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52,147	https://en.wikipedia.org/wiki/Sawtooth%20wave	The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform. The convention is that a sawtooth wave ramps upward and then sharply drops. In a reverse (or inverse) sawtooth wave, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave. The equivalent piecewise linear functions based on the floor function of time t is an example of a sawtooth wave with period 1. A more general form, in the range −1 to 1, and with period p, is This sawtooth function has the same phase as the sine function. While a square wave is constructed from only odd harmonics, a sawtooth wave's sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency. Because it contains all the integer harmonics, it is one of the best waveforms to use for subtractive synthesis of musical sounds, particularly bowed string instruments like violins and cellos, since the slip-stick behavior of the bow drives the strings with a sawtooth-like motion. A sawtooth can be constructed using additive synthesis. For period p and amplitude a, the following infinite Fourier series converge to a sawtooth and a reverse (inverse) sawtooth wave: In digital synthesis, these series are only summed over k such that the highest harmonic, Nmax, is less than the Nyquist frequency (half the sampling frequency). This summation can generally be more efficiently calculated with a fast Fourier transform. If the waveform is digitally created directly in the time domain using a non-bandlimited form, such as y = x − floor(x), infinite harmonics are sampled and the resulting tone contains aliasing distortion. An audio demonstration of a sawtooth played at 440 Hz (A4) and 880 Hz (A5) and 1,760 Hz (A6) is available below. Both bandlimited (non-aliased) and aliased tones are presented. Applications Sawtooth waves are known for their use in electronic music. The sawtooth and square waves are among the most common waveforms used to create sounds with subtractive analog and virtual analog music synthesizers. Sawtooth waves are used in switched-mode power supplies. In the regulator chip the feedback signal from the output is continuously compared to a high-frequency sawtooth to generate a new duty cycle PWM signal on the output of the comparator. In the field of computer science, particularly in automation and robotics, allows to calculate sums and differences of angles while avoiding discontinuities at 360° and 0°. The sawtooth wave is the form of the vertical and horizontal deflection signals used to generate a raster on CRT-based television or monitor screens. Oscilloscopes also use a sawtooth wave for their horizontal deflection, though they typically use electrostatic deflection. On the wave's "ramp", the magnetic field produced by the deflection yoke drags the electron beam across the face of the CRT, creating a scan line. On the wave's "cliff", the magnetic field suddenly collapses, causing the electron beam to return to its resting position as quickly as possible. The current applied to the deflection yoke is adjusted by various means (transformers, capacitors, center-tapped windings) so that the half-way voltage on the sawtooth's cliff is at the zero mark, meaning that a negative current will cause deflection in one direction, and a positive current deflection in the other; thus, a center-mounted deflection yoke can use the whole screen area to depict a trace. The horizontal frequency is 15.734 kHz on NTSC, 15.625 kHz for PAL and SECAM. The vertical deflection system operates the same way as the horizontal, though at a much lower frequency (59.94 Hz on NTSC, 50 Hz for PAL and SECAM). The ramp portion of the wave must appear as a straight line. If otherwise, it indicates that the current isn't increasing linearly, and therefore that the magnetic field produced by the deflection yoke is not linear. As a result, the electron beam will accelerate during the non-linear portions. This would result in a television image "squished" in the direction of the non-linearity. Extreme cases will show marked brightness increases, since the electron beam spends more time on that side of the picture. The first television receivers had controls allowing users to adjust the picture's vertical or horizontal linearity. Such controls were not present on later sets as the stability of electronic components had improved. See also List of periodic functions Sine wave Square wave Triangle wave Pulse wave Sound Wave Zigzag References External links Waveforms Fourier series	Sawtooth wave	[ "Physics" ]	1,039	[ "Waves", "Physical phenomena", "Waveforms" ]
52,151	https://en.wikipedia.org/wiki/Triangle%20wave	A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse). Definitions Definition A triangle wave of period p that spans the range [0, 1] is defined as where is the floor function. This can be seen to be the absolute value of a shifted sawtooth wave. For a triangle wave spanning the range the expression becomes A more general equation for a triangle wave with amplitude and period using the modulo operation and absolute value is For example, for a triangle wave with amplitude 5 and period 4: A phase shift can be obtained by altering the value of the term, and the vertical offset can be adjusted by altering the value of the term. As this only uses the modulo operation and absolute value, it can be used to simply implement a triangle wave on hardware electronics. Note that in many programming languages, the % operator is a remainder operator (with result the same sign as the dividend), not a modulo operator; the modulo operation can be obtained by using ((x % p) + p) % p in place of x % p. In e.g. JavaScript, this results in an equation of the form 4a/p Math.abs((((x - p/4) % p) + p) % p - p/2) - a. Relation to the square wave The triangle wave can also be expressed as the integral of the square wave: Expression in trigonometric functions A triangle wave with period p and amplitude a can be expressed in terms of sine and arcsine (whose value ranges from −π/2 to π/2): The identity can be used to convert from a triangle "sine" wave to a triangular "cosine" wave. This phase-shifted triangle wave can also be expressed with cosine and arccosine: Expressed as alternating linear functions Another definition of the triangle wave, with range from −1 to 1 and period p, is Harmonics It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by ) and multiplying the amplitude of the harmonics by one over the square of their mode number, (which is equivalent to one over the square of their relative frequency to the fundamental). The above can be summarised mathematically as follows: where is the number of harmonics to include in the approximation, is the independent variable (e.g. time for sound waves), is the fundamental frequency, and is the harmonic label which is related to its mode number by . This infinite Fourier series converges quickly to the triangle wave as tends to infinity, as shown in the animation. Arc length The arc length per period for a triangle wave, denoted by s, is given in terms of the amplitude a and period length p by See also List of periodic functions Sine wave Square wave Sawtooth wave Pulse wave Sound Triangle function Wave Zigzag References Fourier series Waveforms	Triangle wave	[ "Physics" ]	685	[ "Waves", "Physical phenomena", "Waveforms" ]
52,202	https://en.wikipedia.org/wiki/Magic%20square	In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The "order" of the magic square is the number of integers along one side (n), and the constant sum is called the "magic constant". If the array includes just the positive integers , the magic square is said to be "normal". Some authors take "magic square" to mean "normal magic square". Magic squares that include repeated entries do not fall under this definition and are referred to as "trivial". Some well-known examples, including the Sagrada Família magic square and the Parker square, are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant, this gives a semimagic square (sometimes called orthomagic square). The mathematical study of a magic square typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century. Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations. History The third-order magic square was known to Chinese mathematicians as early as 190 BCE, and explicitly given by the first century of the common era. The first dateable instance of the fourth-order magic square occurred in 587 CE in India. Specimens of magic squares of order 3 to 9 appear in an encyclopedia from Baghdad , the Encyclopedia of the Brethren of Purity (Rasa'il Ikhwan al-Safa). By the end of 12th century, the general methods for constructing magic squares were well established. Around this time, some of these squares were increasingly used in conjunction with magic letters, as in Shams Al-ma'arif, for occult purposes. In India, all the fourth-order pandiagonal magic squares were enumerated by Narayana in 1356. Magic squares were made known to Europe through translation of Arabic sources as occult objects during the Renaissance, and the general theory had to be re-discovered independent of prior developments in China, India, and Middle East. Also notable are the ancient cultures with a tradition of mathematics and numerology that did not discover the magic squares: Greeks, Babylonians, Egyptians, and Pre-Columbian Americans. Chinese While ancient references to the pattern of even and odd numbers in the 3×3 magic square appear in the I Ching, the first unequivocal instance of this magic square appears in the chapter called Mingtang (Bright Hall) of a 1st-century book Da Dai Liji (Record of Rites by the Elder Dai), which purported to describe ancient Chinese rites of the Zhou dynasty. These numbers also occur in a possibly earlier mathematical text called Shushu jiyi (Memoir on Some Traditions of Mathematical Art), said to be written in 190 BCE. This is the earliest appearance of a magic square on record; and it was mainly used for divination and astrology. The 3×3 magic square was referred to as the "Nine Halls" by earlier Chinese mathematicians. The identification of the 3×3 magic square to the legendary Luoshu chart was only made in the 12th century, after which it was referred to as the Luoshu square. The oldest surviving Chinese treatise that displays magic squares of order larger than 3 is Yang Hui's Xugu zheqi suanfa (Continuation of Ancient Mathematical Methods for Elucidating the Strange) written in 1275. The contents of Yang Hui's treatise were collected from older works, both native and foreign; and he only explains the construction of third and fourth-order magic squares, while merely passing on the finished diagrams of larger squares. He gives a magic square of order 3, two squares for each order of 4 to 8, one of order nine, and one semi-magic square of order 10. He also gives six magic circles of varying complexity. The above magic squares of orders 3 to 9 are taken from Yang Hui's treatise, in which the Luo Shu principle is clearly evident. The order 5 square is a bordered magic square, with central 3×3 square formed according to Luo Shu principle. The order 9 square is a composite magic square, in which the nine 3×3 sub squares are also magic. After Yang Hui, magic squares frequently occur in Chinese mathematics such as in Ding Yidong's Dayan suoyin (), Cheng Dawei's Suanfa tongzong (1593), Fang Zhongtong's Shuduyan (1661) which contains magic circles, cubes and spheres, Zhang Chao's Xinzhai zazu (), who published China's first magic square of order ten, and lastly Bao Qishou's Binaishanfang ji (), who gave various three dimensional magic configurations. However, despite being the first to discover the magic squares and getting a head start by several centuries, the Chinese development of the magic squares are much inferior compared to the Indian, Middle Eastern, or European developments. The high point of Chinese mathematics that deals with the magic squares seems to be contained in the work of Yang Hui; but even as a collection of older methods, this work is much more primitive, lacking general methods for constructing magic squares of any order, compared to a similar collection written around the same time by the Byzantine scholar Manuel Moschopoulos. This is possibly because of the Chinese scholars' enthralment with the Lo Shu principle, which they tried to adapt to solve higher squares; and after Yang Hui and the fall of Yuan dynasty, their systematic purging of the foreign influences in Chinese mathematics. Japan Japan and China have similar mathematical traditions and have repeatedly influenced each other in the history of magic squares. The Japanese interest in magic squares began after the dissemination of Chinese works—Yang Hui's Suanfa and Cheng Dawei's Suanfa tongzong—in the 17th century, and as a result, almost all the wasans devoted their time to its study. In the 1660 edition of Ketsugi-sho, Isomura Kittoku gave both odd and even ordered bordered magic squares as well as magic circles; while the 1684 edition of the same book contained a large section on magic squares, demonstrating that he had a general method for constructing bordered magic squares. In Jinko-ki (1665) by Muramatsu Kudayu Mosei, both magic squares and magic circles are displayed. The largest square Mosei constructs is of 19th order. Various magic squares and magic circles were also published by Nozawa Teicho in Dokai-sho (1666), Sato Seiko in Kongenki (1666), and Hosino Sanenobu in Ko-ko-gen Sho (1673). One of Seki Takakazu's Seven Books (Hojin Yensan) (1683) is devoted completely to magic squares and circles. This is the first Japanese book to give a general treatment of magic squares in which the algorithms for constructing odd, singly even and doubly even bordered magic squares are clearly described. In 1694 and 1695, Yueki Ando gave different methods to create the magic squares and displayed squares of order 3 to 30. A fourth-order magic cube was constructed by Yoshizane Tanaka (1651–1719) in Rakusho-kikan (1683). The study of magic squares was continued by Seki's pupils, notably by Katahiro Takebe, whose squares were displayed in the fourth volume of Ichigen Kappo by Shukei Irie, Yoshisuke Matsunaga in Hojin-Shin-jutsu, Yoshihiro Kurushima in Kyushi Iko who rediscovered a method to produce the odd squares given by Agrippa, and Naonobu Ajima. Thus by the beginning of the 18th century, the Japanese mathematicians were in possession of methods to construct magic squares of arbitrary order. After this, attempts at enumerating the magic squares was initiated by Nushizumi Yamaji. India The 3×3 magic square first appears in India in Gargasamhita by Garga, who recommends its use to pacify the nine planets (navagraha). The oldest version of this text dates from 100 CE, but the passage on planets could not have been written earlier than 400 CE. The first dateable instance of 3×3 magic square in India occur in a medical text Siddhayog () by Vrnda, which was prescribed to women in labor in order to have easy delivery. The oldest dateable fourth order magic square in the world is found in an encyclopaedic work written by Varahamihira around 587 CE called Brhat Samhita. The magic square is constructed for the purpose of making perfumes using 4 substances selected from 16 different substances. Each cell of the square represents a particular ingredient, while the number in the cell represents the proportion of the associated ingredient, such that the mixture of any four combination of ingredients along the columns, rows, diagonals, and so on, gives the total volume of the mixture to be 18. Although the book is mostly about divination, the magic square is given as a matter of combinatorial design, and no magical properties are attributed to it. The special features of this magic square were commented on by Bhattotpala () The square of Varahamihira as given above has sum of 18. Here the numbers 1 to 8 appear twice in the square. It is a pan-diagonal magic square. Four different magic squares can be obtained by adding 8 to one of the two sets of 1 to 8 sequence. The sequence is selected such that the number 8 is added exactly twice in each row, each column and each of the main diagonals. One of the possible magic squares shown in the right side. This magic square is remarkable in that it is a 90 degree rotation of a magic square that appears in the 13th century Islamic world as one of the most popular magic squares. The construction of 4th-order magic square is detailed in a work titled Kaksaputa, composed by the alchemist Nagarjuna around 10th century CE. All of the squares given by Nagarjuna are 4×4 magic squares, and one of them is called Nagarjuniya after him. Nagarjuna gave a method of constructing 4×4 magic square using a primary skeleton square, given an odd or even magic sum. The Nagarjuniya square is given below, and has the sum total of 100. The Nagarjuniya square is a pan-diagonal magic square. The Nagarjuniya square is made up of two arithmetic progressions starting from 6 and 16 with eight terms each, with a common difference between successive terms as 4. When these two progressions are reduced to the normal progression of 1 to 8, the adjacent square is obtained. Around 12th-century, a 4×4 magic square was inscribed on the wall of Parshvanath temple in Khajuraho, India. Several Jain hymns teach how to make magic squares, although they are undateable. As far as is known, the first systematic study of magic squares in India was conducted by Thakkar Pheru, a Jain scholar, in his Ganitasara Kaumudi (c. 1315). This work contains a small section on magic squares which consists of nine verses. Here he gives a square of order four, and alludes to its rearrangement; classifies magic squares into three (odd, evenly even, and oddly even) according to its order; gives a square of order six; and prescribes one method each for constructing even and odd squares. For the even squares, Pheru divides the square into component squares of order four, and puts the numbers into cells according to the pattern of a standard square of order four. For odd squares, Pheru gives the method using horse move or knight's move. Although algorithmically different, it gives the same square as the De la Loubere's method. The next comprehensive work on magic squares was taken up by Narayana Pandit, who in the fourteenth chapter of his Ganita Kaumudi (1356) gives general methods for their construction, along with the principles governing such constructions. It consists of 55 verses for rules and 17 verses for examples. Narayana gives a method to construct all the pan-magic squares of fourth order using knight's move; enumerates the number of pan-diagonal magic squares of order four, 384, including every variation made by rotation and reflection; three general methods for squares having any order and constant sum when a standard square of the same order is known; two methods each for constructing evenly even, oddly even, and of squares when the sum is given. While Narayana describes one older method for each species of square, he claims the method of superposition for evenly even and odd squares and a method of interchange for oddly even squares to be his own invention. The superposition method was later re-discovered by De la Hire in Europe. In the last section, he conceives of other figures, such as circles, rectangles, and hexagons, in which the numbers may be arranged to possess properties similar to those of magic squares. Below are some of the magic squares constructed by Narayana: The order 8 square is interesting in itself since it is an instance of the most-perfect magic square. Incidentally, Narayana states that the purpose of studying magic squares is to construct yantra, to destroy the ego of bad mathematicians, and for the pleasure of good mathematicians. The subject of magic squares is referred to as bhadraganita and Narayana states that it was first taught to men by god Shiva. Middle East, North Africa, Muslim Iberia Although the early history of magic squares in Persia and Arabia is not known, it has been suggested that they were known in pre-Islamic times. It is clear, however, that the study of magic squares was common in medieval Islam, and it was thought to have begun after the introduction of chess into the region. The first dateable appearance of a magic square of order 3 occurs in Jābir ibn Hayyān's (fl. c. 721 – c. 815) Kitab al-mawazin al-Saghir (The Small Book of Balances) where the magic square and its related numerology is associated with alchemy. While it is known that treatises on magic squares were written in the 9th century, the earliest extant treaties date from the 10th-century: one by Abu'l-Wafa al-Buzjani () and another by Ali b. Ahmad al-Antaki (). These early treatises were purely mathematical, and the Arabic designation for magic squares used is wafq al-a'dad, which translates as harmonious disposition of the numbers. By the end of 10th century, the two treatises by Buzjani and Antaki makes it clear that the Middle Eastern mathematicians had understood how to construct bordered squares of any order as well as simple magic squares of small orders (n ≤ 6) which were used to make composite magic squares. A specimen of magic squares of orders 3 to 9 devised by Middle Eastern mathematicians appear in an encyclopedia from Baghdad , the Rasa'il Ikhwan al-Safa (the Encyclopedia of the Brethren of Purity). The squares of order 3 to 7 from Rasa'il are given below: The 11th century saw the finding of several ways to construct simple magic squares for odd and evenly-even orders; the more difficult case of evenly-odd case (n = 4k + 2) was solved by Ibn al-Haytham with k even (c. 1040), and completely by the beginning of 12th century, if not already in the latter half of the 11th century. Around the same time, pandiagonal squares were being constructed. Treaties on magic squares were numerous in the 11th and 12th century. These later developments tended to be improvements on or simplifications of existing methods. From the 13th century, magic squares were increasingly put to occult purposes. However, much of these later texts written for occult purposes merely depict certain magic squares and mention their attributes, without describing their principle of construction, with only some authors keeping the general theory alive. One such occultist was the Algerian Ahmad al-Buni (c. 1225), who gave general methods on constructing bordered magic squares; some others were the 17th century Egyptian Shabramallisi and the 18th century Nigerian al-Kishnawi. The magic square of order three was described as a child-bearing charm since its first literary appearances in the alchemical works of Jābir ibn Hayyān (fl. c. 721 – c. 815) and al-Ghazālī (1058–1111) and it was preserved in the tradition of the planetary tables. The earliest occurrence of the association of seven magic squares to the virtues of the seven heavenly bodies appear in Andalusian scholar Ibn Zarkali's (known as Azarquiel in Europe) (1029–1087) Kitāb tadbīrāt al-kawākib (Book on the Influences of the Planets). A century later, the Algerian scholar Ahmad al-Buni attributed mystical properties to magic squares in his highly influential book Shams al-Ma'arif (The Book of the Sun of Gnosis and the Subtleties of Elevated Things), which also describes their construction. This tradition about a series of magic squares from order three to nine, which are associated with the seven planets, survives in Greek, Arabic, and Latin versions. There are also references to the use of magic squares in astrological calculations, a practice that seems to have originated with the Arabs. Latin Europe Unlike in Persia and Arabia, better documentation exists of how the magic squares were transmitted to Europe. Around 1315, influenced by Arab sources, the Greek Byzantine scholar Manuel Moschopoulos wrote a mathematical treatise on the subject of magic squares, leaving out the mysticism of his Middle Eastern predecessors, where he gave two methods for odd squares and two methods for evenly even squares. Moschopoulos was essentially unknown to the Latin Europe until the late 17th century, when Philippe de la Hire rediscovered his treatise in the Royal Library of Paris. However, he was not the first European to have written on magic squares; and the magic squares were disseminated to rest of Europe through Spain and Italy as occult objects. The early occult treaties that displayed the squares did not describe how they were constructed. Thus the entire theory had to be rediscovered. Magic squares had first appeared in Europe in Kitāb tadbīrāt al-kawākib (Book on the Influences of the Planets) written by Ibn Zarkali of Toledo, Al-Andalus, as planetary squares by 11th century. The magic square of three was discussed in numerological manner in early 12th century by Jewish scholar Abraham ibn Ezra of Toledo, which influenced later Kabbalists. Ibn Zarkali's work was translated as Libro de Astromagia in the 1280s, due to Alfonso X of Castille. In the Alfonsine text, magic squares of different orders are assigned to the respective planets, as in the Islamic literature; unfortunately, of all the squares discussed, the Mars magic square of order five is the only square exhibited in the manuscript. Magic squares surface again in Florence, Italy in the 14th century. A 6×6 and a 9×9 square are exhibited in a manuscript of the Trattato d'Abbaco (Treatise of the Abacus) by Paolo Dagomari. It is interesting to observe that Paolo Dagomari, like Pacioli after him, refers to the squares as a useful basis for inventing mathematical questions and games, and does not mention any magical use. Incidentally, though, he also refers to them as being respectively the Sun's and the Moon's squares, and mentions that they enter astrological calculations that are not better specified. As said, the same point of view seems to motivate the fellow Florentine Luca Pacioli, who describes 3×3 to 9×9 squares in his work De Viribus Quantitatis by the end of 15th century. Europe after 15th century The planetary squares had disseminated into northern Europe by the end of 15th century. For instance, the Cracow manuscript of Picatrix from Poland displays magic squares of orders 3 to 9. The same set of squares as in the Cracow manuscript later appears in the writings of Paracelsus in Archidoxa Magica (1567), although in highly garbled form. In 1514 Albrecht Dürer immortalized a 4×4 square in his famous engraving Melencolia I. Paracelsus' contemporary Heinrich Cornelius Agrippa von Nettesheim published his famous three volume book De occulta philosophia in 1531, where he devoted Chapter 22 of Book II to the planetary squares shown below. The same set of squares given by Agrippa reappear in 1539 in Practica Arithmetice by Girolamo Cardano, where he explains the construction of the odd ordered squares using "diamond method", which was later reproduced by Bachet. The tradition of planetary squares was continued into the 17th century by Athanasius Kircher in Oedipi Aegyptici (1653). In Germany, mathematical treaties concerning magic squares were written in 1544 by Michael Stifel in Arithmetica Integra, who rediscovered the bordered squares, and Adam Riese, who rediscovered the continuous numbering method to construct odd ordered squares published by Agrippa. However, due to the religious upheavals of that time, these work were unknown to the rest of Europe. In 1624 France, Claude Gaspard Bachet described the "diamond method" for constructing Agrippa's odd ordered squares in his book Problèmes Plaisants. During 1640 Bernard Frenicle de Bessy and Pierre Fermat exchanged letters on magic squares and cubes, and in one of the letters Fermat boasts of being able to construct 1,004,144,995,344 magic squares of order 8 by his method. An early account on the construction of bordered squares was given by Antoine Arnauld in his Nouveaux éléments de géométrie (1667). In the two treatise Des quarrez ou tables magiques and Table générale des quarrez magiques de quatre de côté, published posthumously in 1693, twenty years after his death, Bernard Frenicle de Bessy demonstrated that there were exactly 880 distinct magic squares of order four. Frenicle gave methods to construct magic square of any odd and even order, where the even ordered squares were constructed using borders. He also showed that interchanging rows and columns of a magic square produced new magic squares. In 1691, Simon de la Loubère described the Indian continuous method of constructing odd ordered magic squares in his book Du Royaume de Siam, which he had learned while returning from a diplomatic mission to Siam, which was faster than Bachet's method. In an attempt to explain its working, de la Loubere used the primary numbers and root numbers, and rediscovered the method of adding two preliminary squares. This method was further investigated by Abbe Poignard in Traité des quarrés sublimes (1704), by Philippe de La Hire in Mémoires de l'Académie des Sciences for the Royal Academy (1705), and by Joseph Sauveur in Construction des quarrés magiques (1710). Concentric bordered squares were also studied by De la Hire in 1705, while Sauveur introduced magic cubes and lettered squares, which was taken up later by Euler in 1776, who is often credited for devising them. In 1750 d'Ons-le-Bray rediscovered the method of constructing doubly even and singly even squares using bordering technique; while in 1767 Benjamin Franklin published a semi-magic square that had the properties of eponymous Franklin square. By this time the earlier mysticism attached to the magic squares had completely vanished, and the subject was treated as a part of recreational mathematics. In the 19th century, Bernard Violle gave a comprehensive treatment of magic squares in his three volume Traité complet des carrés magiques (1837–1838), which also described magic cubes, parallelograms, parallelopipeds, and circles. Pandiagonal squares were extensively studied by Andrew Hollingworth Frost, who learned it while in the town of Nasik, India, (thus calling them Nasik squares) in a series of articles: On the knight's path (1877), On the General Properties of Nasik Squares (1878), On the General Properties of Nasik Cubes (1878), On the construction of Nasik Squares of any order (1896). He showed that it is impossible to have normal singly-even pandiagonal magic squares. Frederick A.P. Barnard constructed inlaid magic squares and other three dimensional magic figures like magic spheres and magic cylinders in Theory of magic squares and of magic cubes (1888). In 1897, Emroy McClintock published On the most perfect form of magic squares, coining the words pandiagonal square and most perfect square, which had previously been referred to as perfect, or diabolic, or Nasik. Some famous magic squares Luo Shu magic square Legends dating from as early as 650 BCE tell the story of the Lo Shu (洛書) or "scroll of the river Lo". According to the legend, there was at one time in ancient China a huge flood. While the great king Yu was trying to channel the water out to sea, a turtle emerged from it with a curious pattern on its shell: a 3×3 grid in which circular dots of numbers were arranged, such that the sum of the numbers in each row, column and diagonal was the same: 15. According to the legend, thereafter people were able to use this pattern in a certain way to control the river and protect themselves from floods. The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection. Magic square in Parshavnath temple There is a well-known 12th-century 4×4 normal magic square inscribed on the wall of the Parshvanath temple in Khajuraho, India. This is known as the Chautisa Yantra (Chautisa, 34; Yantra, lit. "device"), since its magic sum is 34. It is one of the three 4×4 pandiagonal magic squares and is also an instance of the most-perfect magic square. The study of this square led to the appreciation of pandiagonal squares by European mathematicians in the late 19th century. Pandiagonal squares were referred to as Nasik squares or Jain squares in older English literature. Albrecht Dürer's magic square The order four normal magic square Albrecht Dürer immortalized in his 1514 engraving Melencolia I, referred to above, is believed to be the first seen in European art. The square associated with Jupiter appears as a talisman used to drive away melancholy. It is very similar to Yang Hui's square, which was created in China about 250 years before Dürer's time. As with every order 4 normal magic square, the magic sum is 34. But in the Durer square this sum is also found in each of the quadrants, in the center four squares, and in the corner squares (of the 4×4 as well as the four contained 3×3 grids). This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows (5+9+8+12 and 3+2+15+14), and in four kite or cross shaped quartets (3+5+11+15, 2+10+8+14, 3+9+7+15, and 2+6+12+14). The two numbers in the middle of the bottom row give the date of the engraving: 1514. It has been speculated that the numbers 4,1 bordering the publication date correspond to Durer's initials D,A. But if that had been his intention, he could have inverted the order of columns 1 and 4 to achieve "A1514D" without compromising the square's properties. Dürer's magic square can also be extended to a magic cube. Sagrada Família magic square The Passion façade of the Sagrada Família church in Barcelona, conceptualized by Antoni Gaudí and designed by sculptor Josep Subirachs, features a trivial order 4 magic square: The magic constant of the square is 33, the age of Jesus at the time of the Passion. Structurally, it is very similar to the Melancholia magic square, but it has had the numbers in four of the cells reduced by 1. Trivial squares such as this one are not generally mathematically interesting and only have historical significance. Lee Sallows has pointed out that, due to Subirachs's ignorance of magic square theory, the renowned sculptor made a needless blunder, and supports this assertion by giving several examples of non-trivial 4×4 magic squares showing the desired magic constant of 33. Similarly to Dürer's magic square, the Sagrada Familia's magic square can also be extended to a magic cube. Parker square The Parker square, named after recreational mathematician Matt Parker, is an attempt to create a 33 magic square of squares — a prized unsolved problem since Euler. The Parker square is a trivial semimagic square since it uses some numbers more than once, and the diagonal sums to , not as for all the other rows and columns, and the other diagonal. The Parker square became popular in mathematical culture. The Parker square became a "mascot for people who give it a go, but ultimately fall short". Gardner square The Gardner square, named after recreational mathematician Martin Gardner, similar to the Parker square, is given as a problem to determine a, b, c and d. This solution for a = 74, b = 113, c = 94 and d = 97 gives a semimagic square; the diagonal sums to , not as for all the other rows and columns, and the other diagonal. Properties of magic squares Magic constant The constant that is the sum of any row, or column, or diagonal is called the magic constant or magic sum, M. Every normal magic square has a constant dependent on the order , calculated by the formula . This can be demonstrated by noting that the sum of is . Since the sum of each row is , the sum of rows is , which when divided by the order yields the magic constant as . For normal magic squares of orders n = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). Magic square of order 1 is trivial The 1×1 magic square, with only one cell containing the number 1, is called trivial, because it is typically not under consideration when discussing magic squares; but it is indeed a magic square by definition, if a single cell is regarded as a square of order one. Magic square of order 2 cannot be constructed Normal magic squares of all sizes can be constructed except 2×2 (that is, where order n = 2). Center of mass If the numbers in the magic square are seen as masses located in various cells, then the center of mass of a magic square coincides with its geometric center. Moment of inertia The moment of inertia of a magic square has been defined as the sum over all cells of the number in the cell times the squared distance from the center of the cell to the center of the square; here the unit of measurement is the width of one cell. (Thus for example a corner cell of a 3×3 square has a distance of a non-corner edge cell has a distance of 1, and the center cell has a distance of 0.) Then all magic squares of a given order have the same moment of inertia as each other. For the order-3 case the moment of inertia is always 60, while for the order-4 case the moment of inertia is always 340. In general, for the n×n case the moment of inertia is Birkhoff–von Neumann decomposition Dividing each number of the magic square by the magic constant will yield a doubly stochastic matrix, whose row sums and column sums equal to unity. However, unlike the doubly stochastic matrix, the diagonal sums of such matrices will also equal to unity. Thus, such matrices constitute a subset of doubly stochastic matrix. The Birkhoff–von Neumann theorem states that for any doubly stochastic matrix , there exists real numbers , where and permutation matrices such that This representation may not be unique in general. By Marcus-Ree theorem, however, there need not be more than terms in any decomposition. Clearly, this decomposition carries over to magic squares as well, since a magic square can be recovered from a doubly stochastic matrix by multiplying it by the magic constant. Classification of magic squares While the classification of magic squares can be done in many ways, some useful categories are given below. An n×n square array of integers 1, 2, ..., n2 is called: Semi-magic square when its rows and columns sum to give the magic constant. Simple magic square when its rows, columns, and two diagonals sum to give magic constant and no more. They are also known as ordinary magic squares or normal magic squares. Self-complementary magic square when it is a magic square which when complemented (i.e. each number subtracted from n2 + 1) will give a rotated or reflected version of the original magic square. Associative magic square when it is a magic square with a further property that every number added to the number equidistant, in a straight line, from the center gives n2 + 1. They are also called symmetric magic squares. Associative magic squares do not exist for squares of singly even order. All associative magic square are self-complementary magic squares as well. Pandiagonal magic square when it is a magic square with a further property that the broken diagonals sum to the magic constant. They are also called panmagic squares, perfect squares, diabolic squares, Jain squares, or Nasik squares. Panmagic squares do not exist for singly even orders. However, singly even non-normal squares can be panmagic. Ultra magic square when it is both associative and pandiagonal magic square. Ultra magic square exist only for orders n ≥ 5. Bordered magic square when it is a magic square and it remains magic when the rows and columns on the outer edge are removed. They are also called concentric bordered magic squares if removing a border of a square successively gives another smaller bordered magic square. Bordered magic square do not exist for order 4. Composite magic square when it is a magic square that is created by "multiplying" (in some sense) smaller magic squares, such that the order of the composite magic square is a multiple of the order of the smaller squares. Such squares can usually be partitioned into smaller non-overlapping magic sub-squares. Inlaid magic square when it is a magic square inside which a magic sub-square is embedded, regardless of construction technique. The embedded magic sub-squares are themselves referred to as inlays. Most-perfect magic square when it is a pandiagonal magic square with two further properties (i) each 2×2 subsquare add to 1/k of the magic constant where n = 4k, and (ii) all pairs of integers distant n/2 along any diagonal (major or broken) are complementary (i.e. they sum to n2 + 1). The first property is referred to as compactness, while the second property is referred to as completeness. Most-perfect magic squares exist only for squares of doubly even order. All the pandiagonal squares of order 4 are also most perfect. Franklin magic square when it is a doubly even magic square with three further properties (i) every bent diagonal adds to the magic constant, (ii) every half row and half column starting at an outside edge adds to half the magic constant, and (iii) the square is compact. Multimagic square when it is a magic square that remains magic even if all its numbers are replaced by their k-th power for 1 ≤ k ≤ P. They are also known as P-multimagic square or satanic squares. They are also referred to as bimagic squares, trimagic squares, tetramagic squares, and pentamagic squares when the value of P is 2, 3, 4, and 5 respectively. Enumeration of magic squares Low-order squares There is only one (trivial) magic square of order 1 and no magic square of order 2. As mentioned above, the set of normal squares of order three constitutes a single equivalence class-all equivalent to the Lo Shu square. Thus there is basically just one normal magic square of order 3. The number of different n × n magic squares for n from 1 to 6, not counting rotations and reflections is: 1, 0, 1, 880, 275305224, 17753889197660635632. The number for n = 6 had previously been estimated to be Magic tori Cross-referenced to the above sequence, a new classification enumerates the magic tori that display these magic squares. The number of magic tori of order n from 1 to 5, is: 1, 0, 1, 255, 251449712 . Higher-order squares and tori The number of distinct normal magic squares rapidly increases for higher orders. The 880 magic squares of order 4 are displayed on 255 magic tori of order 4 and the 275,305,224 squares of order 5 are displayed on 251,449,712 magic tori of order 5. The numbers of magic tori and distinct normal squares are not yet known for orders beyond 5 and 6, respectively. Algorithms tend to only generate magic squares of a certain type or classification, making counting all possible magic squares quite difficult. Since traditional counting methods have proven unsuccessful, statistical analysis using the Monte Carlo method has been applied. The basic principle applied to magic squares is to randomly generate n × n matrices of elements 1 to n2 and check if the result is a magic square. The probability that a randomly generated matrix of numbers is a magic square is then used to approximate the number of magic squares. More intricate versions of the Monte Carlo method, such as the exchange Monte Carlo, and Monte Carlo backtracking have produced even more accurate estimations. Using these methods it has been shown that the probability of magic squares decreases rapidly as n increases. Using fitting functions give the curves seen to the right. Transformations that preserve the magic property For any magic square The sum of any two magic squares of the same order by matrix addition is a magic square. A magic square remains magic when all of its numbers undergo the same linear transformation (i.e., a function of the form ). For example, a magic square remains magic when its numbers are multiplied by any constant. Moreover, a magic square remains magic when a constant is added or subtracted to its numbers, or if its numbers are subtracted from a constant. In particular, if every element in a normal magic square of order is subtracted from , the complement of the original square is obtained. In the example below, each element of the magic square on the left is subtracted from 17 to obtain the complement magic square on the right. A magic square remains magic when transformed by any element of , the symmetry group of a square (see ). Every combination of one or more rotations of 90 degrees, reflections, or both produce eight trivially distinct squares which are generally considered equivalent. The eight such squares are said to make up a single equivalence class. The eight equivalent magic squares for the 3×3 magic square are shown below: A magic square of order remains magic when both its rows and columns are symmetrically permuted by such that for . Every permutation of the rows or columns preserves all row and column sums, but generally not the two diagonal sums. If the same permutation is applied to both the rows and columns, then diagonal element in row and column is mapped to row and column which is on the same diagonal; therefore, applying the same permutation to rows and columns preserves the main (upper left to lower right) diagonal sum. If the permutation is symmetric as described, then the diagonal element in row and column is mapped to row and column which is on the same diagonal; therefore, applying the same symmetric permutation to both rows and columns preserves both diagonal sums. For even , there are such symmetric permutations, and for odd. In the example below, the original magic square on the left has its rows and columns symmetrically permuted by resulting in the magic square on the right. A magic square of order remains magic when rows and are exchanged and columns and are exchanged because this is a symmetric permutation of the form described above. In the example below, the square on the right is obtained by interchanging the 1st and 4th rows and columns of the original square on the left. A magic square of order remains magic when rows and are exchanged, rows and are exchanged, columns and are exchanged, and columns and are exchanged where because this is another symmetric permutation of the form described above. In the example below, the left square is the original square, while the right square is the new square obtained by this transformation. In the middle square, rows 1 and 2 and rows 3 and 4 have been swapped. The final square on the right is obtained by interchanging columns 1 and 2 and columns 3 and 4 of the middle square. In this particular example, this transform rotates the quadrants 180 degrees. The middle square is also magic because the original square is associative. A magic square remains magic when its quadrants are diagonally interchanged because this is another symmetric permutation of the form described above. For even-order , permute the rows and columns by permutation where for , and for . For odd-order , permute rows and columns by permutation where for , and for . For odd ordered square, the halves of the central row and column are also interchanged. Examples for order 4 and 5 magic squares are given below: For associative magic squares An associative magic square remains associative when two rows or columns equidistant from the center are interchanged. For an even square, there are n/2 pairs of rows or columns that can be interchanged; thus 2n/2 × 2n/2 = 2n equivalent magic squares by combining such interchanges can be obtained. For odd square, there are (n - 1)/2 pairs of rows or columns that can be interchanged; and 2n-1 equivalent magic squares obtained by combining such interchanges. Interchanging all the rows flips the square vertically (i.e. reflected along the horizontal axis), while interchanging all the columns flips the square horizontally (i.e. reflected along the vertical axis). In the example below, a 4×4 associative magic square on the left is transformed into a square on the right by interchanging the second and third row, yielding the famous Durer's magic square. An associative magic square remains associative when two same sided rows (or columns) are interchanged along with corresponding other sided rows (or columns). For an even square, since there are n/2 same sided rows (or columns), there are n(n - 2)/8 pairs of such rows (or columns) that can be interchanged. Thus, 2n(n-2)/8 × 2n(n-2)/8 = 2n(n-2)/4 equivalent magic squares can be obtained by combining such interchanges. For odd square, since there are (n - 1)/2 same sided rows or columns, there are (n - 1)(n - 3)/8 pairs of such rows or columns that can be interchanged. Thus, there are 2(n - 1)(n - 3)/8 × 2(n - 1)(n - 3)/8 = 2(n - 1)(n - 3)/4 equivalent magic squares obtained by combining such interchanges. Interchanging all the same sided rows flips each quadrants of the square vertically, while interchanging all the same sided columns flips each quadrant of the square horizontally. In the example below, the original square is on the left, whose rows 1 and 2 are interchanged with each other, along with rows 3 and 4, to obtain the transformed square on the right. An associative magic square remains associative when its entries are replaced with corresponding numbers from a set of s arithmetic progressions with the same common difference among r terms, such that r × s = n2, and whose initial terms are also in arithmetic progression, to obtain a non-normal magic square. Here either s or r should be a multiple of n. Let us have s arithmetic progressions given by where a is the initial term, c is the common difference of the arithmetic progressions, and d is the common difference among the initial terms of each progression. The new magic constant will be If s = r = n, then follows the simplification With a = c = 1 and d = n, the usual M = n(n2+1)/2 is obtained. For given M the required a, c, and d can be found by solving the linear Diophantine equation. In the examples below, there are order 4 normal magic squares on the left most side. The second square is a corresponding non-normal magic square with r = 8, s = 2, a = 1, c = 1, and d = 10 such that the new magic constant is M = 38. The third square is an order 5 normal magic square, which is a 90 degree clockwise rotated version of the square generated by De la Loubere method. On the right most side is a corresponding non-normal magic square with a = 4, c = 1, and d = 6 such that the new magic constant is M = 90. For pan-diagonal magic squares A pan-diagonal magic square remains a pan-diagonal magic square under cyclic shifting of rows or of columns or both. This allows us to position a given number in any one of the n2 cells of an n order square. Thus, for a given pan-magic square, there are n2 equivalent pan-magic squares. In the example below, the original square on the left is transformed by shifting the first row to the bottom to obtain a new pan-magic square in the middle. Next, the 1st and 2nd column of the middle pan-magic square is circularly shifted to the right to obtain a new pan-magic square on the right. For bordered magic squares A bordered magic square remains a bordered magic square after permuting the border cells in the rows or columns, together with their corresponding complementary terms, keeping the corner cells fixed. Since the cells in each row and column of every concentric border can be permuted independently, when the order n ≥ 5 is odd, there are ((n-2)! × (n-4)! × ··· × 3!)2 equivalent bordered squares. When n ≥ 6 is even, there are ((n-2)! × (n-4)! × ··· × 4!)2 equivalent bordered squares. In the example below, a square of order 5 is given whose border row has been permuted and (3!)2 = 36 such equivalent squares can be obtained. A bordered magic square remains a bordered magic square after each of its concentric borders are independently rotated or reflected with respect to the central core magic square. If there are b borders, then this transform will yield 8b equivalent squares. In the example below of the 5×5 magic square, the border has been rotated 90 degrees anti-clockwise. For composite magic squares A composite magic square remains a composite magic square when the embedded magic squares undergo transformations that do not disturb the magic property (e.g. rotation, reflection, shifting of rows and columns, and so on). Special methods of construction Over the millennia, many ways to construct magic squares have been discovered. These methods can be classified as general methods and special methods, in the sense that general methods allow us to construct more than a single magic square of a given order, whereas special methods allow us to construct just one magic square of a given order. Special methods are specific algorithms whereas general methods may require some trial-and-error. Special methods are the most simple ways to construct magic squares. They follow certain algorithms which generate regular patterns of numbers in a square. The correctness of these special methods can be proved using one of the general methods given in later sections. After a magic square has been constructed using a special method, the transformations described in the previous section can be applied to yield further magic squares. Special methods are usually referred to using the name of the author(s) (if known) who described the method, for e.g. De la Loubere's method, Starchey's method, Bachet's method, etc. Magic squares are believed to exist for all orders, except for order 2. Magic squares can be classified according to their order as odd, doubly even (n divisible by four), and singly even (n even, but not divisible by four). This classification is based on the fact that entirely different techniques need to be employed to construct these different species of squares. Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist, including John Horton Conway's LUX method for magic squares and the Strachey method for magic squares. A method for constructing a magic square of order 3 In the 19th century, Édouard Lucas devised the general formula for order 3 magic squares. Consider the following table made up of positive integers a, b and c: These nine numbers will be distinct positive integers forming a magic square with the magic constant 3c so long as 0 < a < b < c − a and b ≠ 2a. Moreover, every 3×3 magic square of distinct positive integers is of this form. In 1997 Lee Sallows discovered that leaving aside rotations and reflections, then every distinct parallelogram drawn on the Argand diagram defines a unique 3×3 magic square, and vice versa, a result that had never previously been noted. A method for constructing a magic square of odd order A method for constructing magic squares of odd order was published by the French diplomat de la Loubère in his book, A new historical relation of the kingdom of Siam (Du Royaume de Siam, 1693), in the chapter entitled The problem of the magical square according to the Indians. The method operates as follows: The method prescribes starting in the central column of the first row with the number 1. After that, the fundamental movement for filling the squares is diagonally up and right, one step at a time. If a square is filled with a multiple of the order n, one moves vertically down one square instead, then continues as before. When an "up and to the right" move would leave the square, it is wrapped around to the last row or first column, respectively. Starting from other squares rather than the central column of the first row is possible, but then only the row and column sums will be identical and result in a magic sum, whereas the diagonal sums will differ. The result will thus be a semimagic square and not a true magic square. Moving in directions other than north east can also result in magic squares. A method of constructing a magic square of doubly even order Doubly even means that n is an even multiple of an even integer; or 4p (e.g. 4, 8, 12), where p is an integer. Generic pattern All the numbers are written in order from left to right across each row in turn, starting from the top left hand corner. Numbers are then either retained in the same place or interchanged with their diametrically opposite numbers in a certain regular pattern. In the magic square of order four, the numbers in the four central squares and one square at each corner are retained in the same place and the others are interchanged with their diametrically opposite numbers. A construction of a magic square of order 4 Starting from top left, go left to right through each row of the square, counting each cell from 1 to 16 and filling the cells along the diagonals with its corresponding number. Once the bottom right cell is reached, continue by going right to left, starting from the bottom right of the table through each row, and fill in the non-diagonal cells counting up from 1 to 16 with its corresponding number. As shown below: An extension of the above example for Orders 8 and 12 First generate a pattern table, where a '1' indicates selecting from the square where the numbers are written in order 1 to n2 (left-to-right, top-to-bottom), and a '0' indicates selecting from the square where the numbers are written in reverse order n2 to 1. For M = 4, the pattern table is as shown below (third matrix from left). With the unaltered cells (cells with '1') shaded, a criss-cross pattern is obtained. The patterns are a) there are equal number of '1's and '0's in each row and column; b) each row and each column are "palindromic"; c) the left- and right-halves are mirror images; and d) the top- and bottom-halves are mirror images (c and d imply b). The pattern table can be denoted using hexadecimals as (9, 6, 6, 9) for simplicity (1-nibble per row, 4 rows). The simplest method of generating the required pattern for higher ordered doubly even squares is to copy the generic pattern for the fourth-order square in each four-by-four sub-squares. For M = 8, possible choices for the pattern are (99, 66, 66, 99, 99, 66, 66, 99); (3C, 3C, C3, C3, C3, C3, 3C, 3C); (A5, 5A, A5, 5A, 5A, A5, 5A, A5) (2-nibbles per row, 8 rows). For M = 12, the pattern table (E07, E07, E07, 1F8, 1F8, 1F8, 1F8, 1F8, 1F8, E07, E07, E07) yields a magic square (3-nibbles per row, 12 rows.) It is possible to count the number of choices one has based on the pattern table, taking rotational symmetries into account. Method of superposition The earliest discovery of the superposition method was made by the Indian mathematician Narayana in the 14th century. The same method was later re-discovered and studied in early 18th century Europe by de la Loubere, Poignard, de La Hire, and Sauveur; and the method is usually referred to as de la Hire's method. Although Euler's work on magic square was unoriginal, he famously conjectured the impossibility of constructing the evenly odd ordered mutually orthogonal Graeco-Latin squares. This conjecture was disproved in the mid 20th century. For clarity of exposition, two important variations of this method can be distinguished. Euler's method This method consists in constructing two preliminary squares, which when added together gives the magic square. As a running example, a 3×3 magic square is considered. Each number of the 3×3 natural square by a pair of numbers can be labeled as where every pair of Greek and Latin alphabets, e.g. αa, are meant to be added together, i.e. αa = α + a. Here, (α, β, γ) = (0, 3, 6) and (a, b, c) = (1, 2, 3). The numbers 0, 3, and 6 are referred to as the root numbers while the numbers 1, 2, and 3 are referred to as the primary numbers. An important general constraint here is a Greek letter is paired with a Latin letter only once. Thus, the original square can now be split into two simpler squares: The lettered squares are referred to as Greek square or Latin square if they are filled with Greek or Latin letters, respectively. A magic square can be constructed by ensuring that the Greek and Latin squares are magic squares too. The converse of this statement is also often, but not always (e.g. bordered magic squares), true: A magic square can be decomposed into a Greek and a Latin square, which are themselves magic squares. Thus the method is useful for both synthesis as well as analysis of a magic square. Lastly, by examining the pattern in which the numbers are laid out in the finished square, it is often possible to come up with a faster algorithm to construct higher order squares that replicate the given pattern, without the necessity of creating the preliminary Greek and Latin squares. During the construction of the 3×3 magic square, the Greek and Latin squares with just three unique terms are much easier to deal with than the original square with nine different terms. The row sum and the column sum of the Greek square will be the same, α + β + γ, if each letter appears exactly once in a given column or a row. This can be achieved by cyclic permutation of α, β, and γ. Satisfaction of these two conditions ensures that the resulting square is a semi-magic square; and such Greek and Latin squares are said to be mutually orthogonal to each other. For a given order n, there are at most n - 1 squares in a set of mutually orthogonal squares, not counting the variations due to permutation of the symbols. This upper bound is exact when n is a prime number. In order to construct a magic square, we should also ensure that the diagonals sum to magic constant. For this, we have a third condition: either all the letters should appear exactly once in both the diagonals; or in case of odd ordered squares, one of the diagonals should consist entirely of the middle term, while the other diagonal should have all the letters exactly once. The mutually orthogonal Greek and Latin squares that satisfy the first part of the third condition (that all letters appear in both the diagonals) are said to be mutually orthogonal doubly diagonal Graeco-Latin squares. Odd squares: For the 3×3 odd square, since α, β, and γ are in arithmetic progression, their sum is equal to the product of the square's order and the middle term, i.e. α + β + γ = 3 β. Thus, the diagonal sums will be equal if we have βs in the main diagonal and α, β, γ in the skew diagonal. Similarly, for the Latin square. The resulting Greek and Latin squares and their combination will be as below. The Latin square is just a 90 degree anti-clockwise rotation of the Greek square (or equivalently, flipping about the vertical axis) with the corresponding letters interchanged. Substituting the values of the Greek and Latin letters will give the 3×3 magic square. For the odd squares, this method explains why the Siamese method (method of De la Loubere) and its variants work. This basic method can be used to construct odd ordered magic squares of higher orders. To summarise: For odd ordered squares, to construct Greek square, place the middle term along the main diagonal, and place the rest of the terms along the skew diagonal. The remaining empty cells are filled by diagonal moves. The Latin square can be constructed by rotating or flipping the Greek square, and replacing the corresponding alphabets. The magic square is obtained by adding the Greek and Latin squares. A peculiarity of the construction method given above for the odd magic squares is that the middle number (n2 + 1)/2 will always appear at the center cell of the magic square. Since there are (n - 1)! ways to arrange the skew diagonal terms, we can obtain (n - 1)! Greek squares this way; same with the Latin squares. Also, since each Greek square can be paired with (n - 1)! Latin squares, and since for each of Greek square the middle term may be arbitrarily placed in the main diagonal or the skew diagonal (and correspondingly along the skew diagonal or the main diagonal for the Latin squares), we can construct a total of 2 × (n - 1)! × (n - 1)! magic squares using this method. For n = 3, 5, and 7, this will give 8, 1152, and 1,036,800 different magic squares, respectively. Dividing by 8 to neglect equivalent squares due to rotation and reflections, we obtain 1, 144, and 129,600 essentially different magic squares, respectively. As another example, the construction of 5×5 magic square is given. Numbers are directly written in place of alphabets. The numbered squares are referred to as primary square or root square if they are filled with primary numbers or root numbers, respectively. The numbers are placed about the skew diagonal in the root square such that the middle column of the resulting root square has 0, 5, 10, 15, 20 (from bottom to top). The primary square is obtained by rotating the root square counter-clockwise by 90 degrees, and replacing the numbers. The resulting square is an associative magic square, in which every pair of numbers symmetrically opposite to the center sum up to the same value, 26. For e.g., 16+10, 3+23, 6+20, etc. In the finished square, 1 is placed at center cell of bottom row, and successive numbers are placed via elongated knight's move (two cells right, two cells down), or equivalently, bishop's move (two cells diagonally down right). When a collision occurs, the break move is to move one cell up. All the odd numbers occur inside the central diamond formed by 1, 5, 25 and 21, while the even numbers are placed at the corners. The occurrence of the even numbers can be deduced by copying the square to the adjacent sides. The even numbers from four adjacent squares will form a cross. A variation of the above example, where the skew diagonal sequence is taken in different order, is given below. The resulting magic square is the flipped version of the famous Agrippa's Mars magic square. It is an associative magic square and is the same as that produced by Moschopoulos's method. Here the resulting square starts with 1 placed in the cell which is to the right of the centre cell, and proceeds as De la Loubere's method, with downwards-right move. When a collision occurs, the break move is to shift two cells to the right. In the previous examples, for the Greek square, the second row can be obtained from the first row by circularly shifting it to the right by one cell. Similarly, the third row is a circularly shifted version of the second row by one cell to the right; and so on. Likewise, the rows of the Latin square is circularly shifted to the left by one cell. The row shifts for the Greek and Latin squares are in mutually opposite direction. It is possible to circularly shift the rows by more than one cell to create the Greek and Latin square. For odd ordered squares, whose order is not divisible by three, we can create the Greek squares by shifting a row by two places to the left or to the right to form the next row. The Latin square is made by flipping the Greek square along the main diagonal and interchanging the corresponding letters. This gives us a Latin square whose rows are created by shifting the row in the direction opposite to that of the Greek square. A Greek square and a Latin square should be paired such that their row shifts are in mutually opposite direction. The magic square is obtained by adding the Greek and Latin squares. When the order also happens to be a prime number, this method always creates pandiagonal magic square. This essentially re-creates the knight's move. All the letters will appear in both the diagonals, ensuring correct diagonal sum. Since there are n! permutations of the Greek letters by which we can create the first row of the Greek square, there are thus n! Greek squares that can be created by shifting the first row in one direction. Likewise, there are n! such Latin squares created by shifting the first row in the opposite direction. Since a Greek square can be combined with any Latin square with opposite row shifts, there are n! × n! such combinations. Lastly, since the Greek square can be created by shifting the rows either to the left or to the right, there are a total of 2 × n! × n! magic squares that can be formed by this method. For n = 5 and 7, since they are prime numbers, this method creates 28,800 and 50,803,200 pandiagonal magic squares. Dividing by 8 to neglect equivalent squares due to rotation and reflections, we obtain 3,600 and 6,350,400 equivalent squares. Further dividing by n2 to neglect equivalent panmagic squares due to cyclic shifting of rows or columns, we obtain 144 and 129,600 essentially different panmagic squares. For order 5 squares, these are the only panmagic square there are. The condition that the square's order not be divisible by 3 means that we cannot construct squares of orders 9, 15, 21, 27, and so on, by this method. In the example below, the square has been constructed such that 1 is at the center cell. In the finished square, the numbers can be continuously enumerated by the knight's move (two cells up, one cell right). When collision occurs, the break move is to move one cell up, one cell left. The resulting square is a pandiagonal magic square. This square also has a further diabolical property that any five cells in quincunx pattern formed by any odd sub-square, including wrap around, sum to the magic constant, 65. For e.g., 13+7+1+20+24, 23+1+9+15+17, 13+21+10+19+2 etc. Also the four corners of any 5×5 square and the central cell, as well as the middle cells of each side together with the central cell, including wrap around, give the magic sum: 13+10+19+22+1 and 20+24+12+8+1. Lastly the four rhomboids that form elongated crosses also give the magic sum: 23+1+9+24+8, 15+1+17+20+12, 14+1+18+13+19, 7+1+25+22+10. Such squares with 1 at the center cell are also called God's magic squares in Islamic amulet design, where the center cell is either left blank or filled with God's name. We can also combine the Greek and Latin squares constructed by different methods. In the example below, the primary square is made using knight's move. We have re-created the magic square obtained by De la Loubere's method. As before, we can form 8 × (n - 1)! × n! magic squares by this combination. For n = 5 and 7, this will create 23,040 and 29,030,400 magic squares. After dividing by 8 in order to neglect equivalent squares due to rotation and reflection, we get 2,880 and 3,628,800 squares. For order 5 squares, these three methods give a complete census of the number of magic squares that can be constructed by the method of superposition. Neglecting the rotation and reflections, the total number of magic squares of order 5 produced by the superposition method is 144 + 3,600 + 2,880 = 6,624. Even squares: We can also construct even ordered squares in this fashion. Since there is no middle term among the Greek and Latin alphabets for even ordered squares, in addition to the first two constraint, for the diagonal sums to yield the magic constant, all the letters in the alphabet should appear in the main diagonal and in the skew diagonal. An example of a 4×4 square is given below. For the given diagonal and skew diagonal in the Greek square, the rest of the cells can be filled using the condition that each letter appear only once in a row and a column. Using these two Graeco-Latin squares, we can construct 2 × 4! × 4! = 1,152 magic squares. Dividing by 8 to eliminate equivalent squares due to rotation and reflections, we get 144 essentially different magic squares of order 4. These are the only magic squares constructible by the Euler method, since there are only two mutually orthogonal doubly diagonal Graeco-Latin squares of order 4. Similarly, an 8×8 magic square can be constructed as below. Here the order of appearance of the numbers is not important; however the quadrants imitate the layout pattern of the 4×4 Graeco-Latin squares. Euler's method has given rise to the study of Graeco-Latin squares. Euler's method for constructing magic squares is valid for any order except 2 and 6. Variations: Magic squares constructed from mutually orthogonal doubly diagonal Graeco-Latin squares are interesting in themselves since the magic property emerges from the relative position of the alphabets in the square, and not due to any arithmetic property of the value assigned to them. This means that we can assign any value to the alphabets of such squares and still obtain a magic square. This is the basis for constructing squares that display some information (e.g. birthdays, years, etc.) in the square and for creating "reversible squares". For example, we can display the number π ≈ at the bottom row of a 4×4 magic square using the Graeco-Latin square given above by assigning (α, β, γ, δ) = (10, 0, 90, 15) and (a, b, c, d) = (0, 2, 3, 4). We will obtain the following non-normal magic square with the magic sum 124: Narayana-De la Hire's method for even orders Narayana-De la Hire's method for odd square is the same as that of Euler's. However, for even squares, we drop the second requirement that each Greek and Latin letter appear only once in a given row or column. This allows us to take advantage of the fact that the sum of an arithmetic progression with an even number of terms is equal to the sum of two opposite symmetric terms multiplied by half the total number of terms. Thus, when constructing the Greek or Latin squares, for even ordered squares, a letter can appear n/2 times in a column but only once in a row, or vice versa. As a running example, if we take a 4×4 square, where the Greek and Latin terms have the values (α, β, γ, δ) = (0, 4, 8, 12) and (a, b, c, d) = (1, 2, 3, 4), respectively, then we have α + β + γ + δ = 2 (α + δ) = 2 (β + γ). Similarly, a + b + c + d = 2 (a + d) = 2 (b + c). This means that the complementary pair α and δ (or β and γ) can appear twice in a column (or a row) and still give the desired magic sum. Thus, we can construct: For even ordered squares, the Greek magic square is made by first placing the Greek alphabets along the main diagonal in some order. The skew diagonal is then filled in the same order or by picking the terms that are complementary to the terms in the main diagonal. Finally, the remaining cells are filled column wise. Given a column, we use the complementary terms in the diagonal cells intersected by that column, making sure that they appear only once in a given row but n/2 times in the given column. The Latin square is obtained by flipping or rotating the Greek square and interchanging the corresponding alphabets. The final magic square is obtained by adding the Greek and Latin squares. In the example given below, the main diagonal (from top left to bottom right) is filled with sequence ordered as α, β, γ, δ, while the skew diagonal (from bottom left to top right) filled in the same order. The remaining cells are then filled column wise such that the complementary letters appears only once within a row, but twice within a column. In the first column, since α appears on the 1st and 4th row, the remaining cells are filled with its complementary term δ. Similarly, the empty cells in the 2nd column are filled with γ; in 3rd column β; and 4th column α. Each Greek letter appears only once along the rows, but twice along the columns. As such, the row sums are α + β + γ + δ while the column sums are either 2 (α + δ) or 2 (β + γ). Likewise for the Latin square, which is obtained by flipping the Greek square along the main diagonal and interchanging the corresponding letters. The above example explains why the "criss-cross" method for doubly even magic square works. Another possible 4×4 magic square, which is also pan-diagonal as well as most-perfect, is constructed below using the same rule. However, the diagonal sequence is chosen such that all four letters α, β, γ, δ appear inside the central 2×2 sub-square. Remaining cells are filled column wise such that each letter appears only once within a row. In the 1st column, the empty cells need to be filled with one of the letters selected from the complementary pair α and δ. Given the 1st column, the entry in the 2nd row can only be δ since α is already there in the 2nd row; while, in the 3rd row the entry can only be α since δ is already present in the 3rd row. We proceed similarly until all cells are filled. The Latin square given below has been obtained by flipping the Greek square along the main diagonal and replacing the Greek alphabets with corresponding Latin alphabets. We can use this approach to construct singly even magic squares as well. However, we have to be more careful in this case since the criteria of pairing the Greek and Latin alphabets uniquely is not automatically satisfied. Violation of this condition leads to some missing numbers in the final square, while duplicating others. Thus, here is an important proviso: For singly even squares, in the Greek square, check the cells of the columns which is vertically paired to its complement. In such a case, the corresponding cell of the Latin square must contain the same letter as its horizontally paired cell. Below is a construction of a 6×6 magic square, where the numbers are directly given, rather than the alphabets. The second square is constructed by flipping the first square along the main diagonal. Here in the first column of the root square the 3rd cell is paired with its complement in the 4th cells. Thus, in the primary square, the numbers in the 1st and 6th cell of the 3rd row are same. Likewise, with other columns and rows. In this example the flipped version of the root square satisfies this proviso. As another example of a 6×6 magic square constructed this way is given below. Here the diagonal entries are arranged differently. The primary square is constructed by flipping the root square about the main diagonal. In the second square the proviso for singly even square is not satisfied, leading to a non-normal magic square (third square) where the numbers 3, 13, 24, and 34 are duplicated while missing the numbers 4, 18, 19, and 33. The last condition is a bit arbitrary and may not always need to be invoked, as in this example, where in the root square each cell is vertically paired with its complement: As one more example, we have generated an 8×8 magic square. Unlike the criss-cross pattern of the earlier section for evenly even square, here we have a checkered pattern for the altered and unaltered cells. Also, in each quadrant the odd and even numbers appear in alternating columns. Variations: A number of variations of the basic idea are possible: a complementary pair can appear n/2 times or less in a column. That is, a column of a Greek square can be constructed using more than one complementary pair. This method allows us to imbue the magic square with far richer properties. The idea can also be extended to the diagonals too. An example of an 8×8 magic square is given below. In the finished square each of four quadrants are pan-magic squares as well, each quadrant with same magic constant 130. Method of borders Bordering method for order 3 In this method, the objective is to wrap a border around a smaller magic square which serves as a core. Consider the 3×3 square for example. Subtracting the middle number 5 from each number 1, 2, ..., 9, we obtain 0, ± 1, ± 2, ± 3, and ± 4, which we will, for lack of better words, following S. Harry White, refer to as bone numbers. The magic constant of a magic square, which we will refer to as the skeleton square, made by these bone numbers will be zero since adding all the rows of a magic square will give nM = Σ k = 0; thus M = 0. It is not difficult to argue that the middle number should be placed at the center cell: let x be the number placed in the middle cell, then the sum of the middle column, middle row, and the two diagonals give Σ k + 3 x = 4 M. Since Σ k = 3 M, we have x = M / 3. Here M = 0, so x = 0. Putting the middle number 0 in the center cell, we want to construct a border such that the resulting square is magic. Let the border be given by: Since the sum of each row, column, and diagonals must be a constant (which is zero), we have a + a* = 0, b + b* = 0, u + u* = 0, v + v* = 0. Now, if we have chosen a, b, u, and v, then we have a* = - a, b* = - b, u* = - u, and v* = - v. This means that if we assign a given number to a variable, say a = 1, then its complement will be assigned to a, i.e. a = - 1. Thus out of eight unknown variables, it is sufficient to specify the value of only four variables. We will consider a, b, u, and v as independent variables, while a, b, u, and v as dependent variables. This allows us to consider a bone number ± x as a single number regardless of sign because (1) its assignment to a given variable, say a, will automatically imply that the same number of opposite sign will be shared with its complement a, and (2) two independent variables, say a and b, cannot be assigned the same bone number. But how should we choose a, b, u, and v? We have the sum of the top row and the sum of the right column as u + a + v = 0, v + b + u = 0. Since 0 is an even number, there are only two ways that the sum of three integers will yield an even number: 1) if all three were even, or 2) if two were odd and one was even. Since in our choice of numbers we only have two even non-zero number (± 2 and ± 4), the first statement is false. Hence, it must be the case that the second statement is true: that two of the numbers are odd and one even. The only way that both the above two equations can satisfy this parity condition simultaneously, and still be consistent with the set of numbers we have, is when u and v are odd. For on the contrary, if we had assumed u and a to be odd and v to be even in the first equation, then u* = - u will be odd in the second equation, making b odd as well, in order to satisfy the parity condition. But this requires three odd numbers (u, a, and b), contradicting the fact that we only have two odd numbers (± 1 and ± 3) which we can use. This proves that the odd bone numbers occupy the corners cells. When converted to normal numbers by adding 5, this implies that the corners of a 3×3 magic square are all occupied by even numbers. Thus, taking u = 1 and v = 3, we have a = - 4 and b = - 2. Hence, the finished skeleton square will be as in the left. Adding 5 to each number, we get the finished magic square. Similar argument can be used to construct larger squares. Since there does not exist a 2×2 magic square around which we can wrap a border to construct a 4×4 magic square, the next smallest order for which we can construct bordered square is the order 5. Bordering method for order 5 Consider the fifth-order square. For this, we have a 3×3 magic core, around which we will wrap a magic border. The bone numbers to be used will be ± 5, ± 6, ± 7, ± 8, ± 9, ± 10, ± 11, and ± 12. Disregarding the signs, we have 8 bone numbers, 4 of which are even and 4 of which are odd. In general, for a square of any order n, there will be 4(n - 1) border cells, which are to be filled using 2(n - 1) bone numbers. Let the magic border be given as As before, we should place a bone number and its complement opposite to each other, so that the magic sum will be zero. It is sufficient to determine the numbers u, v, a, b, c, d, e, f to describe the magic border. As before, we have the two constraint equations for the top row and right column: u + a + b + c + v = 0 v + d + e + f + u* = 0. Multiple solutions are possible. The standard procedure is to first try to determine the corner cells, after which we will try to determine the rest of the border. There are 28 ways of choosing two numbers from the set of 8 bone numbers for the corner cells u and v. However, not all pairs are admissible. Among the 28 pairs, 16 pairs are made of an even and an odd number, 6 pairs have both as even numbers, while 6 pairs have them both as odd numbers. We can prove that the corner cells u and v cannot have an even and an odd number. This is because if this were so, then the sums u + v and v + u* will be odd, and since 0 is an even number, the sums a + b + c and d + e + f should be odd as well. The only way that the sum of three integers will result in an odd number is when 1) two of them are even and one is odd, or 2) when all three are odd. Since the corner cells are assumed to be odd and even, neither of these two statements are compatible with the fact that we only have 3 even and 3 odd bone numbers at our disposal. This proves that u and v cannot have different parity. This eliminates 16 possibilities. Using similar type reasoning we can also draw some conclusions about the sets {a, b, c} and {d, e, f}. If u and v are both even, then both the sets should have two odd numbers and one even number. If u and v are both odd, then one of the sets should have three even numbers while the other set should have one even number and two odd numbers. As a running example, consider the case when both u and v are even. The 6 possible pairs are: (6, 8), (6, 10), (6, 12), (8, 10), (8, 12), and (10, 12). Since the sums u + v and v + u* are even, the sums a + b + c and d + e + f should be even as well. The only way that the sum of three integers will result in an even number is when 1) two of them are odd and one is even, or 2) when all three are even. The fact that the two corner cells are even means that we have only 2 even numbers at our disposal. Thus, the second statement is not compatible with this fact. Hence, it must be the case that the first statement is true: two of the three numbers should be odd, while one be even. Now let a, b, d, e be odd numbers while c and f be even numbers. Given the odd bone numbers at our disposal: ± 5, ± 7, ± 9, and ± 11, their differences range from D = { ± 2, ± 4, ± 6} while their sums range from S = {± 12, ± 14, ± 16, ± 18, ± 20}. It is also useful to have a table of their sum and differences for later reference. Now, given the corner cells (u, v), we can check its admissibility by checking if the sums u + v + c and v + u* + f fall within the set D or S. The admissibility of the corner numbers is a necessary but not a sufficient condition for the solution to exist. For example, if we consider the pair (u, v) = (8, 12), then u + v = 20 and v + u* = 6; and we will have ± 6 and ± 10 even bone numbers at our disposal. Taking c = ± 6, we have the sum u + v + c to be 26 and 14, depending on the sign of ± 6 taken, both of which do not fall within the sets D or S. Likewise, taking c = ± 10, we have the sum u + v + c to be 30 and 10, both of which again do not fall within the sets D or S. Thus, the pair (8, 12) is not admissible. By similar process of reasoning, we can also rule out the pair (6, 12). As another example, if we consider the pair (u, v) = (10, 12), then u + v = 22 and v + u* = 2; and we will have ± 6 and ± 8 even bone numbers at our disposal. Taking c = ± 6, we have the sum u + v + c to be 28 and 16. While 28 does not fall within the sets D or S, 16 falls in set S. By inspection, we find that if (a, b) = (-7, -9), then a + b = -16; and it will satisfy the first constraint equation. Also, taking f = ± 8, we have the sum v + u* + f to be 10 and -6. While 10 does not fall within the sets D or S, -6 falls in set D. Since -7 and -9 have already been assigned to a and b, clearly (d, e) = (-5, 11) so that d + e = 6; and it will satisfy the second constraint equation. Likewise, taking c = ± 8, we have the sum u + v + c to be 30 and 14. While 30 does not fall within the sets D or S, 14 falls in set S. By inspection, we find that if (a, b) = (-5, -9), then a + b = -14. Also, taking f = ± 6, we have the sum v + u* + f to be 8 and -4. While 8 does not fall within the sets D or S, -4 falls in set D. Clearly, (d, e) = (-7, 11) so that d + e = 4, and the second constraint equation will be satisfied. Hence the corner pair (u, v) = (10, 12) is admissible; and it admits two solutions: (a, b, c, d, e, f) = (-7, -9, -6, -5, 11, -8) and (a, b, c, d, e, f) = ( -5, -9, -8, -7, 11, -6). The finished skeleton squares are given below. The magic square is obtained by adding 13 to each cells. Using similar process of reasoning, we can construct the following table for the values of u, v, a, b, c, d, e, f expressed as bone numbers as given below. There are only 6 possible choices for the corner cells, which leads to 10 possible border solutions. Given this group of 10 borders, we can construct 10×8×(3!)2 = 2880 essentially different bordered magic squares. Here the bone numbers ± 5, ..., ± 12 were consecutive. More bordered squares can be constructed if the numbers are not consecutive. If non-consecutive bone numbers were also used, then there are a total of 605 magic borders. Thus, the total number of order 5 essentially different bordered magic squares (with consecutive and non-consecutive numbers) is 174,240. See history. The number of fifth-order magic squares constructible via the bordering method is about 26 times larger than via the superposition method. Continuous enumeration methods Exhaustive enumeration of all the borders of a magic square of a given order, as done previously, is very tedious. As such a structured solution is often desirable, which allows us to construct a border for a square of any order. Below we give three algorithms for constructing border for odd, doubly even, and singly even squares. These continuous enumeration algorithms were discovered in 10th century by Arab scholars; and their earliest surviving exposition comes from the two treatises by al-Buzjani and al-Antaki, although they themselves were not the discoverers. Since then many more such algorithms have been discovered. Odd-ordered squares: The following is the algorithm given by al-Buzjani to construct a border for odd squares. A peculiarity of this method is that for order n square, the two adjacent corners are numbers n - 1 and n + 1. Starting from the cell above the lower left corner, we put the numbers alternately in left column and bottom row until we arrive at the middle cell. The next number is written in the middle cell of the bottom row just reached, after which we fill the cell in the upper left corner, then the middle cell of the right column, then the upper right corner. After this, starting from the cell above middle cell of the right column already filled, we resume the alternate placement of the numbers in the right column and the top row. Once half of the border cells are filled, the other half are filled by numbers complementary to opposite cells. The subsequent inner borders is filled in the same manner, until the square of order 3 is filled. Below is an example for 9th-order square. Doubly even order: The following is the method given by al-Antaki. Consider an empty border of order n = 4k with k ≥ 3. The peculiarity of this algorithm is that the adjacent corner cells are occupied by numbers n and n - 1. Starting at the upper left corner cell, we put the successive numbers by groups of four, the first one next to the corner, the second and the third on the bottom, and the fourth at the top, and so on until there remains in the top row (excluding the corners) six empty cells. We then write the next two numbers above and the next four below. We then fill the upper corners, first left then right. We place the next number below the upper right corner in the right column, the next number on the other side in the left column. We then resume placing groups of four consecutive numbers in the two columns as before. Once half of the border cells are filled, the other half are filled by numbers complementary to opposite cells. The example below gives the border for order 16 square. For order 8 square, we just begin directly with the six cells. Singly even order: For singly even order, we have the algorithm given by al-Antaki. Here the corner cells are occupied by n and n - 1. Below is an example of 10th-order square. Start by placing 1 at the bottom row next to the left corner cell, then place 2 in the top row. After this, place 3 at the bottom row and turn around the border in anti-clockwise direction placing the next numbers, until n - 2 is reached on the right column. The next two numbers are placed in the upper corners (n - 1 in upper left corner and n in upper right corner). Then, the next two numbers are placed on the left column, then we resume the cyclic placement of the numbers until half of all the border cells are filled. Once half of the border cells are filled, the other half are filled by numbers complementary to opposite cells. Method of composition For squares of order m × n where m, n > 2 This is a method reminiscent of the Kronecker product of two matrices, that builds an nm × nm magic square from an n × n magic square and an m × m magic square. The "product" of two magic squares creates a magic square of higher order than the two multiplicands. Let the two magic squares be of orders m and n. The final square will be of order m × n. Divide the square of order m × n into m × m sub-squares, such that there are a total of n2 such sub-squares. In the square of order n, reduce by 1 the value of all the numbers. Multiply these reduced values by m2, and place the results in the corresponding sub-squares of the m × n whole square. The squares of order m are added n2 times to the sub-squares of the final square. The peculiarity of this construction method is that each magic subsquare will have different magic sums. The square made of such magic sums from each magic subsquare will again be a magic square. The smallest composite magic square of order 9, composed of two order 3 squares is given below. Since each of the 3×3 sub-squares can be independently rotated and reflected into 8 different squares, from this single 9×9 composite square we can derive 89 = 134,217,728 essentially different 9×9 composite squares. Plenty more composite magic squares can also be derived if we select non-consecutive numbers in the magic sub-squares, like in Yang Hui's version of the 9×9 composite magic square. The next smallest composite magic squares of order 12, composed of magic squares of order 3 and 4 are given below. For the base squares, there is only one essentially different 3rd order square, while there 880 essentially different 4th-order squares that we can choose from. Each pairing can produce two different composite squares. Since each magic sub-squares in each composite square can be expressed in 8 different forms due to rotations and reflections, there can be 1×880×89 + 880×1×816 ≈ 2.476×1017 essentially different 12×12 composite magic squares created this way, with consecutive numbers in each sub-square. In general, if there are cm and cn essentially different magic squares of order m and n, then we can form cm × cn × ( 8m2 + 8n2) composite squares of order mn, provided m ≠ n. If m = n, then we can form (cm)2 × 8m2 composite squares of order m2. For squares of doubly even order When the squares are of doubly even order, we can construct a composite magic square in a manner more elegant than the above process, in the sense that every magic subsquare will have the same magic constant. Let n be the order of the main square and m the order of the equal subsquares. The subsquares are filled one by one, in any order, with a continuous sequence of m2/2 smaller numbers (i.e. numbers less than or equal to n2/2) together with their complements to n2 + 1. Each subsquare as a whole will yield the same magic sum. The advantage of this type of composite square is that each subsquare is filled in the same way and their arrangement is arbitrary. Thus, the knowledge of a single construction of even order will suffice to fill the whole square. Furthermore, if the subsquares are filled in the natural sequence, then the resulting square will be pandiagonal. The magic sum of the subsquares is related to the magic sum of the whole square by where n = km. In the examples below, we have divided the order 12 square into nine subsquares of order 4 filled each with eight smaller numbers and, in the corresponding bishop's cells (two cells diagonally across, including wrap arounds, in the 4×4 subsquare), their complements to n2 + 1 = 145. Each subsquare is pandiagonal with magic constant 290; while the whole square on the left is also pandiagonal with magic constant 870. In another example below, we have divided the order 12 square into four order 6 squares. Each of the order 6 squares are filled with eighteen small numbers and their complements using bordering technique given by al-Antaki. If we remove the shaded borders of the order 6 subsquares and form an order 8 square, then this order 8 square is again a magic square. In its full generality, we can take any m2/2 smaller numbers together with their complements to n2 + 1 to fill the subsquares, not necessarily in continuous sequence. Medjig-method for squares of even order 2n, where n > 2 In this method a magic square is "multiplied" with a medjig square to create a larger magic square. The namesake of this method derives from mathematical game called medjig created by Willem Barink in 2006, although the method itself is much older. An early instance of a magic square constructed using this method occurs in Yang Hui's text for order 6 magic square. The LUX method to construct singly even magic squares is a special case of the medjig method, where only 3 out of 24 patterns are used to construct the medjig square. The pieces of the medjig puzzle are 2×2 squares on which the numbers 0, 1, 2 and 3 are placed. There are three basic patterns by which the numbers 0, 1, 2 and 3 can be placed in a 2×2 square, where 0 is at the top left corner: Each pattern can be reflected and rotated to obtain 8 equivalent patterns, giving us a total of 3×8 = 24 patterns. The aim of the puzzle is to take n2 medjig pieces and arrange them in an n × n medjig square in such a way that each row, column, along with the two long diagonals, formed by the medjig square sums to 3n, the magic constant of the medjig square. An n × n medjig square can create a 2n × 2n magic square where n > 2. Given an n×n medjig square and an n×n magic square base, a magic square of order 2n×2n can be constructed as follows: Each cell of an n×n magic square is associated with a corresponding 2×2 subsquare of the medjig square Fill each 2×2 subsquares of the medjig square with the four numbers from 1 to 4n2 that equal the original number modulo n2, i.e. x+n2y where x is the corresponding number from the magic square and y is a number from 0 to 3 in the 2×2 subsquares. Assuming that we have an initial magic square base, the challenge lies in constructing a medjig square. For reference, the sums of each medjig piece along the rows, columns and diagonals, denoted in italics, are: Doubly even squares: The smallest even ordered medjig square is of order 2 with magic constant 6. While it is possible to construct a 2×2 medjig square, we cannot construct a 4×4 magic square from it since 2×2 magic squares required to "multiply" it does not exist. Nevertheless, it is worth constructing these 2×2 medjig squares. The magic constant 6 can be partitioned into two parts in three ways as 6 = 5 + 1 = 4 + 2 = 3 + 3. There exist 96 such 2×2 medjig squares. In the examples below, each 2×2 medjig square is made by combining different orientations of a single medjig piece. We can use the 2×2 medjig squares to construct larger even ordered medjig squares. One possible approach is to simply combine the 2×2 medjig squares together. Another possibility is to wrap a smaller medjig square core with a medjig border. The pieces of a 2×2 medjig square can form the corner pieces of the border. Yet another possibility is to append a row and a column to an odd ordered medjig square. An example of an 8×8 magic square is constructed below by combining four copies of the left most 2×2 medjig square given above: The next example is constructed by bordering a 2×2 medjig square core. Singly even squares: Medjig square of order 1 does not exist. As such, the smallest odd ordered medjig square is of order 3, with magic constant 9. There are only 7 ways of partitioning the integer 9, our magic constant, into three parts. If these three parts correspond to three of the medjig pieces in a row, column or diagonal, then the relevant partitions for us are: 9 = 1 + 3 + 5 = 1 + 4 + 4 = 2 + 3 + 4 = 2 + 2 + 5 = 3 + 3 + 3. A 3×3 medjig square can be constructed with some trial-and-error, as in the left most square below. Another approach is to add a row and a column to a 2×2 medjig square. In the middle square below, a left column and bottom row has been added, creating an L-shaped medjig border, to a 2×2 medjig square given previously. The right most square below is essentially same as the middle square, except that the row and column has been added in the middle to form a cross while the pieces of 2×2 medjig square are placed at the corners. Once a 3×3 medjig square has been constructed, it can be converted into a 6×6 magic square. For example, using the left most 3×3 medjig square given above: There are 1,740,800 such 3×3 medjig squares. An easy approach to construct higher order odd medjig square is by wrapping a smaller odd ordered medjig square with a medjig border, just as with even ordered medjig squares. Another approach is to append a row and a column to an even ordered medjig square. Approaches such as the LUX method can also be used. In the example below, a 5×5 medjig square is created by wrapping a medjig border around a 3×3 medjig square given previously: Solving partially completed magic squares Solving partially completed magic squares is a popular mathematical pastime. The techniques needed are similar to those used in Sudoku or KenKen puzzles, and involve deducing the values of unfilled squares using logic and permutation group theory (Sudoku grids are not magic squares but are based on a related idea called Graeco-Latin squares). Variations of the magic square Extra constraints Certain extra restrictions can be imposed on magic squares. If raising each number to the nth power yields another magic square, the result is a bimagic (n = 2), a trimagic (n = 3), or, in general, a multimagic square. A magic square in which the number of letters in the name of each number in the square generates another magic square is called an alphamagic square. There are magic squares consisting entirely of primes. Rudolf Ondrejka (1928–2001) discovered the following 3×3 magic square of primes, in this case nine Chen primes: The Green–Tao theorem implies that there are arbitrarily large magic squares consisting of primes. The following "reversible magic square" has a magic constant of 264 both upside down and right way up: When the extra constraint is to display some date, especially a birth date, then such magic squares are called birthday magic square. An early instance of such birthday magic square was created by Srinivasa Ramanujan. He created a 4×4 square in which he entered his date of birth in D–M–C-Y format in the top row and the magic happened with additions and subtractions of numbers in squares. Not only do the rows, columns, and diagonals add up to the same number, but the four corners, the four middle squares (17, 9, 24, 89), the first and last rows two middle numbers (12, 18, 86, 23), and the first and last columns two middle numbers (88, 10, 25, 16) all add up to the sum of 139. Multiplicative magic squares Instead of adding the numbers in each row, column and diagonal, one can apply some other operation. For example, a multiplicative magic square has a constant product of numbers. A multiplicative magic square can be derived from an additive magic square by raising 2 (or any other integer) to the power of each element, because the logarithm of the product of 2 numbers is the sum of logarithm of each. Alternatively, if any 3 numbers in a line are 2a, 2b and 2c, their product is 2a+b+c, which is constant if a+b+c is constant, as they would be if a, b and c were taken from ordinary (additive) magic square. For example, the original Lo-Shu magic square becomes: Other examples of multiplicative magic squares include: Multiplicative magic squares of complex numbers Still using Ali Skalli's non iterative method, it is possible to produce an infinity of multiplicative magic squares of complex numbers belonging to set. On the example below, the real and imaginary parts are integer numbers, but they can also belong to the entire set of real numbers . The product is: −352,507,340,640 − 400,599,719,520 i. Additive-multiplicative magic and semimagic squares Additive-multiplicative magic squares and semimagic squares satisfy properties of both ordinary and multiplicative magic squares and semimagic squares, respectively. It is unknown if any additive-multiplicative magic squares smaller than 7×7 exist, but it has been proven that no 3×3 or 4×4 additive-multiplicative magic squares and no 3×3 additive-multiplicative semimagic squares exist. Geometric magic squares Magic squares may be constructed which contain geometric shapes instead of numbers. Such squares, known as geometric magic squares, were invented and named by Lee Sallows in 2001. In the example shown the shapes appearing are two dimensional. It was Sallows' discovery that all magic squares are geometric, the numbers that appear in numerical magic squares can be interpreted as a shorthand notation which indicates the lengths of straight line segments that are the geometric 'shapes' occurring in the square. That is, numerical magic squares are that special case of a geometric magic square using one dimensional shapes. Area magic squares In 2017, following initial ideas of William Walkington and Inder Taneja, the first linear area magic square (L-AMS) was constructed by Walter Trump. Other magic shapes Other two dimensional shapes than squares can be considered. The general case is to consider a design with N parts to be magic if the N parts are labeled with the numbers 1 through N and a number of identical sub-designs give the same sum. Examples include magic circles, magic rectangles, magic triangles magic stars, magic hexagons, magic diamonds. Going up in dimension results in magic spheres, magic cylinders, magic cubes, magic parallelepiped, magic solids, and other magic hypercubes. Possible magic shapes are constrained by the number of equal-sized, equal-sum subsets of the chosen set of labels. For example, if one proposes to form a magic shape labeling the parts with {1, 2, 3, 4}, the sub-designs will have to be labeled with {1,4} and {2,3}. Related problems n-Queens problem In 1992, Demirörs, Rafraf, and Tanik published a method for converting some magic squares into n-queens solutions, and vice versa. Magic squares in occultism Magic squares of order 3 through 9, assigned to the seven planets, and described as means to attract the influence of planets and their angels (or demons) during magical practices, can be found in several manuscripts all around Europe starting at least since the 15th century. Among the best known, the Liber de Angelis, a magical handbook written around 1440, is included in Cambridge Univ. Lib. MS Dd.xi.45. The text of the Liber de Angelis is very close to that of De septem quadraturis planetarum seu quadrati magici, another handbook of planetary image magic contained in the Codex 793 of the Biblioteka Jagiellońska (Ms BJ 793). The magical operations involve engraving the appropriate square on a plate made with the metal assigned to the corresponding planet, as well as performing a variety of rituals. For instance, the 3×3 square, that belongs to Saturn, has to be inscribed on a lead plate. It will, in particular, help women during a difficult childbirth. In about 1510 Heinrich Cornelius Agrippa wrote De Occulta Philosophia, drawing on the Hermetic and magical works of Marsilio Ficino and Pico della Mirandola. In its 1531 edition, he expounded on the magical virtues of the seven magical squares of orders 3 to 9, each associated with one of the astrological planets, much in the same way as the older texts did. This book was very influential throughout Europe until the Counter-Reformation, and Agrippa's magic squares, sometimes called kameas, continue to be used within modern ceremonial magic in much the same way as he first prescribed. The most common use for these kameas is to provide a pattern upon which to construct the sigils of spirits, angels or demons; the letters of the entity's name are converted into numbers, and lines are traced through the pattern that these successive numbers make on the kamea. In a magical context, the term magic square is also applied to a variety of word squares or number squares found in magical grimoires, including some that do not follow any obvious pattern, and even those with differing numbers of rows and columns. They are generally intended for use as talismans. For instance the following squares are: The Sator square, one of the most famous magic squares found in a number of grimoires including the Key of Solomon; a square "to overcome envy", from The Book of Power; and two squares from The Book of the Sacred Magic of Abramelin the Mage, the first to cause the illusion of a superb palace to appear, and the second to be worn on the head of a child during an angelic invocation: Magic squares in popular culture In Goethe's Faust, the witch's spell used to make a youth elixir for Faust, the , has been interpreted as a construction of a magic square. The English composer Peter Maxwell Davies has used magic squares to structure many of his compositions. For example, his 1975 Ave Maris Stella uses the 9×9 magic square of Moon while his 1977 A Mirror of Whitening Light uses the 8×8 magic square of Mercury to create the entire set of notes and durations for the piece. His other works that employ magic squares include The Lighthouse (1979), Resurrection (1987), Strathclyde Concerto No. 3 for Horn and Trumpet (1989), as well as many of his symphonies. According to Davies' own account: A magic square in a musical composition is not a block of numbers – it is a generating principle, to be learned and known intimately, perceived inwardly as a multi-dimensional projection into that vast (chaotic!) area of the internal ear – the space/time crucible – where music is conceived. ... Projected onto the page, a magic square is a dead, black conglomeration of digits; tune in, and one hears a powerful, orbiting dynamo of musical images, glowing with numen and lumen. Magic squares, including Benjamin Franklin's, appear as clues to the mystery in Katherine Neville's novels The Eight and The Fire. Magic squares play a role in Steve Martin's 2003 novel The Pleasure of My Company. Dürer's magic square and his Melencolia I both also played large roles in Dan Brown's 2009 novel, The Lost Symbol. In the 2011 Korean television drama Deep Rooted Tree, King Sejong is shown attempting to construct a 33×33 magic square using lunch boxes. He ultimately discovers the "pyramid method" and completes the magic square with the help of an army of court attendants. This inspires him to create a more just form of government ruled by reason and words rather than military might. On October 9, 2014, the post office of Macao in the People's Republic of China issued a series of stamps based on magic squares. The figure below shows the stamps featuring the nine magic squares chosen to be in this collection. The metallic artifact at the center of The X-Files episode "Biogenesis" is alleged by Chuck Burks to be a magic square. Mathematician Matt Parker attempted to create a 3×3 magic square using square numbers in a YouTube video on the Numberphile channel. His failed attempt is known as the Parker square. The first season Stargate Atlantis episode "Brotherhood" involves completing a magic square as part of a puzzle guarding a powerful Ancient artefact. Magic Squares are also featured in the 2019 Spanish film Vivir dos veces. See also Antimagic square Arithmetic sequence Associative magic square Combinatorial design Freudenthal magic square John R. Hendricks Hexagonal tortoise problem Latin square Magic circle Magic cube classes Magic polygon Magic series Most-perfect magic square Nasik magic hypercube Prime reciprocal magic square Room square Square matrices Sigil (magic) Sriramachakra Sudoku Unsolved problems in mathematics Vedic square Notes References Magic Squares at Convergence John Lee Fults, Magic Squares. (La Salle, Illinois: Open Court, 1974). Cliff Pickover, The Zen of Magic Squares, Circles, and Stars (Princeton, New Jersey: Princeton University Press) Leonhard Euler, On magic squares Leonhard Euler, Investigations on new type of magic square William H. Benson and Oswald Jacoby, "New Recreations with Magic Squares". (New York: Dover, 1976). Further reading External links Matrices Chinese mathematical discoveries Unsolved problems in mathematics Magic symbols	Magic square	[ "Mathematics" ]	24,700	[ "Matrices (mathematics)", "Unsolved problems in mathematics", "Mathematical problems", "Mathematical objects" ]
52,206	https://en.wikipedia.org/wiki/Nanowire	A nanowire is a nanostructure in the form of a wire with the diameter of the order of a nanometre (10−9 m). More generally, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length. At these scales, quantum mechanical effects are important—which coined the term "quantum wires". Many different types of nanowires exist, including superconducting (e.g. YBCO), metallic (e.g. Ni, Pt, Au, Ag), semiconducting (e.g. silicon nanowires (SiNWs), InP, GaN) and insulating (e.g. SiO2, TiO2). Molecular nanowires are composed of repeating molecular units either organic (e.g. DNA) or inorganic (e.g. Mo6S9−xIx). Characteristics Typical nanowires exhibit aspect ratios (length-to-width ratio) of 1000 or more. As such they are often referred to as one-dimensional (1-D) materials. Nanowires have many interesting properties that are not seen in bulk or 3-D (three-dimensional) materials. This is because electrons in nanowires are quantum confined laterally and thus occupy energy levels that are different from the traditional continuum of energy levels or bands found in bulk materials. A consequence of this quantum confinement in nanowires is that they exhibit discrete values of the electrical conductance. Such discrete values arise from a quantum mechanical constraint on the number electronic transport channels at the nanometer scale, and they are often approximately equal to integer multiples of the quantum of conductance: This conductance is twice the reciprocal of the resistance unit called the von Klitzing constant, defined as and named for Klaus von Klitzing, the discoverer of the integer quantum Hall effect. Examples of nanowires include inorganic molecular nanowires (Mo6S9−xIx, Li2Mo6Se6), which can have a diameter of 0.9 nm and be hundreds of micrometers long. Other important examples are based on semiconductors such as InP, Si, GaN, etc., dielectrics (e.g. SiO2,TiO2), or metals (e.g. Ni, Pt). There are many applications where nanowires may become important in electronic, opto-electronic and nanoelectromechanical devices, as additives in advanced composites, for metallic interconnects in nanoscale quantum devices, as field-emitters and as leads for biomolecular nanosensors. Synthesis There are two basic approaches to synthesizing nanowires: top-down and bottom-up. A top-down approach reduces a large piece of material to small pieces, by various means such as lithography, milling or thermal oxidation. A bottom-up approach synthesizes the nanowire by combining constituent adatoms. Most synthesis techniques use a bottom-up approach. Initial synthesis via either method may often be followed by a nanowire thermal treatment step, often involving a form of self-limiting oxidation, to fine tune the size and aspect ratio of the structures. After the bottom-up synthesis, nanowires can be integrated using pick-and-place techniques. Nanowire production uses several common laboratory techniques, including suspension, electrochemical deposition, vapor deposition, and VLS growth. Ion track technology enables growing homogeneous and segmented nanowires down to 8 nm diameter. As nanowire oxidation rate is controlled by diameter, thermal oxidation steps are often applied to tune their morphology. Suspension A suspended nanowire is a wire produced in a high-vacuum chamber held at the longitudinal extremities. Suspended nanowires can be produced by: The chemical etching of a larger wire The bombardment of a larger wire, typically with highly energetic ions Indenting the tip of a STM in the surface of a metal near its melting point, and then retracting it VLS growth A common technique for creating a nanowire is vapor–liquid–solid method (VLS), which was first reported by Wagner and Ellis in 1964 for silicon whiskers with diameters ranging from hundreds of nm to hundreds of μm. This process can produce high-quality crystalline nanowires of many semiconductor materials, for example, VLS–grown single crystalline silicon nanowires (SiNWs) with smooth surfaces could have excellent properties, such as ultra-large elasticity. This method uses a source material from either laser ablated particles or a feed gas such as silane. VLS synthesis requires a catalyst. For nanowires, the best catalysts are liquid metal (such as gold) nanoclusters, which can either be self-assembled from a thin film by dewetting, or purchased in colloidal form and deposited on a substrate. The source enters these nanoclusters and begins to saturate them. On reaching supersaturation, the source solidifies and grows outward from the nanocluster. Simply turning off the source can adjust the final length of the nanowire. Switching sources while still in the growth phase can create compound nanowires with super-lattices of alternating materials. For example, a method termed ENGRAVE (Encoded Nanowire GRowth and Appearance through VLS and Etching) developed by the Cahoon Lab at UNC-Chapel Hill allows for nanometer-scale morphological control via rapid in situ dopant modulation. A single-step vapour phase reaction at elevated temperature synthesises inorganic nanowires such as Mo6S9−xIx. From another point of view, such nanowires are cluster polymers. Similar to VLS synthesis, VSS (vapor-solid-solid) synthesis of nanowires (NWs) proceeds through thermolytic decomposition of a silicon precursor (typically phenylsilane). Unlike VLS, the catalytic seed remains in solid state when subjected to high temperature annealing of the substrate. This such type of synthesis is widely used to synthesise metal silicide/germanide nanowires through VSS alloying between a copper substrate and a silicon/germanium precursor. Solution-phase synthesis Solution-phase synthesis refers to techniques that grow nanowires in solution. They can produce nanowires of many types of materials. Solution-phase synthesis has the advantage that it can produce very large quantities, compared to other methods. In one technique, the polyol synthesis, ethylene glycol is both solvent and reducing agent. This technique is particularly versatile at producing nanowires of gold, lead, platinum, and silver. The supercritical fluid-liquid-solid growth method can be used to synthesize semiconductor nanowires, e.g., Si and Ge. By using metal nanocrystals as seeds, Si and Ge organometallic precursors are fed into a reactor filled with a supercritical organic solvent, such as toluene. Thermolysis results in degradation of the precursor, allowing release of Si or Ge, and dissolution into the metal nanocrystals. As more of the semiconductor solute is added from the supercritical phase (due to a concentration gradient), a solid crystallite precipitates, and a nanowire grows uniaxially from the nanocrystal seed. Liquid Bridge Induced Self-assembly Protein nanowires in spider silk have been formed by rolling a droplet of spider silk solution over a superhydrophobic pillar structure. Non-catalytic growth The vast majority of nanowire-formation mechanisms are explained through the use of catalytic nanoparticles, which drive the nanowire growth and are either added intentionally or generated during the growth. However, nanowires can be also grown without the help of catalysts, which gives an advantage of pure nanowires and minimizes the number of technological steps. The mechanisms for catalyst-free growth of nanowires (or whiskers) were known from 1950s. The simplest methods to obtain metal oxide nanowires use ordinary heating of the metals, e.g. metal wire heated with battery, by Joule heating in air can be easily done at home. Spontaneous nanowire formation by non-catalytic methods were explained by the dislocation present in specific directions or the growth anisotropy of various crystal faces. More recently, after microscopy advancement, the nanowire growth driven by screw dislocations or twin boundaries were demonstrated. The picture on the right shows a single atomic layer growth on the tip of CuO nanowire, observed by in situ TEM microscopy during the non-catalytic synthesis of nanowire. Atomic-scale nanowires can also form completely self-organised without need for defects. For example, rare-earth silicide (RESi2) nanowires of few nm width and height and several 100 nm length form on silicon(001) substrates which are covered with a sub-monolayer of a rare earth metal and subsequently annealed. The lateral dimensions of the nanowires confine the electrons in such a way that the system resembles a (quasi-)one-dimensional metal. Metallic RESi2 nanowires form on silicon(hhk) as well. This system permits tuning the dimensionality between two-dimensional and one-dimensional by the coverage and the tilt angle of the substrate. DNA-templated metallic nanowire synthesis An emerging field is to use DNA strands as scaffolds for metallic nanowire synthesis. This method is investigated both for the synthesis of metallic nanowires in electronic components and for biosensing applications, in which they allow the transduction of a DNA strand into a metallic nanowire that can be electrically detected. Typically, ssDNA strands are stretched, whereafter they are decorated with metallic nanoparticles that have been functionalised with short complementary ssDNA strands. Crack-Defined Shadow Mask Lithography A simple method to produce nanowires with defined geometries has been recently reported using conventional optical lithography. In this approach, optical lithography is used to generate nanogaps using controlled crack formation. These nanogaps are then used as shadow mask for generating individual nanowires with precise lengths and widths. This technique allows to produce individual nanowires below 20 nm in width in a scalable way out of several metallic and metal oxide materials. Physics Conductivity Several physical reasons predict that the conductivity of a nanowire will be much less than that of the corresponding bulk material. First, there is scattering from the wire boundaries, whose effect will be very significant whenever the wire width is below the free electron mean free path of the bulk material. In copper, for example, the mean free path is 40 nm. Copper nanowires less than 40 nm wide will shorten the mean free path to the wire width. Silver nanowires have very different electrical and thermal conductivity from bulk silver. Nanowires also show other peculiar electrical properties due to their size. Unlike single wall carbon nanotubes, whose motion of electrons can fall under the regime of ballistic transport (meaning the electrons can travel freely from one electrode to the other), nanowire conductivity is strongly influenced by edge effects. The edge effects come from atoms that lay at the nanowire surface and are not fully bonded to neighboring atoms like the atoms within the bulk of the nanowire. The unbonded atoms are often a source of defects within the nanowire, and may cause the nanowire to conduct electricity more poorly than the bulk material. As a nanowire shrinks in size, the surface atoms become more numerous compared to the atoms within the nanowire, and edge effects become more important. The conductance in a nanowire is described as the sum of the transport by separate channels, each having a different electronic wavefunction normal to the wire. The thinner the wire is, the smaller the number of channels available to the transport of electrons. As a result, wires that are only one or a few atoms wide exhibit quantization of the conductance: i.e. the conductance can assume only discrete values that are multiples of the conductance quantum (where e is the elementary charge and h is the Planck constant) (see also Quantum Hall effect). This quantization has been observed by measuring the conductance of a nanowire suspended between two electrodes while pulling it progressively longer: as its diameter reduces, its conductivity decreases in a stepwise fashion and the plateaus correspond approximately to multiples of G0. The quantization of conductivity is more pronounced in semiconductors like Si or GaAs than in metals, because of their lower electron density and lower effective mass. It can be observed in 25 nm wide silicon fins, and results in increased threshold voltage. In practical terms, this means that a MOSFET with such nanoscale silicon fins, when used in digital applications, will need a higher gate (control) voltage to switch the transistor on. Welding To incorporate nanowire technology into industrial applications, researchers in 2008 developed a method of welding nanowires together: a sacrificial metal nanowire is placed adjacent to the ends of the pieces to be joined (using the manipulators of a scanning electron microscope); then an electric current is applied, which fuses the wire ends. The technique fuses wires as small as 10 nm. For nanowires with diameters less than 10 nm, existing welding techniques, which require precise control of the heating mechanism and which may introduce the possibility of damage, will not be practical. Recently scientists discovered that single-crystalline ultrathin gold nanowires with diameters ≈ 3–10 nm can be "cold-welded" together within seconds by mechanical contact alone, and under remarkably low applied pressures (unlike macro- and micro-scale cold welding process). High-resolution transmission electron microscopy and in situ measurements reveal that the welds are nearly perfect, with the same crystal orientation, strength and electrical conductivity as the rest of the nanowire. The high quality of the welds is attributed to the nanoscale sample dimensions, oriented-attachment mechanisms and mechanically assisted fast surface diffusion. Nanowire welds were also demonstrated between gold and silver, and silver nanowires (with diameters ≈ 5–15 nm) at near room temperature, indicating that this technique may be generally applicable for ultrathin metallic nanowires. Combined with other nano- and microfabrication technologies, cold welding is anticipated to have potential applications in the future bottom-up assembly of metallic one-dimensional nanostructures. Mechanical properties The study of nanowire mechanics has boomed since the advent of the atomic force microscope (AFM), and associated technologies which have enabled direct study of the response of the nanowire to an applied load. Specifically, a nanowire can be clamped from one end, and the free end displaced by an AFM tip. In this cantilever geometry, the height of the AFM is precisely known, and the force applied is precisely known. This allows for construction of a force vs. displacement curve, which can be converted to a stress vs. strain curve if the nanowire dimensions are known. From the stress-strain curve, the elastic constant known as the Young's Modulus can be derived, as well as the toughness, and degree of strain-hardening. Young's modulus The elastic component of the stress-strain curve described by the Young's Modulus, has been reported for nanowires, however the modulus depends very strongly on the microstructure. Thus a complete description of the modulus dependence on diameter is lacking. Analytically, continuum mechanics has been applied to estimate the dependence of modulus on diameter: in tension, where is the bulk modulus, is the thickness of a shell layer in which the modulus is surface dependent and varies from the bulk, is the surface modulus, and is the diameter. This equation implies that the modulus increases as the diameter decreases. However, various computational methods such as molecular dynamics have predicted that modulus should decrease as diameter decreases. Experimentally, gold nanowires have been shown to have a Young's modulus which is effectively diameter independent. Similarly, nano-indentation was applied to study the modulus of silver nanowires, and again the modulus was found to be 88 GPa, very similar to the modulus of bulk Silver (85 GPa) These works demonstrated that the analytically determined modulus dependence seems to be suppressed in nanowire samples where the crystalline structure highly resembles that of the bulk system. In contrast, Si solid nanowires have been studied, and shown to have a decreasing modulus with diameter The authors of that work report a Si modulus which is half that of the bulk value, and they suggest that the density of point defects, and or loss of chemical stoichiometry may account for this difference. Yield strength The plastic component of the stress strain curve (or more accurately the onset of plasticity) is described by the yield strength. The strength of a material is increased by decreasing the number of defects in the solid, which occurs naturally in nanomaterials where the volume of the solid is reduced. As a nanowire is shrunk to a single line of atoms, the strength should theoretically increase all the way to the molecular tensile strength. Gold nanowires have been described as 'ultrahigh strength' due to the extreme increase in yield strength, approaching the theoretical value of E/10. This huge increase in yield is determined to be due to the lack of dislocations in the solid. Without dislocation motion, a 'dislocation-starvation' mechanism is in operation. The material can accordingly experience huge stresses before dislocation motion is possible, and then begins to strain-harden. For these reasons, nanowires (historically described as 'whiskers') have been used extensively in composites for increasing the overall strength of a material. Moreover, nanowires continue to be actively studied, with research aiming to translate enhanced mechanical properties to novel devices in the fields of MEMS or NEMS. Possible applications Electronic devices Nanowires have been proposed for use as MOSFETs (MOS field-effect transistors). MOS transistors are used widely as fundamental building elements in today's electronic circuits. As predicted by Moore's law, the dimension of MOS transistors is shrinking smaller and smaller into nanoscale. One of the key challenges of building future nanoscale MOS transistors is ensuring good gate control over the channel. In general, having a wider gate relative to the total transistor length affords greater gate control. Therefore, the high aspect ratio of nanowires potentially allows for good gate control. Due to their one-dimensional structure with unusual optical properties, the nanowire are of interest for photovoltaic devices. Compared with its bulk counterparts, the nanowire solar cells are less sensitive to impurities due to bulk recombination, and thus silicon wafers with lower purity can be used to achieve acceptable efficiency, leading to the reduction on material consumption. After p-n junctions were built with nanowires, the next logical step was to build logic gates. By connecting several p-n junctions together, researchers have been able to create the basis of all logic circuits: the AND, OR, and NOT gates have all been built from semiconductor nanowire crossings. In August 2012, researchers reported constructing the first NAND gate from undoped silicon nanowires. This avoids the problem of how to achieve precision doping of complementary nanocircuits, which is unsolved. They were able to control the Schottky barrier to achieve low-resistance contacts by placing a silicide layer in the metal-silicon interface. It is possible that semiconductor nanowire crossings will be important to the future of digital computing. Though there are other uses for nanowires beyond these, the only ones that actually take advantage of physics in the nanometer regime are electronic. In addition, nanowires are also being studied for use as photon ballistic waveguides as interconnects in quantum dot/quantum effect well photon logic arrays. Photons travel inside the tube, electrons travel on the outside shell. When two nanowires acting as photon waveguides cross each other the juncture acts as a quantum dot. Conducting nanowires offer the possibility of connecting molecular-scale entities in a molecular computer. Dispersions of conducting nanowires in different polymers are being investigated for use as transparent electrodes for flexible flat-screen displays. Because of their high Young's moduli, their use in mechanically enhancing composites is being investigated. Because nanowires appear in bundles, they may be used as tribological additives to improve friction characteristics and reliability of electronic transducers and actuators. Because of their high aspect ratio, nanowires are also suited to dielectrophoretic manipulation, which offers a low-cost, bottom-up approach to integrating suspended dielectric metal oxide nanowires in electronic devices such as UV, water vapor, and ethanol sensors. Due to their large surface-to-volume ratio, physico-chemical reactions are facilitated on the surface of nanowires. Single nanowire devices for gas and chemical sensing The high aspect ratio of nanowires makes this nanostructures suitable for electrochemical sensing with the potential for ultimate sensitivity. One of the challenge for the use of nanowires in commercial products is related to the isolation, handling, and integration of nanowires in an electrical circuit when using the conventional and manual pick-and-place approach, leading to a very limited throughput. Recent developments in the nanowire synthesis methods now allow for parallel production of single nanowire devices with useful applications in electrochemistry, photonics, and gas- and biosensing. Nanowire lasers Nanowire lasers are nano-scaled lasers with potential as optical interconnects and optical data communication on chip. Nanowire lasers are built from III–V semiconductor heterostructures, the high refractive index allows for low optical loss in the nanowire core. Nanowire lasers are subwavelength lasers of only a few hundred nanometers. Nanowire lasers are Fabry–Perot resonator cavities defined by the end facets of the wire with high-reflectivity, recent developments have demonstrated repetition rates greater than 200 GHz offering possibilities for optical chip level communications. Sensing of proteins and chemicals using semiconductor nanowires In an analogous way to FET devices in which the modulation of conductance (flow of electrons/holes) in the semiconductor, between the input (source) and the output (drain) terminals, is controlled by electrostatic potential variation (gate-electrode) of the charge carriers in the device conduction channel, the methodology of a Bio/Chem-FET is based on the detection of the local change in charge density, or so-called "field effect", that characterizes the recognition event between a target molecule and the surface receptor. This change in the surface potential influences the Chem-FET device exactly as a 'gate' voltage does, leading to a detectable and measurable change in the device conduction. When these devices are fabricated using semiconductor nanowires as the transistor element the binding of a chemical or biological species to the surface of the sensor can lead to the depletion or accumulation of charge carriers in the "bulk" of the nanometer diameter nanowire i.e. (small cross section available for conduction channels). Moreover, the wire, which serves as a tunable conducting channel, is in close contact with the sensing environment of the target, leading to a short response time, along with orders of magnitude increase in the sensitivity of the device as a result of the huge S/V ratio of the nanowires. While several inorganic semiconducting materials such as Si, Ge, and metal oxides (e.g. In2O3, SnO2, ZnO, etc.) have been used for the preparation of nanowires, Si is usually the material of choice when fabricating nanowire FET-based chemo/biosensors. Several examples of the use of silicon nanowire(SiNW) sensing devices include the ultra sensitive, real-time sensing of biomarker proteins for cancer, detection of single virus particles, and the detection of nitro-aromatic explosive materials such as 2,4,6-tri-nitrotoluene (TNT) in sensitives superior to these of canines. Silicon nanowires could also be used in their twisted form, as electromechanical devices, to measure intermolecular forces with great precision. Limitations of sensing with silicon nanowire FET devices Generally, the charges on dissolved molecules and macromolecules are screened by dissolved counterions, since in most cases molecules bound to the devices are separated from the sensor surface by approximately 2–12 nm (the size of the receptor proteins or DNA linkers bound to the sensor surface). As a result of the screening, the electrostatic potential that arises from charges on the analyte molecule decays exponentially toward zero with distance. Thus, for optimal sensing, the Debye length must be carefully selected for nanowire FET measurements. One approach of overcoming this limitation employs fragmentation of the antibody-capturing units and control over surface receptor density, allowing more intimate binding to the nanowire of the target protein. This approach proved useful for dramatically enhancing the sensitivity of cardiac biomarkers (e.g. Troponin) detection directly from serum for the diagnosis of acute myocardial infarction. Nanowire assisted transfer of sensitive TEM samples For a minimal introduction of stress and bending to transmission electron microscopy (TEM) samples (lamellae, thin films, and other mechanically and beam sensitive samples), when transferring inside a focused ion beam (FIB), flexible metallic nanowires can be attached to a typically rigid micromanipulator. The main advantages of this method include a significant reduction of sample preparation time (quick welding and cutting of nanowire at low beam current), and minimization of stress-induced bending, Pt contamination, and ion beam damage. This technique is particularly suitable for in situ electron microscopy sample preparation. Corn-like nanowires Corn-like nanowire is a one-dimensional nanowire with interconnected nanoparticles on the surface, providing a large percentage of reactive facets. TiO2 corn-like nanowires were first prepared by a surface modification concept using surface tension stress mechanism through a two consecutive hydrothermal operation, and showed an increase of 12% in dye-sensitized solar cell efficiency the light scattering layer. CdSe corn-like nanowires grown by chemical bath deposition and corn-like γ-Fe2O3@SiO2@TiO2 photocatalysts induced by magnetic dipole interactions have been also reported previously. See also Bacterial nanowires Molecular wire Nanoantenna Nanorod Nanowire battery Non-carbon nanotube Silicon nanowire Solar cell References External links Nanohedron.com \| Nano Image Gallery several images of nanowires are included in the galleries. Stanford's nanowire battery holds 10 times the charge of existing ones Original article on the Quantum Hall Effect: K. v. Klitzing, G. Dorda, and M. Pepper; Phys. Rev. Lett. 45, 494–497 (1980). Strongest theoretical nanowire produced at Australia's University of Melbourne. Penn Engineers Design Electronic Computer Memory in Nanoscale Form That Retrieves Data 1,000 Times Faster. One atom thick, hundreds of nanometers long Pt-nanowires are one of the best examples of self-assembly. (University of Twente) Nanoelectronics Electrical connectors Mesoscopic physics	Nanowire	[ "Physics", "Materials_science" ]	5,768	[ "Quantum mechanics", "Nanoelectronics", "Condensed matter physics", "Nanotechnology", "Mesoscopic physics" ]
52,211	https://en.wikipedia.org/wiki/Superellipse	A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse. In two dimensional Cartesian coordinate system, a superellipse is defined as the set of all points on the curve that satisfy the equationwhere and are positive numbers referred to as semi-diameters or semi-axes of the superellipse, and is a positive parameter that defines the shape. When , the superellipse is an ordinary ellipse. For , the shape is more rectangular with rounded corners, and for , it is more pointed. In the polar coordinate system, the superellipse equation is (the set of all points on the curve satisfy the equation): Specific cases This formula defines a closed curve contained in the rectangle and . The parameters and are the semi-diameters or semi-axes of the curve. The overall shape of the curve is determined by the value of the exponent , as shown in the following table: If , the figure is also called a hypoellipse; if , a hyperellipse. When and , the superellipse is the boundary of a ball of in the -norm. The extreme points of the superellipse are () and (), and its four "corners" are (,), where (sometimes called the "superness"). Mathematical properties When n is a positive rational number (in lowest terms), then each quadrant of the superellipse is a plane algebraic curve of order . In particular, when and n is an even integer, then it is a Fermat curve of degree n. In that case it is non-singular, but in general it will be singular. If the numerator is not even, then the curve is pieced together from portions of the same algebraic curve in different orientations. The curve is given by the parametric equations (with parameter having no elementary geometric interpretation)where each can be chosen separately so that each value of gives four points on the curve. Equivalently, letting range over where the sign function isHere is not the angle between the positive horizontal axis and the ray from the origin to the point, since the tangent of this angle equals while in the parametric expressions Area The area inside the superellipse can be expressed in terms of the gamma function asor in terms of the beta function as Perimeter The perimeter of a superellipse, like that of an ellipse, does not admit closed-form solution purely using elementary functions. Exact solutions for the perimeter of a superellipse exist using infinite summations; these could be truncated to obtain approximate solutions. Numerical integration is another option to obtain perimeter estimates at arbitrary precision. A closed-form approximation obtained via symbolic regression is also an option that balances parsimony and accuracy. Consider a superellipse centered on the origin of a 2D plane. Now, imagine that the superellipse (with shape parameter ) is stretched such that the first quadrant (e.g., , ) is an arc from to , with . Then, the arc length of the superellipse within that single quadrant is approximated as the following function of and : h + (((((n-0.88487077) * h + 0.2588574 / h) ^ exp(n / -0.90069205)) + h) + 0.09919785) ^ (-1.4812293 / n) This single-quadrant arc length approximation is accurate to within ±0.2% for across all values of , and can be used to efficiently estimate the total perimeter of a superellipse. Pedal curve The pedal curve is relatively straightforward to compute. Specifically, the pedal ofis given in polar coordinates by Generalizations The generalization of these shapes can involve several approaches.The generalizations of the superellipse in higher dimensions retain the fundamental mathematical structure of the superellipse while adapting it to different contexts and applications. Higher dimensions The generalizations of the superellipse in higher dimensions retain the fundamental mathematical structure of the superellipse while adapting it to different contexts and applications. A superellipsoid extends the superellipse into three dimensions, creating shapes that vary between ellipsoids and rectangular solids with rounded edges. The superellipsoid is defined as the set of all points that satisfy the equation:where and are positive numbers referred to as the semi-axes of the superellipsoid, and is a positive parameter that defines the shape. A hyperellipsoid is the -dimensional analogue of an ellipsoid (and by extension, a superellipsoid). It is defined as the set of all points that satisfy the equation:where are positive numbers referred to as the semi-axes of the hyperellipsoid, and is a positive parameter that defines the shape. Different exponents Using different exponents for each term in the equation, allowing more flexibility in shape formation. For two-dimensional case the equation is where either equals to or differs from . If , it is the Lamé's superellipses. If , the curve possesses more flexibility of behavior, and is better possible fit to describe some experimental information. For the three-dimensional case, three different positive powers , and can be used in the equation . If , a super-ellipsoid is obtained. If any two or all three powers differ from each other, a solid is obtained that may possess more flexibility in representing real structural data than the super ellipsoid. A three-dimensional super-ellipsoid with , and the semi-diameters , represents the structure of the National Centre for the Performing Arts in China. In the general –dimensional case, the equation is , where In general, may differ from each other. It is the superellipsoid only if . Related shapes Superquadrics are a family of shapes that include superellipsoids as a special case. They are used in computer graphics and geometric modeling to create complex, smooth shapes with easily adjustable parameters. While not a direct generalization of superellipses, hyperspheres also share the concept of extending geometric shapes into higher dimensions. These related shapes demonstrate the versatility and broad applicability of the fundamental principles underlying superellipses. Anisotropic scaling Anisotropic scaling involves scaling the shape differently along different axes, providing additional control over the geometry. This approach can be applied to superellipses, superellipsoids, and their higher-dimensional analogues to produce a wider variety of forms and better fit specific requirements in applications such as computer graphics, structural design, and data visualization. For instance, anisotropic scaling allows the creation of shapes that can model real-world objects more accurately by adjusting the proportions along each axis independently. History The general Cartesian notation of the form comes from the French mathematician Gabriel Lamé (1795–1870), who generalized the equation for the ellipse. Hermann Zapf's typeface Melior, published in 1952, uses superellipses for letters such as o. Thirty years later Donald Knuth would build the ability to choose between true ellipses and superellipses (both approximated by cubic splines) into his Computer Modern type family. The superellipse was named by the Danish poet and scientist Piet Hein (1905–1996) though he did not discover it as it is sometimes claimed. In 1959, city planners in Stockholm, Sweden announced a design challenge for a roundabout in their city square Sergels Torg. Piet Hein's winning proposal was based on a superellipse with n = 2.5 and a/b = 6/5. As he explained it: Sergels Torg was completed in 1967. Meanwhile, Piet Hein went on to use the superellipse in other artifacts, such as beds, dishes, tables, etc. By rotating a superellipse around the longest axis, he created the superegg, a solid egg-like shape that could stand upright on a flat surface, and was marketed as a novelty toy. In 1968, when negotiators in Paris for the Vietnam War could not agree on the shape of the negotiating table, Balinski, Kieron Underwood and Holt suggested a superelliptical table in a letter to the New York Times. The superellipse was used for the shape of the 1968 Azteca Olympic Stadium, in Mexico City. The second floor of the original World Trade Center in New York City consisted of a large, superellipse-shaped overhanging balcony. Waldo R. Tobler developed a map projection, the Tobler hyperelliptical projection, published in 1973, in which the meridians are arcs of superellipses. The logo for news company The Local consists of a tilted superellipse matching the proportions of Sergels Torg. Three connected superellipses are used in the logo of the Pittsburgh Steelers. In computing, mobile operating system iOS uses a superellipse curve for app icons, replacing the rounded corners style used up to version 6. See also Astroid, the superellipse with n = and a = b, is a hypocycloid with four cusps. Deltoid curve, the hypocycloid of three cusps. Squircle, the superellipse with n = 4 and a = b, looks like "The Four-Cornered Wheel." Reuleaux triangle, "The Three-Cornered Wheel." Superformula, a generalization of the superellipse. Superquadrics: superellipsoids and supertoroids, the three-dimensional "relatives" of superellipses. Superelliptic curve, equation of the form Yn = f(X). Lp spaces References External links "Lamé Curve" at MathCurve. "Super Ellipse" on 2dcurves.com Superellipse Calculator & Template Generator Superellipse fitting toolbox in MATLAB C code for fitting superellipses Plane curves	Superellipse	[ "Mathematics" ]	2,110	[ "Planes (geometry)", "Euclidean plane geometry", "Plane curves" ]
52,217	https://en.wikipedia.org/wiki/Free-rider%20problem	In economics, the free-rider problem is a type of market failure that occurs when those who benefit from resources, public goods and common pool resources do not pay for them or under-pay. Free riders may overuse common pool resources by not paying for them, neither directly through fees or tolls, nor indirectly through taxes. Consequently, the common pool resource may be under-produced, overused, or degraded. Additionally, despite evidence that people tend to be cooperative by nature (a prosocial behaviour), the presence of free-riders has been shown to cause cooperation to deteriorate, perpetuating the free-rider problem. In social science, the free-rider problem is the question of how to limit free riding and its negative effects in these situations, such as the free-rider problem of when property rights are not clearly defined and imposed. The free-rider problem is common with public goods which are non-excludable and non-rivalrous. The non-excludability and non-rivalry of public goods results in there being little incentive for consumers to contribute to a collective resource as they enjoy its benefits. A free rider may enjoy a non-excludable and non-rivalrous good such as a government-provided road system without contributing to paying for it. Another example is if a coastal town builds a lighthouse, ships from many regions and countries will benefit from it, even though they are not contributing to its costs, and are thus "free riding" on the navigation aid. A third example of non-excludable and non-rivalrous consumption would be a crowd watching fireworks. The number of viewers, whether they paid for the entertainment or not, does not diminish the fireworks as a resource. In each of these examples, the cost of excluding non-payers would be prohibitive, while the collective consumption of the resource does not decrease how much is available. Although the term "free rider" was first used in economic theory of public goods, similar concepts have been applied to other contexts, including collective bargaining, antitrust law, psychology, political science, and vaccines. For example, some individuals in a team or community may reduce their contributions or performance if they believe that one or more other members of the group may free ride. The economic free-rider problem is equally pertinent within the realm of global politics, often presenting challenges in international cooperation and collective action. In global politics, states are confronted with scenarios where certain actors reap the benefits of collective goods or actions without bearing the costs or contributing to the efforts required to achieve these shared objectives. This phenomenon creates imbalances and hampers cooperative endeavors, particularly in addressing transnational challenges like climate change, global security, or humanitarian crises. For instance, in discussions on climate change mitigation, countries with lesser contributions to greenhouse gas emissions might still benefit from global efforts to reduce emissions, enjoying a stable climate without proportionally shouldering the costs of emission reductions. This creates a disparity between states' contributions and their gains, leading to challenges in negotiating and implementing effective international agreements. The economic free-rider problem's manifestation in global politics underscores the complexities and obstacles encountered in fostering collective action and equitable burden-sharing among nations to address pressing global issues. Incentive The underlying incentive which generates the free-rider problem can be explained via the application of the prisoner's dilemma within the context of contributing to a public good. Suppose two people were to split a contribution to a public service (such as for a fire station) with society benefiting from their contribution. According to the prisoner's dilemma, certain conclusions can be drawn from the results of this scenario: If both parties donate, they both do so out of pocket, and society benefits. If one party doesn't pay (in the hopes that someone else will), they become a free-rider, and the other will have to cover the cost. If the other party also decides to become a free-rider and not pay either, then society receives no benefit. This demonstrates that the free-rider problem is generated by individuals' willingness to let others pay when they themselves can receive the benefit at zero cost. This is reinforced by the economic theory of rational choice, which states that people make choices which they infer will provide them with the greatest benefit. Therefore, if a service or resource is offered for free, then a consumer will not pay for it. Economic issues Free riding is a problem of economic inefficiency when it leads to the underproduction or overconsumption of a good. For example, when people are asked how much they value a particular public good, with that value measured in terms of how much money they would be willing to pay, their tendency is to under-report their valuations. Goods that are subject to free riding are usually characterized by: the inability to exclude non-payers, its consumption by an individual does not impact the availability for others and that the resource in question must be produced and/or maintained. Indeed, if non-payers can be excluded by some mechanism, the good may be transformed into a club good (e.g. if an overused, congested public road is converted to a toll road, or if a free public museum turns into a private, admission fee-charging museum). Free riders become a problem when non-excludable goods are also rivalrous. These goods, categorized as common-pool resources, are characterized by overconsumption when common property regimes are not implemented. Not only can consumers of common-property goods benefit without payment, but consumption by one imposes an opportunity cost on others. The theory of 'Tragedy of the commons' highlights this, in which each consumer acts to maximize their own utility and thereby relies on others to cut back their own consumption. This will lead to overconsumption and even possibly exhaustion or destruction of the good. If too many people start to free ride, a system or service will eventually not have enough resources to operate. Free-riding is experienced when the production of goods does not consider the external costs, particularly the use of ecosystem services. An example of this is global climate change initiatives. As climate change is a global issue and there is no global regime to manage the climate, the benefits of reduced emissions in one country will extend beyond their own countries' borders and impact countries worldwide. However, this has resulted in some countries acting in their own self-interest, limiting their own efforts and free-riding on the work of others. In some countries, citizens and governments do not wish to contribute to the associated effort and costs of mitigation, as they are able to free-ride on the efforts of others. This free rider problem also raises questions in regards to the fairness and ethics of these practices, as countries most likely to suffer the consequences of climate change, are also those who typically emit the least greenhouse gases and have fewer economic resources to contribute to the efforts, such as the small island country of Tuvalu. Theodore Groves and John Ledyard believe that Pareto-optimal allocation of resources in relation to public goods is not compatible with the fundamental incentives belonging to individuals. Therefore, the free-rider problem, according to most scholars, is expected to be an ongoing public issue. For example, Albert O. Hirschman believed that the free-rider problem is a cyclical one for capitalist economies. Hirschman considers the free-rider problem to be related to the shifting interests of people. When stress levels rise on individuals in the workplace and many fear losing their employment, they devote less of their human capital to the public sphere. When public needs then increase, disenchanted consumers become more interested in collective action projects. This leads individuals to organize themselves in various groups and the results are attempts to solve public problems. In effect this reverses the momentum of free riding. Activities often seen as costs in models focused on self-interest are instead seen as benefits for the individuals who were previously dissatisfied consumers seeking their private interests. This cycle will reset itself because as individuals' work for public benefit becomes less praiseworthy, supporters' level of commitment to collective action projects will decrease. With the decrease in support, many will return to private interests, which with time resets the cycle. Supporters of Hirschman's model insist that the important factor in motivating people is that they are compelled by a leader's call to altruism. In John F. Kennedy's inaugural address he implored the American people to "ask not what your country can do for you; ask what you can do for your country." Some economists (for example, Milton Friedman) find these calls to altruism to be nonsensical. Scholars like Friedman do not think the free-rider problem is part of an unchangeable virtuous or vicious circle, but instead seek possible solutions or attempts at improvement elsewhere. Economic and political solutions Assurance contracts An assurance contract is a contract in which participants make a binding pledge to contribute to building a public good, contingent on a quorum of a predetermined size being reached, otherwise the good is not provided and any monetary contributions are refunded. A dominant assurance contract is a variation in which an entrepreneur creates the contract and refunds the initial pledge plus an additional sum of money if the quorum is not reached. The entrepreneur profits by collecting a fee if the quorum is reached and the good is provided. In terms of game theory, this makes pledging to build the public good a dominant strategy: the best move is to abide by the contract regardless of the actions of others. Coasian solution A Coasian solution, named for the economist Ronald Coase, proposes that potential beneficiaries of a public good can negotiate to pool their resources and create it, based on each party's self-interested willingness to pay. His treatise, The Problem of Social Cost (1960), argued that if the transaction costs between potential beneficiaries of a public good are low—that it is easy for potential beneficiaries to find each other and organize pooling their resources based upon the good's value to each of them—that public goods could be produced without government action. Much later, Coase himself wrote that while what had become known as the Coase Theorem had explored the implications of zero-transaction costs, he had actually intended to use this construct as a stepping stone to understand the real world of positive transaction costs, corporations, legal systems and government actions:I examined what would happen in a world in which transaction costs were assumed to be zero. My aim in doing so was not to describe what life would be like in such a world but to provide a simple setting in which to develop the analysis and, what was even more important, to make clear the fundamental role which transaction costs do, and should, play in the fashioning of the institutions which make up the economic system.Coase also wrote:The world of zero transaction costs has often been described as a Coasian world. Nothing could be further from the truth. It is the world of modern economic theory, one which I was hoping to persuade economists to leave. What I did in "The Problem of Social Cost" was simply to shed light on some of its properties. I argued in such a world the allocation of resources would be independent of the legal position, a result which Stigler dubbed the "Coase theorem". Thus, while Coase himself appears to have considered the "Coase theorem" and Coasian solutions as simplified constructs to ultimately consider the real 20th-century world of governments, laws, and corporations, these concepts have become attached to a world where transaction costs were much lower and government intervention would unquestionably be less necessary. Fundraising A minor alternative, especially for information goods, is for the producer to refuse to release a good to the public until payment to cover costs is met. For instance, Stephen King authored chapters of a new novel downloadable for free on his website while stating that he would not release subsequent chapters unless a certain amount of money was raised. Sometimes dubbed holding for ransom, this method of public goods production is a modern application of the street performer protocol for public goods production. Unlike assurance contracts, its success relies largely on social norms to ensure (to some extent) that the threshold is reached and partial contributions are not wasted. One of the purest Coasian solutions today is the new phenomenon of Internet crowdfunding, in which case rules are enforced by computer algorithms and legal contracts, as well as social pressure. For example, on the Kickstarter site, each funder authorizes a credit card purchase to buy a new product or receive other promised benefits, but no money changes hands until the funding goal is met. Because automation and the Internet greatly reduce the transaction costs for pooling resources, project goals of only a few hundred dollars are frequently crowdfunded, far below the costs of soliciting traditional investors. Introducing an exclusion mechanism (club goods) Another solution, which has evolved for information goods, is to introduce exclusion mechanisms which turn public goods into club goods. One well-known example is copyright and patent laws. These laws, which in the 20th century came to be called intellectual property laws, attempt to remove the natural non-excludability by prohibiting reproduction of the good. Although they can address the free rider problem, the downside of these laws is that they imply private monopoly power and thus are not Pareto-optimal. For example, in the United States, the patent rights given to pharmaceutical companies encourage them to charge high prices (above marginal cost) and to advertise to convince patients to persuade their doctors to prescribe the drugs. Likewise, copyright provides an incentive for publishers to take older works out of print so as not to cannibalize revenue from newer works. An example from the entertainment industry is Walt Disney Studios Home Entertainment's "vault" sales practice, and an example from the technology industry is Microsoft's decision to pull Windows XP from the market in mid-2008 to drive revenue from the widely criticized Windows Vista operating system. Intellectual property laws also end up encouraging patent and copyright owners to sue even mild imitators in court and to lobby for the extension of the term of the exclusive rights in a form of rent seeking. These problems with the club-good mechanism arise because the underlying marginal cost of giving the good to more people is low or zero, but because of the limits of price discrimination, those who are unwilling or unable to pay a profit-maximizing price do not gain access to the good. If the costs of the exclusion mechanism are not higher than the gain from the collaboration, club goods can emerge naturally. James M. Buchanan showed in his seminal paper that clubs can be an efficient alternative to government interventions. On the other hand, the inefficiencies and inequities of club goods exclusions sometimes cause potentially excludable club goods to be treated as public goods, and their production financed by some other mechanism. This explains why many such goods, often known as social goods, are often provided or subsidized by governments, co-operatives, or volunteer associations, rather than being left to be supplied by profit-minded entrepreneurs. Joseph Schumpeter claimed that the "excess profits" (or profits over normal profit) generated by the copyright or patent monopoly will attract competitors that would make technological innovations and thereby end the monopoly. This is a continual process referred to as "Schumpeterian creative destruction", and its applicability to different types of public goods is a source of some controversy. Supporters of the theory point to cases such as that of Microsoft, which has been increasing its prices (or lowering its products' quality), predicting that these practices will make increased market shares for Linux and Apple largely inevitable. A nation can be considered akin to a club whose members are its citizens. The government would then be the manager of this club. This is further studied in the theory of the state. Non-altruistic social sanctions (common property regimes) Often on the foundation of game theory, experimental literature suggests that free-riding situations can be improved without any state intervention by seeking to measure the effects of various forms of social sanctions. Peer-to-peer punishment, that is, when members sanction other members that do not contribute to the common pool resource by inflicting a cost on "free-riders", is considered sufficient to establish and maintain cooperation. Social actions come at a cost to the punisher, which discourages individuals from taking action to punish the free-rider. Therefore, punishers often need to be rewarded for following through with their punishment for the resource to be effectively managed. Unlike a prisoner's dilemma where the prisoners are prohibited from communicating and strategizing, people can get together to form "common property regimes" in which the group weighs the costs and benefits of rewarding individuals for sanctioning free riders. So long as the benefits of preserving the resource outweigh the cost of communication and enforcement, members often compensate punishers for sanctioning free riders. While the outcome is not Pareto-optimal, as the group has the additional cost of paying for enforcement, it is often less costly than letting the resource deplete. In the limiting case, where the costs of bargaining and enforcement approach zero, the setup becomes Coasian as the solution approaches the Pareto-optimal solution. Both punishment and regulation by the state work relatively badly under imperfect information, where people cannot observe the behavior of others. Often common property regimes which members establish through bargaining have more information about the specific common pool resource which they are managing than outsiders. For this reason, and because common property regimes can avoid the principal-agent problem, the specific local knowledge within common property regimes typically enables them to outperform regulations designed by outside technical experts. Nevertheless, the best performance is typically achieved when people in common property regimes consult with governments and technical experts while deciding on the rules and design of their firm, thereby combining local and technical knowledge. Altruistic solutions Social norms Psychologically, humans are fundamentally considered as free-riders by others only when benefits are consumed while contributions are withheld. Indicating that in all cultures free-riders are recognised, however, cultural differences exist in the degree of tolerance and how these people dealt with them. The impact of social norms on the free-rider problem differs between cultural contexts, which may lead to a variance between results in research on the free-rider problem when applied cross-culturally. Social norms impact on privately and voluntarily provided public goods; however, is considered to have some level of effect on the problem in many contexts. Social sanctioning, for example, is a norm in and of itself that has a high degree of universality. The goal of much research on the topic of social sanctioning and its effect on the free-rider problem is to explain the altruistic motivation that is observed in various societies. Free riding is often thought of only in terms of positive and negative externalities felt by the public. The impact of social norms on actions and motivations related to altruism are often underestimated in economic solutions and the models from which they are derived. Altruistic social sanctions While non-altruistic social sanctions occur when people establish common property regimes, people sometimes punish free-riders even without being rewarded. The exact nature of motivation remains to be explored. Whether costly punishment can explain cooperation is disputed. Recent research finds that costly punishment is less effective in real world environments. Other research finds that social sanctions cannot be generalized as strategic in the context of public goods. Preferences between secret sanctions (untraceable sanctions between players in the game) and standard sanctions (traceable sanctions including feedback between players in an otherwise identical environment) on free riders did not vary significantly. Rather some individuals preferred to sanction others regardless of secrecy. Other research build on the findings of behavioral economics, finds that in a dilemmatic donation game, donators are motivated by the fear of loss. In the game donators' deposits were only refunded if the donators always punish free riding and non-commitment among other individuals. Pool-punishment (everyone loses their deposit if one donator doesn't punish the free rider) provided more stable results than punishment without consideration of the consensus of the group. Individual-to-individual peer punishment led to less consistently applied social sanctions. Collectively this research, although it is experimental in nature, may prove useful when applied in public policy decisions seeking to improve free-rider problems within society. See also Common pool resource Economic surplus Freedom Riders Forced rider Leech (computing) The Logic of Collective Action Moral hazard Parasitism (social offense) Prisoner's dilemma Tragedy of the commons References Notes Further reading William D. Nordhaus, "A New Solution: the Climate Club" (a review of Gernot Wagner and Martin L. Weitzman, Climate Shock: The Economic Consequences of a Hotter Planet, Princeton University Press, 250 pp, $27.95), The New York Review of Books, vol. LXII, no. 10 (June 4, 2015), pp. 36–39. P. Oliver – Sociology 626 published by Social Science Computing Cooperative University of Wisconsin Market failure Tragedy of the commons Dilemmas	Free-rider problem	[ "Mathematics" ]	4,337	[ "Game theory", "Tragedy of the commons" ]
52,224	https://en.wikipedia.org/wiki/The%20Diamond%20Age	The Diamond Age: Or, A Young Lady's Illustrated Primer is a science fiction novel by American writer Neal Stephenson. It is to some extent a Bildungsroman or coming-of-age story, focused on a young girl named Nell, set in a future world in which nanotechnology affects all aspects of life. The novel deals with themes of education, social class, ethnicity, and the nature of artificial intelligence. The Diamond Age was first published in 1995 by Bantam Books, as a Bantam Spectra hardcover edition. In 1996, it won both the Hugo and Locus Awards, and was shortlisted for the Nebula and other awards. Setting The Diamond Age depicts a near-future world revolutionised by advances in nanotechnology, much as Eric Drexler envisioned it in his 1986 nonfiction book Engines of Creation. Molecular nanotechnology is omnipresent in the novel's world, generally in the form of Matter Compilers and the products that come out of them. The book explicitly recognizes the achievements of several existing nanotechnology researchers: Feynman, Drexler, and Ralph Merkle are seen among characters of the fresco in Merkle-Hall, where new nanotechnological items are designed and constructed. The book contains descriptions of various exotic technologies, such as the chevaline (a mechanical horse that can fold up and is light enough to be carried one-handed), and forecasts the use of technologies that are in development today, such as smart paper that can show personalized news headlines. Major cities have immune systems made up of aerostatic defensive micromachines, and public matter compilers provide basic food, blankets, and water for free to anyone who requests them. Matter compilers receive their raw materials from the Feed, a system analogous to the electrical grid of modern society. The Feed carries streams of both energy and basic molecules, which are rapidly assembled into usable goods by matter compilers. The Source, where the Feed's stream of matter originates, is controlled by the Victorian phyle (though smaller, independent Feeds are possible). The hierarchic nature of the Feed and an alternative, anarchic developing technology, known as the Seed, mirror the cultural conflict between East and West that is depicted in the book. This conflict has an economic element as well, with the Feed representing a centrally-controlled distribution mechanism, while the Seed represents a more flexible, open-ended, decentralized method of creation and organization. Phyles Society in The Diamond Age is dominated by a number of phyles, also sometimes called tribes, which are groups of people often distinguished by shared values, similar ethnic heritage, a common religion, or other cultural similarities. In the extremely globalized future depicted in the novel, these cultural divisions have largely supplanted the system of nation-states that divides the world today. Cities appear divided into sovereign enclaves affiliated or belonging to different phyles within a single metropolis. Most phyles depicted in the novel have a global scope of sovereignty, and maintain segregated enclaves in or near many cities throughout the world. The phyles coexist much like historical nation-states under a system of justice and mutual protection, known as the Common Economic Protocol (CEP). The rules of the CEP are intended to provide for the co-existence of, and peaceful economic activity between, phyles with potentially very different values. The CEP is concerned particularly with upholding rights to personal property, being shown to provide particularly harsh punishment for harming the economic capability of another person. "Thetes" are individuals who are not members of any phyle and are often socially disadvantaged and economically poor, being similar to second-class citizens under the CEP. In the novel, the material needs of nearly all thetes are satisfied by freely available food and clothing, albeit of low quality; thetes without the political connections of a phyle are entitled to similarly low-quality "free justice." The book distinguishes between the four Great Phyles: the Han (consisting of Han Chinese), Nippon (consisting of Japanese), Hindustan (a "riotously diverse collection of microtribes sintered together according to some formula we don't get") and the Neo-Victorian New Atlantis (consisting largely of Anglo-Saxons but also accepting Indians, Africans, and other members of the Anglosphere who identify with the culture). Internally, the New Atlantis phyle is a corporate oligarchy whose "equity lords" rule the organization and its bylaws under allegiance to the vestigial British monarchy. Other phyles are less defined – some intentionally, as with the CryptNet group or the mysterious hive-mind Drummers. Over the course of the story, the Common Economic Protocol sponsors the investigation of clandestine Seed technologies in order to preserve the established order from subversion, using the justification that unrestricted access to Sources would lead to the proliferation of high tech weapons and result in anarchy. Plot summary The protagonist in the story is Nell, a thete (or person without a tribe; equivalent to the lowest working class) living in the Leased Territories, a lowland slum built on the artificial, diamondoid island of New Chusan, located offshore from the mouth of the Yangtze River, northwest of Shanghai. When she is four, Nell's older brother Harv gives her a stolen copy of a highly sophisticated interactive book, Young Lady's Illustrated Primer: a Propædeutic Enchiridion, in which is told the tale of Princess Nell and her various friends, kin, associates, etc., commissioned by the wealthy Neo-Victorian "Equity Lord" Alexander Chung-Sik Finkle-McGraw for his granddaughter, Elizabeth. The story follows Nell's development under the tutelage of the Primer, and to a lesser degree, the lives of Elizabeth Finkle-McGraw and Fiona Hackworth, Neo-Victorian girls who receive other copies. The Primer is intended to steer its reader intellectually toward a more interesting life, as defined by Lord Finkle-McGraw, and growing up to be an effective member of society. The most important quality to achieving an interesting life is deemed to be a subversive attitude towards the status quo. The Primer is designed to react to its owner's environment and teach them what they need to know to survive and develop. The Diamond Age features intersecting story lines: the social downfall of the nanotech engineer designer of the Primer, John Percival Hackworth, who makes an unauthorized copy of the Primer for his own young daughter, Fiona, and Nell's education through her independent work with the Primer after her brother Harv steals it from Hackworth. Hackworth's crime becomes known to Dr. X, the black market engineer whose compiler Hackworth used to create the copy of the Primer, and later Lord Finkle-McGraw. Hackworth is compelled by both to advance their opposing goals. Another storyline follows actress ("ractor") Miranda Redpath, who voices most of the Primer characters who interact with Nell and effectively becomes a surrogate mother to Nell. After Miranda disappears in her quest to find Nell, her storyline continues from the point of view of her boss, Carl Hollywood. The Diamond Age also includes fully narrated educational tales from the Primer that map Nell's individual experience (e.g. her four toy friends) onto archetypal folk tales stored in the primer's database. The story explores the role of technology and personal relationships in child development, and its deeper themes also probe the relative values of cultures. Title "Diamond Age" is an extension of labels for archeological time periods that take central technological materials to define an entire era of human history, such as the Stone Age, the Bronze Age or the Iron Age. Technological visionaries such as Eric Drexler and Ralph Merkle, both of whom receive an honorary mention in The Diamond Age, have argued that if nanotechnology develops the ability to manipulate individual atoms at will, it will become possible to simply assemble diamond structures from carbon atoms, materials also known as diamondoids. Merkle states: "In diamond, then, a dense network of strong bonds creates a strong, light, and stiff material. Indeed, just as we named the Stone Age, the Bronze Age, and the Steel Age after the materials that humans could make, we might call the new technological epoch we are entering the Diamond Age". In the novel, a near future vision of our world, nanotechnology has developed precisely to this point, which enables the cheap production of diamond structures. Characters Nell – The story's protagonist, from the viewpoint of the novel as a coming-of-age story. She is born to Tequila, a lower-class single mother, and, with the help of the nanotech Primer, grows up to become an independent woman and the leader of a new phyle. Harv – Nell's older brother, who plays an important role in the beginning as her protector; he obtains the Primer for his sister by mugging John Percival Hackworth. Harv is forced to leave Nell when she is accepted by the Neo-Victorians, and is later bedridden by asthma caused by the inhalation of dead nanomachines ("toner") in his childhood. Bud – A petty criminal and "thete", or tribeless individual, Bud is Tequila's boyfriend and Nell and Harv's father. He is obsessed with his muscular body, and possesses a cranial weapon implant (known as a "skull gun"), which he uses to mug people. When he robs a couple who are members of the powerful Ashanti phyle, he is executed for this crime early in the novel. Tequila – Nell and Harv's neglectful thete mother. After Bud's death, she has a series of boyfriends who mistreat the children to varying degrees. John Percival Hackworth – The novel's second protagonist. He is a Neo-Victorian nanotech engineer, and develops the code for the Primer. He makes an illicit copy of the Primer for his daughter Fiona, who is Nell's age. When his crime is detected, he is forced to become a double agent in a covert power struggle between the Neo-Victorians and the Chinese Celestial Kingdom. Hackworth is forced to spend ten years with a colony of "Drummers," subsuming his personality into their gestalt intelligence (similar but not identical to distributed artificial intelligence) for the development of the Seed, an indigenous nanotechnology that aims to end Chinese dependence on the Victorian-controlled Feed. Fiona Hackworth – Hackworth's daughter, and his motivation for stealing a second copy of the Primer. During Hackworth's decade-long altered consciousness with the Drummers, he is able to maintain a connection with his daughter through the Primer, and when he returns she joins him, eventually choosing to stay with a surrealistic acting troupe in London. Gwendolyn Hackworth – Hackworth's wife and Fiona's mother, who divorces Hackworth during his long absence. Lord Alexander Chung-Sik Finkle-McGraw – A Neo-Victorian "Equity Lord" with the Apthorp conglomerate, who commissions the development of the Primer for his granddaughter Elizabeth. Elizabeth Finkle-McGraw – Lord Finkle-McGraw's granddaughter. It was for her that the project to develop the Illustrated Primer was begun. However, she never became as engrossed in the stories created by the Primer as Nell, and later rebelled against her Neo-Victorian upbringing due in part to the abuse by Miss Stricken, one of her teachers. Elizabeth runs away from her wealthy aristocratic family to join the secretive CryptNet phyle. Lord Finkle-McGraw expresses satisfaction with this outcome to Carl Hollywood, deeming it akin to youthful rebellion. Judge Fang – A New York-born Chinese Confucian judge who sentences Bud to death in the beginning of the book. He also investigates Hackworth's mugging by Harv and his gang. As a civil official with deep Confucian principles, his decision to let Nell keep the stolen primer is one of the pivotal plot elements that allows Nell's story to unfold. The fallout from that choice leads him to question his allegiances to the Coastal Republic (which rules Shanghai and the surrounding area), and he eventually joins the inland Celestial Kingdom. Lieutenant Chang and Miss Pao – Judge Fang's assistants. Dr. X. – A mysterious character who evolves from being an illicit technology specialist and hacker to being a powerful Confucian leader and nefarious force. His name comes from the fact that most westerners cannot pronounce his Chinese name; he encourages people to instead call him by the first letter of his name. Constable Moore - Constable of the Dovetail community, semi-retired soldier, and Nell's adoptive father/guardian. Miranda Redpath – A "ractor" (actor in interactive movies) who, by performing in the stories of Nell's Primer, effectively becomes a mother figure for Nell. Carl Hollywood – A theatrical company director and Miranda's boss and adviser. He becomes more important towards the end of the novel, helping Miranda on her quest to find Nell, and aiding the escape of Coastal Republic refugees from the encroaching anti-Western Fists of the Celestial Kingdom. Nell appoints him as a trusted advisor of her new phyle. Miss Matheson – The head teacher at the academy where Nell, Fiona, and Elizabeth attend. She instructs Nell to find her own path. Miss Stricken – An authoritarian teacher at Miss Matheson's Academy who frequently uses corporal punishment on the students for minor infractions. During a confrontation with Nell, Stricken attempts to strike her with the ruler only to be immediately disarmed due to Nell's physical training by the Primer. This leads to her, Elizabeth and Fiona all being placed in detention, where they are forced to mindlessly copy from textbooks. Reception Reviews Michael Berry of the San Francisco Chronicle wrote: "Stephenson's world-building skills are extraordinary, and while he sometimes lets his narrative ramble or grow complicated, he can be depended upon to serve up plenty of clever extrapolations." Gerald Jonas of The New York Times: "While the final chapters of the novel veer toward the stylistic excesses that marred Snow Crash, Mr. Stephenson mostly holds to his theme." Marc Laidlaw of Wired magazine praised the characters, the setting, and called the "rich and polished, the inventiveness unceasing" but found it ultimately disappointing saying Stephenson "gave himself an enormous task and nearly succeeded in all respects, instead of "merely" most of them." Awards In 1996, it won both the Hugo and Locus Awards, and was shortlisted for the Nebula and other awards. Allusions to other works and genres Charles Dickens. The novel's neo-Victorian setting, as well as its narrative form, particularly the chapter headings, suggest a relation to the work of Charles Dickens. The protagonist's name points directly to Little Nell from Dickens' 1840 novel The Old Curiosity Shop. Judge Dee mysteries. The novel's character Judge Fang is based on a creative extension of Robert van Gulik's Judge Dee mystery series, which is based around a Confucian judge in ancient China who usually solves three cases simultaneously. The Judge Dee stories are based on the tradition of Chinese mysteries, transposing key elements into Western detective fiction. The Wizard of Oz. When Nell enters the castle of King Coyote in the Primer's final challenge for her, she encounters an enormous computer apparently designed to think and placed in charge of the kingdom. The computer is named "Wizard 0.2", a typographical allusion to The Wonderful Wizard of Oz. In that book, the Wizard puts on a grand appearance but is later revealed to be merely a man hiding behind a curtain. In similar fashion, Wizard 0.2 creates an impressive light show as it apparently processes data, but it is revealed that the computer's decisions are in fact made by King Coyote himself. Proposed television adaptation In January 2007, the Sci-Fi Channel announced a planned six-hour miniseries based on The Diamond Age. According to a June 2009 report in Variety, Zoë Green had been hired to write the series, with George Clooney and Grant Heslov of Smokehouse Productions as executive producers on the project. Allusions to The Diamond Age During the early stages of its development, the Amazon Kindle e-reader was codenamed "Fiona", as a deliberate reference to the Illustrated Primer and Fiona Hackworth. See also Molecular nanotechnology Nanotechnology in fiction Post-scarcity Technological singularity References Bibliography 1995 American novels Novels by Neal Stephenson Hugo Award for Best Novel–winning works Cyberpunk novels 1995 science fiction novels Novels set in Shanghai American steampunk novels Anarchist fiction Postcyberpunk novels American science fiction novels American bildungsromans Fiction about nanotechnology Novels about artificial intelligence Bantam Spectra books	The Diamond Age	[ "Materials_science" ]	3,500	[ "Fiction about nanotechnology", "Nanotechnology" ]
52,227	https://en.wikipedia.org/wiki/SourceForge	SourceForge is a web service founded by Geoffrey B. Jeffery, Tim Perdue, and Drew Streib in November 1999. The software provides a centralized online platform for managing and hosting open-source software projects, and a directory for comparing and reviewing business software that lists over 101,600 business software titles. It provides source code repository hosting, bug tracking, mirroring of downloads for load balancing, a wiki for documentation, developer and user mailing lists, user-support forums, user-written reviews and ratings, a news bulletin, micro-blog for publishing project updates, and other features. SourceForge was one of the first to offer this service free of charge to open-source projects. Since 2012, the website has run on Apache Allura software. SourceForge offers free hosting and free access to tools for developers of free and open-source software. , the SourceForge repository claimed to host more than 502,000 projects and had more than 3.7 million registered users. Concept SourceForge is a web-based source code repository. It acts as a centralized location for free and open-source software projects. It was the first to offer this service for free to open-source projects. Project developers have access to centralized storage and tools for managing projects, though it is best known for providing revision control systems such as CVS, SVN, Bazaar, Git and Mercurial. Major features (amongst others) include project wikis, metrics and analysis, access to a MySQL database, and unique sub-domain URLs (in the form http://project-name.sourceforge.net). The vast number of users at SourceForge.net (over three million as of 2013) exposes prominent projects to a variety of developers and can create a positive feedback loop. As a project's activity rises, SourceForge.net's internal ranking system makes it more visible to other developers through SourceForge directory and Enterprise Directory. Given that many open-source projects fail due to lack of developer support, exposure to such a large community of developers can continually breathe new life into a project. Revenue model SourceForge's traditional revenue model is through advertising banner sales on their site. In 2006, SourceForge Inc. reported quarterly takings of US$6.5 million. In 2009, SourceForge reported a gross quarterly income of US$23 million through media and e-commerce streams. In 2011, a revenue of US$20 million was reported for the combined value of the SourceForge, slashdot and freecode holdings, prior to SourceForge's acquisition. Since 2013, additional revenue generation schemes, such as bundleware models, have been trialled, with the goal of increasing SourceForge's revenue. The result has in some cases been the appearance of malware bundled with SourceForge downloads. On February 9, 2016, SourceForge announced they had eliminated their DevShare program practice of bundling installers with project downloads. Negative community reactions to the partnership program led to a review of the program, which was nonetheless opened up to all SourceForge projects on February 7, 2014. The program was canceled by new owners BIZX, LLC on February 9, 2016. On May 17, 2016, they announced that it would scan all projects for malware and display warnings on downloads. History SourceForge, founded in 1999 by VA Software, was the first provider of a centralized location for free and open-source software developers to control and manage software development and offering this service without charge. The software running the SourceForge site was released as free software in January 2000 and was later named SourceForge Alexandria. The last release under a free license was made in November 2001. After the dot-com bubble, SourceForge was later powered by the proprietary SourceForge Enterprise Edition, a separate product re-written in Java which was marketed for offshore outsourcing. SourceForge has been temporarily banned in China three times: in September 2002, in July 2008 (for about a month) and on August 6, 2012 (for several days). In November 2008, SourceForge was sued by the French collection society Société civile des Producteurs de Phonogrammes en France (SPPF) for hosting downloads of the file sharing application Shareaza. In 2009, SourceForge announced a new site platform known as Allura, which would be an extensible, open source platform licensed under the Apache License, utilizing components such as Python and MongoDB, and offering REST APIs. In June 2012, the Allura project was donated to the Apache Software Foundation as Apache Allura. In September 2012, SourceForge, Slashdot, and Freecode were acquired from Geeknet by the online job site Dice.com for $20 million, and incorporated into a subsidiary known as Slashdot Media. In July 2015, Dice announced that it planned to sell SourceForge and Slashdot, and, in January 2016, the two sites were sold to the San Diego–based BIZX, LLC for an undisclosed amount. In December 2019, BIZX rebranded as Slashdot Media. On September 26, 2012, it was reported that attackers had compromised a SourceForge mirror, and modified a download of phpMyAdmin to add security exploits. Adware controversy In July 2013, SourceForge announced that it would provide project owners with an optional feature called DevShare, which places closed-source ad-supported content into the binary installers and gives the project part of the ad revenue. Opinions of this new feature varied; some complained about users not being as aware of what they are getting or being able to trust the downloaded content, whereas others saw it as a reasonably harmless option that keeps individual projects and users in control. In November 2013, GIMP, a free image manipulation program, removed its download from SourceForge, citing misleading download buttons that potentially confuse customers as well as SourceForge's own Windows installer, which bundles potentially unwanted programs with GIMP. In a statement, GIMP called SourceForge a "once useful and trustworthy place to develop and host FLOSS applications" that now faces "a problem with the ads they allow on their sites". In May 2015, SourceForge took control of pages for five projects that had migrated to other hosting sites and replaced the project downloads with adware-laden downloads, including GIMP. This came despite SourceForge's commitment in November 2013 to never bundle adware with project downloads without developers' consent. On June 1, 2015, SourceForge claimed that they had stopped coupling "third party offers" with unmaintained SourceForge projects. Since this announcement was made, a number of other developers have reported that their SourceForge projects had been taken over by SourceForge staff accounts (but have not had binaries edited), including nmap and VLC media player. On June 18, 2015, SourceForge announced that SourceForge-maintained mirrored projects were removed and anticipated the formation of a Community Panel to review their mirroring practices. No such Community Panel ever materialized, but SourceForge discontinued DevShare and the bundling of installers after SourceForge was sold to BizX in early 2016. On May 17, 2016, SourceForge announced that they were now scanning all projects for malware and displaying warnings on projects detected to have malware. Project of the Month Since 2002, SourceForge has featured a pair of Projects of the Month, one chosen by its community and the other by its staff, but these have not been updated since December 2020. Usage , the SourceForge repository hosted more than 300,000 projects and had more than 3 million registered users, although not all were active. The domain sourceforge.net attracted at least 33 million visitors by August 2009 according to a Compete.com survey. Country restrictions In its terms of use, SourceForge states that its services are not available to users in countries on the sanction list of the U.S. Office of Foreign Assets Control (including Cuba, Iran, North Korea, Sudan and Syria). Since 2008 the secure server used for making contributions to the site has blocked access from those countries. In January 2010, the site had blocked all access from those countries, including downloads. Any IP address that appeared to belong to one of those countries could not use the site. By the following month, SourceForge relaxed the restrictions so that individual projects could indicate whether or not SourceForge should block their software from download to those countries. This, however, had been reversed by November 2020 for North Korea and other countries. Crimea has been blocked since February 1, 2015. See also Comparison of source-code-hosting facilities References External links "The SourceForge Story", by James Maguire (2007-10-17) Free software websites Geeknet Internet properties established in 1999 Internet services supporting OpenID Open-source software hosting facilities	SourceForge	[ "Technology" ]	1,841	[ "Computing websites", "Free software websites" ]
52,247	https://en.wikipedia.org/wiki/Fourier%20transform	In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced sine and cosine transforms (which correspond to the imaginary and real components of the modern Fourier transform) in his study of heat transfer, where Gaussian functions appear as solutions of the heat equation. The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically more sophisticated viewpoint. The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 'position space' to a function of momentum (or a function of space and time to a function of 4-momentum). This idea makes the spatial Fourier transform very natural in the study of waves, as well as in quantum mechanics, where it is important to be able to represent wave solutions as functions of either position or momentum and sometimes both. In general, functions to which Fourier methods are applicable are complex-valued, and possibly vector-valued. Still further generalization is possible to functions on groups, which, besides the original Fourier transform on or , notably includes the discrete-time Fourier transform (DTFT, group = ), the discrete Fourier transform (DFT, group = ) and the Fourier series or circular Fourier transform (group = , the unit circle ≈ closed finite interval with endpoints identified). The latter is routinely employed to handle periodic functions. The fast Fourier transform (FFT) is an algorithm for computing the DFT. Definition The Fourier transform of a complex-valued (Lebesgue) integrable function on the real line, is the complex valued function , defined by the integral Evaluating the Fourier transform for all values of produces the frequency-domain function, and it converges at all frequencies to a continuous function tending to zero at infinity. If decays with all derivatives, i.e., then converges for all frequencies and, by the Riemann–Lebesgue lemma, also decays with all derivatives. First introduced in Fourier's Analytical Theory of Heat., the corresponding inversion formula for "sufficiently nice" functions is given by the Fourier inversion theorem, i.e., The functions and are referred to as a Fourier transform pair. A common notation for designating transform pairs is: for example By analogy, the Fourier series can be regarded as abstract Fourier transform on the group of integers. That is, the synthesis of a sequence of complex numbers is defined by the Fourier transform such that are given by the inversion formula, i.e., the analysis for some complex-valued, -periodic function defined on a bounded interval . When the constituent frequencies are a continuum: and . In other words, on the finite interval the function has a discrete decomposition in the periodic functions . On the infinite interval the function has a continuous decomposition in periodic functions . Lebesgue integrable functions A measurable function is called (Lebesgue) integrable if the Lebesgue integral of its absolute value is finite: If is Lebesgue integrable then the Fourier transform, given by , is well-defined for all . Furthermore, is bounded, uniformly continuous and (by the Riemann–Lebesgue lemma) zero at infinity. The space is the space of measurable functions for which the norm is finite, modulo the equivalence relation of equality almost everywhere. The Fourier transform is one-to-one on . However, there is no easy characterization of the image, and thus no easy characterization of the inverse transform. In particular, is no longer valid, as it was stated only under the hypothesis that decayed with all derivatives. While defines the Fourier transform for (complex-valued) functions in , it is not well-defined for other integrability classes, most importantly the space of square-integrable functions . For example, the function is in but not and therefore the Lebesgue integral does not exist. However, the Fourier transform on the dense subspace admits a unique continuous extension to a unitary operator on . This extension is important in part because, unlike the case of , the Fourier transform is an automorphism of the space . In such cases, the Fourier transform can be obtained explicitly by regularizing the integral, and then passing to a limit. In practice, the integral is often regarded as an improper integral instead of a proper Lebesgue integral, but sometimes for convergence one needs to use weak limit or principal value instead of the (pointwise) limits implicit in an improper integral. and each gives three rigorous ways of extending the Fourier transform to square integrable functions using this procedure. A general principle in working with the Fourier transform is that Gaussians are dense in , and the various features of the Fourier transform, such as its unitarity, are easily inferred for Gaussians. Many of the properties of the Fourier transform, can then be proven from two facts about Gaussians: that is its own Fourier transform; and that the Gaussian integral A feature of the Fourier transform is that it is a homomorphism of Banach algebras from equipped with the convolution operation to the Banach algebra of continuous functions under the (supremum) norm. The conventions chosen in this article are those of harmonic analysis, and are characterized as the unique conventions such that the Fourier transform is both unitary on and an algebra homomorphism from to , without renormalizing the Lebesgue measure. Angular frequency (ω) When the independent variable () represents time (often denoted by ), the transform variable () represents frequency (often denoted by ). For example, if time is measured in seconds, then frequency is in hertz. The Fourier transform can also be written in terms of angular frequency, whose units are radians per second. The substitution into produces this convention, where function is relabeled Unlike the definition, the Fourier transform is no longer a unitary transformation, and there is less symmetry between the formulas for the transform and its inverse. Those properties are restored by splitting the factor evenly between the transform and its inverse, which leads to another convention: Variations of all three conventions can be created by conjugating the complex-exponential kernel of both the forward and the reverse transform. The signs must be opposites. Background History In 1822, Fourier claimed (see ) that any function, whether continuous or discontinuous, can be expanded into a series of sines. That important work was corrected and expanded upon by others to provide the foundation for the various forms of the Fourier transform used since. Complex sinusoids In general, the coefficients are complex numbers, which have two equivalent forms (see Euler's formula): The product with () has these forms: which conveys both amplitude and phase of frequency Likewise, the intuitive interpretation of is that multiplying by has the effect of subtracting from every frequency component of function Only the component that was at frequency can produce a non-zero value of the infinite integral, because (at least formally) all the other shifted components are oscillatory and integrate to zero. (see ) It is noteworthy how easily the product was simplified using the polar form, and how easily the rectangular form was deduced by an application of Euler's formula. Negative frequency Euler's formula introduces the possibility of negative And is defined Only certain complex-valued have transforms (See Analytic signal. A simple example is ) But negative frequency is necessary to characterize all other complex-valued found in signal processing, partial differential equations, radar, nonlinear optics, quantum mechanics, and others. For a real-valued has the symmetry property (see below). This redundancy enables to distinguish from But of course it cannot tell us the actual sign of because and are indistinguishable on just the real numbers line. Fourier transform for periodic functions The Fourier transform of a periodic function cannot be defined using the integral formula directly. In order for integral in to be defined the function must be absolutely integrable. Instead it is common to use Fourier series. It is possible to extend the definition to include periodic functions by viewing them as tempered distributions. This makes it possible to see a connection between the Fourier series and the Fourier transform for periodic functions that have a convergent Fourier series. If is a periodic function, with period , that has a convergent Fourier series, then: where are the Fourier series coefficients of , and is the Dirac delta function. In other words, the Fourier transform is a Dirac comb function whose teeth are multiplied by the Fourier series coefficients. Sampling the Fourier transform The Fourier transform of an integrable function can be sampled at regular intervals of arbitrary length These samples can be deduced from one cycle of a periodic function which has Fourier series coefficients proportional to those samples by the Poisson summation formula: The integrability of ensures the periodic summation converges. Therefore, the samples can be determined by Fourier series analysis: When has compact support, has a finite number of terms within the interval of integration. When does not have compact support, numerical evaluation of requires an approximation, such as tapering or truncating the number of terms. Units The frequency variable must have inverse units to the units of the original function's domain (typically named or ). For example, if is measured in seconds, should be in cycles per second or hertz. If the scale of time is in units of seconds, then another Greek letter is typically used instead to represent angular frequency (where ) in units of radians per second. If using for units of length, then must be in inverse length, e.g., wavenumbers. That is to say, there are two versions of the real line: one which is the range of and measured in units of and the other which is the range of and measured in inverse units to the units of These two distinct versions of the real line cannot be equated with each other. Therefore, the Fourier transform goes from one space of functions to a different space of functions: functions which have a different domain of definition. In general, must always be taken to be a linear form on the space of its domain, which is to say that the second real line is the dual space of the first real line. See the article on linear algebra for a more formal explanation and for more details. This point of view becomes essential in generalizations of the Fourier transform to general symmetry groups, including the case of Fourier series. That there is no one preferred way (often, one says "no canonical way") to compare the two versions of the real line which are involved in the Fourier transform—fixing the units on one line does not force the scale of the units on the other line—is the reason for the plethora of rival conventions on the definition of the Fourier transform. The various definitions resulting from different choices of units differ by various constants. In other conventions, the Fourier transform has in the exponent instead of , and vice versa for the inversion formula. This convention is common in modern physics and is the default for Wolfram Alpha, and does not mean that the frequency has become negative, since there is no canonical definition of positivity for frequency of a complex wave. It simply means that is the amplitude of the wave instead of the wave (the former, with its minus sign, is often seen in the time dependence for Sinusoidal plane-wave solutions of the electromagnetic wave equation, or in the time dependence for quantum wave functions). Many of the identities involving the Fourier transform remain valid in those conventions, provided all terms that explicitly involve have it replaced by . In Electrical engineering the letter is typically used for the imaginary unit instead of because is used for current. When using dimensionless units, the constant factors might not even be written in the transform definition. For instance, in probability theory, the characteristic function of the probability density function of a random variable of continuous type is defined without a negative sign in the exponential, and since the units of are ignored, there is no 2 either: (In probability theory, and in mathematical statistics, the use of the Fourier—Stieltjes transform is preferred, because so many random variables are not of continuous type, and do not possess a density function, and one must treat not functions but distributions, i.e., measures which possess "atoms".) From the higher point of view of group characters, which is much more abstract, all these arbitrary choices disappear, as will be explained in the later section of this article, which treats the notion of the Fourier transform of a function on a locally compact Abelian group. Properties Let and represent integrable functions Lebesgue-measurable on the real line satisfying: We denote the Fourier transforms of these functions as and respectively. Basic properties The Fourier transform has the following basic properties: Linearity Time shifting Frequency shifting Time scaling The case leads to the time-reversal property: Symmetry When the real and imaginary parts of a complex function are decomposed into their even and odd parts, there are four components, denoted below by the subscripts RE, RO, IE, and IO. And there is a one-to-one mapping between the four components of a complex time function and the four components of its complex frequency transform: From this, various relationships are apparent, for example: The transform of a real-valued function is the conjugate symmetric function Conversely, a conjugate symmetric transform implies a real-valued time-domain. The transform of an imaginary-valued function is the conjugate antisymmetric function and the converse is true. The transform of a conjugate symmetric function is the real-valued function and the converse is true. The transform of a conjugate antisymmetric function is the imaginary-valued function and the converse is true. Conjugation (Note: the ∗ denotes complex conjugation.) In particular, if is real, then is even symmetric (aka Hermitian function): And if is purely imaginary, then is odd symmetric: Real and imaginary parts Zero frequency component Substituting in the definition, we obtain: The integral of over its domain is known as the average value or DC bias of the function. Uniform continuity and the Riemann–Lebesgue lemma The Fourier transform may be defined in some cases for non-integrable functions, but the Fourier transforms of integrable functions have several strong properties. The Fourier transform of any integrable function is uniformly continuous and By the Riemann–Lebesgue lemma, However, need not be integrable. For example, the Fourier transform of the rectangular function, which is integrable, is the sinc function, which is not Lebesgue integrable, because its improper integrals behave analogously to the alternating harmonic series, in converging to a sum without being absolutely convergent. It is not generally possible to write the inverse transform as a Lebesgue integral. However, when both and are integrable, the inverse equality holds for almost every . As a result, the Fourier transform is injective on . Plancherel theorem and Parseval's theorem Let and be integrable, and let and be their Fourier transforms. If and are also square-integrable, then the Parseval formula follows: where the bar denotes complex conjugation. The Plancherel theorem, which follows from the above, states that Plancherel's theorem makes it possible to extend the Fourier transform, by a continuity argument, to a unitary operator on . On , this extension agrees with original Fourier transform defined on , thus enlarging the domain of the Fourier transform to (and consequently to for ). Plancherel's theorem has the interpretation in the sciences that the Fourier transform preserves the energy of the original quantity. The terminology of these formulas is not quite standardised. Parseval's theorem was proved only for Fourier series, and was first proved by Lyapunov. But Parseval's formula makes sense for the Fourier transform as well, and so even though in the context of the Fourier transform it was proved by Plancherel, it is still often referred to as Parseval's formula, or Parseval's relation, or even Parseval's theorem. See Pontryagin duality for a general formulation of this concept in the context of locally compact abelian groups. Convolution theorem The Fourier transform translates between convolution and multiplication of functions. If and are integrable functions with Fourier transforms and respectively, then the Fourier transform of the convolution is given by the product of the Fourier transforms and (under other conventions for the definition of the Fourier transform a constant factor may appear). This means that if: where denotes the convolution operation, then: In linear time invariant (LTI) system theory, it is common to interpret as the impulse response of an LTI system with input and output , since substituting the unit impulse for yields . In this case, represents the frequency response of the system. Conversely, if can be decomposed as the product of two square integrable functions and , then the Fourier transform of is given by the convolution of the respective Fourier transforms and . Cross-correlation theorem In an analogous manner, it can be shown that if is the cross-correlation of and : then the Fourier transform of is: As a special case, the autocorrelation of function is: for which Differentiation Suppose is an absolutely continuous differentiable function, and both and its derivative are integrable. Then the Fourier transform of the derivative is given by More generally, the Fourier transformation of the th derivative is given by Analogously, , so By applying the Fourier transform and using these formulas, some ordinary differential equations can be transformed into algebraic equations, which are much easier to solve. These formulas also give rise to the rule of thumb " is smooth if and only if quickly falls to 0 for ." By using the analogous rules for the inverse Fourier transform, one can also say " quickly falls to 0 for if and only if is smooth." Eigenfunctions The Fourier transform is a linear transform which has eigenfunctions obeying with A set of eigenfunctions is found by noting that the homogeneous differential equation leads to eigenfunctions of the Fourier transform as long as the form of the equation remains invariant under Fourier transform. In other words, every solution and its Fourier transform obey the same equation. Assuming uniqueness of the solutions, every solution must therefore be an eigenfunction of the Fourier transform. The form of the equation remains unchanged under Fourier transform if can be expanded in a power series in which for all terms the same factor of either one of arises from the factors introduced by the differentiation rules upon Fourier transforming the homogeneous differential equation because this factor may then be cancelled. The simplest allowable leads to the standard normal distribution. More generally, a set of eigenfunctions is also found by noting that the differentiation rules imply that the ordinary differential equation with constant and being a non-constant even function remains invariant in form when applying the Fourier transform to both sides of the equation. The simplest example is provided by which is equivalent to considering the Schrödinger equation for the quantum harmonic oscillator. The corresponding solutions provide an important choice of an orthonormal basis for and are given by the "physicist's" Hermite functions. Equivalently one may use where are the "probabilist's" Hermite polynomials, defined as Under this convention for the Fourier transform, we have that In other words, the Hermite functions form a complete orthonormal system of eigenfunctions for the Fourier transform on . However, this choice of eigenfunctions is not unique. Because of there are only four different eigenvalues of the Fourier transform (the fourth roots of unity ±1 and ±) and any linear combination of eigenfunctions with the same eigenvalue gives another eigenfunction. As a consequence of this, it is possible to decompose as a direct sum of four spaces , , , and where the Fourier transform acts on simply by multiplication by . Since the complete set of Hermite functions provides a resolution of the identity they diagonalize the Fourier operator, i.e. the Fourier transform can be represented by such a sum of terms weighted by the above eigenvalues, and these sums can be explicitly summed: This approach to define the Fourier transform was first proposed by Norbert Wiener. Among other properties, Hermite functions decrease exponentially fast in both frequency and time domains, and they are thus used to define a generalization of the Fourier transform, namely the fractional Fourier transform used in time–frequency analysis. In physics, this transform was introduced by Edward Condon. This change of basis functions becomes possible because the Fourier transform is a unitary transform when using the right conventions. Consequently, under the proper conditions it may be expected to result from a self-adjoint generator via The operator is the number operator of the quantum harmonic oscillator written as It can be interpreted as the generator of fractional Fourier transforms for arbitrary values of , and of the conventional continuous Fourier transform for the particular value with the Mehler kernel implementing the corresponding active transform. The eigenfunctions of are the Hermite functions which are therefore also eigenfunctions of Upon extending the Fourier transform to distributions the Dirac comb is also an eigenfunction of the Fourier transform. Inversion and periodicity Under suitable conditions on the function , it can be recovered from its Fourier transform . Indeed, denoting the Fourier transform operator by , so , then for suitable functions, applying the Fourier transform twice simply flips the function: , which can be interpreted as "reversing time". Since reversing time is two-periodic, applying this twice yields , so the Fourier transform operator is four-periodic, and similarly the inverse Fourier transform can be obtained by applying the Fourier transform three times: . In particular the Fourier transform is invertible (under suitable conditions). More precisely, defining the parity operator such that , we have: These equalities of operators require careful definition of the space of functions in question, defining equality of functions (equality at every point? equality almost everywhere?) and defining equality of operators – that is, defining the topology on the function space and operator space in question. These are not true for all functions, but are true under various conditions, which are the content of the various forms of the Fourier inversion theorem. This fourfold periodicity of the Fourier transform is similar to a rotation of the plane by 90°, particularly as the two-fold iteration yields a reversal, and in fact this analogy can be made precise. While the Fourier transform can simply be interpreted as switching the time domain and the frequency domain, with the inverse Fourier transform switching them back, more geometrically it can be interpreted as a rotation by 90° in the time–frequency domain (considering time as the -axis and frequency as the -axis), and the Fourier transform can be generalized to the fractional Fourier transform, which involves rotations by other angles. This can be further generalized to linear canonical transformations, which can be visualized as the action of the special linear group on the time–frequency plane, with the preserved symplectic form corresponding to the uncertainty principle, below. This approach is particularly studied in signal processing, under time–frequency analysis. Connection with the Heisenberg group The Heisenberg group is a certain group of unitary operators on the Hilbert space of square integrable complex valued functions on the real line, generated by the translations and multiplication by , . These operators do not commute, as their (group) commutator is which is multiplication by the constant (independent of ) (the circle group of unit modulus complex numbers). As an abstract group, the Heisenberg group is the three-dimensional Lie group of triples , with the group law Denote the Heisenberg group by . The above procedure describes not only the group structure, but also a standard unitary representation of on a Hilbert space, which we denote by . Define the linear automorphism of by so that . This can be extended to a unique automorphism of : According to the Stone–von Neumann theorem, the unitary representations and are unitarily equivalent, so there is a unique intertwiner such that This operator is the Fourier transform. Many of the standard properties of the Fourier transform are immediate consequences of this more general framework. For example, the square of the Fourier transform, , is an intertwiner associated with , and so we have is the reflection of the original function . Complex domain The integral for the Fourier transform can be studied for complex values of its argument . Depending on the properties of , this might not converge off the real axis at all, or it might converge to a complex analytic function for all values of , or something in between. The Paley–Wiener theorem says that is smooth (i.e., -times differentiable for all positive integers ) and compactly supported if and only if is a holomorphic function for which there exists a constant such that for any integer , for some constant . (In this case, is supported on .) This can be expressed by saying that is an entire function which is rapidly decreasing in (for fixed ) and of exponential growth in (uniformly in ). (If is not smooth, but only , the statement still holds provided .) The space of such functions of a complex variable is called the Paley—Wiener space. This theorem has been generalised to semisimple Lie groups. If is supported on the half-line , then is said to be "causal" because the impulse response function of a physically realisable filter must have this property, as no effect can precede its cause. Paley and Wiener showed that then extends to a holomorphic function on the complex lower half-plane which tends to zero as goes to infinity. The converse is false and it is not known how to characterise the Fourier transform of a causal function. Laplace transform The Fourier transform is related to the Laplace transform , which is also used for the solution of differential equations and the analysis of filters. It may happen that a function for which the Fourier integral does not converge on the real axis at all, nevertheless has a complex Fourier transform defined in some region of the complex plane. For example, if is of exponential growth, i.e., for some constants , then convergent for all , is the two-sided Laplace transform of . The more usual version ("one-sided") of the Laplace transform is If is also causal, and analytical, then: Thus, extending the Fourier transform to the complex domain means it includes the Laplace transform as a special case in the case of causal functions—but with the change of variable . From another, perhaps more classical viewpoint, the Laplace transform by its form involves an additional exponential regulating term which lets it converge outside of the imaginary line where the Fourier transform is defined. As such it can converge for at most exponentially divergent series and integrals, whereas the original Fourier decomposition cannot, enabling analysis of systems with divergent or critical elements. Two particular examples from linear signal processing are the construction of allpass filter networks from critical comb and mitigating filters via exact pole-zero cancellation on the unit circle. Such designs are common in audio processing, where highly nonlinear phase response is sought for, as in reverb. Furthermore, when extended pulselike impulse responses are sought for signal processing work, the easiest way to produce them is to have one circuit which produces a divergent time response, and then to cancel its divergence through a delayed opposite and compensatory response. There, only the delay circuit in-between admits a classical Fourier description, which is critical. Both the circuits to the side are unstable, and do not admit a convergent Fourier decomposition. However, they do admit a Laplace domain description, with identical half-planes of convergence in the complex plane (or in the discrete case, the Z-plane), wherein their effects cancel. In modern mathematics the Laplace transform is conventionally subsumed under the aegis Fourier methods. Both of them are subsumed by the far more general, and more abstract, idea of harmonic analysis. Inversion Still with , if is complex analytic for , then by Cauchy's integral theorem. Therefore, the Fourier inversion formula can use integration along different lines, parallel to the real axis. Theorem: If for , and for some constants , then for any . This theorem implies the Mellin inversion formula for the Laplace transformation, for any , where is the Laplace transform of . The hypotheses can be weakened, as in the results of Carleson and Hunt, to being , provided that be of bounded variation in a closed neighborhood of (cf. Dini test), the value of at be taken to be the arithmetic mean of the left and right limits, and that the integrals be taken in the sense of Cauchy principal values. versions of these inversion formulas are also available. Fourier transform on Euclidean space The Fourier transform can be defined in any arbitrary number of dimensions . As with the one-dimensional case, there are many conventions. For an integrable function , this article takes the definition: where and are -dimensional vectors, and is the dot product of the vectors. Alternatively, can be viewed as belonging to the dual vector space , in which case the dot product becomes the contraction of and , usually written as . All of the basic properties listed above hold for the -dimensional Fourier transform, as do Plancherel's and Parseval's theorem. When the function is integrable, the Fourier transform is still uniformly continuous and the Riemann–Lebesgue lemma holds. Uncertainty principle Generally speaking, the more concentrated is, the more spread out its Fourier transform must be. In particular, the scaling property of the Fourier transform may be seen as saying: if we squeeze a function in , its Fourier transform stretches out in . It is not possible to arbitrarily concentrate both a function and its Fourier transform. The trade-off between the compaction of a function and its Fourier transform can be formalized in the form of an uncertainty principle by viewing a function and its Fourier transform as conjugate variables with respect to the symplectic form on the time–frequency domain: from the point of view of the linear canonical transformation, the Fourier transform is rotation by 90° in the time–frequency domain, and preserves the symplectic form. Suppose is an integrable and square-integrable function. Without loss of generality, assume that is normalized: It follows from the Plancherel theorem that is also normalized. The spread around may be measured by the dispersion about zero defined by In probability terms, this is the second moment of about zero. The uncertainty principle states that, if is absolutely continuous and the functions and are square integrable, then The equality is attained only in the case where is arbitrary and so that is -normalized. In other words, where is a (normalized) Gaussian function with variance , centered at zero, and its Fourier transform is a Gaussian function with variance . In fact, this inequality implies that: for any , . In quantum mechanics, the momentum and position wave functions are Fourier transform pairs, up to a factor of the Planck constant. With this constant properly taken into account, the inequality above becomes the statement of the Heisenberg uncertainty principle. A stronger uncertainty principle is the Hirschman uncertainty principle, which is expressed as: where is the differential entropy of the probability density function : where the logarithms may be in any base that is consistent. The equality is attained for a Gaussian, as in the previous case. Sine and cosine transforms Fourier's original formulation of the transform did not use complex numbers, but rather sines and cosines. Statisticians and others still use this form. An absolutely integrable function for which Fourier inversion holds can be expanded in terms of genuine frequencies (avoiding negative frequencies, which are sometimes considered hard to interpret physically) by This is called an expansion as a trigonometric integral, or a Fourier integral expansion. The coefficient functions and can be found by using variants of the Fourier cosine transform and the Fourier sine transform (the normalisations are, again, not standardised): and Older literature refers to the two transform functions, the Fourier cosine transform, , and the Fourier sine transform, . The function can be recovered from the sine and cosine transform using together with trigonometric identities. This is referred to as Fourier's integral formula. Spherical harmonics Let the set of homogeneous harmonic polynomials of degree on be denoted by . The set consists of the solid spherical harmonics of degree . The solid spherical harmonics play a similar role in higher dimensions to the Hermite polynomials in dimension one. Specifically, if for some in , then . Let the set be the closure in of linear combinations of functions of the form where is in . The space is then a direct sum of the spaces and the Fourier transform maps each space to itself and is possible to characterize the action of the Fourier transform on each space . Let (with in ), then where Here denotes the Bessel function of the first kind with order . When this gives a useful formula for the Fourier transform of a radial function. This is essentially the Hankel transform. Moreover, there is a simple recursion relating the cases and allowing to compute, e.g., the three-dimensional Fourier transform of a radial function from the one-dimensional one. Restriction problems In higher dimensions it becomes interesting to study restriction problems for the Fourier transform. The Fourier transform of an integrable function is continuous and the restriction of this function to any set is defined. But for a square-integrable function the Fourier transform could be a general class of square integrable functions. As such, the restriction of the Fourier transform of an function cannot be defined on sets of measure 0. It is still an active area of study to understand restriction problems in for . It is possible in some cases to define the restriction of a Fourier transform to a set , provided has non-zero curvature. The case when is the unit sphere in is of particular interest. In this case the Tomas–Stein restriction theorem states that the restriction of the Fourier transform to the unit sphere in is a bounded operator on provided . One notable difference between the Fourier transform in 1 dimension versus higher dimensions concerns the partial sum operator. Consider an increasing collection of measurable sets indexed by : such as balls of radius centered at the origin, or cubes of side . For a given integrable function , consider the function defined by: Suppose in addition that . For and , if one takes , then converges to in as tends to infinity, by the boundedness of the Hilbert transform. Naively one may hope the same holds true for . In the case that is taken to be a cube with side length , then convergence still holds. Another natural candidate is the Euclidean ball . In order for this partial sum operator to converge, it is necessary that the multiplier for the unit ball be bounded in . For it is a celebrated theorem of Charles Fefferman that the multiplier for the unit ball is never bounded unless . In fact, when , this shows that not only may fail to converge to in , but for some functions , is not even an element of . Fourier transform on function spaces The definition of the Fourier transform naturally extends from to . That is, if then the Fourier transform is given by This operator is bounded as which shows that its operator norm is bounded by . The Riemann–Lebesgue lemma shows that if then its Fourier transform actually belongs to the space of continuous functions which vanish at infinity, i.e., . Furthermore, the image of under is a strict subset of . Similarly to the case of one variable, the Fourier transform can be defined on . The Fourier transform in is no longer given by an ordinary Lebesgue integral, although it can be computed by an improper integral, i.e., where the limit is taken in the sense. Furthermore, is a unitary operator. For an operator to be unitary it is sufficient to show that it is bijective and preserves the inner product, so in this case these follow from the Fourier inversion theorem combined with the fact that for any we have In particular, the image of is itself under the Fourier transform. On other Lp For , the Fourier transform can be defined on by Marcinkiewicz interpolation, which amounts to decomposing such functions into a fat tail part in plus a fat body part in . In each of these spaces, the Fourier transform of a function in is in , where is the Hölder conjugate of (by the Hausdorff–Young inequality). However, except for , the image is not easily characterized. Further extensions become more technical. The Fourier transform of functions in for the range requires the study of distributions. In fact, it can be shown that there are functions in with so that the Fourier transform is not defined as a function. Tempered distributions One might consider enlarging the domain of the Fourier transform from by considering generalized functions, or distributions. A distribution on is a continuous linear functional on the space of compactly supported smooth functions (i.e. bump functions), equipped with a suitable topology. Since is dense in , the Plancherel theorem allows one to extend the definition of the Fourier transform to general functions in by continuity arguments. The strategy is then to consider the action of the Fourier transform on and pass to distributions by duality. The obstruction to doing this is that the Fourier transform does not map to . In fact the Fourier transform of an element in can not vanish on an open set; see the above discussion on the uncertainty principle. The Fourier transform can also be defined for tempered distributions , dual to the space of Schwartz functions . A Schwartz function is a smooth function that decays at infinity, along with all of its derivatives, hence and: The Fourier transform is an automorphism of the Schwartz space and, by duality, also an automorphism of the space of tempered distributions. The tempered distributions include well-behaved functions of polynomial growth, distributions of compact support as well as all the integrable functions mentioned above. For the definition of the Fourier transform of a tempered distribution, let and be integrable functions, and let and be their Fourier transforms respectively. Then the Fourier transform obeys the following multiplication formula, Every integrable function defines (induces) a distribution by the relation So it makes sense to define the Fourier transform of a tempered distribution by the duality: Extending this to all tempered distributions gives the general definition of the Fourier transform. Distributions can be differentiated and the above-mentioned compatibility of the Fourier transform with differentiation and convolution remains true for tempered distributions. Generalizations Fourier–Stieltjes transform on measurable spaces The Fourier transform of a finite Borel measure on is given by the continuous function: and called the Fourier-Stieltjes transform due to its connection with the Riemann-Stieltjes integral representation of (Radon) measures. If is the probability distribution of a random variable then its Fourier–Stieltjes transform is, by definition, a characteristic function. If, in addition, the probability distribution has a probability density function, this definition is subject to the usual Fourier transform. Stated more generally, when is absolutely continuous with respect to the Lebesgue measure, i.e., then and the Fourier-Stieltjes transform reduces to the usual definition of the Fourier transform. That is, the notable difference with the Fourier transform of integrable functions is that the Fourier-Stieltjes transform need not vanish at infinity, i.e., the Riemann–Lebesgue lemma fails for measures. Bochner's theorem characterizes which functions may arise as the Fourier–Stieltjes transform of a positive measure on the circle. One example of a finite Borel measure that is not a function is the Dirac measure. Its Fourier transform is a constant function (whose value depends on the form of the Fourier transform used). Locally compact abelian groups The Fourier transform may be generalized to any locally compact abelian group, i.e., an abelian group that is also a locally compact Hausdorff space such that the group operation is continuous. If is a locally compact abelian group, it has a translation invariant measure , called Haar measure. For a locally compact abelian group , the set of irreducible, i.e. one-dimensional, unitary representations are called its characters. With its natural group structure and the topology of uniform convergence on compact sets (that is, the topology induced by the compact-open topology on the space of all continuous functions from to the circle group), the set of characters is itself a locally compact abelian group, called the Pontryagin dual of . For a function in , its Fourier transform is defined by The Riemann–Lebesgue lemma holds in this case; is a function vanishing at infinity on . The Fourier transform on is an example; here is a locally compact abelian group, and the Haar measure on can be thought of as the Lebesgue measure on [0,1). Consider the representation of on the complex plane that is a 1-dimensional complex vector space. There are a group of representations (which are irreducible since is 1-dim) where for . The character of such representation, that is the trace of for each and , is itself. In the case of representation of finite group, the character table of the group are rows of vectors such that each row is the character of one irreducible representation of , and these vectors form an orthonormal basis of the space of class functions that map from to by Schur's lemma. Now the group is no longer finite but still compact, and it preserves the orthonormality of character table. Each row of the table is the function of and the inner product between two class functions (all functions being class functions since is abelian) is defined as with the normalizing factor . The sequence is an orthonormal basis of the space of class functions . For any representation of a finite group , can be expressed as the span ( are the irreps of ), such that . Similarly for and , . The Pontriagin dual is and for , is its Fourier transform for . Gelfand transform The Fourier transform is also a special case of Gelfand transform. In this particular context, it is closely related to the Pontryagin duality map defined above. Given an abelian locally compact Hausdorff topological group , as before we consider space , defined using a Haar measure. With convolution as multiplication, is an abelian Banach algebra. It also has an involution * given by Taking the completion with respect to the largest possibly -norm gives its enveloping -algebra, called the group -algebra of . (Any -norm on is bounded by the norm, therefore their supremum exists.) Given any abelian -algebra , the Gelfand transform gives an isomorphism between and , where is the multiplicative linear functionals, i.e. one-dimensional representations, on with the weak-* topology. The map is simply given by It turns out that the multiplicative linear functionals of , after suitable identification, are exactly the characters of , and the Gelfand transform, when restricted to the dense subset is the Fourier–Pontryagin transform. Compact non-abelian groups The Fourier transform can also be defined for functions on a non-abelian group, provided that the group is compact. Removing the assumption that the underlying group is abelian, irreducible unitary representations need not always be one-dimensional. This means the Fourier transform on a non-abelian group takes values as Hilbert space operators. The Fourier transform on compact groups is a major tool in representation theory and non-commutative harmonic analysis. Let be a compact Hausdorff topological group. Let denote the collection of all isomorphism classes of finite-dimensional irreducible unitary representations, along with a definite choice of representation on the Hilbert space of finite dimension for each . If is a finite Borel measure on , then the Fourier–Stieltjes transform of is the operator on defined by where is the complex-conjugate representation of acting on . If is absolutely continuous with respect to the left-invariant probability measure on , represented as for some , one identifies the Fourier transform of with the Fourier–Stieltjes transform of . The mapping defines an isomorphism between the Banach space of finite Borel measures (see rca space) and a closed subspace of the Banach space consisting of all sequences indexed by of (bounded) linear operators for which the norm is finite. The "convolution theorem" asserts that, furthermore, this isomorphism of Banach spaces is in fact an isometric isomorphism of C-algebras into a subspace of . Multiplication on is given by convolution of measures and the involution defined by and has a natural -algebra structure as Hilbert space operators. The Peter–Weyl theorem holds, and a version of the Fourier inversion formula (Plancherel's theorem) follows: if , then where the summation is understood as convergent in the sense. The generalization of the Fourier transform to the noncommutative situation has also in part contributed to the development of noncommutative geometry. In this context, a categorical generalization of the Fourier transform to noncommutative groups is Tannaka–Krein duality, which replaces the group of characters with the category of representations. However, this loses the connection with harmonic functions. Alternatives In signal processing terms, a function (of time) is a representation of a signal with perfect time resolution, but no frequency information, while the Fourier transform has perfect frequency resolution, but no time information: the magnitude of the Fourier transform at a point is how much frequency content there is, but location is only given by phase (argument of the Fourier transform at a point), and standing waves are not localized in time – a sine wave continues out to infinity, without decaying. This limits the usefulness of the Fourier transform for analyzing signals that are localized in time, notably transients, or any signal of finite extent. As alternatives to the Fourier transform, in time–frequency analysis, one uses time–frequency transforms or time–frequency distributions to represent signals in a form that has some time information and some frequency information – by the uncertainty principle, there is a trade-off between these. These can be generalizations of the Fourier transform, such as the short-time Fourier transform, fractional Fourier transform, Synchrosqueezing Fourier transform, or other functions to represent signals, as in wavelet transforms and chirplet transforms, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform. Example The following figures provide a visual illustration of how the Fourier transform's integral measures whether a frequency is present in a particular function. The first image depicts the function which is a 3 Hz cosine wave (the first term) shaped by a Gaussian envelope function (the second term) that smoothly turns the wave on and off. The next 2 images show the product which must be integrated to calculate the Fourier transform at +3 Hz. The real part of the integrand has a non-negative average value, because the alternating signs of and oscillate at the same rate and in phase, whereas and oscillate at the same rate but with orthogonal phase. The absolute value of the Fourier transform at +3 Hz is 0.5, which is relatively large. When added to the Fourier transform at -3 Hz (which is identical because we started with a real signal), we find that the amplitude of the 3 Hz frequency component is 1. However, when you try to measure a frequency that is not present, both the real and imaginary component of the integral vary rapidly between positive and negative values. For instance, the red curve is looking for 5 Hz. The absolute value of its integral is nearly zero, indicating that almost no 5 Hz component was in the signal. The general situation is usually more complicated than this, but heuristically this is how the Fourier transform measures how much of an individual frequency is present in a function To re-enforce an earlier point, the reason for the response at Hz is because and are indistinguishable. The transform of would have just one response, whose amplitude is the integral of the smooth envelope: whereas is Applications Linear operations performed in one domain (time or frequency) have corresponding operations in the other domain, which are sometimes easier to perform. The operation of differentiation in the time domain corresponds to multiplication by the frequency, so some differential equations are easier to analyze in the frequency domain. Also, convolution in the time domain corresponds to ordinary multiplication in the frequency domain (see Convolution theorem). After performing the desired operations, transformation of the result can be made back to the time domain. Harmonic analysis is the systematic study of the relationship between the frequency and time domains, including the kinds of functions or operations that are "simpler" in one or the other, and has deep connections to many areas of modern mathematics. Analysis of differential equations Perhaps the most important use of the Fourier transformation is to solve partial differential equations. Many of the equations of the mathematical physics of the nineteenth century can be treated this way. Fourier studied the heat equation, which in one dimension and in dimensionless units is The example we will give, a slightly more difficult one, is the wave equation in one dimension, As usual, the problem is not to find a solution: there are infinitely many. The problem is that of the so-called "boundary problem": find a solution which satisfies the "boundary conditions" Here, and are given functions. For the heat equation, only one boundary condition can be required (usually the first one). But for the wave equation, there are still infinitely many solutions which satisfy the first boundary condition. But when one imposes both conditions, there is only one possible solution. It is easier to find the Fourier transform of the solution than to find the solution directly. This is because the Fourier transformation takes differentiation into multiplication by the Fourier-dual variable, and so a partial differential equation applied to the original function is transformed into multiplication by polynomial functions of the dual variables applied to the transformed function. After is determined, we can apply the inverse Fourier transformation to find . Fourier's method is as follows. First, note that any function of the forms satisfies the wave equation. These are called the elementary solutions. Second, note that therefore any integral satisfies the wave equation for arbitrary . This integral may be interpreted as a continuous linear combination of solutions for the linear equation. Now this resembles the formula for the Fourier synthesis of a function. In fact, this is the real inverse Fourier transform of and in the variable . The third step is to examine how to find the specific unknown coefficient functions and that will lead to satisfying the boundary conditions. We are interested in the values of these solutions at . So we will set . Assuming that the conditions needed for Fourier inversion are satisfied, we can then find the Fourier sine and cosine transforms (in the variable ) of both sides and obtain and Similarly, taking the derivative of with respect to and then applying the Fourier sine and cosine transformations yields and These are four linear equations for the four unknowns and , in terms of the Fourier sine and cosine transforms of the boundary conditions, which are easily solved by elementary algebra, provided that these transforms can be found. In summary, we chose a set of elementary solutions, parametrized by , of which the general solution would be a (continuous) linear combination in the form of an integral over the parameter . But this integral was in the form of a Fourier integral. The next step was to express the boundary conditions in terms of these integrals, and set them equal to the given functions and . But these expressions also took the form of a Fourier integral because of the properties of the Fourier transform of a derivative. The last step was to exploit Fourier inversion by applying the Fourier transformation to both sides, thus obtaining expressions for the coefficient functions and in terms of the given boundary conditions and . From a higher point of view, Fourier's procedure can be reformulated more conceptually. Since there are two variables, we will use the Fourier transformation in both and rather than operate as Fourier did, who only transformed in the spatial variables. Note that must be considered in the sense of a distribution since is not going to be : as a wave, it will persist through time and thus is not a transient phenomenon. But it will be bounded and so its Fourier transform can be defined as a distribution. The operational properties of the Fourier transformation that are relevant to this equation are that it takes differentiation in to multiplication by and differentiation with respect to to multiplication by where is the frequency. Then the wave equation becomes an algebraic equation in : This is equivalent to requiring unless . Right away, this explains why the choice of elementary solutions we made earlier worked so well: obviously will be solutions. Applying Fourier inversion to these delta functions, we obtain the elementary solutions we picked earlier. But from the higher point of view, one does not pick elementary solutions, but rather considers the space of all distributions which are supported on the (degenerate) conic . We may as well consider the distributions supported on the conic that are given by distributions of one variable on the line plus distributions on the line as follows: if is any test function, where , and , are distributions of one variable. Then Fourier inversion gives, for the boundary conditions, something very similar to what we had more concretely above (put , which is clearly of polynomial growth): and Now, as before, applying the one-variable Fourier transformation in the variable to these functions of yields two equations in the two unknown distributions (which can be taken to be ordinary functions if the boundary conditions are or ). From a calculational point of view, the drawback of course is that one must first calculate the Fourier transforms of the boundary conditions, then assemble the solution from these, and then calculate an inverse Fourier transform. Closed form formulas are rare, except when there is some geometric symmetry that can be exploited, and the numerical calculations are difficult because of the oscillatory nature of the integrals, which makes convergence slow and hard to estimate. For practical calculations, other methods are often used. The twentieth century has seen the extension of these methods to all linear partial differential equations with polynomial coefficients, and by extending the notion of Fourier transformation to include Fourier integral operators, some non-linear equations as well. Fourier-transform spectroscopy The Fourier transform is also used in nuclear magnetic resonance (NMR) and in other kinds of spectroscopy, e.g. infrared (FTIR). In NMR an exponentially shaped free induction decay (FID) signal is acquired in the time domain and Fourier-transformed to a Lorentzian line-shape in the frequency domain. The Fourier transform is also used in magnetic resonance imaging (MRI) and mass spectrometry. Quantum mechanics The Fourier transform is useful in quantum mechanics in at least two different ways. To begin with, the basic conceptual structure of quantum mechanics postulates the existence of pairs of complementary variables, connected by the Heisenberg uncertainty principle. For example, in one dimension, the spatial variable of, say, a particle, can only be measured by the quantum mechanical "position operator" at the cost of losing information about the momentum of the particle. Therefore, the physical state of the particle can either be described by a function, called "the wave function", of or by a function of but not by a function of both variables. The variable is called the conjugate variable to . In classical mechanics, the physical state of a particle (existing in one dimension, for simplicity of exposition) would be given by assigning definite values to both and simultaneously. Thus, the set of all possible physical states is the two-dimensional real vector space with a -axis and a -axis called the phase space. In contrast, quantum mechanics chooses a polarisation of this space in the sense that it picks a subspace of one-half the dimension, for example, the -axis alone, but instead of considering only points, takes the set of all complex-valued "wave functions" on this axis. Nevertheless, choosing the -axis is an equally valid polarisation, yielding a different representation of the set of possible physical states of the particle. Both representations of the wavefunction are related by a Fourier transform, such that or, equivalently, Physically realisable states are , and so by the Plancherel theorem, their Fourier transforms are also . (Note that since is in units of distance and is in units of momentum, the presence of the Planck constant in the exponent makes the exponent dimensionless, as it should be.) Therefore, the Fourier transform can be used to pass from one way of representing the state of the particle, by a wave function of position, to another way of representing the state of the particle: by a wave function of momentum. Infinitely many different polarisations are possible, and all are equally valid. Being able to transform states from one representation to another by the Fourier transform is not only convenient but also the underlying reason of the Heisenberg uncertainty principle. The other use of the Fourier transform in both quantum mechanics and quantum field theory is to solve the applicable wave equation. In non-relativistic quantum mechanics, Schrödinger's equation for a time-varying wave function in one-dimension, not subject to external forces, is This is the same as the heat equation except for the presence of the imaginary unit . Fourier methods can be used to solve this equation. In the presence of a potential, given by the potential energy function , the equation becomes The "elementary solutions", as we referred to them above, are the so-called "stationary states" of the particle, and Fourier's algorithm, as described above, can still be used to solve the boundary value problem of the future evolution of given its values for . Neither of these approaches is of much practical use in quantum mechanics. Boundary value problems and the time-evolution of the wave function is not of much practical interest: it is the stationary states that are most important. In relativistic quantum mechanics, Schrödinger's equation becomes a wave equation as was usual in classical physics, except that complex-valued waves are considered. A simple example, in the absence of interactions with other particles or fields, is the free one-dimensional Klein–Gordon–Schrödinger–Fock equation, this time in dimensionless units, This is, from the mathematical point of view, the same as the wave equation of classical physics solved above (but with a complex-valued wave, which makes no difference in the methods). This is of great use in quantum field theory: each separate Fourier component of a wave can be treated as a separate harmonic oscillator and then quantized, a procedure known as "second quantization". Fourier methods have been adapted to also deal with non-trivial interactions. Finally, the number operator of the quantum harmonic oscillator can be interpreted, for example via the Mehler kernel, as the generator of the Fourier transform . Signal processing The Fourier transform is used for the spectral analysis of time-series. The subject of statistical signal processing does not, however, usually apply the Fourier transformation to the signal itself. Even if a real signal is indeed transient, it has been found in practice advisable to model a signal by a function (or, alternatively, a stochastic process) which is stationary in the sense that its characteristic properties are constant over all time. The Fourier transform of such a function does not exist in the usual sense, and it has been found more useful for the analysis of signals to instead take the Fourier transform of its autocorrelation function. The autocorrelation function of a function is defined by This function is a function of the time-lag elapsing between the values of to be correlated. For most functions that occur in practice, is a bounded even function of the time-lag and for typical noisy signals it turns out to be uniformly continuous with a maximum at . The autocorrelation function, more properly called the autocovariance function unless it is normalized in some appropriate fashion, measures the strength of the correlation between the values of separated by a time lag. This is a way of searching for the correlation of with its own past. It is useful even for other statistical tasks besides the analysis of signals. For example, if represents the temperature at time , one expects a strong correlation with the temperature at a time lag of 24 hours. It possesses a Fourier transform, This Fourier transform is called the power spectral density function of . (Unless all periodic components are first filtered out from , this integral will diverge, but it is easy to filter out such periodicities.) The power spectrum, as indicated by this density function , measures the amount of variance contributed to the data by the frequency . In electrical signals, the variance is proportional to the average power (energy per unit time), and so the power spectrum describes how much the different frequencies contribute to the average power of the signal. This process is called the spectral analysis of time-series and is analogous to the usual analysis of variance of data that is not a time-series (ANOVA). Knowledge of which frequencies are "important" in this sense is crucial for the proper design of filters and for the proper evaluation of measuring apparatuses. It can also be useful for the scientific analysis of the phenomena responsible for producing the data. The power spectrum of a signal can also be approximately measured directly by measuring the average power that remains in a signal after all the frequencies outside a narrow band have been filtered out. Spectral analysis is carried out for visual signals as well. The power spectrum ignores all phase relations, which is good enough for many purposes, but for video signals other types of spectral analysis must also be employed, still using the Fourier transform as a tool. Other notations Other common notations for include: In the sciences and engineering it is also common to make substitutions like these: So the transform pair can become A disadvantage of the capital letter notation is when expressing a transform such as or which become the more awkward and In some contexts such as particle physics, the same symbol may be used for both for a function as well as it Fourier transform, with the two only distinguished by their argument I.e. would refer to the Fourier transform because of the momentum argument, while would refer to the original function because of the positional argument. Although tildes may be used as in to indicate Fourier transforms, tildes may also be used to indicate a modification of a quantity with a more Lorentz invariant form, such as , so care must be taken. Similarly, often denotes the Hilbert transform of . The interpretation of the complex function may be aided by expressing it in polar coordinate form in terms of the two real functions and where: is the amplitude and is the phase (see arg function). Then the inverse transform can be written: which is a recombination of all the frequency components of . Each component is a complex sinusoid of the form whose amplitude is and whose initial phase angle (at ) is . The Fourier transform may be thought of as a mapping on function spaces. This mapping is here denoted and is used to denote the Fourier transform of the function . This mapping is linear, which means that can also be seen as a linear transformation on the function space and implies that the standard notation in linear algebra of applying a linear transformation to a vector (here the function ) can be used to write instead of . Since the result of applying the Fourier transform is again a function, we can be interested in the value of this function evaluated at the value for its variable, and this is denoted either as or as . Notice that in the former case, it is implicitly understood that is applied first to and then the resulting function is evaluated at , not the other way around. In mathematics and various applied sciences, it is often necessary to distinguish between a function and the value of when its variable equals , denoted . This means that a notation like formally can be interpreted as the Fourier transform of the values of at . Despite this flaw, the previous notation appears frequently, often when a particular function or a function of a particular variable is to be transformed. For example, is sometimes used to express that the Fourier transform of a rectangular function is a sinc function, or is used to express the shift property of the Fourier transform. Notice, that the last example is only correct under the assumption that the transformed function is a function of , not of . As discussed above, the characteristic function of a random variable is the same as the Fourier–Stieltjes transform of its distribution measure, but in this context it is typical to take a different convention for the constants. Typically characteristic function is defined As in the case of the "non-unitary angular frequency" convention above, the factor of 2 appears in neither the normalizing constant nor the exponent. Unlike any of the conventions appearing above, this convention takes the opposite sign in the exponent. Computation methods The appropriate computation method largely depends how the original mathematical function is represented and the desired form of the output function. In this section we consider both functions of a continuous variable, and functions of a discrete variable (i.e. ordered pairs of and values). For discrete-valued the transform integral becomes a summation of sinusoids, which is still a continuous function of frequency ( or ). When the sinusoids are harmonically related (i.e. when the -values are spaced at integer multiples of an interval), the transform is called discrete-time Fourier transform (DTFT). Discrete Fourier transforms and fast Fourier transforms Sampling the DTFT at equally-spaced values of frequency is the most common modern method of computation. Efficient procedures, depending on the frequency resolution needed, are described at . The discrete Fourier transform (DFT), used there, is usually computed by a fast Fourier transform (FFT) algorithm. Analytic integration of closed-form functions Tables of closed-form Fourier transforms, such as and , are created by mathematically evaluating the Fourier analysis integral (or summation) into another closed-form function of frequency ( or ). When mathematically possible, this provides a transform for a continuum of frequency values. Many computer algebra systems such as Matlab and Mathematica that are capable of symbolic integration are capable of computing Fourier transforms analytically. For example, to compute the Fourier transform of one might enter the command into Wolfram Alpha. Numerical integration of closed-form continuous functions Discrete sampling of the Fourier transform can also be done by numerical integration of the definition at each value of frequency for which transform is desired. The numerical integration approach works on a much broader class of functions than the analytic approach. Numerical integration of a series of ordered pairs If the input function is a series of ordered pairs, numerical integration reduces to just a summation over the set of data pairs. The DTFT is a common subcase of this more general situation. Tables of important Fourier transforms The following tables record some closed-form Fourier transforms. For functions and denote their Fourier transforms by and . Only the three most common conventions are included. It may be useful to notice that entry 105 gives a relationship between the Fourier transform of a function and the original function, which can be seen as relating the Fourier transform and its inverse. Functional relationships, one-dimensional The Fourier transforms in this table may be found in or . Square-integrable functions, one-dimensional The Fourier transforms in this table may be found in , , or . Distributions, one-dimensional The Fourier transforms in this table may be found in or . Two-dimensional functions Formulas for general -dimensional functions See also Analog signal processing Beevers–Lipson strip Constant-Q transform Discrete Fourier transform DFT matrix Fast Fourier transform Fourier integral operator Fourier inversion theorem Fourier multiplier Fourier series Fourier sine transform Fourier–Deligne transform Fourier–Mukai transform Fractional Fourier transform Indirect Fourier transform Integral transform Hankel transform Hartley transform Laplace transform Least-squares spectral analysis Linear canonical transform List of Fourier-related transforms Mellin transform Multidimensional transform NGC 4622, especially the image NGC 4622 Fourier transform . Nonlocal operator Quantum Fourier transform Quadratic Fourier transform Short-time Fourier transform Spectral density Spectral density estimation Symbolic integration Time stretch dispersive Fourier transform Transform (mathematics) Notes Citations References (translated from French) (translated from Russian) (translated from Russian) (translated from Russian) (translated from Russian) ; also available at Fundamentals of Music Processing, Section 2.1, pages 40–56 External links Encyclopedia of Mathematics Fourier Transform in Crystallography Fourier analysis Integral transforms Unitary operators Joseph Fourier Mathematical physics	Fourier transform	[ "Physics", "Mathematics" ]	14,466	[ "Applied mathematics", "Theoretical physics", "Mathematical physics" ]
52,293	https://en.wikipedia.org/wiki/Origami	) is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word to refer to designs which use cuts. In the detailed Japanese classification, origami is divided into stylized ceremonial origami (儀礼折り紙, girei origami) and recreational origami (遊戯折り紙, yūgi origami), and only recreational origami is generally recognized as origami. In Japan, ceremonial origami is generally called "origata" (:ja:折形) to distinguish it from recreational origami. The term "origata" is one of the old terms for origami. The small number of basic origami folds can be combined in a variety of ways to make intricate designs. The best-known origami model is the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be of different colors, prints, or patterns. Traditional Japanese origami, which has been practiced since the Edo period (1603–1868), has often been less strict about these conventions, sometimes cutting the paper or using nonsquare shapes to start with. The principles of origami are also used in stents, packaging, and other engineering applications. Etymology The word "origami" is a compound of two smaller words: "ori" (root verb "oru"), meaning to fold, and "kami", meaning paper. Until recently, not all forms of paper folding were grouped under the word origami. Before that, paper folding for play was known by a variety of names, including "orikata" or "origata" (折形), "orisue" (折据), "orimono" (折物), "tatamigami" (畳紙) and others. History Distinct paperfolding traditions arose in Europe, China, and Japan which have been well-documented by historians. These seem to have been mostly separate traditions, until the 20th century. Ceremonial origami (origata) By the 7th century, paper had been introduced to Japan from China via the Korean Peninsula, and the Japanese developed washi by improving the method of making paper in the Heian period. The papermaking technique developed in Japan around 805 to 809 was called nagashi-suki (流し漉き), a method of adding mucilage to the process of the conventional tame-suki (溜め漉き) technique to form a stronger layer of paper fibers. With the development of Japanese papermaking technology and the widespread use of paper, folded paper began to be used for decorations and tools for religious ceremonies such as gohei, ōnusa (:ja:大麻 (神道)) and shide at Shinto shrines. Religious decorations made of paper and the way gifts were wrapped in folded paper gradually became stylized and established as ceremonial origami. During the Heian period, the Imperial court established a code of etiquette for wrapping money and goods used in ceremonies with folded paper, and a code of etiquette for wrapping gifts. In the Muromachi period from the 1300s to the 1400s, various forms of decorum were developed by the Ogasawara clan and Ise clans (:ja:伊勢氏), completing the prototype of Japanese folded-paper decorum that continues to this day. The Ise clan presided over the decorum of the inside of the palace of the Ashikaga Shogunate, and in particular, Ise Sadachika (:ja:伊勢貞親) during the reign of the eighth Shogun, Ashikaga Yoshimasa (足利義政), greatly influenced the development of the decorum of the daimyo and samurai classes, leading to the development of various stylized forms of ceremonial origami. The shapes of ceremonial origami created in this period were geometric, and the shapes of noshi to be attached to gifts at feasts and weddings, and origami that imitated butterflies to be displayed on sake vessels, were quite different from those of later generations of recreational origami whose shapes captured the characteristics of real objects and living things. The "noshi" wrapping, and the folding of female and male butterflies, which are still used for weddings and celebrations, are a continuation and development of a tradition that began in the Muromachi period. A reference in a poem by Ihara Saikaku from 1680 describes the origami butterflies used during Shinto weddings to represent the bride and groom. Recreational origami 1500s－1800s It is not certain when play-made paper models, now commonly known as origami, began in Japan. However, the kozuka of a Japanese sword made by Gotō Eijō (後藤栄乗) between the end of the 1500s and the beginning of the 1600s was decorated with a picture of a crane made of origami, and it is believed that origami for play existed by the Sengoku period or the early Edo period. In 1747, during the Edo period, a book titled Ranma zushiki (欄間図式) was published, which contained various designs of the ranma (:ja:欄間), a decoration of Japanese architecture. This included origami of various designs, including paper models of cranes, which are still well known today. It is thought that by this time, many people were familiar with origami for play, which modern people recognize as origami. During this period, origami was commonly called orikata (折形) or orisue (折据) and was often used as a pattern on kimonos and decorations. Hiden senbazuru orikata (:ja:秘傳千羽鶴折形), published in 1797, is the oldest known technical book on origami for play. The book contains 49 origami pieces created by a Buddhist monk named Gidō (:ja:義道) in Ise Province, whose works were named and accompanied by kyōka (狂歌, comic tanka) by author Akisato Ritō (秋里籬島). These pieces were far more technically advanced than their predecessors, suggesting that origami culture had become more sophisticated. Gido continued to produce origami after the publication of his book, leaving at least 158 highly skilled masterpieces for posterity. In 1976, Kuwana City in Mie Prefecture, Gido's hometown, designated 49 of the methods described in the Hiden senbazuru orikata as Intangible Cultural Properties of Kuwana City. Kuwana City has also certified qualified persons who are able to correctly produce these works and have in-depth knowledge of the art. Kuwana City has published some of the origami production methods on YouTube. From the late Edo period to the Bakumatu period, origami that imitated the six legendary Japanese poets, rokkasen (六歌仙) listed in the Kokin Wakashū (古今和歌集) compiled in the 900s and the characters in Chūshingura became popular, but today they are rarely used as subjects for origami. In Europe, there was a well-developed genre of napkin folding, which flourished during the 17th and 18th centuries. After this period, this genre declined and was mostly forgotten; historian Joan Sallas attributes this to the introduction of porcelain, which replaced complex napkin folds as a dinner-table status symbol among nobility. However, some of the techniques and bases associated with this tradition continued to be a part of European culture; folding was a significant part of Friedrich Fröbel's "Kindergarten" method, and the designs published in connection with his curriculum are stylistically similar to the napkin fold repertoire. Another example of early origami in Europe is the "pajarita," a stylized bird whose origins date from at least the nineteenth century. Since 1800s When Japan opened its borders in the 1860s, as part of a modernization strategy, they imported Fröbel's Kindergarten system—and with it, German ideas about paperfolding. This included the ban on cuts, and the starting shape of a bicolored square. These ideas, and some of the European folding repertoire, were integrated into the Japanese tradition. Before this, traditional Japanese sources use a variety of starting shapes, often had cuts, and if they had color or markings, these were added after the model was folded. In Japan, the first kindergarten was established in 1875, and origami was promoted as part of early childhood education. The kindergarten's 1877 regulations listed 25 activities, including origami subjects. Shōkokumin (小国民), a magazine for boys, frequently published articles on origami. Origami Zusetsu (折紙図説), published in 1908, clearly distinguished ceremonial origami from recreational origami. These books and magazines carried both the traditional Japanese style of origami and the style inspired by Fröbel. In the early 1900s, Akira Yoshizawa, Kosho Uchiyama, and others began creating and recording original origami works. Akira Yoshizawa in particular was responsible for a number of innovations, such as wet-folding and the Yoshizawa–Randlett diagramming system, and his work inspired a renaissance of the art form. In 1974, origami was offered in the USSR as an additional activity for elementary school children. During the 1980s a number of folders started systematically studying the mathematical properties of folded forms, which led to a rapid increase in the complexity of origami models. Starting in the late 20th century, there has been a renewed interest in understanding the behavior of folding matter, both artistically and scientifically. The "new origami," which distinguishes it from old craft practices, has had a rapid evolution due to the contribution of computational mathematics and the development of techniques such as box-pleating, tessellations and wet-folding. Artists like Robert J. Lang, Erik Demaine, Sipho Mabona, Giang Dinh, Paul Jackson, and others, are frequently cited for advancing new applications of the art. The computational facet and the interchanges through social networks, where new techniques and designs are introduced, have raised the profile of origami in the 21st century. Techniques and materials Techniques Many origami books begin with a description of basic origami techniques which are used to construct the models. This includes simple diagrams of basic folds like valley and mountain folds, pleats, reverse folds, squash folds, and sinks. There are also standard named bases which are used in a wide variety of models, for instance the bird base is an intermediate stage in the construction of the flapping bird. Additional bases are the preliminary base (square base), fish base, waterbomb base, and the frog base. Origami paper Almost any laminar (flat) material can be used for folding; the only requirement is that it should hold a crease. Origami paper, often referred to as "kami" (Japanese for paper), is sold in prepackaged squares of various sizes ranging from 2.5 cm (1 in) to 25 cm (10 in) or more. It is commonly colored on one side and white on the other; however, dual coloured and patterned versions exist and can be used effectively for color-changed models. Origami paper weighs slightly less than copy paper, making it suitable for a wider range of models. Normal copy paper with weights of 70–90 g/m2 (19–24 lb) can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of 100 g/m2 (approx. 25 lb) or more can be wet-folded. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when it is dry. Foil-backed paper, as its name implies, is a sheet of thin foil glued to a sheet of thin paper. Related to this is tissue foil, which is made by gluing a thin piece of tissue paper to kitchen aluminium foil. A second piece of tissue can be glued onto the reverse side to produce a tissue/foil/tissue sandwich. Foil-backed paper is available commercially, but not tissue foil; it must be handmade. Both types of foil materials are suitable for complex models. is the traditional origami paper used in Japan. Washi is generally tougher than ordinary paper made from wood pulp, and is used in many traditional arts. Washi is commonly made using fibres from the bark of the gampi tree, the mitsumata shrub (Edgeworthia papyrifera), or the paper mulberry but can also be made using bamboo, hemp, rice, and wheat. Artisan papers such as unryu, lokta, hanji, gampi, kozo, saa, and abaca have long fibers and are often extremely strong. As these papers are floppy to start with, they are often backcoated or resized with methylcellulose or wheat paste before folding. Also, these papers are extremely thin and compressible, allowing for thin, narrowed limbs as in the case of insect models. Paper money from various countries is also popular to create origami with; this is known variously as Dollar Origami, Orikane, and Money Origami. Tools It is common to fold using a flat surface, but some folders like doing it in the air with no tools, especially when displaying the folding. Some folders believe that no tool should be used when folding. However a couple of tools can help especially with the more complex models. For instance a bone folder allows sharp creases to be made in the paper easily, paper clips can act as extra pairs of fingers, and tweezers can be used to make small folds. When making complex models from origami crease patterns, it can help to use a ruler and ballpoint embosser to score the creases. Completed models can be sprayed so that they keep their shape better, and a spray is needed when wet folding. Types Action origami In addition to the more common still-life origami, there are also moving object designs; origami can move. Action origami includes origami that flies, requires inflation to complete, or, when complete, uses the kinetic energy of a person's hands, applied at a certain region on the model, to move another flap or limb. Some argue that, strictly speaking, only the latter is really "recognized" as action origami. Action origami, first appearing with the traditional Japanese flapping bird, is quite common. One example is Robert Lang's instrumentalists; when the figures' heads are pulled away from their bodies, their hands will move, resembling the playing of music. Modular origami Modular origami consists of putting a number of identical pieces together to form a complete model. Often the individual pieces are simple, but the final assembly may be more difficult. Many modular origami models are decorative folding balls such as kusudama, which differ from classical origami in that the pieces may be held together using thread or glue. Chinese paper folding, a cousin of origami, includes a similar style called golden venture folding where large numbers of pieces are put together to create elaborate models. This style is most commonly known as "3D origami". However, that name did not appear until Joie Staff published a series of books titled 3D Origami, More 3D Origami, and More and More 3D Origami. This style originated from some Chinese refugees while they were detained in America and is also called Golden Venture folding from the ship they came on. Wet-folding Wet-folding is an origami technique for producing models with gentle curves rather than geometric straight folds and flat surfaces. The paper is dampened so it can be moulded easily, and the final model keeps its shape when it dries. It can be used, for instance, to produce very natural looking animal models. Size, an adhesive that is crisp and hard when dry, but dissolves in water when wet and becoming soft and flexible, is often applied to the paper either at the pulp stage while the paper is being formed, or on the surface of a ready sheet of paper. The latter method is called external sizing and most commonly uses Methylcellulose, or MC, paste, or various plant starches. Pureland origami Pureland origami adds the restrictions that only simple mountain/valley folds may be used, and all folds must have straightforward locations. It was developed by John Smith in the 1970s to help inexperienced folders or those with limited motor skills. Some designers also like the challenge of creating within the very strict constraints. Origami tessellations Origami tessellation is a branch that has grown in popularity after 2000. A tessellation is a collection of figures filling a plane with no gaps or overlaps. In origami tessellations, pleats are used to connect molecules such as twist folds together in a repeating fashion. During the 1960s, Shuzo Fujimoto was the first to explore twist fold tessellations in any systematic way, coming up with dozens of patterns and establishing the genre in the origami mainstream. Around the same time period, Ron Resch patented some tessellation patterns as part of his explorations into kinetic sculpture and developable surfaces, although his work was not known by the origami community until the 1980s. Chris Palmer is an artist who has extensively explored tessellations after seeing the Zilij patterns in the Alhambra, and has found ways to create detailed origami tessellations out of silk. Robert Lang and Alex Bateman are two designers who use computer programs to create origami tessellations. The first international convention devoted to origami tessellations was hosted in Brasília (Brazil) in 2006, and the first instruction book on tessellation folding patterns was published by Eric Gjerde in 2008. Since then, the field has grown very quickly. Tessellation artists include Polly Verity (Scotland); Joel Cooper, Christine Edison, Ray Schamp and Goran Konjevod from the US; Roberto Gretter (Italy); Christiane Bettens (Switzerland); Carlos Natan López (Mexico); and Jorge C. Lucero (Brazil). Kirigami Kirigami is a Japanese term for paper cutting. Cutting was often used in traditional Japanese origami, but modern innovations in technique have made the use of cuts unnecessary. Most origami designers no longer consider models with cuts to be origami, instead using the term Kirigami to describe them. This change in attitude occurred during the 1960s and 70s, so early origami books often use cuts, but for the most part they have disappeared from the modern origami repertoire, and most modern books do not even mention cutting. Strip folding Strip folding is a combination of paper folding and paper weaving. A common example of strip folding is called the Lucky Star, also called Chinese lucky star, dream star, wishing star, or simply origami star. Another common fold is the Moravian Star which is made by strip folding in 3-dimensional design to include 16 spikes. Teabag folding Teabag folding is credited to Dutch artist Tiny van der Plas, who developed the technique in 1992 as a papercraft art for embellishing greeting cards. It uses small square pieces of paper (e.g., a tea bag wrapper) bearing symmetrical designs that are folded in such a way that they interlock and produce a three-dimensional version of the underlying design. The basic kite fold is used to produce rosettes that are a 3 dimensional version of the 2D design. The basic rosette design requires eight matching squares to be folded into the 'kite' design. Mathematics teachers find the designs very useful as a practical way of demonstrating some basic properties of symmetry. Mathematics and technical origami Mathematics and practical applications The practice and study of origami encapsulates several subjects of mathematical interest. For instance, the problem of flat-foldability (whether a crease pattern can be folded into a 2-dimensional model) has been a topic of considerable mathematical study. A number of technological advances have come from insights obtained through paper folding. For example, techniques have been developed for the deployment of car airbags and stent implants from a folded position. The problem of rigid origami ("if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we still fold the model?") has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites. Origami can be used to construct various geometrical designs not possible with compass and straightedge constructions. For instance paper folding may be used for angle trisection and doubling the cube. Technical origami Technical origami, known in Japanese as , is an origami design approach in which the model is conceived as an engineered crease pattern, rather than developed through trial-and-error. With advances in origami mathematics, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs. This method of origami design was developed by Robert Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with a full complement of fingers and toes, and the like. The crease pattern is a layout of the creases required to form the structure of the model. Paradoxically enough, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the model. What is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. By opening up a folded model, you can observe the structures that comprise it; the study of these structures led to a number of crease-pattern-oriented design approaches The pattern of allocations is referred to as the 'circle-packing' or 'polygon-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. Once this figure is computed, the creases which are then used to obtain the base structure can be added. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures. As a circle encloses the maximum amount of area for a given perimeter, circle packing allows for maximum efficiency in terms of paper usage. However, other polygonal shapes can be used to solve the packing problem as well. The use of polygonal shapes other than circles is often motivated by the desire to find easily locatable creases (such as multiples of 22.5 degrees) and hence an easier folding sequence as well. One popular offshoot of the circle packing method is box-pleating, where squares are used instead of circles. As a result, the crease pattern that arises from this method contains only 45 and 90 degree angles, which often makes for a more direct folding sequence. Origami-related computer programs A number of computer aids to origami such as TreeMaker and Oripa, have been devised. TreeMaker allows new origami bases to be designed for special purposes and Oripa tries to calculate the folded shape from the crease pattern. Ethics and copyright Copyright in origami designs and the use of models has become an increasingly important issue in the origami community, as the internet has made the sale and distribution of pirated designs very easy. It is considered good etiquette to always credit the original artist and the folder when displaying origami models. It has been claimed that all commercial rights to designs and models are typically reserved by origami artists; however, the degree to which this can be enforced has been disputed. Under such a view, a person who folds a model using a legally obtained design could publicly display the model unless such rights were specifically reserved, whereas folding a design for money or commercial use of a photo for instance would require consent. The Origami Authors and Creators group was set up to represent the copyright interests of origami artists and facilitate permissions requests. However, a court in Japan has asserted that the folding method of an origami model "comprises an idea and not a creative expression, and thus is not protected under the copyright law". Further, the court stated that "the method to folding origami is in the public domain; one cannot avoid using the same folding creases or the same arrows to show the direction in which to fold the paper". Therefore, it is legal to redraw the folding instructions of a model of another author even if the redrawn instructions share similarities to the original ones, as long as those similarities are "functional in nature". The redrawn instructions may be published (and even sold) without necessity of any permission from the original author. Origami in various meanings From a global perspective, the term 'origami' refers to the folding of paper to shape objects for entertainment purposes, but it has historically been used in various ways in Japan. For example, the term 'origami' also refers to the certificate of authenticity that accompanies a Japanese sword or tea utensil. The people of the Hon'ami clan, who were the authority on Japanese sword appraisal from the Muromachi period to the Edo period, responded to the requests of the shogun, daimyo and samurai by appraising Japanese swords, determining when and by which school the sword was made, whether the inscription on the nakago was genuine or not, and what the price was, and then issuing origami with the results written on it. This has led to the Japanese word 'origami tsuki' (折り紙付き) meaning 'origami is attached' meaning that the quality of the object or the ability of the person is sufficiently high. The term 'origami' also referred to a specific style of old documents in Japan. The paper folded vertically is called 'tategami' (竪紙), while the paper folded horizontally is called 'origami', and origami has a lower status than tategami. This style of letter began to be used at the end of the Heian period, and in the Kamakura period it was used as a complaint, and origami came to refer to the complaint itself. Furthermore, during the Muromachi period, origami was often used as a command document or a catalog of gifts, and it came to refer to the catalog of gifts itself. Gallery These pictures show examples of various types of origami. In popular culture In House of Cards season 1, episode 6, Claire Underwood gives a homeless man cash, and he later returns it folded into the shape of a bird. Claire then begins making origami animals, and in episode 7 she gives several to Peter Russo for his children. In Blade Runner, Gaff folds origami throughout the movie, and an origami unicorn he folds forms a major plot point. The philosophy and plot of the science fiction story "Ghostweight" by Yoon Ha Lee revolve around origami. In it, origami serves as a metaphor for history: "It is not true that the dead cannot be folded. Square becomes kite becomes swan; history becomes rumor becomes song. Even the act of remembrance creases the truth". A major element of the plot is the weaponry called jerengjen of space mercenaries, which unfold from flat shapes: "In the streets, jerengjen unfolded prettily, expanding into artillery with dragon-shaped shadows and sleek four-legged assault robots with wolf-shaped shadows. In the skies, jerengjen unfolded into bombers with kestrel-shaped shadows." The story says that the word means the art of paper folding in the mercenaries' main language. In an interview, when asked about the subject, the author tells that he became fascinated with dimensions since reading the novel Flatland. In Scooby-Doo! and the Samurai Sword, Scooby and Shaggy learn origami, which proves crucial in finding the Sword of Doom. In Kubo and the Two Strings, the main protagonist Kubo can magically manipulate origami with music from his shamisen. In Naruto Shippuden, Konan, the only female member of the Akatsuki, uses origami jutsu, in which she uses her chakra to bring origami to life and use them as weapons. The 2010 video game Heavy Rain has an antagonist known as the origami killer. In the BBC television program QI, it is reported that origami in the form it is commonly known, where paper is folded without being cut or glued likely originated in Germany and was imported to Japan as late as 1860 when Japan opened its borders (However, it is confirmed that paper cranes using this technique have existed in Japan since the Edo period before 1860). Paper Mario: The Origami King is a 2020 Nintendo Switch game featuring Mario series characters in an origami-themed world. Origami Yoda is a children's book series by Tom Angleberger about a group of middle school students who construct origami finger puppets resembling Star Wars characters. See also Chinese paper folding Fold-forming Furoshiki Japanese art List of origamists Origamic architecture Paper craft Paper fortune teller Paper plane Pop-up book References Further reading Kunihiko Kasahara (1988). Origami Omnibus: Paper Folding for Everybody. Tokyo: Japan Publications, Inc. A book for a more advanced origamian; this book presents many more complicated ideas and theories, as well as related topics in geometry and culture, along with model diagrams. Kunihiko Kasahara and Toshie Takahama (1987). Origami for the Connoisseur. Tokyo: Japan Publications, Inc. Satoshi Kamiya (2005). Works by Satoshi Kamiya, 1995–2003. Tokyo: Origami House An extremely complex book for the elite origamian, most models take 100+ steps to complete. Includes his famous Divine Dragon Bahamut and Ancient Dragons. Instructions are in Japanese and English. Kunihiko Kasahara (2001). Extreme Origami. Michael LaFosse. Origamido : Masterworks of Paper Folding Nick Robinson (2004). Encyclopedia of Origami. Quarto. . A book full of stimulating designs. External links Articles containing video clips Japanese inventions Japanese words and phrases Leisure activities Paper art	Origami	[ "Mathematics" ]	6,488	[ "Recreational mathematics", "Paper folding" ]
52,313	https://en.wikipedia.org/wiki/MathML	Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content, and is one of a number of mathematical markup languages. Its aim is to natively integrate mathematical formulae into World Wide Web pages and other documents. It is part of HTML5 and standardised by ISO/IEC since 2015. History Following some experiments in the Arena browser based on proposals for mathematical markup in HTML, MathML 1 was released as a W3C recommendation in April 1998 as the first XML language to be recommended by the W3C. Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. Implementations of the specification appeared in Amaya 1.1, Mozilla 1.0 and Opera 9.5. In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C Math Working Group. MathML was originally designed before the finalization of XML namespaces. However, it was assigned a namespace immediately after the Namespace Recommendation was completed, and for XML use, the elements should be in the namespace with namespace URL http://www.w3.org/1998/Math/MathML. When MathML is used in HTML (as opposed to XML) this namespace is automatically inferred by the HTML parser and need not be specified in the document. MathML version 3 Version 3 of the MathML specification was released as a W3C recommendation on 20 October 2010. A recommendation of A MathML for CSS Profile was later released on 7 June 2011; this is a subset of MathML suitable for CSS formatting. Another subset, Strict Content MathML, provides a subset of content MathML with a uniform structure and is designed to be compatible with OpenMath. Other content elements are defined in terms of a transformation to the strict subset. New content elements include which associates bound variables () to expressions, for example a summation index. The new element allows structure sharing. The development of MathML 3.0 went through a number of stages. In June 2006, the W3C rechartered the MathML Working Group to produce a MathML 3 Recommendation until February 2008, and in November 2008 extended the charter to April 2010. A sixth Working Draft of the MathML 3 revision was published in June 2009. On 10 August 2010 version 3 graduated to become a "Proposed Recommendation" rather than a draft. An implementation of MathML 2 landed in WebKit around this same time, with a Chromium implementation following a couple of years later, although that implementation was removed from Chromium after less than a year. The Second Edition of MathML 3.0 was published as a W3C Recommendation on 10 April 2014. The specification was approved as an ISO/IEC international standard 40314:2015 on 23 June 2015. Also in 2015, the MathML Association was founded to support the adoption of the MathML standard. At that time, according to a member of the MathJax team, none of the major browser makers paid any of their developers for any MathML-rendering work; whatever support existed was overwhelmingly the result of unpaid volunteer time/work. MathML Core In August 2021, a new specification called MathML Core was published, described as the “core subset of Mathematical Markup Language, or MathML, that is suitable for browser implementation.” MathML Core set itself apart from MathML 3.0 by including detailed rendering rules and integration with CSS, automated browser support testing resources, and focusing on a fundamental subset of MathML. An implementation was added to Chromium at the beginning of 2023. Presentation and semantics MathML deals not only with the presentation but also the meaning of formula components (the latter part of MathML is known as "Content MathML"). Because the meaning of the equation is preserved separate from the presentation, how the content is communicated can be left up to the user. For example, web pages with MathML embedded in them can be viewed as normal web pages with many browsers, but visually impaired users can also have the same MathML read to them through the use of screen readers (e.g. using the VoiceOver in Safari). JAWS from version 16 onward supports MathML voicing as well as braille output. The quality of rendering of MathML in a browser depends on the installed fonts. The STIX Fonts project have released a comprehensive set of mathematical fonts under an open license. The Cambria Math font supplied with Microsoft Windows had slightly more limited support. A valid MathML document typically consists of the XML declaration, DOCTYPE declaration, and document element. The document body then contains MathML expressions which appear in elements as needed in the document. Often, MathML will be embedded in more general documents, such as HTML, DocBook, or other XML-based formats. Presentation MathML Presentation MathML focuses on the display of an equation, and has about 30 elements. The elements' names all begin with . A Presentation MathML expression is built up out of tokens that are combined using higher-level elements, which control their layout. Finer details of presentation are affected by close to 50 attributes. Token elements generally only contain characters (not other elements). They include: – identifiers; – operators; – numbers; – text. Note, however, that these token elements may be used as extension points, allowing markup in host languages. MathML in HTML5 allows most inline HTML markup in mtext, and is conforming, with the HTML markup being used within the MathML to mark up the embedded text (making the first word bold in this example). These are combined using layout elements, that generally contain only elements. They include: – a horizontal row of items; , , and others – superscripts, limits over and under operators like sums, etc.; – fractions; and – roots; – surrounding content with fences, such as parentheses. As usual in HTML and XML, many entities are available for specifying special symbols by name, such as and . An interesting feature of MathML is that entities also exist to express normally-invisible operators, such as (or the shorthand ) for implicit multiplication. They are: (to distinguish from in ); (to distinguish from in ); (vice versa); (to distinguish from in ). The full specification of MathML entities is closely coordinated with the corresponding specifications for use with HTML and XML in general. Thus, the expression requires two layout elements: one to create the overall horizontal row and one for the superscripted exponent. However, the individual tokens also have to be identified as identifiers (), operators (), or numbers (). Adding the token markup, the full form ends up as <mrow> <mi>a</mi> <mo>⁢</mo> <msup><mi>x</mi><mn>2</mn></msup> <mo>+</mo><mi>b</mi><mo>⁢</mo><mi>x</mi> <mo>+</mo><mi>c</mi> </mrow> A complete document that consists of just the MathML example above, is shown here: <?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE math PUBLIC "-//W3C//DTD MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mi>a</mi> <mo>⁢</mo> <msup><mi>x</mi><mn>2</mn></msup> <mo>+</mo><mi>b</mi><mo>⁢</mo><mi>x</mi> <mo>+</mo><mi>c</mi> </mrow> </math> Content MathML Content MathML focuses on the semantics, or meaning, of the expression rather than its layout. Central to Content MathML is the element that represents function application. The function being applied is the first child element under , and its operands or parameters are the remaining child elements. Content MathML uses only a few attributes. Tokens such as identifiers and numbers are individually marked up, much as for Presentation MathML, but with elements such as and . Rather than being merely another type of token, operators are represented by specific elements, whose mathematical semantics are known to MathML: , , etc. There are over a hundred different elements for different functions and operators. For example, represents and represents . The elements representing operators and functions are empty elements, because their operands are the other elements under the containing . The expression could be represented as <math> <apply> <plus/> <apply> <times/> <ci>a</ci> <apply> <power/> <ci>x</ci> <cn>2</cn> </apply> </apply> <apply> <times/> <ci>b</ci> <ci>x</ci> </apply> <ci>c</ci> </apply> </math> Content MathML is nearly isomorphic to expressions in a functional language such as Scheme and other dialects of Lisp. amounts to Scheme's , and the many operator and function elements amount to Scheme functions. With this trivial literal transformation, plus un-tagging the individual tokens, the example above becomes: (plus (times a (power x 2)) (times b x) c) This reflects the long-known close relationship between XML element structures, and LISP or Scheme S-expressions. Wikidata annotation in Content MathML According to the OM Society, OpenMath Content Dictionaries can be employed as collections of symbols and identifiers with declarations of their semanticsnames, descriptions and rules. A 2018 paper presented at the SIGIR conference proposed that the semantic knowledge base Wikidata could be used as an OpenMath Content Dictionary to link semantic elements of a mathematical formula to unique and language-independent Wikidata items. Example The well-known quadratic formula could be represented in Presentation MathML as an expression tree made up from layout elements like or : <math mode="display" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mo form="prefix">−</mo> <mi>b</mi> <mo>&pm;</mo> <msqrt> <msup><mi>b</mi><mn>2</mn></msup> <mo>−</mo> <mn>4</mn><mo>⁢</mo><mi>a</mi><mo>⁢</mo><mi>c</mi> </msqrt> </mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex"><!-- TeX --> x = \frac{-b\pm\sqrt{b^2-4ac}}{2a} </annotation> <annotation encoding="StarMath 5.0"> x = {-b plusminus sqrt {b^2 - 4 ac}} over {2 a} </annotation> <!-- More annotations can be written: application/x-troff-eqn for eqn, application/x-asciimath for AsciiMath... --> <!-- Semantic MathML go under <annotation-xml encoding="MathML-Content">. --> </semantics> </math> This example uses the element, which can be used to embed a semantic annotation in non-XML format, for example to store the formula in the format used by an equation editor such as StarMath or the markup using LaTeX syntax. The field is usually a MIME type, although most of the equation encodings don't have such a registration; freeform text may be used in such cases. Although less compact than other formats, the XML structuring of MathML makes its content widely usable and accessible, allows near-instant display in applications such as web browsers, and facilitates an interpretation of its meaning in mathematical software products. MathML is not intended to be written or edited directly by humans. Embedding MathML in HTML/XHTML files MathML, being XML, can be embedded inside other XML files such as XHTML files using XML namespaces. <?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>Example of MathML embedded in an XHTML file</title> <meta name="description" content="Example of MathML embedded in an XHTML file"/> </head> <body> <h1>Example of MathML embedded in an XHTML file</h1> <p> The area of a circle is <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>π<!-- π --></mi> <mo>⁢<!-- ⁢ --></mo> <msup> <mi>r</mi> <mn>2</mn> </msup> </math>. </p> </body> </html> Inline MathML is also supported in HTML5 files. There is no need to specify namespaces as there was in XHTML. <!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <title>Example of MathML embedded in an HTML5 file</title> </head> <body> <h1>Example of MathML embedded in an HTML5 file</h1> <p> The area of a circle is <math> <mi>π</mi> <mo>⁢</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> </math>. </p> </body> </html> Other standards Another standard called OpenMath that has been more specifically designed (largely by the same people who devised Content MathML) for storing formulae semantically can be used to complement MathML. OpenMath data can be embedded in MathML using the element. OpenMath content dictionaries can be used to define the meaning of elements. The following would define P1(x) to be the first Legendre polynomial: <apply> <csymbol encoding="OpenMath" definitionURL="http://www.openmath.org/cd/contrib/cd/orthpoly1.xhtml#legendreP"> <msub><mi>P</mi><mn>1</mn></msub> </csymbol> <ci>x</ci> </apply> The OMDoc format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, and examples, to complete theories and even entire text books. Formulae in OMDoc documents can either be written in Content MathML or in OpenMath; for presentation, they are converted to Presentation MathML. The ISO/IEC standard Office Open XML (OOXML) defines a different XML math syntax, derived from Microsoft Office products. However, it is partially compatible through XSL Transformations. See also CSS List of document markup languages Comparison of document markup languages Formula editors LaTeX2HTML LaTeXML KaTeXJavaScript library that converts LaTeX to MathML MathJaxJavaScript library that converts LaTeX to MathML References Further reading Specifications W3C Recommendation: Mathematical Markup Language (MathML) 1.01 Specification W3C Recommendation: Mathematical Markup Language (MathML) Version 2.0 (Second Edition) W3C Recommendation: Mathematical Markup Language (MathML) Version 3.0 (Third Edition) External links W3C Math Home – Contains the specifications, a FAQ, and a list of supporting software. – A collection of XSLT programs for handling MathML (e.g. converting Content MathML to Presentation MathML, converting Presentation MathML to TeX) Articles with example Scheme (programming language) code Mathematical markup languages World Wide Web Consortium standards XML markup languages XML-based standards	MathML	[ "Mathematics", "Technology" ]	3,813	[ "MathML", "Computer standards", "Mathematical markup languages", "XML-based standards" ]
52,327	https://en.wikipedia.org/wiki/Cyclic%20group	In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently n or Zn, not to be confused with the commutative ring of -adic numbers), that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as an integer power of g in multiplicative notation, or as an integer multiple of g in additive notation. This element g is called a generator of the group. Every infinite cyclic group is isomorphic to the additive group of Z, the integers. Every finite cyclic group of order n is isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation is commutative), and every finitely generated abelian group is a direct product of cyclic groups. Every cyclic group of prime order is a simple group, which cannot be broken down into smaller groups. In the classification of finite simple groups, one of the three infinite classes consists of the cyclic groups of prime order. The cyclic groups of prime order are thus among the building blocks from which all groups can be built. Definition and notation For any element g in any group G, one can form the subgroup that consists of all its integer powers: , called the cyclic subgroup generated by g. The order of g is \|⟨g⟩\|, the number of elements in ⟨g⟩, conventionally abbreviated as \|g\|, as ord(g), or as o(g). That is, the order of an element is equal to the order of the cyclic subgroup that it generates. A cyclic group is a group which is equal to one of its cyclic subgroups: for some element g, called a generator of G. For a finite cyclic group G of order n we have , where e is the identity element and whenever (mod n); in particular , and . An abstract group defined by this multiplication is often denoted Cn, and we say that G is isomorphic to the standard cyclic group Cn. Such a group is also isomorphic to Z/nZ, the group of integers modulo n with the addition operation, which is the standard cyclic group in additive notation. Under the isomorphism χ defined by the identity element e corresponds to 0, products correspond to sums, and powers correspond to multiples. For example, the set of complex 6th roots of unity: forms a group under multiplication. It is cyclic, since it is generated by the primitive root that is, G = ⟨z⟩ = { 1, z, z2, z3, z4, z5 } with z6 = 1. Under a change of letters, this is isomorphic to (structurally the same as) the standard cyclic group of order 6, defined as C6 = ⟨g⟩ = with multiplication gj · gk = gj+k (mod 6), so that g6 = g0 = e. These groups are also isomorphic to Z/6Z = with the operation of addition modulo 6, with zk and gk corresponding to k. For example, corresponds to , and corresponds to , and so on. Any element generates its own cyclic subgroup, such as ⟨z2⟩ = of order 3, isomorphic to C3 and Z/3Z; and ⟨z5⟩ = { e, z5, z10 = z4, z15 = z3, z20 = z2, z25 = z } = G, so that z5 has order 6 and is an alternative generator of G. Instead of the quotient notations Z/nZ, Z/(n), or Z/n, some authors denote a finite cyclic group as Zn, but this clashes with the notation of number theory, where Zp denotes a p-adic number ring, or localization at a prime ideal. On the other hand, in an infinite cyclic group , the powers gk give distinct elements for all integers k, so that G = , and G is isomorphic to the standard group and to Z, the additive group of the integers. An example is the first frieze group. Here there are no finite cycles, and the name "cyclic" may be misleading. To avoid this confusion, Bourbaki introduced the term monogenous group for a group with a single generator and restricted "cyclic group" to mean a finite monogenous group, avoiding the term "infinite cyclic group". Examples Integer and modular addition The set of integers Z, with the operation of addition, forms a group. It is an infinite cyclic group, because all integers can be written by repeatedly adding or subtracting the single number 1. In this group, 1 and −1 are the only generators. Every infinite cyclic group is isomorphic to Z. For every positive integer n, the set of integers modulo n, again with the operation of addition, forms a finite cyclic group, denoted Z/nZ. A modular integer i is a generator of this group if i is relatively prime to n, because these elements can generate all other elements of the group through integer addition. (The number of such generators is φ(n), where φ is the Euler totient function.) Every finite cyclic group G is isomorphic to Z/nZ, where n = is the order of the group. The addition operations on integers and modular integers, used to define the cyclic groups, are the addition operations of commutative rings, also denoted Z and Z/nZ or Z/(n). If p is a prime, then Z/pZ is a finite field, and is usually denoted Fp or GF(p) for Galois field. Modular multiplication For every positive integer n, the set of the integers modulo n that are relatively prime to n is written as (Z/nZ)×; it forms a group under the operation of multiplication. This group is not always cyclic, but is so whenever n is 1, 2, 4, a power of an odd prime, or twice a power of an odd prime . This is the multiplicative group of units of the ring Z/nZ; there are φ(n) of them, where again φ is the Euler totient function. For example, (Z/6Z)× = , and since 6 is twice an odd prime this is a cyclic group. In contrast, (Z/8Z)× = is a Klein 4-group and is not cyclic. When (Z/nZ)× is cyclic, its generators are called primitive roots modulo n. For a prime number p, the group (Z/pZ)× is always cyclic, consisting of the non-zero elements of the finite field of order p. More generally, every finite subgroup of the multiplicative group of any field is cyclic. Rotational symmetries The set of rotational symmetries of a polygon forms a finite cyclic group. If there are n different ways of moving the polygon to itself by a rotation (including the null rotation) then this symmetry group is isomorphic to Z/nZ. In three or higher dimensions there exist other finite symmetry groups that are cyclic, but which are not all rotations around an axis, but instead rotoreflections. The group of all rotations of a circle (the circle group, also denoted S1) is not cyclic, because there is no single rotation whose integer powers generate all rotations. In fact, the infinite cyclic group C∞ is countable, while S1 is not. The group of rotations by rational angles is countable, but still not cyclic. Galois theory An nth root of unity is a complex number whose nth power is 1, a root of the polynomial . The set of all nth roots of unity forms a cyclic group of order n under multiplication. The generators of this cyclic group are the nth primitive roots of unity; they are the roots of the nth cyclotomic polynomial. For example, the polynomial factors as , where ; the set = forms a cyclic group under multiplication. The Galois group of the field extension of the rational numbers generated by the nth roots of unity forms a different group, isomorphic to the multiplicative group (Z/nZ)× of order φ(n), which is cyclic for some but not all n (see above). A field extension is called a cyclic extension if its Galois group is cyclic. For fields of characteristic zero, such extensions are the subject of Kummer theory, and are intimately related to solvability by radicals. For an extension of finite fields of characteristic p, its Galois group is always finite and cyclic, generated by a power of the Frobenius mapping. Conversely, given a finite field F and a finite cyclic group G, there is a finite field extension of F whose Galois group is G. Subgroups All subgroups and quotient groups of cyclic groups are cyclic. Specifically, all subgroups of Z are of the form ⟨m⟩ = mZ, with m a positive integer. All of these subgroups are distinct from each other, and apart from the trivial group {0} = 0Z, they all are isomorphic to Z. The lattice of subgroups of Z is isomorphic to the dual of the lattice of natural numbers ordered by divisibility. Thus, since a prime number p has no nontrivial divisors, pZ is a maximal proper subgroup, and the quotient group Z/pZ is simple; in fact, a cyclic group is simple if and only if its order is prime. All quotient groups Z/nZ are finite, with the exception For every positive divisor d of n, the quotient group Z/nZ has precisely one subgroup of order d, generated by the residue class of n/d. There are no other subgroups. Additional properties Every cyclic group is abelian. That is, its group operation is commutative: (for all g and h in G). This is clear for the groups of integer and modular addition since , and it follows for all cyclic groups since they are all isomorphic to these standard groups. For a finite cyclic group of order n, gn is the identity element for any element g. This again follows by using the isomorphism to modular addition, since for every integer k. (This is also true for a general group of order n, due to Lagrange's theorem.) For a prime power , the group is called a primary cyclic group. The fundamental theorem of abelian groups states that every finitely generated abelian group is a finite direct product of primary cyclic and infinite cyclic groups. Because a cyclic group is abelian, each of its conjugacy classes consists of a single element. A cyclic group of order n therefore has n conjugacy classes. If d is a divisor of n, then the number of elements in Z/nZ which have order d is φ(d), and the number of elements whose order divides d is exactly d. If G is a finite group in which, for each , G contains at most n elements of order dividing n, then G must be cyclic. The order of an element m in Z/nZ is n/gcd(n,m). If n and m are coprime, then the direct product of two cyclic groups Z/nZ and Z/mZ is isomorphic to the cyclic group Z/nmZ, and the converse also holds: this is one form of the Chinese remainder theorem. For example, Z/12Z is isomorphic to the direct product under the isomorphism ; but it is not isomorphic to , in which every element has order at most 6. If p is a prime number, then any group with p elements is isomorphic to the simple group Z/pZ. A number n is called a cyclic number if Z/nZ is the only group of order n, which is true exactly when . The sequence of cyclic numbers include all primes, but some are composite such as 15. However, all cyclic numbers are odd except 2. The cyclic numbers are: 1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 123, 127, 131, 133, 137, 139, 141, 143, ... The definition immediately implies that cyclic groups have group presentation and for finite n. Associated objects Representations The representation theory of the cyclic group is a critical base case for the representation theory of more general finite groups. In the complex case, a representation of a cyclic group decomposes into a direct sum of linear characters, making the connection between character theory and representation theory transparent. In the positive characteristic case, the indecomposable representations of the cyclic group form a model and inductive basis for the representation theory of groups with cyclic Sylow subgroups and more generally the representation theory of blocks of cyclic defect. Cycle graph A cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups. A cycle graph for a cyclic group is simply a circular graph, where the group order is equal to the number of nodes. A single generator defines the group as a directional path on the graph, and the inverse generator defines a backwards path. A trivial path (identity) can be drawn as a loop but is usually suppressed. Z2 is sometimes drawn with two curved edges as a multigraph. A cyclic group Zn, with order n, corresponds to a single cycle graphed simply as an n-sided polygon with the elements at the vertices. Cayley graph A Cayley graph is a graph defined from a pair (G,S) where G is a group and S is a set of generators for the group; it has a vertex for each group element, and an edge for each product of an element with a generator. In the case of a finite cyclic group, with its single generator, the Cayley graph is a cycle graph, and for an infinite cyclic group with its generator the Cayley graph is a doubly infinite path graph. However, Cayley graphs can be defined from other sets of generators as well. The Cayley graphs of cyclic groups with arbitrary generator sets are called circulant graphs. These graphs may be represented geometrically as a set of equally spaced points on a circle or on a line, with each point connected to neighbors with the same set of distances as each other point. They are exactly the vertex-transitive graphs whose symmetry group includes a transitive cyclic group. Endomorphisms The endomorphism ring of the abelian group Z/nZ is isomorphic to Z/nZ itself as a ring. Under this isomorphism, the number r corresponds to the endomorphism of Z/nZ that maps each element to the sum of r copies of it. This is a bijection if and only if r is coprime with n, so the automorphism group of Z/nZ is isomorphic to the unit group (Z/nZ)×. Similarly, the endomorphism ring of the additive group of Z is isomorphic to the ring Z. Its automorphism group is isomorphic to the group of units of the ring Z, which is . Tensor product and Hom of cyclic groups The tensor product can be shown to be isomorphic to . So we can form the collection of group homomorphisms from Z/mZ to Z/nZ, denoted , which is itself a group. For the tensor product, this is a consequence of the general fact that , where R is a commutative ring with unit and I and J are ideals of the ring. For the Hom group, recall that it is isomorphic to the subgroup of consisting of the elements of order dividing m. That subgroup is cyclic of order , which completes the proof. Related classes of groups Several other classes of groups have been defined by their relation to the cyclic groups: Virtually cyclic groups A group is called virtually cyclic if it contains a cyclic subgroup of finite index (the number of cosets that the subgroup has). In other words, any element in a virtually cyclic group can be arrived at by multiplying a member of the cyclic subgroup and a member of a certain finite set. Every cyclic group is virtually cyclic, as is every finite group. An infinite group is virtually cyclic if and only if it is finitely generated and has exactly two ends; an example of such a group is the direct product of Z/nZ and Z, in which the factor Z has finite index n. Every abelian subgroup of a Gromov hyperbolic group is virtually cyclic. Procyclic groups A profinite group is called procyclic if it can be topologically generated by a single element. Examples of profinite groups include the profinite integers or the p-adic integers for a prime number p. Locally cyclic groups A locally cyclic group is a group in which each finitely generated subgroup is cyclic. An example is the additive group of the rational numbers: every finite set of rational numbers is a set of integer multiples of a single unit fraction, the inverse of their lowest common denominator, and generates as a subgroup a cyclic group of integer multiples of this unit fraction. A group is locally cyclic if and only if its lattice of subgroups is a distributive lattice. Cyclically ordered groups A cyclically ordered group is a group together with a cyclic order preserved by the group structure. Every cyclic group can be given a structure as a cyclically ordered group, consistent with the ordering of the integers (or the integers modulo the order of the group). Every finite subgroup of a cyclically ordered group is cyclic. Metacyclic and polycyclic groups A metacyclic group is a group containing a cyclic normal subgroup whose quotient is also cyclic. These groups include the cyclic groups, the dicyclic groups, and the direct products of two cyclic groups. The polycyclic groups generalize metacyclic groups by allowing more than one level of group extension. A group is polycyclic if it has a finite descending sequence of subgroups, each of which is normal in the previous subgroup with a cyclic quotient, ending in the trivial group. Every finitely generated abelian group or nilpotent group is polycyclic. See also Cycle graph (group) Cyclic module Cyclic sieving Prüfer group (countably infinite analogue) Circle group (uncountably infinite analogue) Footnotes Notes Citations References Further reading External links Milne, Group theory, http://www.jmilne.org/math/CourseNotes/gt.html An introduction to cyclic groups Cyclic groups of small order on GroupNames Every cyclic group is abelian Abelian group theory Properties of groups	Cyclic group	[ "Mathematics" ]	3,996	[ "Mathematical structures", "Algebraic structures", "Properties of groups" ]
52,357	https://en.wikipedia.org/wiki/Eroticism	Eroticism () is a quality that causes sexual feelings, as well as a philosophical contemplation concerning the aesthetics of sexual desire, sensuality, and romantic love. That quality may be found in any form of artwork, including painting, sculpture, photography, drama, film, music, or literature. It may also be found in advertising. The term may also refer to a state of sexual arousal or anticipation of such – an insistent sexual impulse, desire, or pattern of thoughts. As French novelist Honoré de Balzac stated, eroticism is dependent not just upon an individual's sexual morality, but also the culture and time in which an individual resides. Definitions Because the nature of what is erotic is fluid, early definitions of the term attempted to conceive eroticism as some form of sensual or romantic love or as the human sex drive (libido); for example, the Encyclopédie of 1755 states that the erotic "is an epithet which is applied to everything with a connection to the love of the sexes; one employs it particularly to characterize...a dissoluteness, an excess". Libertine literature such as those by John Wilmot, 2nd Earl of Rochester evoked eroticism to the readers. Because eroticism is wholly dependent on the viewer's culture and personal tastes pertaining to what, exactly, defines the erotic, critics have often confused eroticism with pornography, with anti-pornography activist Andrea Dworkin saying, "Erotica is simply high-class pornography; better produced, better conceived, better executed, better packaged, designed for a better class of consumer." This confusion, as Lynn Hunt writes, "demonstrate[s] the difficulty of drawing... a clear generic demarcation between the erotic and the pornographic": "the history of the separation of pornography from eroticism... remains to be written". Audre Lorde recognises eroticism and pornography as “two diametrically opposed uses of the sexual”, defining the erotic as “a measure between the beginnings of our sense of self and the chaos of our strongest feelings.” In her 1978 essay, Uses of the Erotic: The Erotic as Power, Lorde identifies the erotic as a source of creative power that is deeply rooted in a spiritual plane of unrecognised or unexpressed feeling and sensation. Psychoanalytical approach Influenced by Sigmund Freud, psychotherapists have turned to Greek philosophy for an understanding of eros' heightened aesthetic. For Plato, Eros takes an almost transcendent manifestation when the subject seeks to go beyond itself and form a communion with the object/other: "the true order of going...to the things of love, is to use the beauties of earth as steps...to all fair forms, and from fair forms to fair actions, and from fair actions to fair notions, until from fair notions he arrives at the notion of absolute beauty". French philosophy Modern French conceptions of eroticism can be traced to the Age of Enlightenment, when "in the eighteenth century, dictionaries defined the erotic as that which concerned love...eroticism was the intrusion into the public sphere of something that was at base private". This theme of intrusion or transgression was taken up in the twentieth century by the French philosopher Georges Bataille, who argued that eroticism performs a function of dissolving boundaries between human subjectivity and humanity, a transgression that dissolves the rational world but is always temporary, as well as that, "Desire in eroticism is the desire that triumphs over the taboo. It presupposes man in conflict with himself". For Bataille, as well as many French theorists, "Eroticism, unlike simple sexual activity, is a psychological quest...eroticism is assenting to life even in death". Non-heterosexual Queer theory and LGBTQ studies consider the concept from a non-heterosexual perspective, viewing psychoanalytical and modernist views of eroticism as both archaic and heterosexist, written primarily by and for a "handful of elite, heterosexual, bourgeois men" who "mistook their own repressed sexual proclivities" as the norm. Theorists like Eve Kosofsky Sedgwick, Gayle S. Rubin and Marilyn Frye all write extensively about eroticism from a heterosexual, lesbian and separatist point of view, respectively, seeing eroticism as both a political force and cultural critique for marginalized groups, or as Mario Vargas Llosa summarized: "Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual's sovereignty". Audre Lorde, a lesbian Caribbean-American writer and outspoken feminist, called the erotic a source of power specifically identified with the female, often corrupted or distorted by oppression, since it poses the challenge of change. "For women, this has meant a suppression of the erotic as a considered source of power and information within our lives". In "The Uses of the Erotic" within Sister Outsider, she discusses how the erotic comes from the sharing of joy, "whether physical, emotional, psychic, or intellectual" and provides the basis on which understanding provides a foundation for acknowledging difference. Lorde suggests that if we suppress the erotic rather than recognize its presence, it takes on a different form. Rather than enjoying and sharing with one another, it becomes objectifying, which she says translates into abuse as we attempt to hide and suppress our experiences. See also Beauty Erogenous zone Eros Erotic art Erotica History of erotic depictions History of nude art Homoeroticism Limit-experience Nudity Pin-up girl Pornography Romance Sexual intercourse Sex-positive movement References Human sexuality Concepts in aesthetics Pornography Video	Eroticism	[ "Biology" ]	1,184	[ "Human sexuality", "Behavior", "Sexuality", "Human behavior" ]
52,358	https://en.wikipedia.org/wiki/Imaginary%20unit	The imaginary unit or unit imaginary number () is a mathematical constant that is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of and , just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter is sometimes used instead. For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by instead of , because is commonly used to denote electric current. Terminology Square roots of negative numbers are called imaginary because in early-modern mathematics, only what are now called real numbers, obtainable by physical measurements or basic arithmetic, were considered to be numbers at all – even negative numbers were treated with skepticism – so the square root of a negative number was previously considered undefined or nonsensical. The name imaginary is generally credited to René Descartes, and Isaac Newton used the term as early as 1670. The notation was introduced by Leonhard Euler. A unit is an undivided whole, and unity or the unit number is the number one (). Definition The imaginary unit is defined solely by the property that its square is −1: With defined this way, it follows directly from algebra that and are both square roots of −1. Although the construction is called "imaginary", and although the concept of an imaginary number may be intuitively more difficult to grasp than that of a real number, the construction is valid from a mathematical standpoint. Real number operations can be extended to imaginary and complex numbers, by treating as an unknown quantity while manipulating an expression (and using the definition to replace any occurrence of with ). Higher integral powers of are thus and so on, cycling through the four values , , , and . As with any non-zero real number, As a complex number, can be represented in rectangular form as , with a zero real component and a unit imaginary component. In polar form, can be represented as (or just ), with an absolute value (or magnitude) of 1 and an argument (or angle) of radians. (Adding any integer multiple of to this angle works as well.) In the complex plane, which is a special interpretation of a Cartesian plane, is the point located one unit from the origin along the imaginary axis (which is orthogonal to the real axis). vs. Being a quadratic polynomial with no multiple root, the defining equation has distinct solutions, which are equally valid and which happen to be additive and multiplicative inverses of each other. Although the two solutions are distinct numbers, their properties are indistinguishable; there is no property that one has that the other does not. One of these two solutions is labelled (or simply ) and the other is labelled , though it is inherently ambiguous which is which. The only differences between and arise from this labelling. For example, by convention is said to have an argument of and is said to have an argument of related to the convention of labelling orientations in the Cartesian plane relative to the positive -axis with positive angles turning anticlockwise in the direction of the positive -axis. Also, despite the signs written with them, neither nor is inherently positive or negative in the sense that real numbers are. A more formal expression of this indistinguishability of and is that, although the complex field is unique (as an extension of the real numbers) up to isomorphism, it is unique up to a isomorphism. That is, there are two field automorphisms of the complex numbers that keep each real number fixed, namely the identity and complex conjugation. For more on this general phenomenon, see Galois group. Matrices Using the concepts of matrices and matrix multiplication, complex numbers can be represented in linear algebra. The real unit and imaginary unit can be represented by any pair of matrices and satisfying and Then a complex number can be represented by the matrix and all of the ordinary rules of complex arithmetic can be derived from the rules of matrix arithmetic. The most common choice is to represent and by the identity matrix and the matrix , Then an arbitrary complex number can be represented by: More generally, any real-valued matrix with a trace of zero and a determinant of one squares to , so could be chosen for . Larger matrices could also be used; for example, could be represented by the identity matrix and could be represented by any of the Dirac matrices for spatial dimensions. Root of Polynomials (weighted sums of the powers of a variable) are a basic tool in algebra. Polynomials whose coefficients are real numbers form a ring, denoted an algebraic structure with addition and multiplication and sharing many properties with the ring of integers. The polynomial has no real-number roots, but the set of all real-coefficient polynomials divisible by forms an ideal, and so there is a quotient ring This quotient ring is isomorphic to the complex numbers, and the variable expresses the imaginary unit. Graphic representation The complex numbers can be represented graphically by drawing the real number line as the horizontal axis and the imaginary numbers as the vertical axis of a Cartesian plane called the complex plane. In this representation, the numbers and are at the same distance from , with a right angle between them. Addition by a complex number corresponds to translation in the plane, while multiplication by a unit-magnitude complex number corresponds to rotation about the origin. Every similarity transformation of the plane can be represented by a complex-linear function Geometric algebra In the geometric algebra of the Euclidean plane, the geometric product or quotient of two arbitrary vectors is a sum of a scalar (real number) part and a bivector part. (A scalar is a quantity with no orientation, a vector is a quantity oriented like a line, and a bivector is a quantity oriented like a plane.) The square of any vector is a positive scalar, representing its length squared, while the square of any bivector is a negative scalar. The quotient of a vector with itself is the scalar , and when multiplied by any vector leaves it unchanged (the identity transformation). The quotient of any two perpendicular vectors of the same magnitude, , which when multiplied rotates the divisor a quarter turn into the dividend, , is a unit bivector which squares to , and can thus be taken as a representative of the imaginary unit. Any sum of a scalar and bivector can be multiplied by a vector to scale and rotate it, and the algebra of such sums is isomorphic to the algebra of complex numbers. In this interpretation points, vectors, and sums of scalars and bivectors are all distinct types of geometric objects. More generally, in the geometric algebra of any higher-dimensional Euclidean space, a unit bivector of any arbitrary planar orientation squares to , so can be taken to represent the imaginary unit . Proper use The imaginary unit was historically written and still is in some modern works. However, great care needs to be taken when manipulating formulas involving radicals. The radical sign notation is reserved either for the principal square root function, which is defined for only real or for the principal branch of the complex square root function. Attempting to apply the calculation rules of the principal (real) square root function to manipulate the principal branch of the complex square root function can produce false results: Generally, the calculation rules and are guaranteed to be valid only for real, positive values of and . When or is real but negative, these problems can be avoided by writing and manipulating expressions like , rather than . For a more thorough discussion, see the articles Square root and Branch point. Properties As a complex number, the imaginary unit follows all of the rules of complex arithmetic. Imaginary integers and imaginary numbers When the imaginary unit is repeatedly added or subtracted, the result is some integer times the imaginary unit, an imaginary integer; any such numbers can be added and the result is also an imaginary integer: Thus, the imaginary unit is the generator of a group under addition, specifically an infinite cyclic group. The imaginary unit can also be multiplied by any arbitrary real number to form an imaginary number. These numbers can be pictured on a number line, the imaginary axis, which as part of the complex plane is typically drawn with a vertical orientation, perpendicular to the real axis which is drawn horizontally. Gaussian integers Integer sums of the real unit and the imaginary unit form a square lattice in the complex plane called the Gaussian integers. The sum, difference, or product of Gaussian integers is also a Gaussian integer: Quarter-turn rotation When multiplied by the imaginary unit , any arbitrary complex number in the complex plane is rotated by a quarter turn or ) anticlockwise. When multiplied by , any arbitrary complex number is rotated by a quarter turn clockwise. In polar form: In rectangular form, Integer powers The powers of repeat in a cycle expressible with the following pattern, where is any integer: Thus, under multiplication, is a generator of a cyclic group of order 4, a discrete subgroup of the continuous circle group of the unit complex numbers under multiplication. Written as a special case of Euler's formula for an integer , With a careful choice of branch cuts and principal values, this last equation can also apply to arbitrary complex values of , including cases like . Roots Just like all nonzero complex numbers, has two distinct square roots which are additive inverses. In polar form, they are In rectangular form, they are Squaring either expression yields The three cube roots of are For a general positive integer , the -th roots of are, for The value associated with is the principal -th root of . The set of roots equals the corresponding set of roots of unity rotated by the principal -th root of . These are the vertices of a regular polygon inscribed within the complex unit circle. Exponential and logarithm The complex exponential function relates complex addition in the domain to complex multiplication in the codomain. Real values in the domain represent scaling in the codomain (multiplication by a real scalar) with representing multiplication by , while imaginary values in the domain represent rotation in the codomain (multiplication by a unit complex number) with representing a rotation by radian. The complex exponential is thus a periodic function in the imaginary direction, with period and image at points for all integers , a real multiple of the lattice of imaginary integers. The complex exponential can be broken into even and odd components, the hyperbolic functions and or the trigonometric functions and : Euler's formula decomposes the exponential of an imaginary number representing a rotation: This fact can be used to demonstrate, among other things, the apparently counterintuitive result that is a real number. The quotient with appropriate scaling, can be represented as an infinite partial fraction decomposition as the sum of reciprocal functions translated by imaginary integers: Other functions based on the complex exponential are well-defined with imaginary inputs. For example, a number raised to the power is: Because the exponential is periodic, its inverse the complex logarithm is a multi-valued function, with each complex number in the domain corresponding to multiple values in the codomain, separated from each-other by any integer multiple of One way of obtaining a single-valued function is to treat the codomain as a cylinder, with complex values separated by any integer multiple of treated as the same value; another is to take the domain to be a Riemann surface consisting of multiple copies of the complex plane stitched together along the negative real axis as a branch cut, with each branch in the domain corresponding to one infinite strip in the codomain. Functions depending on the complex logarithm therefore depend on careful choice of branch to define and evaluate clearly. For example, if one chooses any branch where then when is a positive real number, Factorial The factorial of the imaginary unit is most often given in terms of the gamma function evaluated at : The magnitude and argument of this number are: See also Hyperbolic unit Right versor in quaternions Notes References Further reading External links at Complex numbers Algebraic numbers Quadratic irrational numbers Mathematical constants	Imaginary unit	[ "Mathematics" ]	2,584	[ "Mathematical objects", "Algebraic numbers", "nan", "Complex numbers", "Mathematical constants", "Numbers" ]
52,373	https://en.wikipedia.org/wiki/Center-pivot%20irrigation	Center-pivot irrigation (sometimes called central pivot irrigation), also called water-wheel and circle irrigation, is a method of crop irrigation in which equipment rotates around a pivot and crops are watered with sprinklers. A circular area centered on the pivot is irrigated, often creating a circular pattern in crops when viewed from above (sometimes referred to as crop circles, not to be confused with those formed by circular flattening of a section of a crop in a field). Most center pivots were initially water-powered, however today most are propelled by electric motors. Center-pivot irrigation systems are beneficial due to their ability to efficiently use water and optimize a farm's yield. The systems are highly effective on large land fields. History On March 23, 1914 James A. Norton of Odebolt, Iowa, filed the patent for the center pivot irrigation system. On August 17, 1915, it was granted as patent #1150144. The patent drawings shows multiple pairs of wheels supporting a pipe that is moved in a circle around a center pivot point. The description is: Watering arrangements making use of movable installations on wheels or the like movable around a pivot centre. Center-pivot irrigation was invented in 1940 by the farmer Frank Zybach, who lived in Strasburg, Colorado. It is recognized as an effective method to improve water distribution to fields. In 1952, Zybach went into business with A. E. Trowbridge, a friend, Ethan James Olson, from Columbus, Nebraska. Trowbridge put up $25,000 () and got 49% of the patent rights. Zybach moved back from Colorado to Columbus, opened a shop, hired a few men, moved the height of the pipe up to , and went into business. In the first two years of operation, they sold only 19 systems. The early designs were finicky and few farmers understood the systems. Zybach kept improving his designs and focused on making his machines better, rather than attempting to sell systems with problems. Zybach saw success with modified designs, which improved the systems operational efficiency. In 1954, he licensed his patent to Robert Daugherty and his company, Valley Manufacturing. Daugherty's engineers spent the next decade refining Zybach's innovation, making it sturdier, taller, and more reliable, and converting it from a hydraulic power system to electric drive. Daugherty's company went on to grow into Valmont Industries, with Valley Irrigation being its subsidiary. Overview Center pivot irrigation is a form of overhead sprinkler irrigation consisting of several segments of pipe (usually galvanized steel or aluminum) with sprinklers positioned along their length, joined together and supported by trusses, and mounted on wheeled towers. The machine moves in a circular pattern and is fed with water from the pivot point at the center of the circle. For a center pivot to be used, the terrain needs to be reasonably flat; but one major advantage of center pivots over alternative systems that use gravity flow is the ability to function in undulating country. This advantage has resulted in increased irrigated acreage and water use in some areas. The system is used in parts of the United States, Australia, New Zealand, Brazil, and in desert areas such as the Sahara and the Middle East. Center pivots are typically less than in length (circle radius) with the most common size being the standard machine, which covers about of land. Originally, most center pivots were water-powered. These were replaced by hydraulic systems and electric motor-driven systems, usually driven by a motor mounted at each tower. The outside set of wheels sets the pace for the rotation. The inner sets of wheels are mounted at hubs between two segments and use angle sensors (microswitches) to detect when the bend at the joint exceeds a certain threshold. When the angle is too large, the wheels rotate to keep the segments aligned. Typical periods for a full rotation include three days; while other sources have the outer edge of the structure moving at per minute, which would equate to 14 to 21 hours for one full rotation of a system. To achieve uniform application, center pivots require a variable emitter flow rate across the radius of the machine. Since the outer-most spans (or towers) travel farther in a given time period than the innermost spans, nozzle sizes are smallest at the inner spans and increase with distance from the pivot point. Aerial views show fields of circles created by tracings of quarter-mile or half-mile (400 or 800 m) radial irrigation pipes, which consume up to several thousands of gallons per minute." Most center pivot systems now have drops hanging from a U-shaped pipe called a gooseneck attached at the top of the pipe with sprinkler heads that are positioned a few feet (at most) above the crop, thus limiting evaporative losses and wind drift. There are many different nozzle configurations available including static plate, moving plate and part circle. Pressure regulators are typically installed upstream of each nozzle to ensure each is operating at the correct design pressure. Drops can also be used with drag hoses or bubblers that deposit the water directly on the ground between crops. This type of system is known as LEPA (Low Energy Precision Application) and is often associated with the construction of small dams along the furrow length (termed furrow diking/dyking). Crops may be planted either in straight rows or in circles to conform to the travel of the irrigation system. Linear or lateral move irrigation machines Irrigation equipment can also be configured to move in a straight line, where it is termed a lateral move, linear move, wheel move or side-roll irrigation system. In these systems the water is supplied by an irrigation channel running the length of the field. The channel is positioned either at one side or in a line through the center. The motor and pump equipment are mounted on a cart by the supply channel. The cart travels with the machine. Farmers might choose lateral-move irrigation to keep existing rectangular fields. This can help them convert from furrow irrigation. Lateral-move irrigation is far less common, relies on more complex guidance systems, and requires additional management compared to center pivot irrigation. Lateral-move irrigation is common in Australia. There, systems are usually between 500 and 1,000 meters long. Benefits Center-pivot irrigation uses less labor than many other surface irrigation methods, such as furrow irrigation. It also has lower labor costs than ground-irrigation techniques that require digging of channels. Also, center-pivot irrigation can reduce the amount of soil tillage. Therefore, it helps reduce water runoff and soil erosion that can occur with ground irrigation. Less tillage also encourages more organic materials and crop residue to decompose back into the soil. It also reduces soil compaction. In the United States early settlers of the semiarid High Plains were plagued by crop failures due to cycles of drought, culminating in the disastrous Dust Bowl of the 1930s. Only after World War II when center pivot irrigation became available did the land mass of the High Plains aquifer system transform into one of the most agriculturally productive regions in the world. Negative effects Groundwater levels decrease when the rate of extraction by irrigation exceeds the rate of recharge. By 2013 it was shown that counterintuitively, as the water consumption efficiency of center-pivot irrigation improved over the years, farmers planted more intensively, irrigated more land, and grew thirstier crops. This is an example of Jevons paradox. In parts of the United States, sixty years of the profitable business of intensive farming using huge center-pivot irrigators has emptied parts of the Ogallala Aquifer (also known as the High Plains Aquifer). One of the world's largest aquifers, it covers an area of approximately in portions of the eight states of South Dakota, Nebraska, Wyoming, Colorado, Kansas, Oklahoma, New Mexico, and Texas, beneath the Great Plains in the United States. The total water extraction from center-pivot irrigation in the area is estimated to be about 5.42 million acre-feet of water per year. In 1950, irrigated cropland covered . With the use of center-pivot irrigation, nearly of land were irrigated in Kansas alone. At some places, during maximum extraction, the water table dropped more than per year. In extreme cases, wells had to be greatly deepened to reach the steadily falling water table. In some places in the Texas Panhandle, the water table has been drained (dewatered). "Vast stretches of Texas farmland lying over the aquifer no longer support irrigation. In west-central Kansas, up to a fifth of the irrigated farmland along a swath of the aquifer has already gone dry." It would take hundreds to thousands of years of rainfall to replace the groundwater in the dried up aquifer. Role in culture In the 21st century, recognition of the significance of the High Plains Aquifer has led to increased coverage from regional and international journalists. A May 2013 New York Times article "Wells dry, fertile plains turn to dust" recounts the relentless decline of parts of the High Plains Aquifer System. Writer Emily Woodson characterized the increased use of the center pivot irrigation system as part of a profound attitude shift towards modernism (expensive tractors, center-pivot irrigation, dangerous new pesticides) and away from traditional farming that took place in the mid-1970s and 1980s in the United States. A new generation chose high-risk, high-reward crops such as irrigated corn or peanuts, which require large quantities of groundwater, fertilizer and chemicals. The new family farm corporations turned many pastures into new cropland and were more interested in rising land prices than water conservation. See also Irrigation management Irrigation in Saudi Arabia Water management Fossil water Hydrogeology References Additional sources External links "The Ogallala Aquifer" Manjula V. Guru, Agricultural Policy Specialist and James E. Horne, President & CEO, The Kerr Center for Sustainable Agriculture, Poteau, Oklahoma USGS High Plains Regional Groundwater Study A Legal Fight in Texas over the Ogallala Aquifer Kansas Geological Survey information on the High Plains / Ogallala Aquifer Rapid Recharge of Parts of the High Plains Aquifer Indicated by a Reconnaissance Study in Oklahoma Irrigation Circles	Center-pivot irrigation	[ "Mathematics" ]	2,154	[ "Circles", "Pi" ]
52,376	https://en.wikipedia.org/wiki/Axiom%20of%20extensionality	The axiom of extensionality, also called the axiom of extent, is an axiom used in many forms of axiomatic set theory, such as Zermelo–Fraenkel set theory. The axiom defines what a set is. Informally, the axiom means that the two sets A and B are equal if and only if A and B have the same members. In ZF set theory In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: or in words: If the sets and have the same members, then they are the same set. In , all members of sets are themselves sets, but not in set theory with urelements. The axiom's usefulness can be seen from the fact that, if one accepts that , where is a set and is a formula that occurs free in but doesn't, then the axiom assures that there is a unique set whose members are precisely whatever objects (urelements or sets, as the case may be) satisfy the formula . The converse of the axiom, , follows from the substitution property of equality. Despite this, the axiom is sometimes given directly as a biconditional, i.e., as . In NF set theory Quine's New Foundations (NF) set theory, in Quine's original presentations of it, treats the symbol for equality or identity as shorthand either for "if a set contains the left side of the equals sign as a member, then it also contains the right side of the equals sign as a member" (as defined in 1937), or for "an object is an element of the set on the left side of the equals sign if, and only if, it is also an element of the set on the right side of the equals sign" (as defined in 1951). That is, is treated as shorthand either for , as in the original 1937 paper, or for , as in Quine's Mathematical Logic (1951). The second version of the definition is exactly equivalent to the antecedent of the ZF axiom of extensionality, and the first version of the definition is still very similar to it. By contrast, however, the ZF set theory takes the symbol for identity or equality as a primitive symbol of the formal language, and defines the axiom of extensionality in terms of it. (In this paragraph, the statements of both versions of the definition were paraphrases, and quotation marks were only used to set the statements apart.) In Quine's New Foundations for Mathematical Logic (1937), the original paper of NF, the name "principle of extensionality" is given to the postulate P1, , which, for readability, may be restated as . The definition D8, which defines the symbol for identity or equality, defines as shorthand for . In his Mathematical Logic (1951), having already developed quasi-quotation, Quine defines as shorthand for (definition D10), and does not define an axiom or principle "of extensionality" at all. Thomas Forster, however, ignores these fine distinctions, and considers NF to accept the axiom of extensionality in its ZF form. In ZU set theory In the Scott–Potter (ZU) set theory, the "extensionality principle" is given as a theorem rather than an axiom, which is proved from the definition of a "collection". In set theory with ur-elements An ur-element is a member of a set that is not itself a set. In the Zermelo–Fraenkel axioms, there are no ur-elements, but they are included in some alternative axiomatisations of set theory. Ur-elements can be treated as a different logical type from sets; in this case, makes no sense if is an ur-element, so the axiom of extensionality simply applies only to sets. Alternatively, in untyped logic, we can require to be false whenever is an ur-element. In this case, the usual axiom of extensionality would then imply that every ur-element is equal to the empty set. To avoid this consequence, we can modify the axiom of extensionality to apply only to nonempty sets, so that it reads: That is: Given any set A and any set B, if A is a nonempty set (that is, if there exists a member X of A), then if A and B have precisely the same members, then they are equal. Yet another alternative in untyped logic is to define itself to be the only element of whenever is an ur-element. While this approach can serve to preserve the axiom of extensionality, the axiom of regularity will need an adjustment instead. See also Extensionality Set theory Glossary of set theory References Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. . Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. . Notes Axioms of set theory Urelements	Axiom of extensionality	[ "Mathematics" ]	1,096	[ "Axioms of set theory", "Mathematical axioms" ]
52,381	https://en.wikipedia.org/wiki/Thermite	Thermite () is a pyrotechnic composition of metal powder and metal oxide. When ignited by heat or chemical reaction, thermite undergoes an exothermic reduction-oxidation (redox) reaction. Most varieties are not explosive, but can create brief bursts of heat and high temperature in a small area. Its form of action is similar to that of other fuel-oxidizer mixtures, such as black powder. Thermites have diverse compositions. Fuels include aluminium, magnesium, titanium, zinc, silicon, and boron. Aluminium is common because of its high boiling point and low cost. Oxidizers include bismuth(III) oxide, boron(III) oxide, silicon(IV) oxide, chromium(III) oxide, manganese(IV) oxide, iron(III) oxide, iron(II,III) oxide, copper(II) oxide, and lead(II,IV) oxide. In a thermochemical survey comprising twenty-five metals and thirty-two metal oxides, 288 out of 800 binary combinations were characterized by adiabatic temperatures greater than 2000 K. Combinations like these, which possess the thermodynamic potential to produce very high temperatures, are either already known to be reactive or are plausible thermitic systems. The first thermite reaction was discovered in 1893 by the German chemist Hans Goldschmidt, who obtained a patent for his process. Today, thermite is used mainly for thermite welding, particularly for welding together railway tracks. Thermites have also been used in metal refining, disabling munitions, and in incendiary weapons. Some thermite-like mixtures are used as pyrotechnic initiators in fireworks. Chemical reactions In the following example, elemental aluminium reduces the oxide of another metal, in this common example iron oxide, because aluminium forms stronger and more stable bonds with oxygen than iron: Fe2O3 + 2 Al → 2 Fe + Al2O3 The products are aluminium oxide, elemental iron, and a large amount of heat. The reactants are commonly powdered and mixed with a binder to keep the material solid and prevent separation. Other metal oxides can be used, such as chromium oxide, to generate the given metal in its elemental form. For example, a copper thermite reaction using copper oxide and elemental aluminium can be used for creating electric joints in a process called cadwelding, that produces elemental copper (it may react violently): 3 CuO + 2 Al → 3 Cu + Al2O3 Thermites with nanosized particles are described by a variety of terms, such as metastable intermolecular composites, super-thermite, nano-thermite, and nanocomposite energetic materials. History The thermite () reaction was discovered in 1893 and patented in 1895 by German chemist Hans Goldschmidt. Consequently, the reaction is sometimes called the "Goldschmidt reaction" or "Goldschmidt process". Goldschmidt was originally interested in producing very pure metals by avoiding the use of carbon in smelting, but he soon discovered the value of thermite in welding. The first commercial application of thermite was the welding of tram tracks in Essen in 1899. Types Red iron(III) oxide (Fe2O3, commonly known as rust) is the most common iron oxide used in thermite. Black iron(II,III) oxide (Fe3O4, magnetite) also works. Other oxides are occasionally used, such as MnO2 in manganese thermite, Cr2O3 in chromium thermite, SiO2 (quartz) in silicon thermite, or copper(II) oxide in copper thermite, but only for specialized purposes. All of these examples use aluminium as the reactive metal. Fluoropolymers can be used in special formulations, Teflon with magnesium or aluminium being a relatively common example. Magnesium/Teflon/Viton is another pyrolant of this type. Combinations of dry ice (frozen carbon dioxide) and reducing agents such as magnesium, aluminium and boron follow the same chemical reaction as with traditional thermite mixtures, producing metal oxides and carbon. Despite the very low temperature of a dry ice thermite mixture, such a system is capable of being ignited with a flame. When the ingredients are finely divided, confined in a pipe and armed like a traditional explosive, this cryo-thermite is detonatable and a portion of the carbon liberated in the reaction emerges in the form of diamond. In principle, any reactive metal could be used instead of aluminium. This is rarely done, because the properties of aluminium are nearly ideal for this reaction: It forms a passivation layer making it safer to handle than many other reactive metals. Its relatively low melting point (660 °C) means that it is easy to melt the metal, so that the reaction can occur mainly in the liquid phase, thus it proceeds fairly quickly. Its high boiling point (2519 °C) enables the reaction to reach very high temperatures, since several processes tend to limit the maximum temperature to just below the boiling point. Such a high boiling point is common among transition metals (e.g., iron and copper boil at 2887 and 2582 °C, respectively), but is especially unusual among the highly reactive metals (cf. magnesium and sodium, which boil at 1090 and 883 °C, respectively). Further, the low density of the aluminium oxide formed as a result of the reaction tends to leave it floating on the resultant pure metal. This is particularly important for reducing contamination in a weld. Although the reactants are stable at room temperature, they burn with an extremely intense exothermic reaction when they are heated to ignition temperature. The products emerge as liquids due to the high temperatures reached (up to 2500 °C (4532°F) with iron(III) oxide)—although the actual temperature reached depends on how quickly heat can escape to the surrounding environment. Thermite contains its own supply of oxygen and does not require any external source of air. Consequently, it cannot be smothered, and may ignite in any environment given sufficient initial heat. It burns well while wet, and cannot be easily extinguished with water—though enough water to remove sufficient heat may stop the reaction. Small amounts of water boil before reaching the reaction. Even so, thermite is used for welding under water. The thermites are characterized by almost complete absence of gas production during burning, high reaction temperature, and production of molten slag. The fuel should have high heat of combustion and produce oxides with low melting point and high boiling point. The oxidizer should contain at least 25% oxygen, have high density, low heat of formation, and produce metal with low melting and high boiling points (so the energy released is not consumed in evaporation of reaction products). Organic binders can be added to the composition to improve its mechanical properties, but they tend to produce endothermic decomposition products, causing some loss of reaction heat and production of gases. The temperature achieved during the reaction determines the outcome. In an ideal case, the reaction produces a well-separated melt of metal and slag. For this, the temperature must be high enough to melt both reaction products, the resulting metal and the fuel oxide. Too low a temperature produces a mixture of sintered metal and slag; too high a temperature (above the boiling point of any reactant or product) leads to rapid production of gas, dispersing the burning reaction mixture, sometimes with effects similar to a low-yield explosion. In compositions intended for production of metal by aluminothermic reaction, these effects can be counteracted. Too low a reaction temperature (e.g., when producing silicon from sand) can be boosted with addition of a suitable oxidizer (e.g., sulfur in aluminium-sulfur-sand compositions); too high a temperature can be reduced by using a suitable coolant or slag flux. The flux often used in amateur compositions is calcium fluoride, as it reacts only minimally, has relatively low melting point, low melt viscosity at high temperatures (therefore increasing fluidity of the slag) and forms a eutectic with alumina. Too much flux, however, dilutes the reactants to the point of not being able to sustain combustion. The type of metal oxide also has dramatic influence to the amount of energy produced; the higher the oxide, the higher the amount of energy produced. A good example is the difference between manganese(IV) oxide and manganese(II) oxide, where the former produces too high temperature and the latter is barely able to sustain combustion; to achieve good results, a mixture with proper ratio of both oxides can be used. The reaction rate can be also tuned with particle sizes; coarser particles burn slower than finer particles. The effect is more pronounced with the particles requiring heating to higher temperature to start reacting. This effect is pushed to the extreme with nano-thermites. The temperature achieved in the reaction in adiabatic conditions, when no heat is lost to the environment, can be estimated using Hess’s law – by calculating the energy produced by the reaction itself (subtracting the enthalpy of the reactants from the enthalpy of the products) and subtracting the energy consumed by heating the products (from their specific heat, when the materials only change their temperature, and their enthalpy of fusion and eventually enthalpy of vaporization, when the materials melt or boil). In real conditions, the reaction loses heat to the environment, the achieved temperature is therefore somewhat lower. The heat transfer rate is finite, so the faster the reaction is, the closer to adiabatic condition it runs and the higher is the achieved temperature. Iron thermite The most common composition is iron thermite. The oxidizer used is usually either iron(III) oxide or iron(II,III) oxide. The former produces more heat. The latter is easier to ignite, likely due to the crystal structure of the oxide. Addition of copper or manganese oxides can significantly improve the ease of ignition. The density of prepared thermite is often as low as 0.7 g/cm3. This, in turn, results in relatively poor energy density (about 3 kJ/cm3), rapid burn times, and spray of molten iron due to the expansion of trapped air. Thermite can be pressed to densities as high as 4.9 g/cm3 (almost 16 kJ/cm3) with slow burning speeds (about 1 cm/s). Pressed thermite has higher melting power, i.e. it can melt a steel cup where a low-density thermite would fail. Iron thermite with or without additives can be pressed into cutting devices that have heat-resistant casing and a nozzle. Oxygen-balanced iron thermite 2Al + Fe2O3 has theoretical maximum density of 4.175 g/cm3 an adiabatic burn temperature of 3135 K or 2862 °C or 5183 °F (with phase transitions included, limited by iron, which boils at 3135 K), the aluminium oxide is (briefly) molten and the produced iron is mostly liquid with part of it being in gaseous form - 78.4 g of iron vapor per kg of thermite are produced. The energy content is 945.4 cal/g (3 956 J/g). The energy density is 16,516 J/cm3. The original mixture, as invented, used iron oxide in the form of mill scale. The composition was very difficult to ignite. Copper thermite Copper thermite can be prepared using either copper(I) oxide (Cu2O, red) or copper(II) oxide (CuO, black). The burn rate tends to be very fast and the melting point of copper is relatively low, so the reaction produces a significant amount of molten copper in a very short time. Copper(II) thermite reactions can be so fast that it can be considered a type of flash powder. An explosion can occur, which sends a spray of copper drops to considerable distances. Oxygen-balanced mixture has theoretical maximum density of 5.109 g/cm3, adiabatic flame temperature 2843 K (phase transitions included) with the aluminium oxide being molten and copper in both liquid and gaseous form; 343 g of copper vapor per kg of this thermite are produced. The energy content is 974 cal/g. Copper(I) thermite has industrial uses in e.g., welding of thick copper conductors (cadwelding). This kind of welding is being evaluated also for cable splicing on the US Navy fleet, for use in high-current systems, e.g., electric propulsion. Oxygen-balanced mixture has theoretical maximum density of 5.280 g/cm3, adiabatic flame temperature 2843 K (phase transitions included) with the aluminium oxide being molten and copper in both liquid and gaseous form; 77.6 g of copper vapor per kg of this thermite are produced. The energy content is 575.5 cal/g. Thermates Thermate composition is a thermite enriched with a salt-based oxidizer (usually nitrates, e.g., barium nitrate, or peroxides). In contrast with thermites, thermates burn with evolution of flame and gases. The presence of the oxidizer makes the mixture easier to ignite and improves penetration of target by the burning composition, as the evolved gas is projecting the molten slag and providing mechanical agitation. This mechanism makes thermate more suitable than thermite for incendiary purposes and for emergency destruction of sensitive equipment (e.g., cryptographic devices), as thermite's effect is more localized. Ignition Metals, under the right conditions, burn in a process similar to the combustion of wood or gasoline. In fact, rust is the result of oxidation of steel or iron at very slow rates. A thermite reaction results when the correct mixtures of metallic fuels combine and ignite. Ignition itself requires extremely high temperatures. Ignition of a thermite reaction normally requires a sparkler or easily obtainable magnesium ribbon, but may require persistent efforts, as ignition can be unreliable and unpredictable. These temperatures cannot be reached with conventional black powder fuses, nitrocellulose rods, detonators, pyrotechnic initiators, or other common igniting substances. Even when the thermite is hot enough to glow bright red, it does not ignite, as it has a very high ignition temperature. Starting the reaction is possible using a propane torch if done correctly. Often, strips of magnesium metal are used as fuses. Because metals burn without releasing cooling gases, they can potentially burn at extremely high temperatures. Reactive metals such as magnesium can easily reach temperatures sufficiently high for thermite ignition. Magnesium ignition remains popular among amateur thermite users, mainly because it can be easily obtained, but a piece of the burning strip can fall off into the mixture, resulting in premature ignition. The reaction between potassium permanganate and glycerol or ethylene glycol is used as an alternative to the magnesium method. When these two substances mix, a spontaneous reaction begins, slowly increasing the temperature of the mixture until it produces flames. The heat released by the oxidation of glycerine is sufficient to initiate a thermite reaction. Apart from magnesium ignition, some amateurs also choose to use sparklers to ignite the thermite mixture. These reach the necessary temperatures and provide enough time before the burning point reaches the sample. This can be a dangerous method, as the iron sparks, like the magnesium strips, burn at thousands of degrees and can ignite the thermite, though the sparkler itself is not in contact with it. This is especially dangerous with finely powdered thermite. Match heads burn hot enough to ignite thermite. Use of match heads enveloped with aluminium foil and a sufficiently long viscofuse/electric match leading to the match heads is possible. Similarly, finely powdered thermite can be ignited by a flint spark lighter, as the sparks are burning metal (in this case, the highly reactive rare-earth metals lanthanum and cerium). Therefore, it is unsafe to strike a lighter close to thermite. Civilian uses Thermite reactions have many uses. It is not an explosive; instead, it operates by exposing a very small area to extremely high temperatures. Intense heat focused on a small spot can be used to cut through metal or weld metal components together both by melting metal from the components, and by injecting molten metal from the thermite reaction itself. Thermite may be used for repair by the welding in-place of thick steel sections such as locomotive axle-frames where the repair can take place without removing the part from its installed location. Thermite can be used for quickly cutting or welding steel such as rail tracks, without requiring complex or heavy equipment. However, defects such as slag inclusions and voids (holes) are often present in such welded junctions, so great care is needed to operate the process successfully. The numerical analysis of thermite welding of rails has been approached similar to casting cooling analysis. Both this finite element analysis and experimental analysis of thermite rail welds has shown that weld gap is the most influential parameter affecting defect formation. Increasing weld gap has been shown to reduce shrinkage cavity formation and cold lap welding defects, and increasing preheat and thermite temperature further reduces these defects. However, reducing these defects promotes a second form of defect: microporosity. Care must also be taken to ensure that the rails remain straight, without resulting in dipped joints, which can cause wear on high speed and heavy axle load lines. Studies to make the hardness of thermite welds to repair tracks have made improvements to the hardness to compare more to the original tracks while keeping its portable nature. As the reaction of thermite is oxidation-reduction and environmentally friendly, it has started to be adapted into use for sealing oil wells instead of using concrete. Though thermite is usually in a powder-state, a diluted mixture can reduce damage to the surroundings during the process, though too much alumina can risk hurting the integrity of the seal. A higher concentration of mixture was needed to melt the plastic of a model tube, making it a favorable mixture. Other experiments have been done to simulate the heat flux of the well sealing to predict the temperature on the surface of the seal over time. A thermite reaction, when used to purify the ores of some metals, is called the , or aluminothermic reaction. An adaptation of the reaction, used to obtain pure uranium, was developed as part of the Manhattan Project at Ames Laboratory under the direction of Frank Spedding. It is sometimes called the Ames process. Copper thermite is used for welding together thick copper wires for the purpose of electrical connections. It is used extensively by the electrical utilities and telecommunications industries (exothermic welded connections). Military uses Thermite hand grenades and charges are typically used by armed forces in both an anti-materiel role and in the partial destruction of equipment, the latter being common when time is not available for safer or more thorough methods. For example, thermite can be used for the emergency destruction of cryptographic equipment when there is a danger that it might be captured by enemy troops. Because standard iron-thermite is difficult to ignite, burns with practically no flame and has a small radius of action, standard thermite is rarely used on its own as an incendiary composition. In general, an increase in the volume of gaseous reaction products of a thermite blend increases the heat transfer rate (and therefore damage) of that particular thermite blend. It is usually used with other ingredients that increase its incendiary effects. Thermate-TH3 is a mixture of thermite and pyrotechnic additives that have been found superior to standard thermite for incendiary purposes. Its composition by weight is generally about 68.7% thermite, 29.0% barium nitrate, 2.0% sulfur, and 0.3% of a binder (such as PBAN). The addition of barium nitrate to thermite increases its thermal effect, produces a larger flame, and significantly reduces the ignition temperature. Although the primary purpose of Thermate-TH3 by the armed forces is as an incendiary anti-materiel weapon, it also has uses in welding together metal components. A classic military use for thermite is disabling artillery pieces, and it has been used for this purpose since World War II, such as at Pointe du Hoc, Normandy. Because it permanently disables artillery pieces without the use of explosive charges, thermite can be used when silence is necessary to an operation. This can be accomplished by inserting one or more armed thermite grenades into the breech, then quickly closing it; this welds the breech shut and makes loading the weapon impossible. During World War II, both German and Allied incendiary bombs used thermite mixtures. Incendiary bombs usually consisted of dozens of thin, thermite-filled canisters (bomblets) ignited by a magnesium fuse. Incendiary bombs created massive damage in numerous cities due to the fires started by the thermite. Cities that primarily consisted of wooden buildings were especially susceptible. These incendiary bombs were used primarily during nighttime air raids. Bombsights could not be used at night, creating the need for munitions that could destroy targets without requiring precision placement. So called Dragon drones equipped with thermite munitions were used by the Ukrainian army during the Russian invasion of Ukraine against Russian positions. Hazards Thermite usage is hazardous due to the extremely high temperatures produced and the extreme difficulty in smothering a reaction once initiated. Small streams of molten iron released in the reaction can travel considerable distances and may melt through metal containers, igniting their contents. Additionally, flammable metals with relatively low boiling points such as zinc (with a boiling point of 907 °C, which is about 1,370 °C below the temperature at which thermite burns) could potentially spray superheated boiling metal violently into the air if near a thermite reaction. If, for some reason, thermite is contaminated with organics, hydrated oxides and other compounds able to produce gases upon heating or reaction with thermite components, the reaction products may be sprayed. Moreover, if the thermite mixture contains enough empty spaces with air and burns fast enough, the super-heated air also may cause the mixture to spray. For this reason it is preferable to use relatively crude powders, so the reaction rate is moderate and hot gases could escape the reaction zone. Preheating of thermite before ignition can easily be done accidentally, for example by pouring a new pile of thermite over a hot, recently ignited pile of thermite slag. When ignited, preheated thermite can burn almost instantaneously, releasing light and heat energy at a much higher rate than normal and causing burns and eye damage at what would normally be a reasonably safe distance. The thermite reaction can take place accidentally in industrial locations where workers use abrasive grinding and cutting wheels with ferrous metals. Using aluminium in this situation produces a mixture of oxides that can explode violently. Mixing water with thermite or pouring water onto burning thermite can cause a steam explosion, spraying hot fragments in all directions. Thermite's main ingredients were also utilized for their individual qualities, specifically reflectivity and heat insulation, in a paint coating or dope for the German zeppelin Hindenburg, possibly contributing to its fiery destruction. This was a theory put forward by the former NASA scientist Addison Bain, and later tested in small scale by the scientific reality-TV show MythBusters with semi-inconclusive results (it was proven not to be the fault of the thermite reaction alone, but instead conjectured to be a combination of that and the burning of hydrogen gas that filled the body of the Hindenburg). The MythBusters program also tested the veracity of a video found on the Internet, whereby a quantity of thermite in a metal bucket was ignited while sitting on top of several blocks of ice, causing a sudden explosion. They were able to confirm the results, finding huge chunks of ice as far as 50 m from the point of explosion. Co-host Jamie Hyneman conjectured that this was due to the thermite mixture aerosolizing, perhaps in a cloud of steam, causing it to burn even faster. Hyneman also voiced skepticism about another theory explaining the phenomenon: that the reaction somehow separated the hydrogen and oxygen in the ice and then ignited them. This explanation claims that the explosion is due to the reaction of high temperature molten aluminium with water. Aluminium reacts violently with water or steam at high temperatures, releasing hydrogen and oxidizing in the process. The speed of that reaction and the ignition of the resulting hydrogen can easily account for the explosion verified. This process is akin to the explosive reaction caused by dropping metallic potassium into water. In popular culture In the episode "A No-Rough-Stuff-Type Deal" of the crime drama television series Breaking Bad, Walter White uses thermite to burn through a security lock in order to steal a methylamine drum from a chemical plant. See also References Further reading External links Thermite Pictures & Videos (Including Exotic Thermite) Video – steel casting with thermite Welding Inorganic reactions Incendiary weapons Pyrotechnic compositions Powders Aluminium	Thermite	[ "Physics", "Chemistry", "Engineering" ]	5,377	[ "Pyrotechnic compositions", "Welding", "Inorganic reactions", "Materials", "Powders", "Mechanical engineering", "Matter" ]
52,385	https://en.wikipedia.org/wiki/Axiom%20of%20pairing	In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory. It was introduced by as a special case of his axiom of elementary sets. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: In words: Given any object A and any object B, there is a set C such that, given any object D, D is a member of C if and only if D is equal to A or D is equal to B. Consequences As noted, what the axiom is saying is that, given two objects A and B, we can find a set C whose members are exactly A and B. We can use the axiom of extensionality to show that this set C is unique. We call the set C the pair of A and B, and denote it {A,B}. Thus the essence of the axiom is: Any two objects have a pair. The set {A,A} is abbreviated {A}, called the singleton containing A. Note that a singleton is a special case of a pair. Being able to construct a singleton is necessary, for example, to show the non-existence of the infinitely descending chains from the Axiom of regularity. The axiom of pairing also allows for the definition of ordered pairs. For any objects and , the ordered pair is defined by the following: Note that this definition satisfies the condition Ordered n-tuples can be defined recursively as follows: Alternatives Non-independence The axiom of pairing is generally considered uncontroversial, and it or an equivalent appears in just about any axiomatization of set theory. Nevertheless, in the standard formulation of the Zermelo–Fraenkel set theory, the axiom of pairing follows from the axiom schema of replacement applied to any given set with two or more elements, and thus it is sometimes omitted. The existence of such a set with two elements, such as { {}, { {} } }, can be deduced either from the axiom of empty set and the axiom of power set or from the axiom of infinity. In the absence of some of the stronger ZFC axioms, the axiom of pairing can still, without loss, be introduced in weaker forms. Weaker In the presence of standard forms of the axiom schema of separation we can replace the axiom of pairing by its weaker version: . This weak axiom of pairing implies that any given objects and are members of some set . Using the axiom schema of separation we can construct the set whose members are exactly and . Another axiom which implies the axiom of pairing in the presence of the axiom of empty set is the axiom of adjunction . It differs from the standard one by use of instead of . Using {} for A and x for B, we get {x} for C. Then use {x} for A and y for B, getting {x,y} for C. One may continue in this fashion to build up any finite set. And this could be used to generate all hereditarily finite sets without using the axiom of union. Stronger Together with the axiom of empty set and the axiom of union, the axiom of pairing can be generalised to the following schema: that is: Given any finite number of objects A1 through An, there is a set C whose members are precisely A1 through An. This set C is again unique by the axiom of extensionality, and is denoted {A1,...,An}. Of course, we can't refer to a finite number of objects rigorously without already having in our hands a (finite) set to which the objects in question belong. Thus, this is not a single statement but instead a schema, with a separate statement for each natural number n. The case n = 1 is the axiom of pairing with A = A1 and B = A1. The case n = 2 is the axiom of pairing with A = A1 and B = A2. The cases n > 2 can be proved using the axiom of pairing and the axiom of union multiple times. For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A1,A2}, the singleton {A3}, and then the pair {{A1,A2},{A3}}. The axiom of union then produces the desired result, {A1,A2,A3}. We can extend this schema to include n=0 if we interpret that case as the axiom of empty set. Thus, one may use this as an axiom schema in the place of the axioms of empty set and pairing. Normally, however, one uses the axioms of empty set and pairing separately, and then proves this as a theorem schema. Note that adopting this as an axiom schema will not replace the axiom of union, which is still needed for other situations. References Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. . Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. . . English translation: . Axioms of set theory de:Zermelo-Fraenkel-Mengenlehre#Die Axiome von ZF und ZFC	Axiom of pairing	[ "Mathematics" ]	1,179	[ "Axioms of set theory", "Mathematical axioms" ]
52,386	https://en.wikipedia.org/wiki/Axiom%20schema%20of%20specification	In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation (Aussonderungsaxiom), subset axiom, axiom of class construction, or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set. Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension''', discussed below. Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory. Statement One instance of the schema is included for each formula φ in the language of set theory with free variables among x, w1, ..., wn, A. So B does not occur free in φ. In the formal language of set theory, the axiom schema is: or in words: Given any set A, there is a set B (a subset of A) such that, given any set x, x is a member of B if and only if x is a member of A and φ holds for x. Note that there is one axiom for every such predicate φ; thus, this is an axiom schema. To understand this axiom schema, note that the set B must be a subset of A. Thus, what the axiom schema is really saying is that, given a set A and a predicate , we can find a subset B of A whose members are precisely the members of A that satisfy . By the axiom of extensionality this set is unique. We usually denote this set using set-builder notation as . Thus the essence of the axiom is: Every subclass of a set that is defined by a predicate is itself a set. The preceding form of separation was introduced in 1930 by Thoralf Skolem as a refinement of a previous, non-first-order<ref>F. R. Drake, Set Theory: An Introduction to Large Cardinals (1974), pp.12--13. ISBN 0 444 10535 2.</ref> form by Zermelo. The axiom schema of specification is characteristic of systems of axiomatic set theory related to the usual set theory ZFC, but does not usually appear in radically different systems of alternative set theory. For example, New Foundations and positive set theory use different restrictions of the axiom of comprehension of naive set theory. The Alternative Set Theory of Vopenka makes a specific point of allowing proper subclasses of sets, called semisets. Even in systems related to ZFC, this scheme is sometimes restricted to formulas with bounded quantifiers, as in Kripke–Platek set theory with urelements. Relation to the axiom schema of replacement The axiom schema of specification is implied by the axiom schema of replacement together with the axiom of empty set. The axiom schema of replacement says that, if a function is definable by a formula , then for any set , there exists a set : . To derive the axiom schema of specification, let be a formula and a set, and define the function such that if is true and if is false, where such that is true. Then the set guaranteed by the axiom schema of replacement is precisely the set required in the axiom schema of specification. If does not exist, then in the axiom schema of specification is the empty set, whose existence (i.e., the axiom of empty set) is then needed. For this reason, the axiom schema of specification is left out of some axiomatizations of ZF (Zermelo–Fraenkel set theory), although some authors, despite the redundancy, include both. Regardless, the axiom schema of specification is notable because it was in Zermelo's original 1908 list of axioms, before Fraenkel invented the axiom of replacement in 1922. Additionally, if one takes ZFC set theory (i.e., ZF with the axiom of choice), removes the axiom of replacement and the axiom of collection, but keeps the axiom schema of specification, one gets the weaker system of axioms called ZC (i.e., Zermelo's axioms, plus the axiom of choice). Unrestricted comprehension The axiom schema of unrestricted comprehension reads: that is: This set is again unique, and is usually denoted as In an unsorted material set theory, the axiom or rule of full or unrestricted comprehension''' says that for any property P, there exists a set {x \| P(x)} of all objects satisfying P.This axiom schema was tacitly used in the early days of naive set theory, before a strict axiomatization was adopted. However, it was later discovered to lead directly to Russell's paradox, by taking to be (i.e., the property that set is not a member of itself). Therefore, no useful axiomatization of set theory can use unrestricted comprehension. Passing from classical logic to intuitionistic logic does not help, as the proof of Russell's paradox is intuitionistically valid. Accepting only the axiom schema of specification was the beginning of axiomatic set theory. Most of the other Zermelo–Fraenkel axioms (but not the axiom of extensionality, the axiom of regularity, or the axiom of choice) then became necessary to make up for some of what was lost by changing the axiom schema of comprehension to the axiom schema of specification – each of these axioms states that a certain set exists, and defines that set by giving a predicate for its members to satisfy, i.e. it is a special case of the axiom schema of comprehension. It is also possible to prevent the schema from being inconsistent by restricting which formulae it can be applied to, such as only stratified formulae in New Foundations (see below) or only positive formulae (formulae with only conjunction, disjunction, quantification and atomic formulae) in positive set theory. Positive formulae, however, typically are unable to express certain things that most theories can; for instance, there is no complement or relative complement in positive set theory. In NBG class theory In von Neumann–Bernays–Gödel set theory, a distinction is made between sets and classes. A class is a set if and only if it belongs to some class . In this theory, there is a theorem schema that reads that is, provided that the quantifiers in the predicate are restricted to sets. This theorem schema is itself a restricted form of comprehension, which avoids Russell's paradox because of the requirement that be a set. Then specification for sets themselves can be written as a single axiom that is, or even more simply In this axiom, the predicate is replaced by the class , which can be quantified over. Another simpler axiom which achieves the same effect is that is, In higher-order settings In a typed language where we can quantify over predicates, the axiom schema of specification becomes a simple axiom. This is much the same trick as was used in the NBG axioms of the previous section, where the predicate was replaced by a class that was then quantified over. In second-order logic and higher-order logic with higher-order semantics, the axiom of specification is a logical validity and does not need to be explicitly included in a theory. In Quine's New Foundations In the New Foundations approach to set theory pioneered by W. V. O. Quine, the axiom of comprehension for a given predicate takes the unrestricted form, but the predicates that may be used in the schema are themselves restricted. The predicate ( is not in ) is forbidden, because the same symbol appears on both sides of the membership symbol (and so at different "relative types"); thus, Russell's paradox is avoided. However, by taking to be , which is allowed, we can form a set of all sets. For details, see stratification. References Further reading Halmos, Paul, Naive Set Theory. Princeton, New Jersey: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. . Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs''. Elsevier. . Notes Axioms of set theory	Axiom schema of specification	[ "Mathematics" ]	1,841	[ "Axioms of set theory", "Mathematical axioms" ]
52,387	https://en.wikipedia.org/wiki/Axiom%20schema%20of%20replacement	In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZF. The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas. Statement Suppose is a definable binary relation (which may be a proper class) such that for every set there is a unique set such that holds. There is a corresponding definable function , where if and only if . Consider the (possibly proper) class defined such that for every set , if and only if there is an with . is called the image of under , and denoted or (using set-builder notation) . The axiom schema of replacement states that if is a definable class function, as above, and is any set, then the image is also a set. This can be seen as a principle of smallness: the axiom states that if is small enough to be a set, then is also small enough to be a set. It is implied by the stronger axiom of limitation of size. Because it is impossible to quantify over definable functions in first-order logic, one instance of the schema is included for each formula in the language of set theory with free variables among ; but is not free in . In the formal language of set theory, the axiom schema is: For the meaning of , see uniqueness quantification. For clarity, in the case of no variables , this simplifies to: So whenever specifies a unique -to- correspondence, akin to a function on , then all reached this way can be collected into a set , akin to . Applications The axiom schema of replacement is not necessary for the proofs of most theorems of ordinary mathematics. Indeed, Zermelo set theory (Z) already can interpret second-order arithmetic and much of type theory in finite types, which in turn are sufficient to formalize the bulk of mathematics. Although the axiom schema of replacement is a standard axiom in set theory today, it is often omitted from systems of type theory and foundation systems in topos theory. At any rate, the axiom schema drastically increases the strength of ZF, both in terms of the theorems it can prove - for example the sets shown to exist - and also in terms of its proof-theoretic consistency strength, compared to Z. Some important examples follow: Using the modern definition due to von Neumann, proving the existence of any limit ordinal greater than ω requires the replacement axiom. The ordinal number ω·2 = ω + ω is the first such ordinal. The axiom of infinity asserts the existence of an infinite set ω = {0, 1, 2, ...}. One may hope to define ω·2 as the union of the sequence {ω, ω + 1, ω + 2,...}. However, arbitrary such classes of ordinals need not be sets - for example, the class of all ordinals is not a set. Replacement now allows one to replace each finite number n in ω with the corresponding ω + n, and thus guarantees that this class is a set. As a clarification, note that one can easily construct a well-ordered set that is isomorphic to ω·2 without resorting to replacement – simply take the disjoint union of two copies of ω, with the second copy greater than the first – but that this is not an ordinal since it is not totally ordered by inclusion. Larger ordinals rely on replacement less directly. For example, ω1, the first uncountable ordinal, can be constructed as follows – the set of countable well orders exists as a subset of by separation and powerset (a relation on A is a subset of , and so an element of the power set . A set of relations is thus a subset of ). Replace each well-ordered set with its ordinal. This is the set of countable ordinals ω1, which can itself be shown to be uncountable. The construction uses replacement twice; once to ensure an ordinal assignment for each well ordered set and again to replace well ordered sets by their ordinals. This is a special case of the result of Hartogs number, and the general case can be proved similarly. In light of the above, the existence of an assignment of an ordinal to every well-ordered set requires replacement as well. Similarly the von Neumann cardinal assignment which assigns a cardinal number to each set requires replacement, as well as axiom of choice. For sets of tuples recursively defined as and for large , the set has too high of a rank for its existence to be provable from set theory with just the axiom of power set, choice and without replacement. Similarly, Harvey Friedman showed that at least some instances of replacement are required to show that Borel games are determined. The proven result is Donald A. Martin's Borel determinacy theorem. A later, more careful analysis by Martin of the result showed that it only requires replacement for functions with domain an arbitrary countable ordinal. ZF with replacement proves the consistency of Z, as the set Vω·2 is a model of Z whose existence can be proved in ZF. The cardinal number is the first one which can be shown to exist in ZF but not in Z. For clarification, note that Gödel's second incompleteness theorem shows that each of these theories contains a sentence, "expressing" the theory's own consistency, that is unprovable in that theory, if that theory is consistent - this result is often loosely expressed as the claim that neither of these theories can prove its own consistency, if it is consistent. Relation to other axiom schemas Simplifications Some simplifications may be made to the axiom schema of replacement to obtain different equivalent versions. Azriel Lévy showed that a version of replacement with parameters removed, i.e. the following schema, is equivalent to the original form. In particular the equivalence holds in the presence of the axioms of extensionality, pairing, union and powerset. Collection The axiom schema of collection is closely related to and frequently confused with the axiom schema of replacement. Over the remainder of the ZF axioms, it is equivalent to the axiom schema of replacement. The axiom of collection is stronger than replacement in the absence of the power set axiom or its constructive counterpart of ZF and is used in the framework of IZF, which lacks the law of excluded middle, instead of Replacement which is weaker. While replacement can be read to say that the image of a function is a set, collection speaks about images of relations and then merely says that some superclass of the relation's image is a set. In other words, the resulting set has no minimality requirement, i.e. this variant also lacks the uniqueness requirement on . That is, the relation defined by is not required to be a function—some may correspond to many 's in . In this case, the image set whose existence is asserted must contain at least one such for each in the original set, with no guarantee that it will contain only one. Suppose that the free variables of are among ; but neither nor is free in . Then the axiom schema is: The axiom schema is sometimes stated without prior restrictions (apart from not occurring free in ) on the predicate, : In this case, there may be elements in that are not associated to any other sets by . However, the axiom schema as stated requires that, if an element of is associated with at least one set , then the image set will contain at least one such . The resulting axiom schema is also called the axiom schema of boundedness. Separation The axiom schema of separation, the other axiom schema in ZFC, is implied by the axiom schema of replacement and the axiom of empty set. Recall that the axiom schema of separation includes for each formula in the language of set theory in which is not free, i.e. that does not mention . The proof is as follows: Either contains some element validating , or it does not. In the latter case, taking the empty set for fulfills the relevant instance of the axiom schema of separation and one is done. Otherwise, choose such a fixed in that validates . Now define for use with replacement. Using function notation for this predicate , it acts as the identity wherever is true and as the constant function wherever is false. By case analysis, the possible values are unique for any , meaning indeed constitutes a class function. In turn, the image of under , i.e. the class , is granted to be a set by the axiom of replacement. This precisely validates the axiom of separation. This result shows that it is possible to axiomatize ZFC with a single infinite axiom schema. Because at least one such infinite schema is required (ZFC is not finitely axiomatizable), this shows that the axiom schema of replacement can stand as the only infinite axiom schema in ZFC if desired. Because the axiom schema of separation is not independent, it is sometimes omitted from contemporary statements of the Zermelo-Fraenkel axioms. Separation is still important, however, for use in fragments of ZFC, because of historical considerations, and for comparison with alternative axiomatizations of set theory. A formulation of set theory that does not include the axiom of replacement will likely include some form of the axiom of separation, to ensure that its models contain a sufficiently rich collection of sets. In the study of models of set theory, it is sometimes useful to consider models of ZFC without replacement, such as the models in von Neumann's hierarchy. The proof given above assumes the law of excluded middle for the proposition that is inhabited by a set validating , and for any when stipulating that the relation is functional. The axiom of separation is explicitly included in constructive set theory, or a bounded variant thereof. Reflection Lévy's reflection principle for ZFC is equivalent to the axiom of replacement, assuming the axiom of infinity. Lévy's principle is as follows: For any and any first-order formula , there exists an such that . This is a schema that consists of countably many statements, one for each formula . Here, means with all quantifiers bounded to , i.e. but with every instance of and replaced with and respectively. History The axiom schema of replacement was not part of Ernst Zermelo's 1908 axiomatisation of set theory (Z). Some informal approximation to it existed in Cantor's unpublished works, and it appeared again informally in Mirimanoff (1917). Its publication by Abraham Fraenkel in 1922 is what makes modern set theory Zermelo-Fraenkel set theory (ZFC). The axiom was independently discovered and announced by Thoralf Skolem later in the same year (and published in 1923). Zermelo himself incorporated Fraenkel's axiom in his revised system he published in 1930, which also included as a new axiom von Neumann's axiom of foundation. Although it is Skolem's first order version of the axiom list that we use today, he usually gets no credit since each individual axiom was developed earlier by either Zermelo or Fraenkel. The phrase “Zermelo-Fraenkel set theory” was first used in print by von Neumann in 1928. Zermelo and Fraenkel had corresponded heavily in 1921; the axiom of replacement was a major topic of this exchange. Fraenkel initiated correspondence with Zermelo sometime in March 1921. However, his letters before the one dated 6 May 1921 are lost. Zermelo first admitted to a gap in his system in a reply to Fraenkel dated 9 May 1921. On 10 July 1921, Fraenkel completed and submitted for publication a paper (published in 1922) that described his axiom as allowing arbitrary replacements: "If M is a set and each element of M is replaced by [a set or an urelement] then M turns into a set again" (parenthetical completion and translation by Ebbinghaus). Fraenkel's 1922 publication thanked Zermelo for helpful arguments. Prior to this publication, Fraenkel publicly announced his new axiom at a meeting of the German Mathematical Society held in Jena on 22 September 1921. Zermelo was present at this meeting; in the discussion following Fraenkel's talk he accepted the axiom of replacement in general terms, but expressed reservations regarding its extent. Thoralf Skolem made public his discovery of the gap in Zermelo's system (the same gap that Fraenkel had found) in a talk he gave on 6 July 1922 at the 5th Congress of Scandinavian Mathematicians, which was held in Helsinki; the proceedings of this congress were published in 1923. Skolem presented a resolution in terms of first-order definable replacements: "Let U be a definite proposition that holds for certain pairs (a, b) in the domain B; assume further, that for every a there exists at most one b such that U is true. Then, as a ranges over the elements of a set Ma, b ranges over all elements of a set Mb." In the same year, Fraenkel wrote a review of Skolem's paper, in which Fraenkel simply stated that Skolem's considerations correspond to his own. Zermelo himself never accepted Skolem's formulation of the axiom schema of replacement. At one point he called Skolem's approach “set theory of the impoverished”. Zermelo envisaged a system that would allow for large cardinals. He also objected strongly to the philosophical implications of countable models of set theory, which followed from Skolem's first-order axiomatization. According to the biography of Zermelo by Heinz-Dieter Ebbinghaus, Zermelo's disapproval of Skolem's approach marked the end of Zermelo's influence on the developments of set theory and logic. References . . . . Citations Axioms of set theory	Axiom schema of replacement	[ "Mathematics" ]	3,110	[ "Axioms of set theory", "Mathematical axioms" ]
52,396	https://en.wikipedia.org/wiki/Public%20holiday	A public holiday, national holiday, federal holiday, statutory holiday, bank holiday or legal holiday is a holiday generally established by law and is usually a non-working day during the year. Types Civic holiday A civic holiday, also known as a civil holiday or work holiday, is a day that is legally recognized and celebrated as a holiday in a particular sovereign state or jurisdictional subdivision of such, e.g., a state or a province. It is usually a day that the legislature, parliament, congress or sovereign has declared by statute, edict or decree as a non-working day when the official arms of government such as the court system are closed. In federal states there may also be different holidays for the constituent states or provinces, as in the United States, where holidays that were established by the federal government are called federal holidays. Such days may or may not be counted in calculating the statute of limitations in legal actions and are usually days when non-custodial parents are given alternating visitation or access to their children from a prior marriage or relationship according to a parenting schedule. The term may also be used to distinguish between days that may be celebrated as secular holidays rather than religious holidays such as the celebration of New Year's Day on January 1 (Gregorian calendar) and January 14 (Julian Calendar) in certain eastern Orthodox Christian countries such as Russia. Bank holiday In the British Isles, bank holidays are days established as public holidays in statute law. In England and Wales, Good Friday and Christmas Day are known as common law holidays, as they have been celebrated by custom since time immemorial. Bank holidays were introduced in the late 19th century to extend the labour rights citizens have on common law holidays to four additional days. Impacts The major social function of public holidays is the co-ordination of leisure time. This co-ordination has costs, such as congestion and overcrowding (in leisure facilities, on transport systems) and benefits (easier for people to arrange social occasions). Public holidays constitute an important part of nation building and become important symbols of the nation. They can build and legitimise the nation and are intended to foster national unity, social cohesion and popular identification. They provide national governments with annual opportunities to reinforce the status of the nation. Sabine Marschall argues that public holidays can be regarded as sites of memory, which preserve particular representations of historical events and particular national or public heroes. By country In some countries, there are national laws that make some or all public holidays paid holidays, and in other countries, there are no such laws, though many firms provide days off as paid or unpaid holidays. They vary by country and may vary by year. With 36 days a year, Nepal is the country with the highest number of public holidays but it observes six working days a week. India ranks second with 21 national holidays, followed by Colombia and the Philippines at 18 each. Likewise, Japan, China and Hong Kong enjoy 17 public breaks a year. Some countries (e.g. Cambodia) with a longer, six-day workweek, have more holidays (28) to compensate. Italy Public holidays in Italy are established by the Italian parliament and, with the exception of city or community patronal days, apply nationwide. These include a mix of national, religious and local observances. As for Whit Monday, there is an exception for South Tyrol. In Italy there are also State commemoration days, which are not public holidays. New Zealand In New Zealand, a national law sets 12 paid public holidays. If a worker works on a public holiday, they are to be paid 1.5 times their regular rate of pay and be given another alternate day off. South Africa Sabie Marschall argues that the revised set of public holidays in post-Apartheid South Africa attempts to produce and celebrate a particular national identity in line with the political goal of the rainbow nation. United States In the United States, there is no national law requiring that employers pay employees who do not work on public holidays (although the U.S. states of Rhode Island and Massachusetts have paid holiday laws). Controversial holidays Some public holidays are controversial. For example, in the United States a federal holiday commemorates explorer Christopher Columbus, who is said to have discovered the Americas by Europeans. This has led to protests at Columbus Day parades and calls for the public holiday to be changed. Some states have adopted the day as Indigenous People's Day rather than Columbus Day. Similarly, Australia day commemorates the day when the First Fleet first arrived in the country on 26 January 1788 at Sydney Cove. This has also led to protests, with some Australians seeing the date as a symbol of the beginning of European oppression towards the indigenous population. The holiday has since garnered the nickname 'Invasion Day.' Whilst the national date has yet to be changed, many Australia day staples, such as citizenship ceremonies and Triple J's Hottest 100, have been moved to alternative dates. See also Bank holiday List of holidays by country :Category:Lists of public holidays by country References	Public holiday	[ "Physics" ]	1,012	[ "Spacetime", "Physical quantities", "Time in government", "Time" ]
52,432	https://en.wikipedia.org/wiki/Xanthine	Xanthine ( or , from Ancient Greek for its yellowish-white appearance; archaically xanthic acid; systematic name 3,7-dihydropurine-2,6-dione) is a purine base found in most human body tissues and fluids, as well as in other organisms. Several stimulants are derived from xanthine, including caffeine, theophylline, and theobromine. Xanthine is a product on the pathway of purine degradation. It is created from guanine by guanine deaminase. It is created from hypoxanthine by xanthine oxidoreductase. It is also created from xanthosine by purine nucleoside phosphorylase. Xanthine is subsequently converted to uric acid by the action of the xanthine oxidase enzyme. Use and production Xanthine is used as a drug precursor for human and animal medications, and is produced as a pesticide ingredient. Clinical significance Derivatives of xanthine (known collectively as xanthines) are a group of alkaloids commonly used for their effects as mild stimulants and as bronchodilators, notably in the treatment of asthma or influenza symptoms. In contrast to other, more potent stimulants like sympathomimetic amines, xanthines mainly act to oppose the actions of adenosine, and increase alertness in the central nervous system. Toxicity Methylxanthines (methylated xanthines), which include caffeine, aminophylline, IBMX, paraxanthine, pentoxifylline, theobromine, theophylline, and 7-methylxanthine (heteroxanthine), among others, affect the airways, increase heart rate and force of contraction, and at high concentrations can cause cardiac arrhythmias. In high doses, they can lead to convulsions that are resistant to anticonvulsants. Methylxanthines induce gastric acid and pepsin secretions in the gastrointestinal tract. Methylxanthines are metabolized by cytochrome P450 in the liver. If swallowed, inhaled, or exposed to the eyes in high amounts, xanthines can be harmful, and they may cause an allergic reaction if applied topically. Pharmacology In in vitro pharmacological studies, xanthines act as both competitive nonselective phosphodiesterase inhibitors and nonselective adenosine receptor antagonists. Phosphodiesterase inhibitors raise intracellular cAMP, activate PKA, inhibit TNF-α synthesis, and leukotriene and reduce inflammation and innate immunity. Adenosine receptor antagonists inhibit sleepiness-inducing adenosine. However, different analogues show varying potency at the numerous subtypes, and a wide range of synthetic xanthines (some nonmethylated) have been developed searching for compounds with greater selectivity for phosphodiesterase enzyme or adenosine receptor subtypes. Pathology People with rare genetic disorders, specifically xanthinuria and Lesch–Nyhan syndrome, lack sufficient xanthine oxidase and cannot convert xanthine to uric acid. Possible formation in absence of life Studies reported in 2008, based on 12C/13C isotopic ratios of organic compounds found in the Murchison meteorite, suggested that xanthine and related chemicals, including the RNA component uracil, have been formed extraterrestrially. In August 2011, a report, based on NASA studies with meteorites found on Earth, was published suggesting xanthine and related organic molecules, including the DNA and RNA components adenine and guanine, were found in outer space. See also DMPX Murchison meteorite Theobromine poisoning Xanthene Xanthone Xanthydrol Kidney stone disease References Enones	Xanthine	[ "Chemistry" ]	835	[ "Alkaloids by chemical classification", "Xanthines" ]
52,435	https://en.wikipedia.org/wiki/Tait%27s%20conjecture	In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 edges and 46 vertices. Several smaller counterexamples, with 21 faces, 57 edges and 38 vertices, were later proved minimal by . The condition that the graph be 3-regular is necessary due to polyhedra such as the rhombic dodecahedron, which forms a bipartite graph with six degree-four vertices on one side and eight degree-three vertices on the other side; because any Hamiltonian cycle would have to alternate between the two sides of the bipartition, but they have unequal numbers of vertices, the rhombic dodecahedron is not Hamiltonian. The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeless cubic planar graphs. In a Hamiltonian cubic planar graph, such an edge coloring is easy to find: use two colors alternately on the cycle, and a third color for all remaining edges. Alternatively, a 4-coloring of the faces of a Hamiltonian cubic planar graph may be constructed directly, using two colors for the faces inside the cycle and two more colors for the faces outside. Tutte's counterexample Tutte's fragment The key to this counter-example is what is now known as Tutte's fragment, shown on the right. If this fragment is part of a larger graph, then any Hamiltonian cycle through the graph must go in or out of the top vertex (and either one of the lower ones). It cannot go in one lower vertex and out the other. The counterexample The fragment can then be used to construct the non-Hamiltonian Tutte graph, by putting together three such fragments as shown on the picture. The "compulsory" edges of the fragments, that must be part of any Hamiltonian path through the fragment, are connected at the central vertex; because any cycle can use only two of these three edges, there can be no Hamiltonian cycle. The resulting Tutte graph is 3-connected and planar, so by Steinitz' theorem it is the graph of a polyhedron. In total it has 25 faces, 69 edges and 46 vertices. It can be realized geometrically from a tetrahedron (the faces of which correspond to the four large faces in the drawing, three of which are between pairs of fragments and the fourth of which forms the exterior) by multiply truncating three of its vertices. Smaller counterexamples As show, there are exactly six 38-vertex non-Hamiltonian polyhedra that have nontrivial three-edge cuts. They are formed by replacing two of the vertices of a pentagonal prism by the same fragment used in Tutte's example. See also Grinberg's theorem, a necessary condition on the existence of a Hamiltonian cycle that can be used to show that a graph forms a counterexample to Tait's conjecture Barnette's conjecture, a still-open refinement of Tait's conjecture stating that every bipartite cubic polyhedral graph is Hamiltonian. Notes References . . Reprinted in Scientific Papers, Vol. II, pp. 85–98. . Partly based on sci.math posting by Bill Taylor, used by permission. External links Disproved conjectures Planar graphs Hamiltonian paths and cycles	Tait's conjecture	[ "Mathematics" ]	750	[ "Statements about planar graphs", "Planes (geometry)", "Planar graphs" ]
52,462	https://en.wikipedia.org/wiki/Observational%20learning	Observational learning is learning that occurs through observing the behavior of others. It is a form of social learning which takes various forms, based on various processes. In humans, this form of learning seems to not need reinforcement to occur, but instead, requires a social model such as a parent, sibling, friend, or teacher with surroundings. Particularly in childhood, a model is someone of authority or higher status in an environment. In animals, observational learning is often based on classical conditioning, in which an instinctive behavior is elicited by observing the behavior of another (e.g. mobbing in birds), but other processes may be involved as well. Human observational learning Many behaviors that a learner observes, remembers, and imitates are actions that models display and display modeling, even though the model may not intentionally try to instill a particular behavior. A child may learn to swear, smack, smoke, and deem other inappropriate behavior acceptable through poor modeling. Albert Bandura claims that children continually learn desirable and undesirable behavior through observational learning. Observational learning suggests that an individual's environment, cognition, and behavior all incorporate and ultimately determine how the individual functions and models. Through observational learning, individual behaviors can spread across a culture through a process called diffusion chain. This basically occurs when an individual first learns a behavior by observing another individual and that individual serves as a model through whom other individuals learn the behavior, and so on. Culture plays a role in whether observational learning is the dominant learning style in a person or community. Some cultures expect children to actively participate in their communities and are therefore exposed to different trades and roles on a daily basis. This exposure allows children to observe and learn the different skills and practices that are valued in their communities. Albert Bandura, who is known for the classic Bobo doll experiment, identified this basic form of learning in 1961. The importance of observational learning lies in helping individuals, especially children, acquire new responses by observing others' behavior. Albert Bandura states that people's behavior could be determined by their environment. Observational learning occurs through observing negative and positive behaviors. Bandura believes in reciprocal determinism in which the environment can influence people's behavior and vice versa. For instance, the Bobo doll experiment shows that the model, in a determined environment, affects children's behavior. In this experiment Bandura demonstrates that one group of children placed in an aggressive environment would act the same way, while the control group and the other group of children placed in a passive role model environment hardly shows any type of aggression. In communities where children's primary mode of learning is through observation, the children are rarely separated from adult activities. This incorporation into the adult world at an early age allows children to use observational learning skills in multiple spheres of life. This learning through observation requires keen attentive abilities. Culturally, they learn that their participation and contributions are valued in their communities. This teaches children that it is their duty, as members of the community, to observe others' contributions so they gradually become involved and participate further in the community. Influential stages and factors The stages of observational learning include exposure to the model, acquiring the model's behaviour and accepting it as one's own. Bandura's social cognitive learning theory states that there are four factors that influence observational learning: Attention: Observers cannot learn unless they pay attention to what's happening around them. This process is influenced by characteristics of the model, such as how much one likes or identifies with the model, and by characteristics of the observer, such as the observer's expectations or level of emotional arousal. Retention/Memory: Observers must not only recognize the observed behavior but also remember it at some later time. This process depends on the observer's ability to code or structure the information in an easily remembered form or to mentally or physically rehearse the model's actions. Initiation/Motor: Observers must be physically and/intellectually capable of producing the act. In many cases, the observer possesses the necessary responses. But sometimes, reproducing the model's actions may involve skills the observer has not yet acquired. It is one thing to carefully watch a circus juggler, but it is quite another to go home and repeat those acts. Motivation: The observer must have motivation to recreate the observed behavior. Bandura clearly distinguishes between learning and performance. Unless motivated, a person does not produce learned behavior. This motivation can come from external reinforcement, such as the experimenter's promise of reward in some of Bandura's studies, or the bribe of a parent. Or it can come from vicarious reinforcement, based on the observation that models are rewarded. High-status models can affect performance through motivation. For example, girls aged 11 to 14 performed better on a motor performance task when they thought it was demonstrated by a high-status cheerleader than by a low-status model. Some have even added a step between attention and retention involving encoding a behavior. Observational learning leads to a change in an individual's behavior along three dimensions: An individual thinks about a situation in a different way and may have incentive to react to it. The change is a result of a person's direct experiences as opposed to being in-born. For the most part, the change an individual has made is permanent. Effect on behavior According to Bandura's social cognitive learning theory, observational learning can affect behavior in many ways, with both positive and negative consequences. It can teach completely new behaviors, for one. It can also increase or decrease the frequency of behaviors that have previously been learned. Observational learning can even encourage behaviors that were previously forbidden (for example, the violent behavior towards the Bobo doll that children imitated in Albert Bandura's study). Observational learning can also influence behaviors that are similar to, but not identical to, the ones being modeled. For example, seeing a model excel at playing the piano may motivate an observer to play the saxophone. Age difference Albert Bandura stressed that developing children learn from different social models, meaning that no two children are exposed to exactly the same modeling influence. From infancy to adolescence, they are exposed to various social models. A 2013 study found that a toddlers' previous social familiarity with a model was not always necessary for learning and that they were also able to learn from observing a stranger demonstrating or modeling a new action to another stranger. It was once believed that babies could not imitate actions until the latter half of the first year. However, a number of studies now report that infants as young as seven days can imitate simple facial expressions. By the latter half of their first year, 9-month-old babies can imitate actions hours after they first see them. As they continue to develop, toddlers around age two can acquire important personal and social skills by imitating a social model. Deferred imitation is an important developmental milestone in a two-year-old, in which children not only construct symbolic representations but can also remember information. Unlike toddlers, children of elementary school age are less likely to rely on imagination to represent an experience. Instead, they can verbally describe the model's behavior. Since this form of learning does not need reinforcement, it is more likely to occur regularly. As age increases, age-related observational learning motor skills may decrease in athletes and golfers. Younger and skilled golfers have higher observational learning compared to older golfers and less skilled golfers. Observational causal learning Humans use observational Moleen causal learning to watch other people's actions and use the information gained to find out how something works and how we can do it ourselves. A study of 25-month-old infants found that they can learn causal relations from observing human interventions. They also learn by observing normal actions not created by intentional human action. Comparisons with imitation Observational learning is presumed to have occurred when an organism copies an improbable action or action outcome that it has observed and the matching behavior cannot be explained by an alternative mechanism. Psychologists have been particularly interested in the form of observational learning known as imitation and in how to distinguish imitation from other processes. To successfully make this distinction, one must separate the degree to which behavioral similarity results from (a) predisposed behavior, (b) increased motivation resulting from the presence of another animal, (c) attention drawn to a place or object, (d) learning about the way the environment works, as distinguished from what we think of as (e) imitation (the copying of the demonstrated behavior). Observational learning differs from imitative learning in that it does not require a duplication of the behavior exhibited by the model. For example, the learner may observe an unwanted behavior and the subsequent consequences, and thus learn to refrain from that behavior. For example, Riopelle (1960) found that monkeys did better with observational learning if they saw the "tutor" monkey make a mistake before making the right choice. Heyes (1993) distinguished imitation and non-imitative social learning in the following way: imitation occurs when animals learn about behavior from observing conspecifics, whereas non-imitative social learning occurs when animals learn about the environment from observing others. Not all imitation and learning through observing is the same, and they often differ in the degree to which they take on an active or passive form. John Dewey describes an important distinction between two different forms of imitation: imitation as an end in itself and imitation with a purpose. Imitation as an end is more akin to mimicry, in which a person copies another's act to repeat that action again. This kind of imitation is often observed in animals. Imitation with a purpose utilizes the imitative act as a means to accomplish something more significant. Whereas the more passive form of imitation as an end has been documented in some European American communities, the other kind of more active, purposeful imitation has been documented in other communities around the world. Observation may take on a more active form in children's learning in multiple Indigenous American communities. Ethnographic anthropological studies in Yucatec Mayan and Quechua Peruvian communities provide evidence that the home or community-centered economic systems of these cultures allow children to witness first-hand, activities that are meaningful to their own livelihoods and the overall well-being of the community. These children have the opportunity to observe activities that are relevant within the context of that community, which gives them a reason to sharpen their attention to the practical knowledge they are exposed to. This does not mean that they have to observe the activities even though they are present. The children often make an active decision to stay in attendance while a community activity is taking place to observe and learn. This decision underscores the significance of this learning style in many indigenous American communities. It goes far beyond learning mundane tasks through rote imitation; it is central to children's gradual transformation into informed members of their communities' unique practices. There was also a study, done with children, that concluded that Imitated behavior can be recalled and used in another situation or the same. Apprenticeship Apprenticeship can involve both observational learning and modelling. Apprentices gain their skills in part through working with masters in their profession and through observing and evaluating the work of their fellow apprentices. Examples include renaissance inventor/painter Leonardo da Vinci and Michelangelo; before succeeding in their profession, they were apprentices. Learning without imitation Michael Tomasello described various ways of observational learning without the process of imitation in animals (ethology): Exposure – Individuals learn about their environment through close proximity to other individuals that have more experience. For example, a young dolphin learning the location of a plethora of fish by staying near its mother. Stimulus enhancement – Individuals become interested in an object from watching others interact with it. Increased interest in an object may result in object manipulation, which facilitates new object-related behaviors by trial-and-error learning. For example, a young killer whale might become interested in playing with a sea lion pup after watching other whales toss the sea lion pup around. After playing with the pup, the killer whale may develop foraging behaviors appropriate to such prey. In this case, the killer whale did not learn to prey on sea lions by observing other whales do so, but rather the killer whale became intrigued after observing other whales play with the pup. After the killer whale became interested, then its interactions with the sea lion resulted in behaviors that provoked future foraging efforts. Goal emulation – Individuals are enticed by the end result of an observed behavior and attempt the same outcome but with a different method. For example, Haggerty (1909) devised an experiment in which a monkey climbed up the side of a cage, stuck its arm into a wooden chute, and pulled a rope in the chute to release food. Another monkey was provided an opportunity to obtain the food after watching a monkey go through this process on four separate occasions. The monkey performed a different method and finally succeeded after trial and error. Peer model influences Observational learning is very beneficial when there are positive, reinforcing peer models involved. Although individuals go through four different stages for observational learning: attention; retention; production; and motivation, this does not simply mean that when an individual's attention is captured that it automatically sets the process in that exact order. One of the most important ongoing stages for observational learning, especially among children, is motivation and positive reinforcement. Performance is enhanced when children are positively instructed on how they can improve a situation and where children actively participate alongside a more skilled person. Examples of this are scaffolding and guided participation. Scaffolding refers to an expert responding contingently to a novice so the novice gradually increases their understanding of a problem. Guided participation refers to an expert actively engaging in a situation with a novice so the novice participates with or observes the adult to understand how to resolve a problem. Cultural Variation Cultural variation can be seen by the extent of information learned or absorbed by children in non-Western cultures through learning by observation. Cultural variation is not restricted only to ethnicity and nationality, but rather, extends to the specific practices within communities. In learning by observation, children use observation to learn without verbal requests for further information, or without direct instruction. For example, children from Mexican heritage families tend to learn and make better use of information observed during classroom demonstration than children of European heritage. Children of European heritage experience the type of learning that separates them from their family and community activities. They instead participate in lessons and other exercises in special settings such as school. Cultural backgrounds differ from each other in which children display certain characteristics in regards to learning an activity. Another example is seen in the immersion of children in some Indigenous communities of the Americas into the adult world and the effects it has on observational learning and the ability to complete multiple tasks simultaneously. This might be due to children in these communities having the opportunity to see a task being completed by their elders or peers and then trying to emulate the task. In doing so they learn to value observation and the skill-building it affords them because of the value it holds within their community. This type of observation is not passive, but reflects the child's intent to participate or learn within a community. Observational learning can be seen taking place in many domains of Indigenous communities. The classroom setting is one significant example, and it functions differently for Indigenous communities compared to what is commonly present in Western schooling. The emphasis of keen observation in favor of supporting participation in ongoing activities strives to aid children to learn the important tools and ways of their community. Engaging in shared endeavors – with both the experienced and inexperienced – allows for the experienced to understand what the inexperienced need in order to grow in regards to the assessment of observational learning. The involvement of the inexperienced, or the children in this matter, can either be furthered by the children's learning or advancing into the activity performed by the assessment of observational learning. Indigenous communities rely on observational learning as a way for their children to be a part of ongoing activities in the community (Tharp, 2006). Although learning in the Indigenous American communities is not always the central focus when participating in an activity, studies have shown that attention in intentional observation differs from accidental observation. Intentional participation is "keen observation and listening in anticipation of, or in the process of engaging in endeavors". This means that when they have the intention of participating in an event, their attention is more focused on the details, compared to when they are accidentally observing. Observational learning can be an active process in many Indigenous American communities. The learner must take initiative to attend to activities going on around them. Children in these communities also take initiative to contribute their knowledge in ways that will benefit their community. For example, in many Indigenous American cultures, children perform household chores without being instructed to do so by adults. Instead, they observe a need for their contributions, understand their role in their community, and take initiative to accomplish the tasks they have observed others doing. The learner's intrinsic motivations play an important role in the child's understanding and construction of meaning in these educational experiences. The independence and responsibility associated with observational learning in many Indigenous American communities are significant reasons why this method of learning involves more than just watching and imitating. A learner must be actively engaged with their demonstrations and experiences in order to fully comprehend and apply the knowledge they obtain. Indigenous communities of the Americas Children from indigenous heritage communities of the Americas often learn through observation, a strategy that can carry over into adulthood. The heightened value towards observation allows children to multi-task and actively engage in simultaneous activities. The exposure to an uncensored adult lifestyle allows children to observe and learn the skills and practices that are valued in their communities. Children observe elders, parents, and siblings complete tasks and learn to participate in them. They are seen as contributors and learn to observe multiple tasks being completed at once and can learn to complete a task while still engaging with other community members without being distracted. Indigenous communities provide more opportunities to incorporate children in everyday life. This can be seen in some Mayan communities where children are given full access to community events, which allows observational learning to occur more often. Other children in Mazahua, Mexico are known to observe ongoing activities intensely . In native northern Canadian and indigenous Mayan communities, children often learn as third-party observers from stories and conversations by others. Most young Mayan children are carried on their mother's back, allowing them to observe their mother's work and see the world as their mother sees it. Often, children in Indigenous American communities assume the majority of the responsibility for their learning. Additionally, children find their own approaches to learning. Children are often allowed to learn without restrictions and with minimal guidance. They are encouraged to participate in the community even if they do not know how to do the work. They are self-motivated to learn and finish their chores. These children act as a second set of eyes and ears for their parents, updating them about the community. Children aged 6 to 8 in an indigenous heritage community in Guadalajara, Mexico participated in hard work, such as cooking or running errands, thus benefiting the whole family, while those in the city of Guadalajara rarely did so. These children participated more in adult regulated activities and had little time to play, while those from the indigenous-heritage community had more time to play and initiate in their after-school activities and had a higher sense of belonging to their community. Children from formerly indigenous communities are more likely to show these aspects than children from cosmopolitan communities are, even after leaving their childhood community Within certain indigenous communities, people do not typically seek out explanations beyond basic observation. This is because they are competent in learning through astute observation and often nonverbally encourage to do so. In a Guatemalan footloom factory, amateur adult weavers observed skilled weavers over the course of weeks without questioning or being given explanations; the amateur weaver moved at their own pace and began when they felt confident. The framework of learning how to weave through observation can serve as a model that groups within a society use as a reference to guide their actions in particular domains of life. Communities that participate in observational learning promote tolerance and mutual understand of those coming from different cultural backgrounds. Other human and animal behavior experiments When an animal is given a task to complete, they are almost always more successful after observing another animal doing the same task before them. Experiments have been conducted on several different species with the same effect: animals can learn behaviors from peers. However, there is a need to distinguish the propagation of behavior and the stability of behavior. Research has shown that social learning can spread a behavior, but there are more factors regarding how a behavior carries across generations of an animal culture. Learning in fish Experiments with ninespine sticklebacks showed that individuals will use social learning to locate food. Social learning in pigeons A study in 1996 at the University of Kentucky used a foraging device to test social learning in pigeons. A pigeon could access the food reward by either pecking at a treadle or stepping on it. Significant correspondence was found between the methods of how the observers accessed their food and the methods the initial model used in accessing the food. Acquiring foraging niches Studies have been conducted at the University of Oslo and University of Saskatchewan regarding the possibility of social learning in birds, delineating the difference between cultural and genetic acquisition. Strong evidence already exists for mate choice, bird song, predator recognition, and foraging. Researchers cross-fostered eggs between nests of blue tits and great tits and observed the resulting behavior through audio-visual recording. Tits raised in the foster family learned their foster family's foraging sites early. This shift—from the sites the tits would among their own kind and the sites they learned from the foster parents—lasted for life. What young birds learn from foster parents, they eventually transmitted to their own offspring. This suggests cultural transmissions of foraging behavior over generations in the wild. Social learning in crows The University of Washington studied this phenomenon with crows, acknowledging the evolutionary tradeoff between acquiring costly information firsthand and learning that information socially with less cost to the individual but at the risk of inaccuracy. The experimenters exposed wild crows to a unique "dangerous face" mask as they trapped, banded, and released 7-15 birds at five different study places around Seattle, WA. An immediate scolding response to the mask after trapping by previously captured crows illustrates that the individual crow learned the danger of that mask. There was a scolding from crows that were captured that had not been captured initially. That response indicates conditioning from the mob of birds that assembled during the capture. Horizontal social learning (learning from peers) is consistent with the lone crows that recognized the dangerous face without ever being captured. Children of captured crow parents were conditioned to scold the dangerous mask, which demonstrates vertical social learning (learning from parents). The crows that were captured directly had the most precise discrimination between dangerous and neutral masks than the crows that learned from the experience of their peers. The ability of crows to learn doubled the frequency of scolding, which spread at least 1.2 km from where the experiment started to over a 5-year period at one site. Propagation of animal culture Researchers at the Département d’Etudes Cognitives, Institut Jean Nicod, Ecole Normale Supérieure acknowledged a difficulty with research in social learning. To count acquired behavior as cultural, two conditions need must be met: the behavior must spread in a social group, and that behavior must be stable across generations. Research has provided evidence that imitation may play a role in the propagation of a behavior, but these researchers believe the fidelity of this evidence is not sufficient to prove the stability of animal culture. Other factors like ecological availability, reward-based factors, content-based factors, and source-based factors might explain the stability of animal culture in a wild rather than just imitation. As an example of ecological availability, chimps may learn how to fish for ants with a stick from their peers, but that behavior is also influenced by the particular type of ants as well as the condition. A behavior may be learned socially, but the fact that it was learned socially does not necessarily mean it will last. The fact that the behavior is rewarding has a role in cultural stability as well. The ability for socially-learned behaviors to stabilize across generations is also mitigated by the complexity of the behavior. Different individuals of a species, like crows, vary in their ability to use a complex tool. Finally, a behavior's stability in animal culture depends on the context in which they learn a behavior. If a behavior has already been adopted by a majority, then the behavior is more likely to carry across generations out of a need for conforming. Animals are able to acquire behaviors from social learning, but whether or not that behavior carries across generations requires more investigation. Hummingbird experiment Experiments with hummingbirds provided one example of apparent observational learning in a non-human organism. Hummingbirds were divided into two groups. Birds in one group were exposed to the feeding of a knowledgeable "tutor" bird; hummingbirds in the other group did not have this exposure. In subsequent tests the birds that had seen a tutor were more efficient feeders than the others. Bottlenose dolphin Herman (2002) suggested that bottlenose dolphins produce goal-emulated behaviors rather than imitative ones. A dolphin that watches a model place a ball in a basket might place the ball in the basket when asked to mimic the behavior, but it may do so in a different manner seen. Rhesus monkey Kinnaman (1902) reported that one rhesus monkey learned to pull a plug from a box with its teeth to obtain food after watching another monkey succeed at this task. Fredman (2012) also performed an experiment on observational behavior. In experiment 1, human-raised monkeys observed a familiar human model open a foraging box using a tool in one of two alternate ways: levering or poking. In experiment 2, mother-raised monkeys viewed similar techniques demonstrated by monkey models. A control group in each population saw no model. In both experiments, independent coders detected which technique experimental subjects had seen, thus confirming social learning. Further analyses examined copying at three levels of resolution. The human-raised monkeys exhibited the greatest learning with the specific tool use technique they saw. Only monkeys who saw the levering model used the lever technique, by contrast with controls and those who witnessed poking. Mother-reared monkeys instead typically ignored the tool and exhibited fidelity at a lower level, tending only to re-create whichever result the model had achieved by either levering or poking. Nevertheless, this level of social learning was associated with significantly greater levels of success in monkeys witnessing a model than in controls, an effect absent in the human-reared population. Results in both populations are consistent with a process of canalization of the repertoire in the direction of the approach witnessed, producing a narrower, socially shaped behavioral profile than among controls who saw no model. Light box experiment Pinkham and Jaswal (2011) did an experiment to see if a child would learn how to turn on a light box by watching a parent. They found that children who saw a parent use their head to turn on the light box tended to do the task in that manner, while children who had not seen the parent used their hands instead. Swimming skill performance When adequate practice and appropriate feedback follow demonstrations, increased skill performance and learning occurs. Lewis (1974) did a study of children who had a fear of swimming and observed how modelling and going over swimming practices affected their overall performance. The experiment spanned nine days, and included many steps. The children were first assessed on their anxiety and swimming skills. Then they were placed into one of three conditional groups and exposed to these conditions over a few days. At the end of each day, all children participated in a group lesson. The first group was a control group where the children watched a short cartoon video unrelated to swimming. The second group was a peer mastery group, which watched a short video of similar-aged children who had very good task performances and high confidence. Lastly, the third group was a peer coping group, whose subjects watched a video of similar-aged children who progressed from low task performances and low confidence statements to high task performances and high confidence statements. The day following the exposures to each condition, the children were reassessed. Finally, the children were also assessed a few days later for a follow-up assessment. Upon reassessment, it was shown that the two model groups who watched videos of children similar in age had successful rates on the skills assessed because they perceived the models as informational and motivational. Do-as-I-do Chimpanzee Flexible methods must be used to assess whether an animal can imitate an action. This led to an approach that teaches animals to imitate by using a command such as "do-as-I-do" or "do this" followed by the action that they are supposed to imitate . Researchers trained chimpanzees to imitate an action that was paired with the command. For example, this might include a researcher saying "do this" paired with clapping hands. This type of instruction has been utilized in a variety of other animals in order to teach imitation actions by utilizing a command or request. Observational learning in Everyday Life Observational learning allows for new skills to be learned in a wide variety of areas. Demonstrations help the modification of skills and behaviors. Learning physical activities When learning skills for physical activities can be anything that is learned that requires physical movement, this can include learning a sport, learning to eat with a fork, or learning to walk. There are multiple important variables that aid in modifying physical skills and psychological responses from an observational learning standpoint. Modeling is a variable in observational learning where the skill level of the model is considered. When someone is supposed to demonstrate a physical skill such as throwing a baseball the model should be able to execute the behavior of throwing the ball flawlessly if the model of learning is a mastery model. Another model to utilize in observational learning is a coping model, which would be a model demonstrating a physical skill that they have not yet mastered or achieved high performance in. Both models are found to be effective and can be utilized depending on the what skills is trying to be demonstrated. These models can be used as interventions to increase observational learning in practice, competition, and rehabilitation situations.Observational learning is also dependent on the learner's intentions and goals where performance can be enhanced by increasing instruction and beneficial feedback depending on the individual's age, personality, and abilities. Neuroscience Recent research in neuroscience has implicated mirror neurons as a neurophysiological basis for observational learning. Mirror neurons were first discovered in 1991 by researchers led by Giacomo Rizzolatti. The scientists had a device connected to a monkey to monitor brain activity. When the scientists came into the lab eating ice cream, the device buzzed. This accidental finding led them to mirror neurons which are an essential part in imitation and observational learning. These specialized visuomotor neurons fire action potentials when an individual performs a motor task and also fire when an individual passively observes another individual performing the same motor task. In observational motor learning, the process begins with a visual presentation of another individual performing a motor task, this acts as a model. The learner then needs to transform the observed visual information into internal motor commands that will allow them to perform the motor task, this is known as visuomotor transformation. Mirror neuron networks provide a mechanism for visuo-motor and motor-visual transformation and interaction. Similar networks of mirror neurons have also been implicated in social learning, motor cognition and social cognition. Clinical Perspective Autism Spectrum Disorder Discrete trial training (DTT) is a structured and systematic approach utilized in helping individuals with autism spectrum disorder learn. Individuals with autism tend to struggle with learning through observation, therefore something that is reinforcing is necessary in order to motivate them to imitate or follow through with the task. When utilizing DTT to teach individuals with autism modeling is utilized to aid in their learning. Modeling would include showing how to reach the correct answer, this could mean showing the steps to a math equation. Utilizing DTT in a group setting also promotes observational learning from peers as well. See also Cognitive imitation Educational psychology Educational technology Hypercorrection Imitation Inference Machine learning Mirroring (psychology) Social learning theory Social learning tools Mathematical models of social learning References Further reading on animal social learning Zentall, T.R. (2006). Imitation: Definitions, evidence, and mechanisms. Animal Cognition, 9 335–353. (A thorough review of different types of social learning) Full text Social learning theory Behavioral concepts Learning Animal cognition	Observational learning	[ "Biology" ]	6,669	[ "Behavior", "Behavioral concepts", "Animals", "Behaviorism", "Social learning theory", "Animal cognition" ]
52,469	https://en.wikipedia.org/wiki/Stephen%20Wolfram	Stephen Wolfram ( ; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his work in computer algebra and theoretical physics. In 2012, he was named a fellow of the American Mathematical Society. As a businessman, he is the founder and CEO of the software company Wolfram Research, where he works as chief designer of Mathematica and the Wolfram Alpha answer engine. Early life Family Stephen Wolfram was born in London in 1959 to Hugo and Sybil Wolfram, both German Jewish refugees to the United Kingdom. His maternal grandmother was British psychoanalyst Kate Friedlander. Wolfram's father, Hugo Wolfram, was a textile manufacturer and served as managing director of the Lurex Company—makers of the fabric Lurex. Wolfram's mother, Sybil Wolfram, was a Fellow and Tutor in Philosophy at Lady Margaret Hall at University of Oxford from 1964 to 1993. Stephen Wolfram is married to a mathematician. They have four children together. Education Wolfram was educated at Eton College, but left prematurely in 1976. As a young child, Wolfram had difficulties learning arithmetic. He entered St. John's College, Oxford, at age 17 and left in 1978 without graduating to attend the California Institute of Technology the following year, where he received a PhD in particle physics in 1980. Wolfram's thesis committee was composed of Richard Feynman, Peter Goldreich, Frank J. Sciulli, and Steven Frautschi, and chaired by Richard D. Field. Early career Wolfram, at the age of 15, began research in applied quantum field theory and particle physics and published scientific papers in peer-reviewed scientific journals; by the time he left Oxford, he had published ten such papers. Following his PhD, Wolfram joined the faculty at Caltech and became the youngest recipient of a MacArthur Fellowship in 1981, at age 21. Later career Complex systems and cellular automata In 1983, Wolfram left for the School of Natural Sciences of the Institute for Advanced Study in Princeton. By that time, he was no longer interested in particle physics. Instead, he began pursuing investigations into cellular automata, mainly with computer simulations. He produced a series of papers investigating the class of elementary cellular automata, conceiving the Wolfram code, a naming system for one-dimensional cellular automata, and a classification scheme for the complexity of their behaviour. He conjectured that the Rule 110 cellular automaton might be Turing complete, which a research assistant to Wolfram, Matthew Cook, later proved correct. Wolfram sued Cook and temporarily blocked publication of the work on Rule 110 for allegedly violating a non-disclosure agreement until Wolfram could publish the work in his controversial book A New Kind of Science. Wolfram's cellular-automata work came to be cited in more than 10,000 papers. In the mid-1980s, Wolfram worked on simulations of physical processes (such as turbulent fluid flow) with cellular automata on the Connection Machine alongside Richard Feynman and helped initiate the field of complex systems. In 1984, he was a participant in the Founding Workshops of the Santa Fe Institute, along with Nobel laureates Murray Gell-Mann, Manfred Eigen, and Philip Warren Anderson, and future laureate Frank Wilczek. In 1986, he founded the Center for Complex Systems Research (CCSR) at the University of Illinois at Urbana–Champaign. In 1987, he founded the journal Complex Systems. Symbolic Manipulation Program Wolfram led the development of the computer algebra system SMP (Symbolic Manipulation Program) in the Caltech physics department during 1979–1981. A dispute with the administration over the intellectual property rights regarding SMP—patents, copyright, and faculty involvement in commercial ventures—eventually led him to resign from Caltech. SMP was further developed and marketed commercially by Inference Corp. of Los Angeles during 1983–1988. Mathematica In 1986, Wolfram left the Institute for Advanced Study for the University of Illinois at Urbana–Champaign, where he had founded their Center for Complex Systems Research, and started to develop the computer algebra system Mathematica, which was released on 23 June 1988, when he left academia. In 1987, he founded Wolfram Research, which continues to develop and market the program. A New Kind of Science From 1992 to 2002, Wolfram worked on his controversial book A New Kind of Science, which presents an empirical study of simple computational systems. Additionally, it argues that for fundamental reasons these types of systems, rather than traditional mathematics, are needed to model and understand complexity in nature. Wolfram's conclusion is that the universe is discrete in its nature, and runs on fundamental laws that can be described as simple programs. He predicts that a realization of this within scientific communities will have a revolutionary influence on physics, chemistry, biology, and most other scientific areas, hence the book's title. The book was met with skepticism and criticism that Wolfram took credit for the work of others and made conclusions without evidence to support them. Wolfram Alpha computational knowledge engine In March 2009, Wolfram announced Wolfram Alpha, an answer engine. Wolfram Alpha launched in May 2009, and a paid-for version with extra features launched in February 2012 that was met with criticism for its high price, which later dropped from $50 to $2. The engine is based on natural language processing and a large library of rules-based algorithms. The application programming interface allows other applications to extend and enhance Wolfram Alpha. Touchpress In 2010, Wolfram co-founded Touchpress with Theodore Gray, Max Whitby, and John Cromie. The company specialised in creating in-depth premium apps and games covering a wide range of educational subjects designed for children, parents, students, and educators. Touchpress published more than 100 apps. The company is no longer active. Wolfram Language In March 2014, at the annual South by Southwest (SXSW) event, Wolfram officially announced the Wolfram Language as a new general multi-paradigm programming language, though it was previously available through Mathematica and not an entirely new programming language. The documentation for the language was pre-released in October 2013 to coincide with the bundling of Mathematica and the Wolfram Language on every Raspberry Pi computer with some controversy because of the proprietary nature of the Wolfram Language. While the Wolfram Language has existed for over 30 years as the primary programming language used in Mathematica, it was not officially named until 2014, and is not widely used. Wolfram Physics Project In April 2020, Wolfram announced the "Wolfram Physics Project" as an effort to reduce and explain all the laws of physics within a paradigm of a hypergraph that is transformed by minimal rewriting rules that obey the Church–Rosser property. The effort is a continuation of the ideas he originally described in A New Kind of Science. Wolfram claims that "From an extremely simple model, we're able to reproduce special relativity, general relativity and the core results of quantum mechanics." Physicists are generally unimpressed with Wolfram's claim, and say his results are non-quantitative and arbitrary. Personal interests and activities Wolfram has a log of personal analytics, including emails received and sent, keystrokes made, meetings and events attended, recordings of phone calls, and even physical movement dating back to the 1980s. In the preface of A New Kind of Science, he noted that he recorded over 100 million keystrokes and 100 mouse miles. He has said that personal analytics "can give us a whole new dimension to experiencing our lives." Wolfram was a scientific consultant for the 2016 film Arrival. He and his son Christopher Wolfram wrote some of the code featured on screen, such as the code in graphics depicting an analysis of the alien logograms, for which they used the Wolfram Language. Bibliography Metamathematics: Foundations & Physicalization, (2022), Wolfram Media, Inc, ASIN:B0BPN7SHN3 Combinators: A Centennial View (2021) A Project to Find the Fundamental Theory of Physics (2020), Publisher: Wolfram Media, Adventures of a Computational Explorer (2019) Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People (2016) Elementary Introduction to the Wolfram Language (2015) The Mathematica Book (multiple editions) Cellular Automata and Complexity: Collected Papers (1994) Theory and Applications of Cellular Automata (1986) References External links Wolfram Foundation Interview of Stephen Wolfram by David Zierler on March 18 and April 17, 2021, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA, www.aip.org/history-programs/niels-bohr-library/oral-histories/46902 1959 births 20th-century American businesspeople 20th-century American mathematicians 20th-century British businesspeople 20th-century British mathematicians 21st-century American businesspeople 21st-century American mathematicians 21st-century British businesspeople 21st-century British mathematicians American computer programmers American computer scientists American people of Hungarian-Jewish descent American technology chief executives American technology company founders American transhumanists Artificial intelligence researchers British emigrants to the United States Jewish British writers British technology chief executives British technology company founders British transhumanists Life extensionists Businesspeople in software California Institute of Technology alumni Cellular automatists Chaos theorists Complex systems scientists Computational physicists English computer programmers English computer scientists English emigrants to the United States English Jews English people of German-Jewish descent English people of Hungarian-Jewish descent Fellows of the American Mathematical Society Graph drawing people Independent scientists Data and information visualization experts Institute for Advanced Study visiting scholars Jewish American scientists Jewish British physicists Jewish American physicists Living people MacArthur Fellows Machine learning researchers Mathematics writers Particle physicists People educated at Eton College People educated at The Dragon School Programming language designers Programming language researchers Researchers in geometric algorithms University of Illinois Urbana-Champaign faculty Wolfram Research people American systems scientists British systems scientists 21st-century American Jews	Stephen Wolfram	[ "Physics" ]	2,042	[ "Particle physicists", "Particle physics", "Computational physicists", "Computational physics" ]
52,487	https://en.wikipedia.org/wiki/Ivan%20Pavlov	Ivan Petrovich Pavlov (, ; 27 February 1936) was a Russian and Soviet experimental neurologist and physiologist known for his discovery of classical conditioning through his experiments with dogs. Education and early life Pavlov was born the first of ten children, in Ryazan, Russian Empire. His father, Peter Dmitrievich Pavlov (1823–1899), was a village Russian Orthodox priest. His mother, Varvara Ivanovna Uspenskaya (1826–1890), was a devoted homemaker. As a child, Pavlov willingly participated in house duties such as doing the dishes and taking care of his siblings. He loved to garden, ride his bicycle, row, swim, and play gorodki; he devoted his summer vacations to these activities. Although able to read by the age of seven, Pavlov did not begin formal schooling until he was 11 years old, due to serious injuries he had sustained when falling from a high wall onto stone pavement. From his childhood days, Pavlov demonstrated intellectual curiosity along with an unusual energy which he referred to as "the instinct for research". Inspired by the progressive ideas which Dmitry Pisarev, a Russian literary critic of the 1860s, and Ivan Sechenov, the father of Russian physiology, were spreading, Pavlov abandoned his religious career and devoted his life to science. In 1870, he enrolled in the physics and mathematics department at the University of Saint Petersburg to study natural science. Pavlov attended the Ryazan church school before entering the local theological seminary. In 1870, however, he left the seminary without graduating to attend the university at St. Petersburg. There he enrolled in the physics and math department and took natural science courses. In his fourth year, his first research project on the physiology of the nerves of the pancreas won him a prestigious university award. In 1875, Pavlov completed his course with an outstanding record and received the degree of Candidate of Natural Sciences. Impelled by his overwhelming interest in physiology, Pavlov decided to continue his studies and proceeded to the Imperial Academy of Medical Surgery. While at the academy, Pavlov became an assistant to his former teacher, Elias von Cyon. He left the department when de Cyon was replaced by another instructor. After some time, Pavlov obtained a position as a laboratory assistant to Konstantin Nikolaevich Ustimovich at the physiological department of the Veterinary Institute. For two years, Pavlov investigated the circulatory system for his medical dissertation. In 1878, Professor S. P. Botkin, a famous Russian clinician, invited the gifted young physiologist to work in the physiological laboratory as the clinic's chief. In 1879, Pavlov graduated from the Medical Military Academy with a gold medal award for his research work. After a competitive examination, Pavlov won a fellowship at the academy for postgraduate work. The fellowship and his position as director of the Physiological Laboratory at Botkin's clinic enabled Pavlov to continue his research work. In 1883, he presented his doctor's thesis on the subject of The centrifugal nerves of the heart and posited the idea of nerves and the basic principles on the trophic function of the nervous system. Additionally, his collaboration with the Botkin Clinic produced evidence of a basic pattern in the regulation of reflexes in the activity of circulatory organs. He was inspired to pursue a scientific career by D. I. Pisarev, a literary critic and natural science advocate of the time and I. M. Sechenov, a Russian physiologist, whom Pavlov described as "the father of physiology". Career Studies in Germany After completing his doctorate, Pavlov went to Germany, where he studied in Leipzig with Carl Ludwig and Eimear Kelly in the Heidenhain laboratories in Breslau. He remained there from 1884 to 1886. Heidenhain was studying digestion in dogs, using an exteriorized section of the stomach. However, Pavlov perfected the technique by overcoming the problem of maintaining the external nerve supply. The exteriorized section became known as the Heidenhain or Pavlov pouch. Return to Russia In 1886, Pavlov returned to Russia to look for a new position. His application for the chair of physiology at the University of Saint Petersburg was rejected. Eventually, Pavlov was offered the chair of pharmacology at Tomsk University in Siberia and at the University of Warsaw in Poland. He did not take up either post. In 1890, he was appointed the role of professor of Pharmacology at the Military Medical Academy and occupied the position for five years. In 1891, Pavlov was invited to the Institute of Experimental Medicine in St. Petersburg to organize and direct the Department of Physiology. Over a 45-year period, under his direction, the institute became one of the most important centers of physiological research in the world. Pavlov continued to direct the Department of Physiology at the institute, while taking up the chair of physiology at the Medical Military Academy in 1895. Pavlov would head the physiology department at the academy continuously for three decades. Nobel Prize Starting in 1901, Pavlov was nominated over four successive years for the Nobel Prize in Physiology or Medicine. He did not win the prize until 1904 because his previous nominations were not specific to any discovery, but based on a variety of laboratory findings. When Pavlov received the Nobel Prize it was specified that he did so "in recognition of his work on the physiology of digestion, through which knowledge on vital aspects of the subject has been transformed and enlarged". Studies of digestion At the Institute of Experimental Medicine, Pavlov carried out his classical experiments on the digestive glands, which would eventually grant him the aforementioned Nobel prize. Pavlov investigated the gastric function of dogs, and later, homeless children, by externalizing a salivary gland so he could collect, measure, and analyze the saliva and what response it had to food under different conditions. He noticed that the dogs tended to salivate before food was actually delivered to their mouths, and set out to investigate this "psychic secretion", as he called it. Pavlov's laboratory housed a full-scale kennel for the experimental canines. Pavlov was interested in observing their long-term physiological processes. This required keeping them alive and healthy to conduct chronic experiments, as he called them. These were experiments over time, designed to understand the normal functions of dogs. This was a new kind of study, because previously experiments had been "acute", meaning that the dog underwent vivisection which ultimately killed it. Pavlov would often remove the esophagus of several dogs and created a fistula in their throats. Other activities A 1921 article by Sergius Morgulis in the journal Science was critical of Pavlov's work, raising concerns about the environment in which these experiments had been performed. Based on a report from H. G. Wells, claiming that Pavlov grew potatoes and carrots in his laboratory the article stated, "It is gratifying to be assured that Professor Pavlov is raising potatoes only as a pastime and still gives the best of his genius to scientific investigation". That same year, Pavlov began holding laboratory meetings known as the 'Wednesday meetings' at which he spoke frankly on many topics, including his views on psychology. These meetings lasted until he died in 1936. Relationship with the Soviet government Pavlov was highly regarded by the Soviet government, and he was able to continue his research. He was praised by Lenin. Despite praise from the Soviet Union government, the money that poured in to support his laboratory, and the honours he was given, Pavlov made no attempts to conceal the disapproval and contempt with which he regarded Soviet Communism. In 1923, he stated that he would not sacrifice even the hind leg of a frog to the type of social experiment that the regime was conducting in Russia. Four years later he wrote to Stalin, protesting at what was being done to Russian intellectuals and saying he was ashamed to be a Russian. After the murder of Sergei Kirov in 1934, Pavlov wrote several letters to Vyacheslav Molotov criticizing the mass persecutions which followed and asking for the reconsideration of cases pertaining to several people he knew personally. In the final years of his life Pavlov's attitude towards the Soviet government softened; without fully endorsing its policies, he praised the Soviet government for its support of scientific institutions. In 1935, a few months before his death, Pavlov read a draft of the 1936 "Stalin Constitution" and expressed his pleasure at the apparent dawn of a more free and democratic Soviet Union. Death and burial Conscious until his final moments, Pavlov asked one of his students to sit beside his bed and to record the circumstances of his dying. He wanted to create unique evidence of subjective experiences of this terminal phase of life. Pavlov died on 27 February 1936 of double pneumonia at the age of 86. He was given a grand funeral, and his study and laboratory were preserved as a museum in his honour. His grave is in the Literatorskie mostki (writers' footways) section of Volkovo Cemetery in St. Petersburg. Reflex system research Pavlov contributed to many areas of physiology and neurological sciences. Most of his work involved research in temperament, conditioning and involuntary reflex actions. Pavlov performed and directed experiments on digestion, eventually publishing The Work of the Digestive Glands in 1897, after 12 years of research. His experiments earned him the 1904 Nobel Prize in Physiology and Medicine. These experiments included surgically extracting portions of the digestive system from nonhuman animals, severing nerve bundles to determine the effects, and implanting fistulas between digestive organs and an external pouch to examine the organ's contents. This research served as a base for broad research on the digestive system. Further work on reflex actions involved involuntary reactions to stress and pain. Nervous system research Pavlov was always interested in biomarkers of temperament types described by Hippocrates and Galen. He called these biomarkers "properties of nervous systems" and identified three main properties: (1) strength, (2) mobility of nervous processes and (3) a balance between excitation and inhibition and derived four types based on these three properties. He extended the definitions of the four temperament types under study at the time: choleric, phlegmatic, sanguine, and melancholic, updating the names to "the strong and impetuous type, the strong equilibrated and quiet type, the strong equilibrated and lively type, and the weak type", respectively. Pavlov and his researchers observed and began the study of transmarginal inhibition (TMI), the body's natural response of shutting down when exposed to overwhelming stress or pain by electric shock. This research showed how all temperament types responded to the stimuli the same way, but different temperaments move through the responses at different times. He commented "that the most basic inherited difference ... was how soon they reached this shutdown point and that the quick-to-shut-down have a fundamentally different type of nervous system." Pavlov carried out experiments on the digestive glands, as well as investigated the gastric function of dogs, and eventually won the Nobel Prize for Physiology or Medicine in 1904, becoming the first Russian Nobel laureate. A survey in the Review of General Psychology, published in 2002, ranked Pavlov as the 24th most cited psychologist of the 20th century. Pavlov's principles of classical conditioning have been found to operate across a variety of behavior therapies and in experimental and clinical settings, such as educational classrooms and even reducing phobias with systematic desensitization. Classical conditioning The basics of Pavlov's classical conditioning serve as a historical backdrop for current learning theories. However, the Russian physiologist's initial interest in classical conditioning occurred almost by accident during one of his experiments on digestion in dogs. Considering that Pavlov worked closely with nonhuman animals throughout many of his experiments, his early contributions were primarily about learning in nonhuman animals. However, the fundamentals of classical conditioning have been examined across many different organisms, including humans. The basic underlying principles of Pavlov's classical conditioning have extended to a variety of settings, such as classrooms and learning environments. Classical conditioning focuses on using preceding conditions to alter behavioral reactions. The principles underlying classical conditioning have influenced preventative antecedent control strategies used in the classroom. Classical conditioning set the groundwork for the present day behavior modification practices, such as antecedent control. Antecedent events and conditions are defined as those conditions occurring before the behavior. Pavlov's early experiments used manipulation of events or stimuli preceding behavior (i.e., a tone) to produce salivation in dogs much like teachers manipulate instruction and learning environments to produce positive behaviors or decrease maladaptive behaviors. Although he did not refer to the tone as an antecedent, Pavlov was one of the first scientists to demonstrate the relationship between environmental stimuli and behavioral responses. Pavlov systematically presented and withdrew stimuli to determine the antecedents that were eliciting responses, which is similar to the ways in which educational professionals conduct functional behavior assessments. Antecedent strategies are supported by empirical evidence to operate implicitly within classroom environments. Antecedent-based interventions are supported by research to be preventative, and to produce immediate reductions in problem behaviors. Awards and honours Pavlov was awarded the Nobel Prize in Physiology or Medicine in 1904. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1907, elected an International Member of the United States National Academy of Sciences in 1908, was awarded the Royal Society's Copley Medal in 1915, and elected an International Member of the American Philosophical Society in 1932. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1907. Pavlov's dog, the Pavlovian session and Pavlov's typology are named in his honour. The asteroid 1007 Pawlowia and the lunar crater Pavlov were also named after him. Legacy The concept for which Pavlov is best known is the "conditioned reflex", or what he called the "conditional reflex", which he developed jointly with his assistant Ivan Tolochinov in 1901; Edwin B. Twitmyer at the University of Pennsylvania in Philadelphia published similar research in 1902, a year before Pavlov published his. The concept was developed after observing the rates of salivation in dogs. Pavlov noticed that his dogs began to salivate in the presence of the technician who normally fed them, rather than simply salivating in the presence of the food. If a buzzer or metronome was sounded before the food was given, the dog would later come to associate the sound with the presentation of the food and salivate upon the presentation of the sound stimulus alone. Tolochinov, whose own term for the phenomenon had been "reflex at a distance", communicated the results at the Congress of Natural Sciences in Helsinki in 1903. Later the same year Pavlov more fully explained the findings, at the 14th International Medical Congress in Madrid, where he read a paper titled The Experimental Psychology and Psychopathology of Animals. As Pavlov's work became known in the West, particularly through the writings of John B. Watson and B. F. Skinner. The idea of "conditioning", as an automatic form of learning, became a key concept in the developing specialism of comparative psychology, and the general approach to psychology that underlay it, behaviorism. Pavlov's work with classical conditioning was of huge influence on how humans perceived themselves, their behavior and learning processes; his studies of classical conditioning continue to be central to modern behavior therapy. The Pavlov Institute of Physiology of the Russian Academy of Sciences was founded by Pavlov in 1925 and named after him following his death. British philosopher Bertrand Russell observed that "[w]hether Pavlov's methods can be made to cover the whole of human behaviour is open to question, but at any rate they cover a very large field and within this field they have shown how to apply scientific methods with quantitative exactitude". Pavlov's research on conditional reflexes greatly influenced not only science, but also popular culture. Pavlovian conditioning is a major theme in Aldous Huxley's dystopian novel, Brave New World (1932), and in Thomas Pynchon's Gravity's Rainbow (1973). It is popularly believed that Pavlov always signalled the occurrence of food by ringing a bell. However, his writings record the use of a wide variety of stimuli, including electric shocks, whistles, metronomes, tuning forks, and a range of visual stimuli, in addition to the ring of a bell. In 1994, A. Charles Catania cast doubt on whether Pavlov ever actually used a bell in his experiments. Littman tentatively attributed the popular imagery to Pavlov's contemporaries Vladimir Mikhailovich Bekhterev and John B. Watson. Roger K. Thomas, of the University of Georgia, however, said they had found "three additional references to Pavlov's use of a bell that strongly challenge Littman's argument". In reply, Littman suggested that Catania's recollection, that Pavlov did not use a bell in research, was "convincing ... and correct". In 1964, the psychologist Hans Eysenck reviewed Pavlov's "Lectures on Conditioned Reflexes" for The BMJ: Volume I – "Twenty-five Years of Objective Study of the Higher Nervous Activity of Animals", Volume II – "Conditioned Reflexes and Psychiatry". Personal life Pavlov married Seraphima Vasilievna Karchevskaya on 1 May 1881. Seraphima, called Sara for short, was born in 1855. They had met in 1878 or 1879 when she went to St. Petersburg to study at the Pedagogical Institute. In her later years, she suffered from ill health and died in 1947. The first nine years of their marriage were marred by financial problems; Pavlov and his wife often had to stay with others to have a home and, for a time, the two lived apart so that they could find hospitality. Although their poverty caused despair, material welfare was a secondary consideration. Sara's first pregnancy ended in a miscarriage. When she conceived again, the couple took precautions, and she safely gave birth to their first child, a boy whom they named Mirchik; Sara became deeply depressed following Mirchik's sudden death in childhood. Pavlov and his wife eventually had four more children: Vladimir, Victor, Vsevolod, and Vera. Their youngest son, Vsevolod, died of pancreatic cancer in 1935, only one year before his father. Pavlov was an atheist. Pavlov's follower E. M. Kreps asked him whether he was religious. Kreps writes that Pavlov smiled and replied: "Listen, good fellow, in regard to [claims of] my religiosity, my belief in God, my church attendance, there is no truth in it; it is sheer fantasy. I was a seminarian, and like the majority of seminarians, I became an unbeliever, an atheist in my school years." See also Brainwashing Georgii Zeliony Orienting response Rostov State Medical University References Sources Further reading External links PBS article Institute of Experimental Medicine article on Pavlov Link to a list of Pavlov's dogs with some pictures Commentary on Pavlov's Conditioned Reflexes from 50 Psychology Classics Ivan Pavlov and his dogs Ivan P. Pavlov: Toward a Scientific Psychology and Psychiatry including the Nobel Lecture on 12 December 1904 Physiology of Digestion 1849 births 1936 deaths 19th-century psychologists 20th-century psychologists Animal trainers Atheists from the Russian Empire Educational theorists from the Russian Empire Ethologists Foreign associates of the National Academy of Sciences Foreign members of the Royal Society Full Members of the Russian Academy of Sciences (1917–1925) Full members of the Saint Petersburg Academy of Sciences Full Members of the USSR Academy of Sciences History of neuroscience Human subject research in Russia Lamarckism Members of the American Philosophical Society Members of the French Academy of Sciences Members of the Royal Irish Academy Members of the Royal Netherlands Academy of Arts and Sciences Nobel laureates from the Russian Empire Nobel laureates in Physiology or Medicine People from Ryazan Psychologists from Saint Petersburg 20th-century Russian psychologists Recipients of the Copley Medal Recipients of the Cothenius Medal Russian scientists Russian atheists Saint Petersburg State University alumni Scientists from Saint Petersburg Soviet physiologists Physiologists from the Russian Empire Soviet psychologists	Ivan Pavlov	[ "Biology" ]	4,319	[ "Behavior", "Ethologists", "Obsolete biology theories", "Lamarckism", "Non-Darwinian evolution", "Ethology", "Biology theories" ]
52,497	https://en.wikipedia.org/wiki/Nobel%20Prize%20in%20Physics	The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901, the others being the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and Nobel Prize in Physiology or Medicine. Physics is traditionally the first award presented in the Nobel Prize ceremony. The prize consists of a medal along with a diploma and a certificate for the monetary award. The front side of the medal displays the same profile of Alfred Nobel depicted on the medals for Physics, Chemistry, and Literature. The first Nobel Prize in Physics was awarded to German physicist Wilhelm Röntgen in recognition of the extraordinary services he rendered by the discovery of X-rays. This award is administered by the Nobel Foundation and is widely regarded as the most prestigious award that a scientist can receive in physics. It is presented in Stockholm at an annual ceremony on the 10th of December, the anniversary of Nobel's death. , a total of 226 individuals have been awarded the prize. Background Alfred Nobel, in his last will and testament, stated that his wealth should be used to create a series of prizes for those who confer the "greatest benefit on mankind" in the fields of physics, chemistry, peace, physiology or medicine, and literature. Though Nobel wrote several wills during his lifetime, the last one was written a year before he died and was signed at the Swedish-Norwegian Club in Paris on 27 November 1895. Nobel bequeathed 94% of his total assets, 31 million Swedish kronor (US$2.9 million, or €2.7 million in 2023), to establish and endow the five Nobel Prizes. Owing to the level of skepticism surrounding the will, it was not until 26 April 1897 that it was approved by the Storting (Norwegian Parliament). The executors of his will were Ragnar Sohlman and Rudolf Lilljequist, who formed the Nobel Foundation to take care of Nobel's fortune and organise the prizes. The members of the Norwegian Nobel Committee who were to award the Peace Prize were appointed soon after the will was approved. The other prize-awarding organisations followed: Karolinska Institutet on 7 June, the Swedish Academy on 9 June, and the Royal Swedish Academy of Sciences on 11 June. The Nobel Foundation then established guidelines for awarding the prizes. In 1900, the Nobel Foundation's newly created statutes were promulgated by King Oscar II. According to Nobel's will, the Royal Swedish Academy of Sciences would award the Prize in Physics. Nomination and selection A maximum of three Nobel laureates and two different works may be selected for the Nobel Prize in Physics. Compared with other Nobel Prizes, the nomination and selection process for the prize in physics is long and rigorous. This is a key reason why it has grown in importance over the years to become the most important prize in Physics. The Nobel laureates are selected by the Nobel Committee for Physics, a Nobel Committee that consists of five members elected by The Royal Swedish Academy of Sciences. During the first stage which begins in September, a group of about 3,000 selected university professors, Nobel Laureates in Physics and Chemistry, and others are sent confidential nomination forms. The completed forms must arrive at the Nobel Committee by 31 January of the following year. The nominees are scrutinized and discussed by experts and are narrowed to approximately fifteen names. The committee submits a report with recommendations on the final candidates to the Academy, where, in the Physics Class, it is further discussed. The Academy then makes the final selection of the Laureates in Physics by a majority vote. The names of the nominees are never publicly announced, and neither are they told that they have been considered for the Prize. Nomination records are sealed for fifty years. While posthumous nominations are not permitted, awards can be made if the individual died in the months between the decision of the committee (typically in October) and the ceremony in December. Prior to 1974, posthumous awards were permitted if the candidate had died after being nominated. The rules for the Nobel Prize in Physics require that the significance of achievements being recognized has been "tested by time". In practice, that means that the lag between the discovery and the award is typically on the order of 20 years and can be much longer. For example, half of the 1983 Nobel Prize in Physics was awarded to Subrahmanyan Chandrasekhar for his work on stellar structure and evolution that was done during the 1930s. As a downside of this tested-by-time rule, not all scientists live long enough for their work to be recognized. Some important scientific discoveries are never considered for a prize, as the discoverers have died by the time the impact of their work is appreciated. Prizes A Physics Nobel Prize laureate is awarded a gold medal, a diploma bearing a citation, and a sum of money. Medals The medal for the Nobel Prize in Physics is identical in design to the Nobel Prize in Chemistry medal. The reverse of the physics and chemistry medals depicts the Goddess of Nature in the form of Isis as she emerges from clouds holding a cornucopia. The Genius of Science holds the veil which covers Nature's "cold and austere face". It was designed by Erik Lindberg and is manufactured by Svenska Medalj in Eskilstuna. It is inscribed "Inventas vitam iuvat excoluisse per artes" ("It is beneficial to have improved (human) life through discovered arts"), an adaptation of "inventas aut qui vitam excoluere per artes" from line 663 of book 6 of the Aeneid by the Roman poet Virgil. A plate below the figures is inscribed with the name of the recipient. The text "REG. ACAD. SCIENT. SUEC." denoting the Royal Swedish Academy of Sciences is inscribed on the reverse. Diplomas Nobel laureates receive a diploma directly from the hands of the King of Sweden. Each diploma is uniquely designed by the prize-awarding institutions for the laureate who receives it. The diploma contains a picture with the name of the laureate and a citation explaining their accomplishments. Award money At the awards ceremony, the laureate is given a document indicating the award sum. The amount of the cash award may differ from year to year, based on the funding available from the Nobel Foundation. For example, in 2009 the total cash awarded was 10 million Swedish Kronor (SEK) (US$1.4 million), but in 2012 following the Great Recession, the amount was 8 million SEK, or US$1.1 million. If there are two laureates in a particular category, the award grant is divided equally between the recipients, but if there are three, the awarding committee may opt to divide the grant equally, or award half to one recipient and a quarter to each of the two others. Ceremony The committee and institution serving as the selection board for the prize typically announce the names of the laureates during the first week of October. The prize is then awarded at formal ceremonies held annually in Stockholm Concert Hall on 10 December, the anniversary of Nobel's death. The laureates receive a diploma, a medal, and a document confirming the prize amount. See also List of Nobel laureates in Physics Fundamental Physics Prize List of physics awards Sakurai Prize, presented by the American Physical Society Wolf Prize in Physics References Citations Sources Friedman, Robert Marc (2001). The Politics of Excellence: Behind the Nobel Prize in Science. New York & Stuttgart: VHPS (Times Books). , . Hillebrand, Claus D. (June 2002). "Nobel Century: A Biographical Analysis of Physics Laureates" . Interdisciplinary Science Reviews 27.2: 87–93. Schmidhuber, Jürgen (2010). Evolution of National Nobel Prize Shares in the 20th Century at arXiv:1009.2634v1 with graphics: National Physics Nobel Prize shares 1901–2009 by citizenship at the time of the award and by country of birth . Lemmel, Birgitta. "The Nobel Prize Medals and the Medal for the Prize in Economics" . nobelprize.org. Copyright © The Nobel Foundation 2006. (An article on the history of the design of the medals.) External links "All Nobel Laureates in Physics" at the Nobel Foundation. "The Nobel Prize Award Ceremonies and Banquets" at the Nobel Foundation. "The Nobel Prize in Physics" at the Nobel Foundation. Physics Physics awards Awards of the Royal Swedish Academy of Sciences	Nobel Prize in Physics	[ "Technology" ]	1,763	[ "Science and technology awards", "Physics awards" ]
52,502	https://en.wikipedia.org/wiki/Nobel%20Prize%20in%20Physiology%20or%20Medicine	The Nobel Prize in Physiology or Medicine () is awarded yearly by the Nobel Assembly at the Karolinska Institute for outstanding discoveries in physiology or medicine. The Nobel Prize is not a single prize, but five separate prizes that, according to Alfred Nobel's 1895 will, are awarded "to those who, during the preceding year, have conferred the greatest benefit to humankind". Nobel Prizes are awarded in the fields of Physics, Medicine or Physiology, Chemistry, Literature, and Peace. The Nobel Prize is presented annually on the anniversary of Alfred Nobel's death, 10 December. As of 2024, 115 Nobel Prizes in Physiology or Medicine have been awarded to 229 laureates, 216 men and 13 women. The first one was awarded in 1901 to the German physiologist, Emil von Behring, for his work on serum therapy and the development of a vaccine against diphtheria. The first woman to receive the Nobel Prize in Physiology or Medicine, Gerty Cori, received it in 1947 for her role in elucidating the metabolism of glucose, important in many aspects of medicine, including treatment of diabetes. The most recent Nobel prize was announced by the Karolinska Institute on 7 October 2024, and has been awarded to Americans Victor Ambros and Gary Ruvkun, for their discovery of microRNA and its role in post-transcriptional gene regulation. The prize consists of a medal along with a diploma and a certificate for the monetary award. The front side of the medal displays the same profile of Alfred Nobel depicted on the medals for Physics, Chemistry, and Literature; the reverse side is unique to this medal. Some awards have been controversial. This includes one to António Egas Moniz in 1949 for the prefrontal lobotomy, bestowed despite protests from the medical establishment. Other controversies resulted from disagreements over who was included in the award. The 1952 prize to Selman Waksman was litigated in court, and half the patent rights were awarded to his co-discoverer Albert Schatz who was not recognised by the prize. Nobel prizes cannot be awarded posthumously. Also, no more than three recipients can receive a Nobel Prize in Physiology or Medicine, a limitation that is sometimes discussed because of an increasing trend for larger teams to conduct important scientific projects. Background Alfred Nobel was born on 21 October 1833 in Stockholm, Sweden, into a family of engineers. He was a chemist, engineer and inventor who amassed a fortune during his lifetime, most of it from his 355 inventions, of which dynamite is the most famous. He was interested in experimental physiology and set up his own labs in France and Italy to conduct experiments in blood transfusions. Keeping abreast of scientific findings, he was generous in his donations to Ivan Pavlov's laboratory in Russia and was optimistic about the progress resulting from scientific discoveries made in laboratories. In 1888, Nobel was surprised to read his own obituary, titled "The merchant of death is dead", in a French newspaper. As it happened, it was Nobel's brother Ludvig who had died, but Nobel, unhappy with the content of the obituary and concerned that his legacy would reflect poorly on him, was inspired to change his will. In his last will, Nobel requested that his money be used to create a series of prizes for those who confer the "greatest benefit on mankind" in physics, chemistry, peace, physiology or medicine, and literature. Though Nobel wrote several wills during his lifetime, the last was written a little over a year before he died in 1896 at the age of 63. Because his will was contested, it was not approved by the Storting (Norwegian Parliament) until 26 April 1897. After Nobel's death, the Nobel Foundation was set up to manage the assets of the bequest. In 1900, the Nobel Foundation's newly created statutes were promulgated by Swedish King Oscar II. According to Nobel's will, the Karolinska Institute in Sweden, a medical school and research centre, is responsible for the Prize in Physiology or Medicine. Today, the prize is commonly referred to as the Nobel Prize in Medicine. Nomination and selection It was important to Nobel that the prize be awarded for a "discovery" and that it be of "greatest benefit on mankind". Per the provisions of the will, only select persons are eligible to nominate individuals for the award. These include members of academies around the world, professors of medicine in Sweden, Denmark, Norway, Iceland, and Finland, as well as professors of selected universities and research institutions in other countries. Past Nobel laureates may also nominate. Until 1977, all professors of Karolinska Institute together decided on the Nobel Prize in Physiology or Medicine. That year, changes in Swedish law forced the institute to make public any documents pertaining to the Nobel Prize, and it was considered necessary to establish a legally independent body for the Prize work. Therefore, the Nobel Assembly was constituted, consisting of 50 professors at Karolinska Institute. It elects the Nobel Committee with five members who evaluate the nominees, the Secretary who is in charge of the organisation, and each year ten adjunct members to assist in the evaluation of candidates. In 1968, a provision was added that no more than three persons may share a Nobel prize. True to its mandate, the committee has chosen researchers working in the basic sciences over those who have made applied science contributions. Harvey Cushing, a pioneering American neurosurgeon who identified Cushing's syndrome, was not awarded the prize, nor was Sigmund Freud, as his psychoanalysis lacks hypotheses that can be experimentally confirmed. The public expected Jonas Salk or Albert Sabin to receive the prize for their development of the polio vaccines, but instead the award went to John Enders, Thomas Weller, and Frederick Robbins whose basic discovery that the polio virus could reproduce in monkey cells in laboratory preparations made the vaccines possible. Through the 1930s, there were frequent prize laureates in classical physiology, but after that, the field began fragmenting into specialities. The last classical physiology laureates were John Eccles, Alan Hodgkin, and Andrew Huxley in 1963 for their findings regarding "unitary electrical events in the central and peripheral nervous system." Prizes A Medicine or Physiology Nobel Prize laureate earns a gold medal, a diploma bearing a citation, and a sum of money. These are awarded during the prize ceremony at the Stockholm Concert Hall. Medals The Physiology and Medicine medal has a portrait of Alfred Nobel in left profile on the obverse. The medal was designed by Erik Lindberg. The reverse of the medal depicts the 'Genius of Medicine holding an open book in her lap, collecting the water pouring out from a rock in order to quench a sick girl's thirst'. It is inscribed "" ("It is beneficial to have improved (human) life through discovered arts") an adaptation of "" from line 663 from book 6 of the Aeneid by the Roman poet Virgil. A plate below the figures is inscribed with the name of the recipient. The text "REG. UNIVERSITAS MED. CHIR. CAROL." denoting the Karolinska Institute is also inscribed on the reverse. Between 1902 and 2010 the Nobel Prize medals were struck by the Myntverket, the Swedish royal mint, located in Eskilstuna. In 2011 the medals were made by the Det Norske Myntverket in Kongsberg. The medals have been made by Svenska Medalj in Eskilstuna since 2012. Diplomas Nobel laureates receive a diploma directly from the King of Sweden. Each diploma is uniquely designed by the prize-awarding institutions for the laureate who receives it. In the case of the Nobel Prize in Physiology or Medicine, that is the Nobel Assembly at Karolinska Institute. Well-known artists and calligraphers from Sweden are commissioned to create it. The diploma contains a picture and text which states the name of the laureate and a citation as to why they received the prize. Award money At the awards ceremony, the laureate is given a document indicating the award sum. The amount of the cash award may differ from year to year, based on the funding available from the Nobel Foundation. For example, in 2009 the total cash awarded was 10 million SEK (US$1.4 million), but in 2012, the amount was 8 million Swedish Krona, or US$1.1 million. If there are two laureates in a particular category, the award grant is divided equally between the recipients, but if there are three, the awarding committee may opt to divide the grant equally, or award half to one recipient and a quarter to each of the two others. Ceremony and banquet The awards are bestowed at a gala ceremony followed by a banquet. The Nobel Banquet is an extravagant affair with the menu, planned months ahead of time, kept secret until the day of the event. The Nobel Foundation chooses the menu after tasting and testing selections submitted by selected chefs of international repute. Currently, it is a three-course dinner, although it was originally six courses in 1901. Each Nobel Prize laureate may bring up to 16 guests. Sweden's royal family attends, and typically the Prime Minister and other members of the government attend as well as representatives of the Nobel family. Laureates The first Nobel Prize in Physiology or Medicine was awarded in 1901 to the German physiologist Emil Adolf von Behring. Behring's discovery of serum therapy in the development of the diphtheria and tetanus vaccines put "in the hands of the physician a victorious weapon against illness and deaths". In 1902, the award went to Ronald Ross for his work on malaria, "by which he has shown how it enters the organism and thereby has laid the foundation for successful research on this disease and methods of combating it". He identified the mosquito as the transmitter of malaria, and worked tirelessly on measures to prevent malaria worldwide. The 1903 prize was awarded to Niels Ryberg Finsen, the first Faroese laureate, "in recognition of his contribution to the treatment of diseases, especially lupus vulgaris, with concentrated light radiation, whereby he has opened a new avenue for medical science". He died within a year after receiving the prize at the age of 43. Ivan Pavlov, whose work Nobel admired and supported, received the prize in 1904 for his work on the physiology of digestion. Subsequently, those selecting the recipients have exercised wide latitude in determining what falls under the umbrella of Physiology or Medicine. The awarding of the prize in 1973 to Nikolaas Tinbergen, Konrad Lorenz, and Karl von Frisch for their observations of animal behavioural patterns could be considered a prize in the behavioural sciences rather than medicine or physiology. Tinbergen expressed surprise in his Nobel Prize acceptance speech at "the unconventional decision of the Nobel Foundation to award this year's prize 'for Physiology or Medicine' to three men who had until recently been regarded as 'mere animal watchers'". Laureates have been awarded the Nobel Prize in a wide range of fields that relate to physiology or medicine. , eight Prizes have been awarded for contributions in the field of signal transduction through G proteins and second messengers. 13 have been awarded for contributions in the field of neurobiology and 13 have been awarded for contributions in Intermediary metabolism. The 100 Nobel Prizes in Physiology or Medicine have been awarded to 195 individuals through 2009. Thirteen women have received the prize: Gerty Cori (1947), Rosalyn Yalow (1977), Barbara McClintock (1983), Rita Levi-Montalcini (1986), Gertrude B. Elion (1988), Christiane Nüsslein-Volhard (1995), Linda B. Buck (2004), Françoise Barré-Sinoussi (2008), Elizabeth H. Blackburn (2009), Carol W. Greider (2009), May-Britt Moser (2014), Tu Youyou (2015) and Katalin Karikó (2023). Only one woman, Barbara McClintock, has received an unshared prize in this category, for the discovery of genetic transposition. Mario Capecchi, Martin Evans, Lucas Pu, and Oliver Smithies were awarded the prize in 2007 for the discovery of a gene targeting procedure (a type of genetic recombination) for introducing homologous recombination in mice, employing embryonic stem cells through the development of the knockout mouse. In 2009, the Nobel Prize was awarded to Elizabeth Blackburn, Carol W. Greider and Jack W. Szostak of the United States for discovering the process by which chromosomes are protected by telomeres (regions of repetitive DNA at the ends of chromosomes) and the enzyme telomerase. Rita Levi-Montalcini, an Italian neurologist, who together with colleague Stanley Cohen, received the 1986 Nobel Prize in Physiology or Medicine for their discovery of Nerve growth factor (NGF), was the first Nobel laureate to reach the 100th birthday. There have been 38 times when the Nobel Prize in Physiology or Medicine was awarded to a single individual, 31 times when it was shared by two, and 33 times there were three laureates (the maximum allowed). Time factor and death Because of the length of time that may pass before the significance of a discovery becomes apparent, some prizes are awarded many years after the initial discovery. Barbara McClintock made her discoveries in 1944, before the structure of the DNA molecule was known; she was not awarded the prize until 1983. Similarly, in 1916 Peyton Rous discovered the role of tumor viruses in chickens, but was not awarded the prize until 50 years later, in 1966. Nobel laureate Carol Greider's research leading to the prize was conducted over 20 years before. She noted that the passage of time is an advantage in the medical sciences, as it may take many years for the significance of a discovery to become apparent. In 2011, Canadian immunologist Ralph M. Steinman was awarded the prize; however, unbeknownst to the committee, he had died three days before the announcement. The committee decided that since the prize was awarded "in good faith," it would be allowed to stand. Controversial inclusions and exclusions Some of the awards have been controversial. The person who was deserving of the 1923 prize for the discovery of insulin as a central hormone for controlling diabetes (awarded only a year after its discovery) has been heatedly debated. It was shared between Frederick Banting and John Macleod; this infuriated Banting who regarded Macleod's involvement as minimal. Macleod was the department head at the University of Toronto but otherwise was not directly involved in the findings. Banting thought his laboratory partner Charles Best, who had shared in the laboratory work of discovery, should have shared the prize with him as well. In fairness, he decided to give half of his prize money to Best. Macleod on his part felt the biochemist James Collip, who joined the laboratory team later, deserved to be included in the award and shared his prize money with him. Some maintain that Nicolae Paulescu, a Romanian professor of physiology at the University of Medicine and Pharmacy in Bucharest, was the first to isolate insulin, in 1916, although his pancrein was an impure aqueous extract unfit for human treatment similar to the one used previously by Israel Kleiner. When Banting published the paper that brought him the Nobel, Paulescu already held a patent for his discovery (10 April 1922, patent no. 6254 (8322) "Pancreina şi procedeul fabricaţiei ei"/"Pancrein and the process of making it", from the Romanian Ministry of Industry and Trade). The Spanish neurophysiologist Fernando de Castro (1896–1967) was the first to describe arterial chemoreceptors and circumscribe them to the carotid body for the respiratory reflexes in 1926–1928. For many experts, this direct disciple of Santiago Ramón y Cajal deserved to share the Nobel Prize 1938 with the awarded Corneille Heymans, but at that time Spain was immersed in the Spanish Civil War and it seems that the Nobel Board even doubted if he was alive or not, being at the front since almost the beginning of the conflict. Heymans himself recognised the merits of De Castro for the Nobel Prize in different occasions, including a famous talk in Montevideo (Uruguay). In 1949, despite protests from the medical establishment, the Portuguese neurologist António Egas Moniz received the Physiology or Medicine Prize for his development of the prefrontal leucotomy, which he promoted by declaring the procedure's success just 10 days postoperative. Due largely to the publicity surrounding the award, it was prescribed without regard for modern medical ethics. Favourable results were reported by such publications as The New York Times. It is estimated that around 40,000 lobotomies were performed in the United States before the procedure's popularity faded. Rosemary Kennedy, the sister of John F. Kennedy, was subjected to the procedure by their father; it incapacitated her to the extent that she needed to be institutionalised for the rest of her life. The 1952 prize, awarded solely to Selman Waksman for his discovery of streptomycin, omitted the recognition some felt due to his co-discoverer Albert Schatz. There was litigation brought by Schatz against Waksman over the details and credit of the streptomycin discovery; Schatz was awarded a substantial settlement, and, together with Waksman, Schatz was to be officially recognised as a co-discoverer of streptomycin as concerned patent rights. He is not a Nobel Prize laureate. The 1962 Prize awarded to James D. Watson, Francis Crick, and Maurice Wilkins—for their work on DNA structure and properties—did not recognise contributing work from others, such as Alec Stokes and Herbert Wilson. In addition, Erwin Chargaff, Oswald Avery, and Rosalind Franklin (whose key DNA x-ray crystallography work was the most detailed yet least acknowledged among the three) contributed directly to the ability of Watson and Crick to solve the structure of the DNA molecule. Avery died in 1955, Franklin died in 1958 and posthumous nominations for the Nobel Prize are not permitted. Files of Nobel Prize nominations show Franklin was not nominated when she was alive. As a result of Watson's misrepresentations of Franklin and her role in the discovery of the double helix in his book The Double Helix, Franklin has come to be portrayed as a classic victim of sexism in science. Chargaff, for his part, was not quiet about his exclusion from the prize, bitterly writing to other scientists about his disillusionment regarding the field of molecular biology. The 2008 award went to Harald zur Hausen in recognition of his discovery that human papillomavirus (HPV) can cause cervical cancer, and to Françoise Barré-Sinoussi and Luc Montagnier for discovering the human immunodeficiency virus (HIV). Whether Robert Gallo or Luc Montagnier deserved more credit for the discovery of the virus that causes AIDS has been a matter of considerable controversy. As it was, Gallo was left out and not awarded a prize. Additionally, there was a scandal when it was learned that Harald zur Hausen was being investigated for having a financial interest in vaccines for the cervical cancer that HPV can cause. AstraZeneca, which had a stake in two lucrative HPV vaccines could benefit financially from the prize, had agreed to sponsor Nobel Media and Nobel Web. According to Times Online, two senior figures in the selection process that chose zur Hausen also had strong links with AstraZeneca. Limits on number of awardees The provision that restricts the maximum number of nominees to three for any one prize, introduced in 1968, has caused considerable controversy. From the 1950s onward, there has been an increasing trend to award the Nobel Prize in Physiology or Medicine to more than one person. There were 59 people who received the prize in the first 50 years of the last century, while 113 individuals received it between 1951 and 2000. This increase could be attributed to the rise of the international scientific community after World War II, resulting in more persons being responsible for the discovery, and nominated for, a particular prize. Also, current biomedical research is more often carried out by teams rather than by scientists working alone, making it unlikely that any one scientist, or even a few, is primarily responsible for a discovery; this has meant that a prize nomination that would have to include more than three contributors is automatically excluded from consideration. Also, deserving contributors may not be nominated at all because the restriction results in a cut-off point of three nominees per prize, leading to controversial exclusions. Years without awards There have been nine years in which the Nobel Prize in Physiology or Medicine was not awarded (1915–1918, 1921, 1925, 1940–1942). Most of these occurred during either World War I (1914–1918) or World War II (1939–1945). In 1939, Nazi Germany forbade Gerhard Domagk from accepting his prize. He was later able to receive the diploma and medal but not the money. See also List of medicine awards List of Nobel laureates in Physiology or Medicine References Citations Sources Further reading External links All Nobel Laureates in Physiology or Medicine at the Nobel Foundation. Official site of the Nobel Foundation. Graphics: National Medicine Nobel Prize shares 1901–2009 by citizenship at the time of the award and by country of birth. From J. Schmidhuber (2010), Evolution of National Nobel Prize Shares in the 20th Century at arXiv:1009.2634v1 Physiology or Medicine Karolinska Institute Medicine awards	Nobel Prize in Physiology or Medicine	[ "Technology" ]	4,462	[ "Science and technology awards", "Medicine awards" ]
52,510	https://en.wikipedia.org/wiki/Mores	Mores (, sometimes ; , plural form of singular , meaning "manner, custom, usage, or habit") are social norms that are widely observed within a particular society or culture. Mores determine what is considered morally acceptable or unacceptable within any given culture. A folkway is what is created through interaction and that process is what organizes interactions through routine, repetition, habit and consistency. William Graham Sumner (1840–1910), an early U.S. sociologist, introduced both the terms "mores" (1898) and "folkways" (1906) into modern sociology. Mores are strict in the sense that they determine the difference between right and wrong in a given society, and people may be punished for their immorality which is common place in many societies in the world, at times with disapproval or ostracizing. Examples of traditional customs and conventions that are mores include lying, cheating, causing harm, alcohol use, drug use, marriage beliefs, gossip, slander, jealousy, disgracing or disrespecting parents, refusal to attend a funeral, politically incorrect humor, sports cheating, vandalism, leaving trash, plagiarism, bribery, corruption, saving face, respecting your elders, religious prescriptions and fiduciary responsibility. Folkways are ways of thinking, acting and behaving in social groups which are agreed upon by the masses and are useful for the ordering of society. Folkways are spread through imitation, oral means or observation, and are meant to encompass the material, spiritual and verbal aspects of culture. Folkways meet the problems of social life; we feel security and order from their acceptance and application. Examples of folkways include: acceptable dress, manners, social etiquette, body language, posture, level of privacy, working hours and five day work week, acceptability of social drinking—abstaining or not from drinking during certain working hours, actions and behaviours in public places, school, university, business and religious institution, ceremonial situations, ritual, customary services and keeping personal space. Terminology The English word morality comes from the same Latin root "mōrēs", as does the English noun moral. However, mores do not, as is commonly supposed, necessarily carry connotations of morality. Rather, morality can be seen as a subset of mores, held to be of central importance in view of their content, and often formalized into some kind of moral code or even into customary law. Etymological derivations include More danico, More judaico, More veneto, Coitus more ferarum, and O tempora, o mores!. The Greek terms equivalent to Latin mores are ethos (ἔθος, ἦθος, 'character') or nomos (νόμος, 'law'). As with the relation of mores to morality, ethos is the basis of the term ethics, while nomos gives the suffix -onomy, as in astronomy. Anthropology The meaning of all these terms extend to all customs of proper behavior in a given society, both religious and profane, from more trivial conventional aspects of custom, etiquette or politeness—"folkways" enforced by gentle social pressure, but going beyond mere "folkways" or conventions in including moral codes and notions of justice—down to strict taboos, behavior that is unthinkable within the society in question, very commonly including incest and murder, but also the commitment of outrages specific to the individual society such as blasphemy. Such religious or sacral customs may vary. Some examples include funerary services, matrimonial services; circumcision and covering of the hair in Judaism, Christian Ten Commandments, New Commandment and the sacraments or for example baptism, and Protestant work ethic, Shahada, prayer, alms, the fast and the pilgrimage as well as modesty in Islam, and religious diet. While cultural universals are by definition part of the mores of every society (hence also called "empty universals"), the customary norms specific to a given society are a defining aspect of the cultural identity of an ethnicity or a nation. Coping with the differences between two sets of cultural conventions is a question of intercultural competence. Differences in the mores of various nations are at the root of ethnic stereotype, or in the case of reflection upon one's own mores, autostereotypes. The customary norms in a given society may include indigenous land rights, honour, filial piety, customary law and the customary international law that affects countries who may not have codified their customary norms. Land rights of indigenous peoples is under customary land tenure, its a system of arrangement in-line with customs and norms. This is the case in colonies. An example of a norm is an culture of honor exists in some societies, where the family is viewed as the main source of honor and the conduct of family members reflects upon their family honor. For instance some writers say in Rome to have an honorable stance, to be equals with someone, existed for those who are most similar to one another (family and friends) this could be due to the competing for public recognition and therefore for personal and public honor, over rhetoric, sport, war, wealth and virtue. To protrude, stand out, be recognized and demonstrate this "A Roman could win such a "competition" by pointing to past evidences of their honor" and "Or, a critic might be refuted by one's performance in a fresh showdown in which one's bona fides could be plainly demonstrated." Honor culture only can exist if the society has for males the shared code, a standard to uphold, guidelines and rules to follow, do not want to break those rules and how to interact successfully and to engage, this exists within a "closed" community of equals. Filial piety is ethics towards one's family, as Fung Yu-lan states "the ideological basis for traditional [Chinese] society" and according to Confucious repay a burden debt back to ones parents or caregiver but its also traditional in another sense so as to fulfill an obligation to ones own ancestors, also to modern scholars it suggests extends an attitude of respect to superiors also, who are deserving to have that respect. See also Culture-bound syndrome Enculturation Euthyphro dilemma, discussing the conflict of sacral and secular mores Habitus (sociology) Nihonjinron "Japanese mores" Piety Political and Moral Sociology: see Luc Boltanski and French Pragmatism Repugnancy costs Value (personal and cultural) References Conformity Consensus reality Deviance (sociology) Morality Social agreement Sociological terminology Folklore	Mores	[ "Biology" ]	1,387	[ "Deviance (sociology)", "Behavior", "Conformity", "Human behavior" ]
52,534	https://en.wikipedia.org/wiki/Axiom%20of%20empty%20set	In axiomatic set theory, the axiom of empty set, also called the axiom of null set and the axiom of existence, is a statement that asserts the existence of a set with no elements. It is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or without the axiom of choice. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: . Or, alternatively, . In words: There is a set such that no element is a member of it. Interpretation We can use the axiom of extensionality to show that there is only one empty set. Since it is unique we can name it. It is called the empty set (denoted by { } or ∅). The axiom, stated in natural language, is in essence: An empty set exists. This formula is a theorem and considered true in every version of set theory. The only controversy is over how it should be justified: by making it an axiom; by deriving it from a set-existence axiom (or logic) and the axiom of separation; by deriving it from the axiom of infinity; or some other method. In some formulations of ZF, the axiom of empty set is actually repeated in the axiom of infinity. However, there are other formulations of that axiom that do not presuppose the existence of an empty set. The ZF axioms can also be written using a constant symbol representing the empty set; then the axiom of infinity uses this symbol without requiring it to be empty, while the axiom of empty set is needed to state that it is in fact empty. Furthermore, one sometimes considers set theories in which there are no infinite sets, and then the axiom of empty set may still be required. However, any axiom of set theory or logic that implies the existence of any set will imply the existence of the empty set, if one has the axiom schema of separation. This is true, since the empty set is a subset of any set consisting of those elements that satisfy a contradictory formula. In many formulations of first-order predicate logic, the existence of at least one object is always guaranteed. If the axiomatization of set theory is formulated in such a logical system with the axiom schema of separation as axioms, and if the theory makes no distinction between sets and other kinds of objects (which holds for ZF, KP, and similar theories), then the existence of the empty set is a theorem. If separation is not postulated as an axiom schema, but derived as a theorem schema from the schema of replacement (as is sometimes done), the situation is more complicated, and depends on the exact formulation of the replacement schema. The formulation used in the axiom schema of replacement article only allows to construct the image F[a] when a is contained in the domain of the class function F; then the derivation of separation requires the axiom of empty set. On the other hand, the constraint of totality of F is often dropped from the replacement schema, in which case it implies the separation schema without using the axiom of empty set (or any other axiom for that matter). References Further reading Burgess, John, 2005. Fixing Frege. Princeton Univ. Press. Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. . Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. . Axioms of set theory de:Zermelo-Fraenkel-Mengenlehre#Die Axiome von ZF und ZFC	Axiom of empty set	[ "Mathematics" ]	848	[ "Axioms of set theory", "Mathematical axioms" ]
52,552	https://en.wikipedia.org/wiki/Axiom%20of%20power%20set	In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set the existence of a set , the power set of , consisting precisely of the subsets of . By the axiom of extensionality, the set is unique. The axiom of power set appears in most axiomatizations of set theory. It is generally considered uncontroversial, although constructive set theory prefers a weaker version to resolve concerns about predicativity. Formal statement The subset relation is not a primitive notion in formal set theory and is not used in the formal language of the Zermelo–Fraenkel axioms. Rather, the subset relation is defined in terms of set membership, . Given this, in the formal language of the Zermelo–Fraenkel axioms, the axiom of power set reads: where y is the power set of x, z is any element of y, w is any member of z. In English, this says: Given any set x, there is a set y such that, given any set z, this set z is a member of y if and only if every element of z is also an element of x. Consequences The power set axiom allows a simple definition of the Cartesian product of two sets and : Notice that and, for example, considering a model using the Kuratowski ordered pair, and thus the Cartesian product is a set since One may define the Cartesian product of any finite collection of sets recursively: The existence of the Cartesian product can be proved without using the power set axiom, as in the case of the Kripke–Platek set theory. Limitations The power set axiom does not specify what subsets of a set exist, only that there is a set containing all those that do. Not all conceivable subsets are guaranteed to exist. In particular, the power set of an infinite set would contain only "constructible sets" if the universe is the constructible universe but in other models of ZF set theory could contain sets that are not constructible. References Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. . Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. . Axioms of set theory de:Zermelo-Fraenkel-Mengenlehre#Die Axiome von ZF und ZFC	Axiom of power set	[ "Mathematics" ]	556	[ "Axioms of set theory", "Mathematical axioms" ]
52,553	https://en.wikipedia.org/wiki/Axiom%20of%20union	In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that for each set x there is a set y whose elements are precisely the elements of the elements of x. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: or in words: Given any set A, there is a set B such that, for any element c, c is a member of B if and only if there is a set D such that c is a member of D and D is a member of A. or, more simply: For any set , there is a set which consists of just the elements of the elements of that set . Relation to Pairing The axiom of union allows one to unpack a set of sets and thus create a flatter set. Together with the axiom of pairing, this implies that for any two sets, there is a set (called their union) that contains exactly the elements of the two sets. Relation to Replacement The axiom of replacement allows one to form many unions, such as the union of two sets. However, in its full generality, the axiom of union is independent from the rest of the ZFC-axioms: Replacement does not prove the existence of the union of a set of sets if the result contains an unbounded number of cardinalities. Together with the axiom schema of replacement, the axiom of union implies that one can form the union of a family of sets indexed by a set. Relation to Separation In the context of set theories which include the axiom of separation, the axiom of union is sometimes stated in a weaker form which only produces a superset of the union of a set. For example, Kunen states the axiom as which is equivalent to Compared to the axiom stated at the top of this section, this variation asserts only one direction of the implication, rather than both directions. Relation to Intersection There is no corresponding axiom of intersection. If is a nonempty set containing , it is possible to form the intersection using the axiom schema of specification as , so no separate axiom of intersection is necessary. (If A is the empty set, then trying to form the intersection of A as {c: for all D in A, c is in D} is not permitted by the axioms. Moreover, if such a set existed, then it would contain every set in the "universe", but the notion of a universal set is antithetical to Zermelo–Fraenkel set theory.) References {{reflist\|refs= <ref name=Zermelo1908>Ernst Zermelo, 1908, "Untersuchungen über die Grundlagen der Mengenlehre I", Mathematische Annalen 65(2), pp. 261–281.English translation: Jean van Heijenoort, 1967, From Frege to Gödel: A Source Book in Mathematical Logic, pp. 199–215 </ref> }} Further reading Paul Halmos, Naive set theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded''. Springer. . Axioms of set theory de:Zermelo-Fraenkel-Mengenlehre#Die Axiome von ZF und ZFC	Axiom of union	[ "Mathematics" ]	750	[ "Axioms of set theory", "Mathematical axioms" ]
52,564	https://en.wikipedia.org/wiki/Partial%20differential%20equation	In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence and smoothness of solutions to the Navier–Stokes equations, named as one of the Millennium Prize Problems in 2000. Partial differential equations are ubiquitous in mathematically oriented scientific fields, such as physics and engineering. For instance, they are foundational in the modern scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics (Schrödinger equation, Pauli equation etc.). They also arise from many purely mathematical considerations, such as differential geometry and the calculus of variations; among other notable applications, they are the fundamental tool in the proof of the Poincaré conjecture from geometric topology. Partly due to this variety of sources, there is a wide spectrum of different types of partial differential equations, where the meaning of a solution depends on the context of the problem, and methods have been developed for dealing with many of the individual equations which arise. As such, it is usually acknowledged that there is no "universal theory" of partial differential equations, with specialist knowledge being somewhat divided between several essentially distinct subfields. Ordinary differential equations can be viewed as a subclass of partial differential equations, corresponding to functions of a single variable. Stochastic partial differential equations and nonlocal equations are, as of 2020, particularly widely studied extensions of the "PDE" notion. More classical topics, on which there is still much active research, include elliptic and parabolic partial differential equations, fluid mechanics, Boltzmann equations, and dispersive partial differential equations. Introduction A function of three variables is "harmonic" or "a solution of the Laplace equation" if it satisfies the condition Such functions were widely studied in the 19th century due to their relevance for classical mechanics, for example the equilibrium temperature distribution of a homogeneous solid is a harmonic function. If explicitly given a function, it is usually a matter of straightforward computation to check whether or not it is harmonic. For instance and are both harmonic while is not. It may be surprising that the two examples of harmonic functions are of such strikingly different form. This is a reflection of the fact that they are not, in any immediate way, special cases of a "general solution formula" of the Laplace equation. This is in striking contrast to the case of ordinary differential equations (ODEs) roughly similar to the Laplace equation, with the aim of many introductory textbooks being to find algorithms leading to general solution formulas. For the Laplace equation, as for a large number of partial differential equations, such solution formulas fail to exist. The nature of this failure can be seen more concretely in the case of the following PDE: for a function of two variables, consider the equation It can be directly checked that any function of the form , for any single-variable functions and whatsoever, will satisfy this condition. This is far beyond the choices available in ODE solution formulas, which typically allow the free choice of some numbers. In the study of PDEs, one generally has the free choice of functions. The nature of this choice varies from PDE to PDE. To understand it for any given equation, existence and uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness theorems for ODE can be somewhat opaque; the existence half is usually unnecessary, since one can directly check any proposed solution formula, while the uniqueness half is often only present in the background in order to ensure that a proposed solution formula is as general as possible. By contrast, for PDE, existence and uniqueness theorems are often the only means by which one can navigate through the plethora of different solutions at hand. For this reason, they are also fundamental when carrying out a purely numerical simulation, as one must have an understanding of what data is to be prescribed by the user and what is to be left to the computer to calculate. To discuss such existence and uniqueness theorems, it is necessary to be precise about the domain of the "unknown function". Otherwise, speaking only in terms such as "a function of two variables", it is impossible to meaningfully formulate the results. That is, the domain of the unknown function must be regarded as part of the structure of the PDE itself. The following provides two classic examples of such existence and uniqueness theorems. Even though the two PDE in question are so similar, there is a striking difference in behavior: for the first PDE, one has the free prescription of a single function, while for the second PDE, one has the free prescription of two functions. Let denote the unit-radius disk around the origin in the plane. For any continuous function on the unit circle, there is exactly one function on such that and whose restriction to the unit circle is given by . For any functions and on the real line , there is exactly one function on such that and with and for all values of . Even more phenomena are possible. For instance, the following PDE, arising naturally in the field of differential geometry, illustrates an example where there is a simple and completely explicit solution formula, but with the free choice of only three numbers and not even one function. If is a function on with then there are numbers , , and with . In contrast to the earlier examples, this PDE is nonlinear, owing to the square roots and the squares. A linear PDE is one such that, if it is homogeneous, the sum of any two solutions is also a solution, and any constant multiple of any solution is also a solution. Definition A partial differential equation is an equation that involves an unknown function of variables and (some of) its partial derivatives. That is, for the unknown function of variables belonging to the open subset of , the -order partial differential equation is defined as where and is the partial derivative operator. Notation When writing PDEs, it is common to denote partial derivatives using subscripts. For example: In the general situation that is a function of variables, then denotes the first partial derivative relative to the -th input, denotes the second partial derivative relative to the -th and -th inputs, and so on. The Greek letter denotes the Laplace operator; if is a function of variables, then In the physics literature, the Laplace operator is often denoted by ; in the mathematics literature, may also denote the Hessian matrix of . Classification Linear and nonlinear equations A PDE is called linear if it is linear in the unknown and its derivatives. For example, for a function of and , a second order linear PDE is of the form where and are functions of the independent variables and only. (Often the mixed-partial derivatives and will be equated, but this is not required for the discussion of linearity.) If the are constants (independent of and ) then the PDE is called linear with constant coefficients. If is zero everywhere then the linear PDE is homogeneous, otherwise it is inhomogeneous. (This is separate from asymptotic homogenization, which studies the effects of high-frequency oscillations in the coefficients upon solutions to PDEs.) Nearest to linear PDEs are semi-linear PDEs, where only the highest order derivatives appear as linear terms, with coefficients that are functions of the independent variables. The lower order derivatives and the unknown function may appear arbitrarily. For example, a general second order semi-linear PDE in two variables is In a quasilinear PDE the highest order derivatives likewise appear only as linear terms, but with coefficients possibly functions of the unknown and lower-order derivatives: Many of the fundamental PDEs in physics are quasilinear, such as the Einstein equations of general relativity and the Navier–Stokes equations describing fluid motion. A PDE without any linearity properties is called fully nonlinear, and possesses nonlinearities on one or more of the highest-order derivatives. An example is the Monge–Ampère equation, which arises in differential geometry. Second order equations The elliptic/parabolic/hyperbolic classification provides a guide to appropriate initial- and boundary conditions and to the smoothness of the solutions. Assuming , the general linear second-order PDE in two independent variables has the form where the coefficients , , ... may depend upon and . If over a region of the -plane, the PDE is second-order in that region. This form is analogous to the equation for a conic section: More precisely, replacing by , and likewise for other variables (formally this is done by a Fourier transform), converts a constant-coefficient PDE into a polynomial of the same degree, with the terms of the highest degree (a homogeneous polynomial, here a quadratic form) being most significant for the classification. Just as one classifies conic sections and quadratic forms into parabolic, hyperbolic, and elliptic based on the discriminant , the same can be done for a second-order PDE at a given point. However, the discriminant in a PDE is given by due to the convention of the term being rather than ; formally, the discriminant (of the associated quadratic form) is , with the factor of 4 dropped for simplicity. (elliptic partial differential equation): Solutions of elliptic PDEs are as smooth as the coefficients allow, within the interior of the region where the equation and solutions are defined. For example, solutions of Laplace's equation are analytic within the domain where they are defined, but solutions may assume boundary values that are not smooth. The motion of a fluid at subsonic speeds can be approximated with elliptic PDEs, and the Euler–Tricomi equation is elliptic where . By change of variables, the equation can always be expressed in the form: where x and y correspond to changed variables. This justifies Laplace equation as an example of this type. (parabolic partial differential equation): Equations that are parabolic at every point can be transformed into a form analogous to the heat equation by a change of independent variables. Solutions smooth out as the transformed time variable increases. The Euler–Tricomi equation has parabolic type on the line where . By change of variables, the equation can always be expressed in the form: where x correspond to changed variables. This justifies heat equation, which are of form , as an example of this type. (hyperbolic partial differential equation): hyperbolic equations retain any discontinuities of functions or derivatives in the initial data. An example is the wave equation. The motion of a fluid at supersonic speeds can be approximated with hyperbolic PDEs, and the Euler–Tricomi equation is hyperbolic where . By change of variables, the equation can always be expressed in the form: where x and y correspond to changed variables. This justifies wave equation as an example of this type. If there are independent variables , a general linear partial differential equation of second order has the form The classification depends upon the signature of the eigenvalues of the coefficient matrix . Elliptic: the eigenvalues are all positive or all negative. Parabolic: the eigenvalues are all positive or all negative, except one that is zero. Hyperbolic: there is only one negative eigenvalue and all the rest are positive, or there is only one positive eigenvalue and all the rest are negative. Ultrahyperbolic: there is more than one positive eigenvalue and more than one negative eigenvalue, and there are no zero eigenvalues. The theory of elliptic, parabolic, and hyperbolic equations have been studied for centuries, largely centered around or based upon the standard examples of the Laplace equation, the heat equation, and the wave equation. However, the classification only depends on linearity of the second-order terms and is therefore applicable to semi- and quasilinear PDEs as well. The basic types also extend to hybrids such as the Euler–Tricomi equation; varying from elliptic to hyperbolic for different regions of the domain, as well as higher-order PDEs, but such knowledge is more specialized. Systems of first-order equations and characteristic surfaces The classification of partial differential equations can be extended to systems of first-order equations, where the unknown is now a vector with components, and the coefficient matrices are by matrices for . The partial differential equation takes the form where the coefficient matrices and the vector may depend upon and . If a hypersurface is given in the implicit form where has a non-zero gradient, then is a characteristic surface for the operator at a given point if the characteristic form vanishes: The geometric interpretation of this condition is as follows: if data for are prescribed on the surface , then it may be possible to determine the normal derivative of on from the differential equation. If the data on and the differential equation determine the normal derivative of on , then is non-characteristic. If the data on and the differential equation do not determine the normal derivative of on , then the surface is characteristic, and the differential equation restricts the data on : the differential equation is internal to . A first-order system is elliptic if no surface is characteristic for : the values of on and the differential equation always determine the normal derivative of on . A first-order system is hyperbolic at a point if there is a spacelike surface with normal at that point. This means that, given any non-trivial vector orthogonal to , and a scalar multiplier , the equation has real roots . The system is strictly hyperbolic if these roots are always distinct. The geometrical interpretation of this condition is as follows: the characteristic form defines a cone (the normal cone) with homogeneous coordinates ζ. In the hyperbolic case, this cone has sheets, and the axis runs inside these sheets: it does not intersect any of them. But when displaced from the origin by η, this axis intersects every sheet. In the elliptic case, the normal cone has no real sheets. Analytical solutions Separation of variables Linear PDEs can be reduced to systems of ordinary differential equations by the important technique of separation of variables. This technique rests on a feature of solutions to differential equations: if one can find any solution that solves the equation and satisfies the boundary conditions, then it is the solution (this also applies to ODEs). We assume as an ansatz that the dependence of a solution on the parameters space and time can be written as a product of terms that each depend on a single parameter, and then see if this can be made to solve the problem. In the method of separation of variables, one reduces a PDE to a PDE in fewer variables, which is an ordinary differential equation if in one variable – these are in turn easier to solve. This is possible for simple PDEs, which are called separable partial differential equations, and the domain is generally a rectangle (a product of intervals). Separable PDEs correspond to diagonal matrices – thinking of "the value for fixed " as a coordinate, each coordinate can be understood separately. This generalizes to the method of characteristics, and is also used in integral transforms. Method of characteristics The characteristic surface in dimensional space is called a characteristic curve. In special cases, one can find characteristic curves on which the first-order PDE reduces to an ODE – changing coordinates in the domain to straighten these curves allows separation of variables, and is called the method of characteristics. More generally, applying the method to first-order PDEs in higher dimensions, one may find characteristic surfaces. Integral transform An integral transform may transform the PDE to a simpler one, in particular, a separable PDE. This corresponds to diagonalizing an operator. An important example of this is Fourier analysis, which diagonalizes the heat equation using the eigenbasis of sinusoidal waves. If the domain is finite or periodic, an infinite sum of solutions such as a Fourier series is appropriate, but an integral of solutions such as a Fourier integral is generally required for infinite domains. The solution for a point source for the heat equation given above is an example of the use of a Fourier integral. Change of variables Often a PDE can be reduced to a simpler form with a known solution by a suitable change of variables. For example, the Black–Scholes equation is reducible to the heat equation by the change of variables Fundamental solution Inhomogeneous equations can often be solved (for constant coefficient PDEs, always be solved) by finding the fundamental solution (the solution for a point source ), then taking the convolution with the boundary conditions to get the solution. This is analogous in signal processing to understanding a filter by its impulse response. Superposition principle The superposition principle applies to any linear system, including linear systems of PDEs. A common visualization of this concept is the interaction of two waves in phase being combined to result in a greater amplitude, for example . The same principle can be observed in PDEs where the solutions may be real or complex and additive. If and are solutions of linear PDE in some function space , then with any constants and are also a solution of that PDE in the same function space. Methods for non-linear equations There are no generally applicable analytical methods to solve nonlinear PDEs. Still, existence and uniqueness results (such as the Cauchy–Kowalevski theorem) are often possible, as are proofs of important qualitative and quantitative properties of solutions (getting these results is a major part of analysis). Nevertheless, some techniques can be used for several types of equations. The -principle is the most powerful method to solve underdetermined equations. The Riquier–Janet theory is an effective method for obtaining information about many analytic overdetermined systems. The method of characteristics can be used in some very special cases to solve nonlinear partial differential equations. In some cases, a PDE can be solved via perturbation analysis in which the solution is considered to be a correction to an equation with a known solution. Alternatives are numerical analysis techniques from simple finite difference schemes to the more mature multigrid and finite element methods. Many interesting problems in science and engineering are solved in this way using computers, sometimes high performance supercomputers. Lie group method From 1870 Sophus Lie's work put the theory of differential equations on a more satisfactory foundation. He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred, to a common source; and that ordinary differential equations which admit the same infinitesimal transformations present comparable difficulties of integration. He also emphasized the subject of transformations of contact. A general approach to solving PDEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions (Lie theory). Continuous group theory, Lie algebras and differential geometry are used to understand the structure of linear and nonlinear partial differential equations for generating integrable equations, to find its Lax pairs, recursion operators, Bäcklund transform and finally finding exact analytic solutions to the PDE. Symmetry methods have been recognized to study differential equations arising in mathematics, physics, engineering, and many other disciplines. Semi-analytical methods The Adomian decomposition method, the Lyapunov artificial small parameter method, and his homotopy perturbation method are all special cases of the more general homotopy analysis method. These are series expansion methods, and except for the Lyapunov method, are independent of small physical parameters as compared to the well known perturbation theory, thus giving these methods greater flexibility and solution generality. Numerical solutions The three most widely used numerical methods to solve PDEs are the finite element method (FEM), finite volume methods (FVM) and finite difference methods (FDM), as well other kind of methods called meshfree methods, which were made to solve problems where the aforementioned methods are limited. The FEM has a prominent position among these methods and especially its exceptionally efficient higher-order version hp-FEM. Other hybrid versions of FEM and Meshfree methods include the generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree finite element method, discontinuous Galerkin finite element method (DGFEM), element-free Galerkin method (EFGM), interpolating element-free Galerkin method (IEFGM), etc. Finite element method The finite element method (FEM) (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge–Kutta, etc. Finite difference method Finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. Finite volume method Similar to the finite difference method or finite element method, values are calculated at discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, surface integrals in a partial differential equation that contain a divergence term are converted to volume integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods conserve mass by design. Neural networks Weak solutions Weak solutions are functions that satisfy the PDE, yet in other meanings than regular sense. The meaning for this term may differ with context, and one of the most commonly used definitions is based on the notion of distributions. An example for the definition of a weak solution is as follows: Consider the boundary-value problem given by: where denotes a second-order partial differential operator in divergence form. We say a is a weak solution if for every , which can be derived by a formal integral by parts. An example for a weak solution is as follows: is a weak solution satisfying in distributional sense, as formally, Theoretical Studies As a branch of pure mathematics, the theoretical studies of PDEs focus on the criteria for a solution to exist, the properties of a solution, and finding its formula is often secondary. Well-posedness Well-posedness refers to a common schematic package of information about a PDE. To say that a PDE is well-posed, one must have: an existence and uniqueness theorem, asserting that by the prescription of some freely chosen functions, one can single out one specific solution of the PDE by continuously changing the free choices, one continuously changes the corresponding solution This is, by the necessity of being applicable to several different PDE, somewhat vague. The requirement of "continuity", in particular, is ambiguous, since there are usually many inequivalent means by which it can be rigorously defined. It is, however, somewhat unusual to study a PDE without specifying a way in which it is well-posed. Regularity Regularity refers to the integrability and differentiability of weak solutions, which can often be represented by Sobolev spaces. This problem arise due to the difficulty in searching for classical solutions. Researchers often tend to find weak solutions at first and then find out whether it is smooth enough to be qualified as a classical solution. Results from functional analysis are often used in this field of study. See also Some common PDEs Acoustic wave equation Burgers' equation Continuity equation Heat equation Helmholtz equation Klein–Gordon equation Jacobi equation Lagrange equation Laplace's equation Maxwell's equations Navier-Stokes equation Poisson's equation Reaction–diffusion system Schrödinger equation Wave equation Types of boundary conditions Dirichlet boundary condition Neumann boundary condition Robin boundary condition Cauchy problem Various topics Jet bundle Laplace transform applied to differential equations List of dynamical systems and differential equations topics Matrix differential equation Numerical partial differential equations Partial differential algebraic equation Recurrence relation Stochastic processes and boundary value problems Notes References . . . . . . . . . . . . . . . . Further reading Nirenberg, Louis (1994). "Partial differential equations in the first half of the century." Development of mathematics 1900–1950 (Luxembourg, 1992), 479–515, Birkhäuser, Basel. External links Partial Differential Equations: Exact Solutions at EqWorld: The World of Mathematical Equations. Partial Differential Equations: Index at EqWorld: The World of Mathematical Equations. Partial Differential Equations: Methods at EqWorld: The World of Mathematical Equations. Example problems with solutions at exampleproblems.com Partial Differential Equations at mathworld.wolfram.com Partial Differential Equations with Mathematica Partial Differential Equations in Cleve Moler: Numerical Computing with MATLAB Partial Differential Equations at nag.com Multivariable calculus Mathematical physics Differential equations	Partial differential equation	[ "Physics", "Mathematics" ]	5,308	[ "Calculus", "Applied mathematics", "Theoretical physics", "Mathematical objects", "Differential equations", "Equations", "Multivariable calculus", "Mathematical physics" ]
52,565	https://en.wikipedia.org/wiki/Partial%20derivative	In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function with respect to the variable is variously denoted by It can be thought of as the rate of change of the function in the -direction. Sometimes, for the partial derivative of with respect to is denoted as Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences. The modern partial derivative notation was created by Adrien-Marie Legendre (1786), although he later abandoned it; Carl Gustav Jacob Jacobi reintroduced the symbol in 1841. Definition Like ordinary derivatives, the partial derivative is defined as a limit. Let be an open subset of and a function. The partial derivative of at the point with respect to the -th variable is defined as Where is the unit vector of -th variable . Even if all partial derivatives exist at a given point , the function need not be continuous there. However, if all partial derivatives exist in a neighborhood of and are continuous there, then is totally differentiable in that neighborhood and the total derivative is continuous. In this case, it is said that is a function. This can be used to generalize for vector valued functions, by carefully using a componentwise argument. The partial derivative can be seen as another function defined on and can again be partially differentiated. If the direction of derivative is repeated, it is called a mixed partial derivative. If all mixed second order partial derivatives are continuous at a point (or on a set), is termed a function at that point (or on that set); in this case, the partial derivatives can be exchanged by Clairaut's theorem: Notation For the following examples, let be a function in , , and . First-order partial derivatives: Second-order partial derivatives: Second-order mixed derivatives: Higher-order partial and mixed derivatives: When dealing with functions of multiple variables, some of these variables may be related to each other, thus it may be necessary to specify explicitly which variables are being held constant to avoid ambiguity. In fields such as statistical mechanics, the partial derivative of with respect to , holding and constant, is often expressed as Conventionally, for clarity and simplicity of notation, the partial derivative function and the value of the function at a specific point are conflated by including the function arguments when the partial derivative symbol (Leibniz notation) is used. Thus, an expression like is used for the function, while might be used for the value of the function at the point However, this convention breaks down when we want to evaluate the partial derivative at a point like In such a case, evaluation of the function must be expressed in an unwieldy manner as or in order to use the Leibniz notation. Thus, in these cases, it may be preferable to use the Euler differential operator notation with as the partial derivative symbol with respect to the -th variable. For instance, one would write for the example described above, while the expression represents the partial derivative function with respect to the first variable. For higher order partial derivatives, the partial derivative (function) of with respect to the -th variable is denoted That is, so that the variables are listed in the order in which the derivatives are taken, and thus, in reverse order of how the composition of operators is usually notated. Of course, Clairaut's theorem implies that as long as comparatively mild regularity conditions on are satisfied. Gradient An important example of a function of several variables is the case of a scalar-valued function on a domain in Euclidean space (e.g., on or In this case has a partial derivative with respect to each variable . At the point , these partial derivatives define the vector This vector is called the gradient of at . If is differentiable at every point in some domain, then the gradient is a vector-valued function which takes the point to the vector . Consequently, the gradient produces a vector field. A common abuse of notation is to define the del operator () as follows in three-dimensional Euclidean space with unit vectors Or, more generally, for -dimensional Euclidean space with coordinates and unit vectors Directional derivative Example Suppose that is a function of more than one variable. For instance, The graph of this function defines a surface in Euclidean space. To every point on this surface, there are an infinite number of tangent lines. Partial differentiation is the act of choosing one of these lines and finding its slope. Usually, the lines of most interest are those that are parallel to the -plane, and those that are parallel to the -plane (which result from holding either or constant, respectively). To find the slope of the line tangent to the function at and parallel to the -plane, we treat as a constant. The graph and this plane are shown on the right. Below, we see how the function looks on the plane . By finding the derivative of the equation while assuming that is a constant, we find that the slope of at the point is: So at , by substitution, the slope is . Therefore, at the point . That is, the partial derivative of with respect to at is , as shown in the graph. The function can be reinterpreted as a family of functions of one variable indexed by the other variables: In other words, every value of defines a function, denoted , which is a function of one variable . That is, In this section the subscript notation denotes a function contingent on a fixed value of , and not a partial derivative. Once a value of is chosen, say , then determines a function which traces a curve on the -plane: In this expression, is a , not a , so is a function of only one real variable, that being . Consequently, the definition of the derivative for a function of one variable applies: The above procedure can be performed for any choice of . Assembling the derivatives together into a function gives a function which describes the variation of in the direction: This is the partial derivative of with respect to . Here '' is a rounded 'd' called the partial derivative symbol; to distinguish it from the letter 'd', '' is sometimes pronounced "partial". Higher order partial derivatives Second and higher order partial derivatives are defined analogously to the higher order derivatives of univariate functions. For the function the "own" second partial derivative with respect to is simply the partial derivative of the partial derivative (both with respect to ): The cross partial derivative with respect to and is obtained by taking the partial derivative of with respect to , and then taking the partial derivative of the result with respect to , to obtain Schwarz's theorem states that if the second derivatives are continuous, the expression for the cross partial derivative is unaffected by which variable the partial derivative is taken with respect to first and which is taken second. That is, or equivalently Own and cross partial derivatives appear in the Hessian matrix which is used in the second order conditions in optimization problems. The higher order partial derivatives can be obtained by successive differentiation Antiderivative analogue There is a concept for partial derivatives that is analogous to antiderivatives for regular derivatives. Given a partial derivative, it allows for the partial recovery of the original function. Consider the example of The so-called partial integral can be taken with respect to (treating as constant, in a similar manner to partial differentiation): Here, the constant of integration is no longer a constant, but instead a function of all the variables of the original function except . The reason for this is that all the other variables are treated as constant when taking the partial derivative, so any function which does not involve will disappear when taking the partial derivative, and we have to account for this when we take the antiderivative. The most general way to represent this is to have the constant represent an unknown function of all the other variables. Thus the set of functions where is any one-argument function, represents the entire set of functions in variables that could have produced the -partial derivative If all the partial derivatives of a function are known (for example, with the gradient), then the antiderivatives can be matched via the above process to reconstruct the original function up to a constant. Unlike in the single-variable case, however, not every set of functions can be the set of all (first) partial derivatives of a single function. In other words, not every vector field is conservative. Applications Geometry The volume of a cone depends on the cone's height and its radius according to the formula The partial derivative of with respect to is which represents the rate with which a cone's volume changes if its radius is varied and its height is kept constant. The partial derivative with respect to equals which represents the rate with which the volume changes if its height is varied and its radius is kept constant. By contrast, the total derivative of with respect to and are respectively The difference between the total and partial derivative is the elimination of indirect dependencies between variables in partial derivatives. If (for some arbitrary reason) the cone's proportions have to stay the same, and the height and radius are in a fixed ratio , This gives the total derivative with respect to , which simplifies to Similarly, the total derivative with respect to is The total derivative with respect to and of the volume intended as scalar function of these two variables is given by the gradient vector Optimization Partial derivatives appear in any calculus-based optimization problem with more than one choice variable. For example, in economics a firm may wish to maximize profit with respect to the choice of the quantities and of two different types of output. The first order conditions for this optimization are . Since both partial derivatives and will generally themselves be functions of both arguments and , these two first order conditions form a system of two equations in two unknowns. Thermodynamics, quantum mechanics and mathematical physics Partial derivatives appear in thermodynamic equations like Gibbs-Duhem equation, in quantum mechanics as in Schrödinger wave equation, as well as in other equations from mathematical physics. The variables being held constant in partial derivatives here can be ratios of simple variables like mole fractions in the following example involving the Gibbs energies in a ternary mixture system: Express mole fractions of a component as functions of other components' mole fraction and binary mole ratios: Differential quotients can be formed at constant ratios like those above: Ratios X, Y, Z of mole fractions can be written for ternary and multicomponent systems: which can be used for solving partial differential equations like: This equality can be rearranged to have differential quotient of mole fractions on one side. Image resizing Partial derivatives are key to target-aware image resizing algorithms. Widely known as seam carving, these algorithms require each pixel in an image to be assigned a numerical 'energy' to describe their dissimilarity against orthogonal adjacent pixels. The algorithm then progressively removes rows or columns with the lowest energy. The formula established to determine a pixel's energy (magnitude of gradient at a pixel) depends heavily on the constructs of partial derivatives. Economics Partial derivatives play a prominent role in economics, in which most functions describing economic behaviour posit that the behaviour depends on more than one variable. For example, a societal consumption function may describe the amount spent on consumer goods as depending on both income and wealth; the marginal propensity to consume is then the partial derivative of the consumption function with respect to income. See also d'Alembert operator Chain rule Curl (mathematics) Divergence Exterior derivative Iterated integral Jacobian matrix and determinant Laplace operator Multivariable calculus Symmetry of second derivatives Triple product rule, also known as the cyclic chain rule. Notes External links Partial Derivatives at MathWorld Multivariable calculus Differential operators	Partial derivative	[ "Mathematics" ]	2,478	[ "Multivariable calculus", "Mathematical analysis", "Differential operators", "Calculus" ]
52,599	https://en.wikipedia.org/wiki/Monoculture	In agriculture, monoculture is the practice of growing one crop species in a field at a time. Monocultures increase ease and efficiency in planting, managing, and harvesting crops short-term, often with the help of machinery. However, monocultures are more susceptible to diseases or pest outbreaks long-term due to localized reductions in biodiversity and nutrient depletion. Crop diversity can be added both in time, as with a crop rotation or sequence, or in space, with a polyculture or intercropping. Monocultures appear in contexts outside of agriculture and food production. Grass lawns are a common form of residential monocultures. Several monocultures, including single-species forest plantations, have become increasingly abundant throughout the tropics following market globalization, impacting local communities. Genetic monocultures refer to crops that have little to no genetic variation. This is achieved using cultivars, made through processes of propagation and selective breeding, and can make populations susceptible to disease. Agroecological practices, silvo-pastoral systems, and mixed-species plantations are common alternatives to monoculture that help preserve biodiversity while maintaining productivity. Agriculture Agricultural monocultures refer to the practice of planting one crop species in a field. Monoculture is widely used in intensive farming and in organic farming. In crop monocultures, each plant in a field has the same standardized planting, maintenance, and harvesting requirements resulting in greater yields and lower costs. When a crop is matched to its well-managed environment, a monoculture can produce higher yields than a polyculture. Modern practices such as monoculture planting and the use of synthesized fertilizers have reduced the amount of additional land needed to produce food, called land sparing. Note that the distinction between monoculture and polyculture is not the same as between monocropping and intercropping. The first two describe diversity in space, as does intercropping. Monocropping and crop rotation describe diversity over time. Environmental impacts Monocultures of perennials, such as African palm oil, sugarcane, tea and pines, can change soil chemistry leading to soil acidification, degradation, and soil-borne diseases, ultimately having a negative impact on agricultural productivity and sustainability. The use of unregulated irrigation practices on popular monocultures, such as soy, can also lead to erosion and water loss. As soil health declines, use of synthetic fertilizers on monocultural fields increases, often having negative implications on human health via chemical run-off. In addition to soil depletion, monocultures can cause significant reductions in biodiversity due to unavailability of resources, native species displacement, and loss of genetic variation. Following large-scale oil palm plantations in Latin America, research has revealed extensive declines in mammal, bird, amphibian, and pollinator diversity, particularly in Colombia and Brazil. Due to insufficient biodiversity and population balance, monocultures are associated with higher rates of disease and pest outbreaks. In response, pesticides are widely applied to agricultural fields, further harming insect and pollinator diversity and human health. Increasing rotations of crop monocultures or using alternatives agricultural practices can help mitigate the risk of disease and attack. Social impacts Environmental consequences of monocultural farming have notable social impacts, commonly concentrated to the reduction of small-scale farmers and pesticide-related health issues. Monoculture is contradictive to several primitive, more sustainable farming practices utilized by small-scale farmers. Following pest outbreaks, over 600 million liters of pesticides are sprayed annually, contaminating nearby small-scale farming and causing communal health decline. Research has revealed increased prevalence of pesticide-related disorders, diseases, and cancers affecting the human neurological, gastrointestinal, skin, and respiratory systems. Agro-extractivism Agro-extractivism is a form of extractivism in which foreign territorial, political, and economical dominance over agriculture is motivated by the large-scale production and exportation of agricultural commodities, often in the form of monocultures. Several monocultures in the Global South, such as sugar and coffee, were first planted in the 1800s following European colonization. These plantations used slave labor, setting a precedent for agriculture being a field dominated by foreign entities in the rest of Latin America and the Caribbean. This social framework has shaped the oppression of Black people and smaller-scale farmers in the face of present-day land acquisition for monocultural use. The large-scale establishment of monocultures in the tropics has led to hindrance of local small-scale farms and indigenous land rights in the forms of reduced food sovereignty, food security, land and water access, and hunting. Land privatization and pressure for monocultural expansion by larger companies takes different forms: silent evictions, violence, and reverse leasing arrangements. Introduction to global trade makes small-scale farmers vulnerable to international demand, prices, and variations in climate affecting crop production. Farmers who make contracts or take out loans with large corporations can face debt and loss of land if they fail to meet certain crop yields or profit. Monocultures are an aspect of agro-extractivism on account of high percentages of the produced crop being exported for processing and marketing by large transnational corporations, often in developed countries. For instance, following the North American Free Trade Agreement (NAFTA), agave production increased three-fold in Mexico from 1995 to 2019 due to foreign consumption, specifically by the United States. Pararguay sees similar demands with soy crops, exporting the majority of production without nutrients returning to native soil. More than 46 million hectares of soy has been planted across South America while over half a million hectares of land are being deforested annually to make land for cultivation. Some international companies relevant in the field of agro-extractivist monocultures are Syngenta and Bayer (biotech), Los Grobo, CRESUD, El Tejar, and Maggi (landowners), and Cargill, ADM, and Bunge (grain and seed providers). Forestry In forestry, monoculture refers to plantations of one species of tree. In many areas of the world, forest monocultures are planted as an efficient way to produce and harvest timber. Because timber harvest from monoculture forests is often an export-driven industry, these plantations can be a form of extractivism. Following deforestation, monoculture afforestation has become increasingly popular due to the necessity for ecosystem services, such as mitigating the effects of climate change via carbon sequestration and gas regulation. Eucalyptus, pines, and acacias are examples of popular monocultures being utilized in the tropics and the Global South following rainforest deforestation. Environmental impacts While forest monocultures are efficient ways of producing timber, studies show single-species forests reduce biodiversity, causing declines in forest productivity and native tree, animal, and insect populations over time. The loss of biodiversity in forest monocultures is associated with lower forest resistance to pathogens, attack by insects, and adverse environmental conditions. Social impacts Monoculture plantations have been shown to have substantial social impacts on local communities. Forest monocultures have motivated migrations across Latin America due to localized water cycle interference, declining soil health, and changes in resource availability. While industrial agriculture can increase employment opportunities, studies show forest plantations often have limited employment opportunities, with most workers coming from outside of the community. Profits made from monoculture plantations historically follow a "boom and bust" trend, temporarily benefitting the community in increased income, revenue, and quality of life until resources are exhausted, with profits rarely distributed back into the deforested land. Environmental changes caused by monoculture forests are particularly felt among indigenous communities given their reliance and connection to the land while additionally becoming subject to land privatization. These lands are frequently acquired through land grabbing and dispossession by large companies in global trade, ultimately reducing rural land, cutting off access to locals, and changing agricultural and community dynamics. Residential monoculture Lawn monoculture in the United States was historically influenced by English gardens and manor-house landscapes, but its inception into the American landscape is fairly recent. Aesthetics drove the evolution of the residential green areas, with turfgrass becoming a popular addition to many American homes. Turfgrass is a nonnative species and requires high levels of maintenance. At the local level, governments and organizations, such as Homeowner Associations, have pressured the maintenance of lawn aesthetics and influenced real estate value. Disagreements in residential maintenance of weeds and lawns have resulted in civil cases or direct aggression against neighbors. High levels of maintenance required for turfgrass created a growing demand for chemical management, i.e. pesticides, herbicides, insecticides. A 1999 study showed that in a sample of urban streams, at least one type of pesticide was found in 99% of the streams. A major risk associated with lawn pesticide use is the exposure to chemicals within the home through the air, clothing, and furniture, which can be more detrimental to children than to the average adult. Genetic monocultures While often referring to the production of the same crop species in a field (space), monoculture can also refer to the planting of a single cultivar across a larger regional area, such that there are numerous plants in the area with an identical genetic makeup to each other. When all plants in a region are genetically similar, a disease to which they have no resistance can destroy entire populations of crops. the wheat leaf rust fungus caused much concern internationally, having already severely affected wheat crops in Uganda and Kenya, and having started to spread in Asia as well. Given the very genetically similar strains of much of the world's wheat crops following the Green Revolution, the impacts of such diseases threaten agricultural production worldwide. Historic examples of genetic monocultures Great Famine of Ireland In Ireland, exclusive use of one variety of potato, the "lumper", led to the Great Famine of 1845–1849. Lumpers provided inexpensive food to feed the Irish masses. Potatoes were propagated vegetatively with little to no genetic variation. When Phytophthora infestans arrived in Ireland from the Americas in 1845, the lumper had no resistance to the disease, leading to the nearly complete failure of the potato crop across Ireland. Bananas Until the 1950s, the Gros Michel cultivar of banana represented almost all bananas consumed in the United States because of their taste, small seeds, and efficiency to produce. Their small seeds, while more appealing than the large ones in other Asian cultivars, were not suitable for planting, meaning all new banana plants had to be grown from the cut suckers of another plant. As a result of this asexual form of planting, all bananas grown had identical genetic makeups which gave them no traits for resistance to Fusarium wilt, a fungal disease that spread quickly throughout the Caribbean where they were being grown. By the beginning of the 1960s, growers had to switch to growing the Cavendish banana, a cultivar grown in a similar way. This cultivar is under similar disease stress since all the bananas are clones of each other and could easily succumb as the Gros Michel did. Cattle Genetic monoculture can also refer to a single breed of farm animal being raised in large-scale concentrated animal feeding operations (CAFOs). Many livestock production systems rely on just a small number of highly specialized breeds. Focusing heavily on a single trait (output) may come at the expense of other desirable traitssuch as fertility, resistance to disease, vigor, and mothering instincts. In the early 1990s, a few Holstein calves were observed to grow poorly and died in the first 6 months of life. They were all found to be homozygous for a mutation in the gene that caused bovine leukocyte adhesion deficiency. This mutation was found at a high frequency in Holstein populations worldwide. (15% among bulls in the US, 10% in Germany, and 16% in Japan.) Researchers studying the pedigrees of affected and carrier animals tracked the source of the mutation to a single bull that was widely used in livestock production. In 1990 there were approximately 4 million Holstein cattle in the US, making the affected population around 600,000 animals. Benefits of genetic diversity Increasing genetic diversity through the introduction of organisms with varying genes can make agricultural and livestock systems more sustainable. By utilizing crops with varying genetic traits for disease and pest resistance, chances of disease outbreak decrease due to the likelihood of neighboring plants having strain-resistant genes. This can aid in increasing crop productivity while decreasing pesticide usage. Alternatives to monoculture Alternatives to monoculture include the consultation of agroecology, silvo-pastoral systems, and mixed-species plantations. Agroecology Agroecology consults the entire food system, considering how agricultural inputs and outputs affect social, environmental, and economic systems. Despite the recent dominance of GMO monoculture crop rotations of soy, corn, and cotton across the deforested Amazon, many Afrodescendant-run farms in Brazil continue to use traditional practices of agroecology that have the capacity to sustain the local community, environment, and economy. Ecosystem-specific ecological damage done by monocultural practices and byproducts, including the use of biocides and soil degradation, can be irreparable. However, the increasing modern prevalence of regenerative farming reinstates crop rotation and natural nutrient cycling to repair biodiversity and improve soil productivity. Silvopasture Silvopasture is a traditional practice that incorporates the use of various trees and forage in pastures to increase land and livestock productivity. Incorporating other plants in pastures, such as tree legumes, has been shown to enhance pollinator activity, benefitting local biodiversity and food security. Silvopastoral systems provide greater pasture species richness and grazing feed, increasing economic and environmental outcomes on various size scales. Mixed-species plantations In several studies, well-managed mixed-species plantations have been shown to produce greater economic outcomes than monocultures with regard to timber sales. Mixed-species forests are also associated with greater carbon sequestration and biodiversity, presenting a possible mitigation tactic against the climate crisis and current global carbon levels. However, mixed-species plantations are less common under the misconception of being more expensive and harder to manage. See also Biodiversity Cash crop Crop diversity Crop rotation Genetically modified organism Intercropping Intensive crop farming Permaculture Polyculture References External links Monoculture and disease Modern Agriculture: Ecological impacts and the possibilities for truly sustainable farming Agricultural terminology Intensive farming	Monoculture	[ "Chemistry" ]	2,971	[ "Eutrophication", "Intensive farming" ]
52,636	https://en.wikipedia.org/wiki/Boiling	Boiling or ebullition is the rapid phase transition from liquid to gas or vapour; the reverse of boiling is condensation. Boiling occurs when a liquid is heated to its boiling point, so that the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. Boiling and evaporation are the two main forms of liquid vapourization. There are two main types of boiling: nucleate boiling where small bubbles of vapour form at discrete points, and critical heat flux boiling where the boiling surface is heated above a certain critical temperature and a film of vapour forms on the surface. Transition boiling is an intermediate, unstable form of boiling with elements of both types. The boiling point of water is 100 °C or 212 °F but is lower with the decreased atmospheric pressure found at higher altitudes. Boiling water is used as a method of making it potable by killing microbes and viruses that may be present. The sensitivity of different micro-organisms to heat varies, but if water is held at for one minute, most micro-organisms and viruses are inactivated. Ten minutes at a temperature of 70 °C (158 °F) is also sufficient to inactivate most bacteria. Boiling water is also used in several cooking methods including boiling, steaming, and poaching. Types Free convection The lowest heat flux seen in boiling is only sufficient to cause [natural convection], where the warmer fluid rises due to its slightly lower density. This condition occurs only when the superheat is very low, meaning that the hot surface near the fluid is nearly the same temperature as the boiling point. Nucleate Nucleate boiling is characterised by the growth of bubbles or pops on a heated surface (heterogeneous nucleation), which rises from discrete points on a surface, whose temperature is only slightly above the temperature of the liquid. In general, the number of nucleation sites is increased by an increasing surface temperature. An irregular surface of the boiling vessel (i.e., increased surface roughness) or additives to the fluid (i.e., surfactants and/or nanoparticles) facilitate nucleate boiling over a broader temperature range, while an exceptionally smooth surface, such as plastic, lends itself to superheating. Under these conditions, a heated liquid may show boiling delay and the temperature may go somewhat above the boiling point without boiling. Homogeneous nucleation, where the bubbles form from the surrounding liquid instead of on a surface, can occur if the liquid is warmer in its center, and cooler at the surfaces of the container. This can be done, for instance, in a microwave oven, which heats the water and not the container. Critical heat flux Critical heat flux (CHF) describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing localised overheating of the heating surface. As the boiling surface is heated above a critical temperature, a film of vapour forms on the surface. Since this vapour film is much less capable of carrying heat away from the surface, the temperature rises very rapidly beyond this point into the transition boiling regime. The point at which this occurs is dependent on the characteristics of boiling fluid and the heating surface in question. Transition Transition boiling may be defined as the unstable boiling, which occurs at surface temperatures between the maximum attainable in nucleate and the minimum attainable in film boiling. The formation of bubbles in a heated liquid is a complex physical process which often involves cavitation and acoustic effects, such as the broad-spectrum hiss one hears in a kettle not yet heated to the point where bubbles boil to the surface. Film If a surface heating the liquid is significantly hotter than the liquid then film boiling will occur, where a thin layer of vapour, which has low thermal conductivity, insulates the surface. This condition of a vapour film insulating the surface from the liquid characterises film boiling. Influence of geometry Pool boiling "Pool boiling" refers to boiling where there is no forced convective flow. Instead, the flow occurs due to density gradients. It can experience any of the regimes mentioned above. Flow boiling "Flow boiling" occurs when the boiling fluid circulates, typically through pipes. Its movement can be powered by pumps, such as in power plants, or by density gradients, such as in a thermosiphon or a heat pipe. Flows in flow boiling are often characterised by a void fraction parameter, which indicates the fraction of the volume in the system that is vapor. One can use this fraction and the densities to calculate the vapor quality, which refers to the mass fraction that is in the gas phase. Flow boiling can be very complex, with heavy influences of density, flow rates, and heat flux, as well as surface tension. The same system may have regions that are liquid, gas, and two-phase flow. Such two phase regimes can lead to some of the best heat transfer coefficients of any system. Confined boiling Confined boiling refers to boiling in confined geometries, typically characterized by a Bond number that compares the gap spacing to the capillary length. Confined boiling regimes begin to play a major role when Bo < 0.5. This boiling regime is dominated by "vapour stem bubbles" left behind after vapour departs. These bubbles act as seeds for vapor growth. Confined boiling typically has higher heat transfer coefficient but a lower CHF than pool boiling. CHF occurs when the vapor momentum force at the two-phase interface balances the combined surface tension and hydrostatic forces, leading to irreversible growth of the dry spot. Confined boiling is particularly promising for electronics cooling. Physics The boiling point of an element at a given pressure is a characteristic attribute of the element. This is also true for many simple compounds including water and simple alcohols. Once boiling has started and provided that boiling remains stable and the pressure is constant, the temperature of the boiling liquid remains constant. This attribute led to the adoption of boiling points as the definition of 100 °C. Distillation Mixtures of volatile liquids have a boiling point specific to that mixture producing vapour with a constant mix of components - the constant boiling mixture. This attribute allows mixtures of liquids to be separated or partly separated by boiling and is best known as a means of separating ethanol from water. Uses Refrigeration and air conditioning Most types of refrigeration and some type of air-conditioning work by compressing a gas so that it becomes liquid and then allowing it to boil. This adsorbs heat from the surroundings cooling the fridge or freezer or cooling the air entering a building. Typical liquids include propane, ammonia, carbon dioxide or nitrogen. For making water potable As a method of disinfecting water, bringing it to its boiling point at , is the oldest and most effective way since it does not affect the taste, it is effective despite contaminants or particles present in it, and is a single step process which eliminates most microbes responsible for causing intestine related diseases. The boiling point of water is at sea level and at normal barometric pressure. In places having a proper water purification system, it is recommended only as an emergency treatment method or for obtaining potable water in the wilderness or in rural areas, as it cannot remove chemical toxins or impurities. The elimination of micro-organisms by boiling follows first-order kinetics—at high temperatures, it is achieved in less time and at lower temperatures, in more time. The heat sensitivity of micro-organisms varies, at , Giardia species (which cause giardiasis) can take ten minutes for complete inactivation, most intestine affecting microbes and E. coli (gastroenteritis) take less than a minute; at boiling point, Vibrio cholerae (cholera) takes ten seconds and hepatitis A virus (causes the symptom of jaundice), one minute. Boiling does not ensure the elimination of all micro-organisms; the bacterial spores Clostridium can survive at but are not water-borne or intestine affecting. Thus for human health, complete sterilization of water is not required. The traditional advice of boiling water for ten minutes is mainly for additional safety, since microbes start getting eliminated at temperatures greater than and bringing it to its boiling point is also a useful indication that can be seen without the help of a thermometer, and by this time, the water is disinfected. Though the boiling point decreases with increasing altitude, it is not enough to affect the disinfecting process. In cooking Boiling is the method of cooking food in boiling water or other water-based liquids such as stock or milk. Simmering is gentle boiling, while in poaching the cooking liquid moves but scarcely bubbles. The boiling point of water is typically considered to be , especially at sea level. Pressure and a change in the composition of the liquid may alter the boiling point of the liquid. High elevation cooking generally takes longer since boiling point is a function of atmospheric pressure. At an elevation of about , water boils at approximately . Depending on the type of food and the elevation, the boiling water may not be hot enough to cook the food properly. Similarly, increasing the pressure as in a pressure cooker raises the temperature of the contents above the open air boiling point. Boil-in-the-bag Also known as "boil-in-bag", this involves heating or cooking ready-made foods sealed in a thick plastic bag. The bag containing the food, often frozen, is submerged in boiling water for a prescribed time. The resulting dishes can be prepared with greater convenience as no pots or pans are dirtied in the process. Such meals are available for camping as well as home dining. Contrast with evaporation At any given temperature, the molecules in a liquid have varying kinetic energies. Some high energy particles on the liquid surface may have enough energy to escape the intermolecular forces of attraction of the liquid and become a gas. This is called evaporation. Evaporation only happens on the surface while boiling happens throughout the liquid. When a liquid reaches its boiling point bubbles of gas form in it which rise into the surface and burst into the air. This process is called boiling. If the boiling liquid is heated more strongly the temperature does not rise but the liquid boils more quickly. This distinction is exclusive to the liquid-to-gas transition; any transition directly from solid to gas is always referred to as sublimation regardless of whether it is at its boiling point or not. See also Phase transition Phase diagram Enthalpy of vaporization Explosive boiling Recovery time (culinary) References Cooking techniques Phase transitions Heat transfer Gases	Boiling	[ "Physics", "Chemistry" ]	2,208	[ "Transport phenomena", "Matter", "Phase transitions", "Physical phenomena", "Heat transfer", "Phases of matter", "Critical phenomena", "Thermodynamics", "Statistical mechanics", "Gases" ]
52,642	https://en.wikipedia.org/wiki/Van%20de%20Graaff%20generator	A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage direct current (DC) electricity at low current levels. It was invented by American physicist Robert J. Van de Graaff in 1929. The potential difference achieved by modern Van de Graaff generators can be as much as 5 megavolts. A tabletop version can produce on the order of 100 kV and can store enough energy to produce visible electric sparks. Small Van de Graaff machines are produced for entertainment, and for physics education to teach electrostatics; larger ones are displayed in some science museums. The Van de Graaff generator was originally developed as a particle accelerator for physics research, as its high potential can be used to accelerate subatomic particles to great speeds in an evacuated tube. It was the most powerful type of accelerator until the cyclotron was developed in the early 1930s. Van de Graaff generators are still used as accelerators to generate energetic particle and X-ray beams for nuclear research and nuclear medicine. The voltage produced by an open-air Van de Graaff machine is limited by arcing and corona discharge to about 5 MV. Most modern industrial machines are enclosed in a pressurized tank of insulating gas; these can achieve potentials as large as about 25 MV. History Background The concept of an electrostatic generator in which charge is mechanically transported in small amounts into the interior of a high-voltage electrode originated with the Kelvin water dropper, invented in 1867 by William Thomson (Lord Kelvin), in which charged drops of water fall into a bucket with the same polarity charge, adding to the charge. In a machine of this type, the gravitational force moves the drops against the opposing electrostatic field of the bucket. Kelvin himself first suggested using a belt to carry the charge instead of water. The first electrostatic machine that used an endless belt to transport charge was constructed in 1872 by Augusto Righi. It used an india rubber belt with wire rings along its length as charge carriers, which passed into a spherical metal electrode. The charge was applied to the belt from the grounded lower roller by electrostatic induction using a charged plate. John Gray also invented a belt machine about 1890. Another more complicated belt machine was invented in 1903 by Juan Burboa. A more immediate inspiration for Van de Graaff was a generator W. F. G. Swann was developing in the 1920s in which charge was transported to an electrode by falling metal balls, thus returning to the principle of the Kelvin water dropper. Initial development The Van de Graaff generator was developed, starting in 1929, by physicist Robert J. Van de Graaff at Princeton University, with help from colleague Nicholas Burke. The first model was demonstrated in October 1929. The first machine used an ordinary tin can, a small motor, and a silk ribbon bought at a five-and-dime store. After that, he went to the chairman of the physics department requesting $100 to make an improved version. He did get the money, with some difficulty. By 1931, he could report achieving 1.5 million volts, saying "The machine is simple, inexpensive, and portable. An ordinary lamp socket provides the only power needed." According to a patent application, it had two 60-cm-diameter charge-accumulation spheres mounted on borosilicate glass columns 180 cm high; the apparatus cost $90 in 1931. Van de Graaff applied for a second patent in December 1931, which was assigned to Massachusetts Institute of Technology in exchange for a share of net income; the patent was later granted. In 1933, Van de Graaff built a 40 ft (12 m) model at MIT's Round Hill facility, the use of which was donated by Colonel Edward H. R. Green. One consequence of the location of this generator in an aircraft hangar was the "pigeon effect": arcing from accumulated droppings on the outer surface of the spheres. Higher energy machines In 1937, the Westinghouse Electric company built a machine, the Westinghouse Atom Smasher capable of generating 5 MeV in Forest Hills, Pennsylvania. It marked the beginning of nuclear research for civilian applications. It was decommissioned in 1958 and was partially demolished in 2015. (The enclosure was laid on its side for safety reasons.) A more recent development is the tandem Van de Graaff accelerator, containing one or more Van de Graaff generators, in which negatively charged ions are accelerated through one potential difference before being stripped of two or more electrons, inside a high-voltage terminal, and accelerated again. An example of a three-stage operation has been built in Oxford Nuclear Laboratory in 1964 of a 10 MV single-ended "injector" and a 6 MV EN tandem. By the 1970s, as much as 14 MV could be achieved at the terminal of a tandem that used a tank of high-pressure sulfur hexafluoride (SF6) gas to prevent sparking by trapping electrons. This allowed the generation of heavy ion beams of several tens of MeV, sufficient to study light-ion direct nuclear reactions. The greatest potential sustained by a Van de Graaff accelerator is 25.5 MV, achieved by the tandem in the Holifield Radioactive Ion Beam Facility in Oak Ridge National Laboratory. A further development is the pelletron, where the rubber or fabric belt is replaced by a chain of short conductive rods connected by insulating links, and the air-ionizing electrodes are replaced by a grounded roller and inductive charging electrode. The chain can be operated at a much greater velocity than a belt, and both the voltage and currents attainable are much greater than with a conventional Van de Graaff generator. The 14 UD Heavy Ion Accelerator at the Australian National University houses a 15 MV pelletron. Its chains are more than 20 m long and can travel faster than . The Nuclear Structure Facility (NSF) at Daresbury Laboratory was proposed in the 1970s, commissioned in 1981, and opened for experiments in 1983. It consisted of a tandem Van de Graaff generator operating routinely at 20 MV, housed in a distinctive building 70 m high. During its lifetime, it accelerated 80 different ion beams for experimental use, ranging from protons to uranium. A particular feature was the ability to accelerate rare isotopic and radioactive beams. Perhaps the most important discovery made using the NSF was that of super-deformed nuclei. These nuclei, when formed from the fusion of lighter elements, rotate very rapidly. The pattern of gamma rays emitted as they slow down provided detailed information about the inner structure of the nucleus. Following financial cutbacks, the NSF closed in 1993. Description A simple Van de Graaff generator consists of a belt of rubber (or a similar flexible dielectric material) moving over two rollers of differing material, one of which is surrounded by a hollow metal sphere. A comb-shaped metal electrode with sharp points (2 and 7 in the diagram), is positioned near each roller. The upper comb (2) is connected to the sphere, and the lower one (7) to ground. When a motor is used to drive the belt, the triboelectric effect causes the transfer of electrons from the dissimilar materials of the belt and the two rollers. In the example shown, the rubber of the belt will become negatively charged while the acrylic glass of the upper roller will become positively charged. The belt carries away negative charge on its inner surface while the upper roller accumulates positive charge. Next, the strong electric field surrounding the positive upper roller (3) induces a very high electric field near the points of the nearby comb (2). At the points of the comb, the field becomes strong enough to ionize air molecules. The electrons from the air molecules are attracted to the outside of the belt, while the positive ions go to the comb. At the comb they are neutralized by electrons from the metal, thus leaving the comb and the attached outer shell (1) with fewer net electrons and a net positive charge. By Gauss's law (as illustrated in the Faraday ice pail experiment), the excess positive charge is accumulated on the outer surface of the outer shell, leaving no electric field inside the shell. Continuing to drive the belt causes further electrostatic induction, which can build up large amounts of charge on the shell. Charge will continue to accumulate until the rate of charge leaving the sphere (through leakage and corona discharge) equals the rate at which new charge is being carried into the sphere by the belt. Outside the terminal sphere, a high electric field results from the high voltage on the sphere, which would prevent the addition of further charge from the outside. However, since electrically charged conductors do not have any electric field inside, charges can be added continuously from the inside without needing to overcome the full potential of the outer shell. The larger the sphere and the farther it is from ground, the higher its peak potential. The sign of the charge (positive or negative) can be controlled by the selection of materials for the belt and rollers. Higher potentials on the sphere can also be achieved by using a voltage source to charge the belt directly, rather than relying solely on the triboelectric effect. A Van de Graaff generator terminal does not need to be sphere-shaped to work, and in fact, the optimum shape is a sphere with an inward curve around the hole where the belt enters. A rounded terminal minimizes the electric field around it, allowing greater potentials to be achieved without ionization of the air, or other dielectric gas, surrounding it. Since a Van de Graaff generator can supply the same small current at almost any level of electrical potential, it is an example of a nearly ideal current source. The maximal achievable potential is roughly equal to the sphere radius R multiplied by the electric field Emax at which corona discharges begin to form within the surrounding gas. For air at standard temperature and pressure (STP) the breakdown field is about . Therefore, a polished spherical electrode in diameter could be expected to develop a maximal voltage of about . This explains why Van de Graaff generators are often made with the largest possible diameter. Use as a particle accelerator The initial motivation for the development of the Van de Graaff generator was as a source of high voltage to accelerate particles for nuclear physics experiments. The high potential difference between the surface of the terminal and ground results in a corresponding electric field. When an ion source is placed near the surface of the sphere (typically within the sphere itself) the field will accelerate charged particles of the appropriate sign away from the sphere. By insulating the generator with pressurized gas, the breakdown voltage can be raised, increasing the maximum energy of accelerated particles. Tandem accelerators Particle-beam Van de Graaff accelerators are often used in a "tandem" configuration with the high potential terminal located at the center of the machine. Negatively charged ions are injected at one end, where they are accelerated by attractive force toward the terminal. When the particles reach the terminal, they are stripped of some electrons to make them positively charged, and are subsequently accelerated by repulsive forces away from the terminal. This configuration results in two accelerations for the cost of one Van de Graaff generator and has the added advantage of leaving the ion source instrumentation accessible near ground potential. Pelletron The pelletron is a style of tandem accelerator designed to overcome some of the disadvantages of using a belt to transfer charge to the high voltage terminal. In the pelletron, the belt is replaced with "pellets", metal spheres joined by insulating links into a chain. This chain of spheres serves the same function as the belt in a traditional Van de Graff accelerator – to convey charge to the high voltage terminal. The separate charged spheres and higher durability of the chain mean that higher voltages can be achieved at the high voltage terminal, and charge can be conveyed to the terminal more quickly. Entertainment and educational generators The largest air-insulated Van de Graaff generator in the world, built by Dr. Van de Graaff in the 1930s, is now displayed permanently at Boston's Museum of Science. With two conjoined aluminium spheres standing on columns tall, this generator can often obtain 2 MV (2 million volts). Shows using the Van de Graaff generator and several Tesla coils are conducted two to three times a day. Many science museums, such as the American Museum of Science and Energy, have small-scale Van de Graaff generators on display, and exploit their static-producing qualities to create "lightning" or make people's hair stand up. Van de Graaff generators are also used in schools and science shows. Comparison with other electrostatic generators Other electrostatic machines such as the Wimshurst machine or Bonetti machine work similarly to the Van De Graaff generator; charge is transported by moving plates, disks, or cylinders to a high voltage electrode. For these generators, however, corona discharge from exposed metal parts at high potentials and poorer insulation result in smaller voltages. In an electrostatic generator, the rate of charge transported (current) to the high-voltage electrode is very small. After the machine is started, the voltage on the terminal electrode increases until the leakage current from the electrode equals the rate of charge transport. Therefore, leakage from the terminal determines the maximum voltage attainable. In the Van de Graaff generator, the belt allows the transport of charge into the interior of a large hollow spherical electrode. This is the ideal shape to minimize leakage and corona discharge, so the Van de Graaff generator can produce the greatest voltage. This is why the Van de Graaff design has been used for all electrostatic particle accelerators. In general, the larger the diameter and the smoother the sphere is, the higher the voltage that can be achieved. Patents — "Electrostatic Generator" — "Apparatus For Reducing Electron Loading In Positive-Ion Accelerators" See also – Metalworking process used to fabricate thin metal spheres References External links How Van de Graaff Generators Work with how to build, HowStuffWorks Interactive Java tutorial – Van de Graaff Generator National High Magnetic Field Laboratory Tandem Van de Graaff Accelerator Western Michigan University Physics Dr. Van de Graaff's huge machine at Museum of Science Van de Graaff Generator Frequently Asked Questions, Science Hobbyist Illustration from Report on Van de Graaff Generator From "Progress Report on the M.I.T. High-Voltage Generator at Round Hill" Nikola Tesla, "". Scientific American, March, 1934. (.doc format) Paolo Brenni,The Van de Graaff Generator – An Electrostatic Machine for the 20th Century Bulletin of the Scientific Instrument Society No. 63 (1999) Charrier Jacques "Le générateur de Van de Graaff". Faculté des Sciences de Nantes. Hellborg, Ragnar, ed. Electrostatic Accelerators: Fundamentals and Applications [N.Y., N.Y.: Springer, 2005]. Available online at: https://books.google.com/books?id=tc6CEuIV1jEC&pg=PA51&lpg=PA51&dq=electrostatic+accelerator+book American Physical Society names ORNL's Holifield Facility historic physics site Accelerator physics American inventions Electrostatic generators 1929 introductions	Van de Graaff generator	[ "Physics" ]	3,187	[ "Applied and interdisciplinary physics", "Accelerator physics", "Experimental physics" ]
52,644	https://en.wikipedia.org/wiki/Cysteine	Cysteine (; symbol Cys or C) is a semiessential proteinogenic amino acid with the formula . The thiol side chain in cysteine enables the formation of disulfide bonds, and often participates in enzymatic reactions as a nucleophile. Cysteine is chiral, but both D and L-cysteine are found in nature. LCysteine is a protein monomer in all biota, and D-cysteine acts as a signaling molecule in mammalian nervous systems. Cysteine is named after its discovery in urine, which comes from the urinary bladder or cyst, from Greek κύστις kýstis, "bladder". The thiol is susceptible to oxidation to give the disulfide derivative cystine, which serves an important structural role in many proteins. In this case, the symbol Cyx is sometimes used. The deprotonated form can generally be described by the symbol Cym as well. When used as a food additive, cysteine has the E number E920. Cysteine is encoded by the codons UGU and UGC. Structure Like other amino acids (not as a residue of a protein), cysteine exists as a zwitterion. Cysteine has chirality in the older / notation based on homology to - and -glyceraldehyde. In the newer R/S system of designating chirality, based on the atomic numbers of atoms near the asymmetric carbon, cysteine (and selenocysteine) have R chirality, because of the presence of sulfur (or selenium) as a second neighbor to the asymmetric carbon atom. The remaining chiral amino acids, having lighter atoms in that position, have S chirality. Replacing sulfur with selenium gives selenocysteine. Dietary sources Cysteinyl is a residue in high-protein foods. Some foods considered rich in cysteine include poultry, eggs, beef, and whole grains. In high-protein diets, cysteine may be partially responsible for reduced blood pressure and stroke risk. Although classified as a nonessential amino acid, in rare cases, cysteine may be essential for infants, the elderly, and individuals with certain metabolic diseases or who suffer from malabsorption syndromes. Cysteine can usually be synthesized by the human body under normal physiological conditions if a sufficient quantity of methionine is available. Industrial sources The majority of -cysteine is obtained industrially by hydrolysis of animal materials, such as poultry feathers or hog hair. Despite widespread rumor, human hair is rarely a source material. Indeed, food additive or cosmetic product manufactures may not legally source from human hair in the European Union. Some animal-originating sources of -cysteine as a food additive contravene kosher, halal, vegan, or vegetarian diets. To avoid this problem, synthetic -cysteine, compliant with Jewish kosher and Muslim halal laws, is also available, albeit at a higher price. The typical synthetic route involves fermentation with an artificial E. coli strain. Alternatively, Evonik (formerly Degussa) introduced a route from substituted thiazolines. Pseudomonas thiazolinophilum hydrolyzes racemic 2amino-Δ2thiazoline-4carboxylic acid to cysteine. Biosynthesis In animals, biosynthesis begins with the amino acid serine. The sulfur is derived from methionine, which is converted to homocysteine through the intermediate S-adenosylmethionine. Cystathionine beta-synthase then combines homocysteine and serine to form the asymmetrical thioether cystathionine. The enzyme cystathionine gamma-lyase converts the cystathionine into cysteine and alpha-ketobutyrate. In plants and bacteria, cysteine biosynthesis also starts from serine, which is converted to O-acetylserine by the enzyme serine transacetylase. The enzyme cysteine synthase, using sulfide sources, converts this ester into cysteine, releasing acetate. Biological functions The cysteine sulfhydryl group is nucleophilic and easily oxidized. The reactivity is enhanced when the thiol is ionized, and cysteine residues in proteins have pKa values close to neutrality, so are often in their reactive thiolate form in the cell. Because of its high reactivity, the sulfhydryl group of cysteine has numerous biological functions. Precursor to the antioxidant glutathione Due to the ability of thiols to undergo redox reactions, cysteine and cysteinyl residues have antioxidant properties. Its antioxidant properties are typically expressed in the tripeptide glutathione, which occurs in humans and other organisms. The systemic availability of oral glutathione (GSH) is negligible; so it must be biosynthesized from its constituent amino acids, cysteine, glycine, and glutamic acid. While glutamic acid is usually sufficient because amino acid nitrogen is recycled through glutamate as an intermediary, dietary cysteine and glycine supplementation can improve synthesis of glutathione. Precursor to iron-sulfur clusters Cysteine is an important source of sulfide in human metabolism. The sulfide in iron-sulfur clusters and in nitrogenase is extracted from cysteine, which is converted to alanine in the process. Metal ion binding Beyond the iron-sulfur proteins, many other metal cofactors in enzymes are bound to the thiolate substituent of cysteinyl residues. Examples include zinc in zinc fingers and alcohol dehydrogenase, copper in the blue copper proteins, iron in cytochrome P450, and nickel in the [NiFe]-hydrogenases. The sulfhydryl group also has a high affinity for heavy metals, so that proteins containing cysteine, such as metallothionein, will bind metals such as mercury, lead, and cadmium tightly. Roles in protein structure In the translation of messenger RNA molecules to produce polypeptides, cysteine is coded for by the UGU and UGC codons. Cysteine has traditionally been considered to be a hydrophilic amino acid, based largely on the chemical parallel between its sulfhydryl group and the hydroxyl groups in the side chains of other polar amino acids. However, the cysteine side chain has been shown to stabilize hydrophobic interactions in micelles to a greater degree than the side chain in the nonpolar amino acid glycine and the polar amino acid serine. In a statistical analysis of the frequency with which amino acids appear in various proteins, cysteine residues were found to associate with hydrophobic regions of proteins. Their hydrophobic tendency was equivalent to that of known nonpolar amino acids such as methionine and tyrosine (tyrosine is polar aromatic but also hydrophobic), those of which were much greater than that of known polar amino acids such as serine and threonine. Hydrophobicity scales, which rank amino acids from most hydrophobic to most hydrophilic, consistently place cysteine towards the hydrophobic end of the spectrum, even when they are based on methods that are not influenced by the tendency of cysteines to form disulfide bonds in proteins. Therefore, cysteine is now often grouped among the hydrophobic amino acids, though it is sometimes also classified as slightly polar, or polar. Most cysteine residues are covalently bonded to other cysteine residues to form disulfide bonds, which play an important role in the folding and stability of some proteins, usually proteins secreted to the extracellular medium. Since most cellular compartments are reducing environments, disulfide bonds are generally unstable in the cytosol with some exceptions as noted below. Disulfide bonds in proteins are formed by oxidation of the sulfhydryl group of cysteine residues. The other sulfur-containing amino acid, methionine, cannot form disulfide bonds. More aggressive oxidants convert cysteine to the corresponding sulfinic acid and sulfonic acid. Cysteine residues play a valuable role by crosslinking proteins, which increases the rigidity of proteins and also functions to confer proteolytic resistance (since protein export is a costly process, minimizing its necessity is advantageous). Inside the cell, disulfide bridges between cysteine residues within a polypeptide support the protein's tertiary structure. Insulin is an example of a protein with cystine crosslinking, wherein two separate peptide chains are connected by a pair of disulfide bonds. Protein disulfide isomerases catalyze the proper formation of disulfide bonds; the cell transfers dehydroascorbic acid to the endoplasmic reticulum, which oxidizes the environment. In this environment, cysteines are, in general, oxidized to cystine and are no longer functional as a nucleophiles. Aside from its oxidation to cystine, cysteine participates in numerous post-translational modifications. The nucleophilic sulfhydryl group allows cysteine to conjugate to other groups, e.g., in prenylation. Ubiquitin ligases transfer ubiquitin to its pendant, proteins, and caspases, which engage in proteolysis in the apoptotic cycle. Inteins often function with the help of a catalytic cysteine. These roles are typically limited to the intracellular milieu, where the environment is reducing, and cysteine is not oxidized to cystine. Evolutionary role of cysteine Cysteine is considered a "newcomer" amino acid, being the 17th amino acid incorporated into the genetic code. Similar to other later-added amino acids such as methionine, tyrosine, and tryptophan, cysteine exhibits strong nucleophilic and redox-active properties. These properties contribute to the depletion of cysteine from respiratory chain complexes, such as Complexes I and IV, since reactive oxygen species (ROS) produced by the respiratory chain can react with the cysteine residues in these complexes, leading to dysfunctional proteins and potentially contributing to aging. The primary response of a protein to ROS is the oxidation of cysteine and the loss of free thiol groups, resulting in increased thiyl radicals and associated protein cross-linking. In contrast, another sulfur-containing, redox-active amino acid, methionine, does not exhibit these biochemical properties and its content is relatively upregulated in mitochondrially encoded proteins. Applications Cysteine, mainly the -enantiomer, is a precursor in the food, pharmaceutical, and personal-care industries. One of the largest applications is the production of flavors. For example, the reaction of cysteine with sugars in a Maillard reaction yields meat flavors. -Cysteine is also used as a processing aid for baking. In the field of personal care, cysteine is used for permanent-wave applications, predominantly in Asia. Again, the cysteine is used for breaking up the disulfide bonds in the hair's keratin. Cysteine is a very popular target for site-directed labeling experiments to investigate biomolecular structure and dynamics. Maleimides selectively attach to cysteine using a covalent Michael addition. Site-directed spin labeling for EPR or paramagnetic relaxation-enhanced NMR also uses cysteine extensively. Reducing toxic effects of alcohol Cysteine has been proposed as a preventive or antidote for some of the negative effects of alcohol, including liver damage and hangover. It counteracts the poisonous effects of acetaldehyde. It binds to acetaldehyde to form the low-toxicity heterocycle methylthioproline. In a rat study, test animals received an LD90 dose of acetaldehyde. Those that received cysteine had an 80% survival rate; when both cysteine and thiamine were administered, all animals survived. The control group had a 10% survival rate. In 2020 an article was published that suggests L-cysteine might also work in humans. N-Acetylcysteine N-Acetyl--cysteine is a derivative of cysteine wherein an acetyl group is attached to the nitrogen atom. This compound is sold as a dietary supplement, and used as an antidote in cases of acetaminophen overdose. Sheep Cysteine is required by sheep to produce wool. It is an essential amino acid that is taken in from their feed. As a consequence, during drought conditions, sheep produce less wool; however, transgenic sheep that can make their own cysteine have been developed. Chemical reactions Being multifunctional, cysteine undergoes a variety of reactions. Much attention has focused on protecting the sulfhydryl group. Methylation of cysteine gives S-methylcysteine. Treatment with formaldehyde gives the thiazolidine thioproline. Cysteine forms a variety of coordination complexes upon treatment with metal ions. Safety Relative to most other amino acids, cysteine is much more toxic. History In 1884 German chemist Eugen Baumann found that when cystine was treated with a reducing agent, cystine revealed itself to be a dimer of a monomer which he named "cysteïne". See also Amino acids Cysteine metabolism Cystinuria Saville reaction Sullivan reaction References Further reading External links Holly (2005). Cystinuria Clearinghouse Cysteine MS Spectrum International Kidney Stone Institute Alpha-Amino acids Proteinogenic amino acids Glucogenic amino acids Sulfur amino acids Thiols Food additives E-number additives Excitatory amino acids	Cysteine	[ "Chemistry" ]	2,973	[ "Organic compounds", "Thiols" ]
52,648	https://en.wikipedia.org/wiki/Camera	A camera is an instrument used to capture and store images and videos, either digitally via an electronic image sensor, or chemically via a light-sensitive material such as photographic film. As a pivotal technology in the fields of photography and videography, cameras have played a significant role in the progression of visual arts, media, entertainment, surveillance, and scientific research. The invention of the camera dates back to the 19th century and has since evolved with advancements in technology, leading to a vast array of types and models in the 21st century. Cameras function through a combination of multiple mechanical components and principles. These include exposure control, which regulates the amount of light reaching the sensor or film; the lens, which focuses the light; the viewfinder, which allows the user to preview the scene; and the film or sensor, which captures the image. Several types of cameras exist, each suited to specific uses and offering unique capabilities. Single-lens reflex (SLR) cameras provide real-time, exact imaging through the lens. Large-format and medium-format cameras offer higher image resolution and are often used in professional and artistic photography. Compact cameras, known for their portability and simplicity, are popular in consumer photography. Rangefinder cameras, with separate viewing and imaging systems, were historically widely used in photojournalism. Motion picture cameras are specialized for filming cinematic content, while digital cameras, which became prevalent in the late 20th and early 21st century, use electronic sensors to capture and store images. The rapid development of smartphone camera technology in the 21st century has blurred the lines between dedicated cameras and multifunctional devices, profoundly influencing how society creates, shares, and consumes visual content. History 19th century Beginning with the use of the camera obscura and transitioning to complex photographic cameras, the evolution of the technology in the 19th century was driven by pioneers like Thomas Wedgwood, Nicéphore Niépce, and Henry Fox Talbot. First using the camera obscura for chemical experiments, they ultimately created cameras specifically for chemical photography, and later reduced the camera's size and optimized lens configurations. The introduction of the daguerreotype process in 1839 facilitated commercial camera manufacturing, with various producers contributing diverse designs. As camera manufacturing became a specialized trade in the 1850s, designs and sizes were standardized. The latter half of the century witnessed the advent of dry plates and roll-film, prompting a shift towards smaller and more cost-effective cameras, epitomized by the original Kodak camera, first produced in 1888. This period also saw significant advancements in lens technology and the emergence of color photography, leading to a surge in camera ownership. 20th century The first half of the 20th century saw continued miniaturization and the integration of new manufacturing materials. After World War I, Germany took the lead in camera development, spearheading industry consolidation and producing precision-made cameras. The industry saw significant product launches such as the Leica camera and the Contax, which were enabled by advancements in film and lens designs. Additionally, there was a marked increase in accessibility to cinematography for amateurs with Eastman Kodak's production of the first 16-mm and 8-mm reversal safety films. The World War II era saw a focus on the development of specialized aerial reconnaissance and instrument-recording equipment, even as the overall pace of non-military camera innovation slowed. In the second half of the century, Japanese manufacturers in particular advanced camera technology. From the introduction of the affordable Ricohflex III TLR in 1952 to the first 35mm SLR with automatic exposure, the Olympus AutoEye in 1960, new designs and features continuously emerged. Electronics became integral to camera design in the 1970s, evident in models like Polaroid's SX-70 and Canon's AE-1. Transition to digital photography marked the late 20th century, culminating in digital camera sales surpassing film cameras in the United States by 2003. In contrast, the film camera industry in the UK, Western Europe, and the USA declined during this period, while manufacturing continued in the USSR, German Democratic Republic, and China, often mimicking Western designs. 21st century The 21st century witnessed the mass adoption of digital cameras and significant improvements in sensor technology. A major revolution came with the incorporation of cameras into smartphones, making photography a commonplace activity. The century also marked the rise of computational photography, using algorithms and AI to enhance image quality. Features like low-light and HDR photography, optical image stabilization, and depth-sensing became common in smartphone cameras. Mechanics Most cameras capture light from the visible spectrum, while specialized cameras capture other portions of the electromagnetic spectrum, such as infrared. All cameras use the same basic design: light enters an enclosed box through a converging or convex lens and an image is recorded on a light-sensitive medium. A shutter mechanism controls the length of time that light enters the camera. Most cameras also have a viewfinder, which shows the scene to be recorded, along with means to adjust various combinations of focus, aperture and shutter speed. Exposure control Aperture Light enters the camera through an aperture, an opening adjusted by overlapping plates called the aperture ring. Typically located in the lens, this opening can be widened or narrowed to alter the amount of light that strikes the film or sensor. The size of the aperture can be set manually, by rotating the lens or adjusting a dial or automatically based on readings from an internal light meter. As the aperture is adjusted, the opening expands and contracts in increments called f-stops. The smaller the f-stop, the more light is allowed to enter the lens, increasing the exposure. Typically, f-stops range from 1.4 to 32 in standard increments: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, and 32. The light entering the camera is halved with each increasing increment. The wider opening at lower f-stops narrows the range of focus so the background is blurry while the foreground is in focus. This depth of field increases as the aperture closes. A narrow aperture results in a high depth of field, meaning that objects at many different distances from the camera will appear to be in focus. What is acceptably in focus is determined by the circle of confusion, the photographic technique, the equipment in use and the degree of magnification expected of the final image. Shutter The shutter, along with the aperture, is one of two ways to control the amount of light entering the camera. The shutter determines the duration that the light-sensitive surface is exposed to light. The shutter opens, light enters the camera and exposes the film or sensor to light, and then the shutter closes. There are two types of mechanical shutters: the leaf-type shutter and the focal-plane shutter. The leaf-type uses a circular iris diaphragm maintained under spring tension inside or just behind the lens that rapidly opens and closes when the shutter is released. More commonly, a focal-plane shutter is used. This shutter operates close to the film plane and employs metal plates or cloth curtains with an opening that passes across the light-sensitive surface. The curtains or plates have an opening that is pulled across the film plane during exposure. The focal-plane shutter is typically used in single-lens reflex (SLR) cameras, since covering the film (rather than blocking the light passing through the lens) allows the photographer to view the image through the lens at all times, except during the exposure itself. Covering the film also facilitates removing the lens from a loaded camera, as many SLRs have interchangeable lenses. A digital camera may use a mechanical or electronic shutter, the latter of which is common in smartphone cameras. Electronic shutters either record data from the entire sensor simultaneously (a global shutter) or record the data line by line across the sensor (a rolling shutter). In movie cameras, a rotary shutter opens and closes in sync with the advancement of each frame of film. The duration for which the shutter is open is called the shutter speed or exposure time. Typical exposure times can range from one second to 1/1,000 of a second, though longer and shorter durations are not uncommon. In the early stages of photography, exposures were often several minutes long. These long exposure times often resulted in blurry images, as a single object is recorded in multiple places across a single image for the duration of the exposure. To prevent this, shorter exposure times can be used. Very short exposure times can capture fast-moving action and eliminate motion blur. However, shorter exposure times require more light to produce a properly exposed image, so shortening the exposure time is not always possible. Like aperture settings, exposure times increment in powers of two. The two settings determine the exposure value (EV), a measure of how much light is recorded during the exposure. There is a direct relationship between the exposure times and aperture settings so that if the exposure time is lengthened one step, but the aperture opening is also narrowed one step, then the amount of light that contacts the film or sensor is the same. Light meter In most modern cameras, the amount of light entering the camera is measured using a built-in light meter or exposure meter. Taken through the lens (called metering), these readings are taken using a panel of light-sensitive semiconductors. They are used to calculate optimal exposure settings. These settings are typically determined automatically as the reading is used by the camera's microprocessor. The reading from the light meter is incorporated with aperture settings, exposure times, and film or sensor sensitivity to calculate the optimal exposure. Light meters typically average the light in a scene to 18% middle gray. More advanced cameras are more nuanced in their metering—weighing the center of the frame more heavily (center-weighted metering), considering the differences in light across the image (matrix metering), or allowing the photographer to take a light reading at a specific point within the image (spot metering). Lens A camera lens is an assembly of multiple optical elements, typically made from high-quality glass. Its primary function is to focus light onto a camera's film or digital sensor, thereby producing an image. This process significantly influences image quality, the overall appearance of the photo, and which parts of the scene are brought into focus. A camera lens is constructed from a series of lens elements, small pieces of glass arranged to form an image accurately on the light-sensitive surface. Each element is designed to reduce optical aberrations, or distortions, such as chromatic aberration (a failure of the lens to focus all colors at the same point), vignetting (darkening of image corners), and distortion (bending or warping of the image). The degree of these distortions can vary depending on the subject of the photo. The focal length of the lens, measured in millimeters, plays a critical role as it determines how much of the scene the camera can capture and how large the objects appear. Wide-angle lenses provide a broad view of the scene, while telephoto lenses capture a narrower view but magnify the objects. The focal length also influences the ease of taking clear pictures handheld, with longer lengths making it more challenging to avoid blur from small camera movements. Two primary types of lenses include zoom and prime lenses. A zoom lens allows for changing its focal length within a certain range, providing the convenience of adjusting the scene capture without moving the camera or changing the lens. A prime lens, in contrast, has a fixed focal length. While less flexible, prime lenses often provide superior image quality, are typically lighter, and perform better in low light. Focus involves adjusting the lens elements to sharpen the image of the subject at various distances. The focus is adjusted through the focus ring on the lens, which moves the lens elements closer or further from the sensor. Autofocus is a feature included in many lenses, which uses a motor within the lens to adjust the focus quickly and precisely based on the lens's detection of contrast or phase differences. This feature can be enabled or disabled using switches on the lens body. Advanced lenses may include mechanical image stabilization systems that move lens elements or the image sensor itself to counteract camera shake, especially beneficial in low-light conditions or at slow shutter speeds. Lens hoods, filters, and caps are accessories used alongside a lens to enhance image quality, protect the lens, or achieve specific effects. Viewfinder The camera's viewfinder provides a real-time approximation of what will be captured by the sensor or film. It assists photographers in aligning, focusing, and adjusting the composition, lighting, and exposure of their shots, enhancing the accuracy of the final image. Viewfinders fall into two primary categories: optical and electronic. Optical viewfinders, commonly found in Single-Lens Reflex (SLR) cameras, use a system of mirrors or prisms to reflect light from the lens to the viewfinder, providing a clear, real-time view of the scene. Electronic viewfinders, typical in mirrorless cameras, project an electronic image onto a small display, offering a wider range of information such as live exposure previews and histograms, albeit at the cost of potential lag and higher battery consumption. Specialized viewfinder systems exist for specific applications, like subminiature cameras for spying or underwater photography. Parallax error, resulting from misalignment between the viewfinder and lens axes, can cause inaccurate representations of the subject's position. While negligible with distant subjects, this error becomes prominent with closer ones. Some viewfinders incorporate parallax-compensating devices to mitigate that issue. Film and sensor Image capture in a camera occurs when light strikes a light-sensitive surface: photographic film or a digital sensor. Housed within the camera body, the film or sensor records the light's pattern when the shutter is briefly opened to allow light to pass during the exposure. Loading film into a film camera is a manual process. The film, typically housed in a cartridge, is loaded into a designated slot in the camera. One end of the film strip, the film leader, is manually threaded onto a take-up spool. Once the back of the camera is closed, the film advance lever or knob is used to ensure the film is correctly placed. The photographer then winds the film, either manually or automatically depending on the camera, to position a blank portion of the film in the path of the light. Each time a photo is taken, the film advance mechanism moves the exposed film out of the way, bringing a new, unexposed section of film into position for the next shot. The film must be advanced after each shot to prevent double exposure — where the same section of film is exposed to light twice, resulting in overlapped images. Once all frames on the film roll have been exposed, the film is rewound back into the cartridge, ready to be removed from the camera for developing. In digital cameras, sensors typically comprise Charge-Coupled Devices (CCDs) or Complementary Metal-Oxide-Semiconductor (CMOS) chips, both of which convert incoming light into electrical charges to form digital images. CCD sensors, though power-intensive, are recognized for their excellent light sensitivity and image quality. Conversely, CMOS sensors offer individual pixel readouts, leading to less power consumption and faster frame rates, with their image quality having improved significantly over time. Digital cameras convert light into electronic data that can be directly processed and stored. The volume of data generated is dictated by the sensor's size and properties, necessitating storage media such as Compact Flash, Memory Sticks, and SD (Secure Digital) cards. Modern digital cameras typically feature a built-in monitor for immediate image review and adjustments. Digital images are also more readily handled and manipulated by computers, offering a significant advantage in terms of flexibility and post-processing potential over traditional film. Camera accessories Flash A flash provides a short burst of bright light during exposure and is a commonly used artificial light source in photography. Most modern flash systems use a battery-powered high-voltage discharge through a gas-filled tube to generate bright light for a very short time (1/1,000 of a second or less). Many flash units measure the light reflected from the flash to help determine the appropriate duration of the flash. When the flash is attached directly to the camera—typically in a slot at the top of the camera (the flash shoe or hot shoe) or through a cable—activating the shutter on the camera triggers the flash, and the camera's internal light meter can help determine the duration of the flash. Additional flash equipment can include a light diffuser, mount and stand, reflector, soft box, trigger and cord. Other accessories Accessories for cameras are mainly used for care, protection, special effects, and functions. Lens hood: used on the end of a lens to block the sun or other light source to prevent glare and lens flare (see also matte box). Lens cap: covers and protects the camera lens when not in use. Lens adapter: allows the use of lenses other than those for which the camera was designed. Filter: allows artificial colors or changes light density. Lens extension tube: allows close focus in macro photography. Care and protection: including camera case and cover, maintenance tools, and screen protector. Camera monitor: provides an off-camera view of the composition with a brighter and more colorful screen, and typically exposes more advanced tools such as framing guides, focus peaking, zebra stripes, waveform monitors (oftentimes as an "RGB parade"), vectorscopes and false color to highlight areas of the image critical to the photographer. Tripod: primarily used for keeping the camera steady while recording video, doing a long exposure, and time-lapse photography. Microscope adapter: used to connect a camera to a microscope to photograph what the microscope is examining. Cable release: used to remotely control the shutter using a remote shutter button that can be connected to the camera via a cable. It can be used to lock the shutter open for the desired period, and it is also commonly used to prevent the camera shake from pressing the built-in camera shutter button. Dew shield: prevents moisture build-up on the lens. UV filter: can protect the front element of a lens from scratches, cracks, smudges, dirt, dust, and moisture while keeping a minimum impact on image quality. Battery and sometimes a charger. Large format cameras use special equipment that includes a magnifier loupe, view finder, angle finder, and focusing rail/truck. Some professional SLRs can be provided with interchangeable finders for eye-level or waist-level focusing, focusing screens, eyecup, data backs, motor-drives for film transportation or external battery packs. Primary types Single-lens reflex (SLR) camera In photography, the single-lens reflex camera (SLR) is provided with a mirror to redirect light from the lens to the viewfinder prior to releasing the shutter for composing and focusing an image. When the shutter is released, the mirror swings up and away, allowing the exposure of the photographic medium, and instantly returns after the exposure is finished. No SLR camera before 1954 had this feature, although the mirror on some early SLR cameras was entirely operated by the force exerted on the shutter release and only returned when the finger pressure was released. The Asahiflex II, released by Japanese company Asahi (Pentax) in 1954, was the world's first SLR camera with an instant return mirror. In the single-lens reflex camera, the photographer sees the scene through the camera lens. This avoids the problem of parallax which occurs when the viewfinder or viewing lens is separated from the taking lens. Single-lens reflex cameras have been made in several formats including sheet film 5x7" and 4x5", roll film 220/120 taking 8,10, 12, or 16 photographs on a 120 roll, and twice that number of a 220 film. These correspond to 6x9, 6x7, 6x6, and 6x4.5 respectively (all dimensions in cm). Notable manufacturers of large format and roll film SLR cameras include Bronica, Graflex, Hasselblad, Seagull, Mamiya and Pentax. However, the most common format of SLR cameras has been 35 mm and subsequently the migration to digital SLR cameras, using almost identical sized bodies and sometimes using the same lens systems. Almost all SLR cameras use a front-surfaced mirror in the optical path to direct the light from the lens via a viewing screen and pentaprism to the eyepiece. At the time of exposure, the mirror is flipped up out of the light path before the shutter opens. Some early cameras experimented with other methods of providing through-the-lens viewing, including the use of a semi-transparent pellicle as in the Canon Pellix and others with a small periscope such as in the Corfield Periflex series. Large-format camera The large-format camera, taking sheet film, is a direct successor of the early plate cameras and remained in use for high-quality photography and technical, architectural, and industrial photography. There are three common types: the view camera, with its monorail and field camera variants, and the press camera. They have extensible bellows with the lens and shutter mounted on a lens plate at the front. Backs taking roll film and later digital backs are available in addition to the standard dark slide back. These cameras have a wide range of movements allowing very close control of focus and perspective. Composition and focusing are done on view cameras by viewing a ground-glass screen which is replaced by the film to make the exposure; they are suitable for static subjects only and are slow to use. Plate camera The earliest cameras produced in significant numbers were plate cameras, using sensitized glass plates. Light entered a lens mounted on a lens board which was separated from the plate by extendible bellows. There were simple box cameras for glass plates but also single-lens reflex cameras with interchangeable lenses and even for color photography (Autochrome Lumière). Many of these cameras had controls to raise, lower, and tilt the lens forwards or backward to control perspective. Focusing of these plate cameras was by the use of a ground glass screen at the point of focus. Because lens design only allowed rather small aperture lenses, the image on the ground glass screen was faint and most photographers had a dark cloth to cover their heads to allow focusing and composition to be carried out more quickly. When focus and composition were satisfactory, the ground glass screen was removed, and a sensitized plate was put in its place protected by a dark slide. To make the exposure, the dark decline was carefully slid out and the shutter opened, and then closed and the dark fall replaced. Glass plates were later replaced by sheet film in a dark slide for sheet film; adapter sleeves were made to allow sheet film to be used in plate holders. In addition to the ground glass, a simple optical viewfinder was often fitted. Medium-format camera Medium-format cameras have a film size between the large-format cameras and smaller 35 mm cameras. Typically these systems use 120 or 220 roll film. The most common image sizes are 6×4.5 cm, 6×6 cm and 6×7 cm; the older 6×9 cm is rarely used. The designs of this kind of camera show greater variation than their larger brethren, ranging from monorail systems through the classic Hasselblad model with separate backs, to smaller rangefinder cameras. There are even compact amateur cameras available in this format. Twin-lens reflex camera Twin-lens reflex cameras used a pair of nearly identical lenses: one to form the image and one as a viewfinder. The lenses were arranged with the viewing lens immediately above the taking lens. The viewing lens projects an image onto a viewing screen which can be seen from above. Some manufacturers such as Mamiya also provided a reflex head to attach to the viewing screen to allow the camera to be held to the eye when in use. The advantage of a TLR was that it could be easily focused using the viewing screen and that under most circumstances the view seen on the viewing screen was identical to that recorded on film. At close distances, however, parallax errors were encountered, and some cameras also included an indicator to show what part of the composition would be excluded. Some TLRs had interchangeable lenses, but as these had to be paired lenses, they were relatively heavy and did not provide the range of focal lengths that the SLR could support. Most TLRs used 120 or 220 films; some used the smaller 127 films. Compact cameras Instant camera After exposure, every photograph is taken through pinch rollers inside the instant camera. Thereby the developer paste contained in the paper 'sandwich' is distributed on the image. After a minute, the cover sheet just needs to be removed and one gets a single original positive image with a fixed format. With some systems, it was also possible to create an instant image negative, from which then could be made copies in the photo lab. The ultimate development was the SX-70 system of Polaroid, in which a row of ten shots – engine driven – could be made without having to remove any cover sheets from the picture. There were instant cameras for a variety of formats, as well as adapters for instant film use in medium- and large-format cameras. Subminiature camera Subminiature cameras were first produced in the twentieth century and use film significantly smaller than 35mm. The expensive 8×11mm Minox, the only type of camera produced by the company from 1937 to 1976, became very widely known and was often used for espionage (the Minox company later also produced larger cameras). Later inexpensive subminiatures were made for general use, some using rewound 16 mm cine film. Image quality with these small film sizes was limited. Folding camera The introduction of films enabled the existing designs for plate cameras to be made much smaller and for the baseplate to be hinged so that it could be folded up, compressing the bellows. These designs were very compact and small models were dubbed vest pocket cameras. One of the smallest and best-selling cameras was the Vest Pocket Kodak, sold in two generations between 1912 and 1934. Folding roll film cameras were preceded by folding plate cameras, more compact than other designs. Box camera Box cameras were introduced as budget-level cameras and had few if any controls. The original box Brownie models had a small reflex viewfinder mounted on the top of the camera and had no aperture or focusing controls and just a simple shutter. Later models such as the Brownie 127 had larger direct view optical viewfinders together with a curved film path to reduce the impact of deficiencies in the lens. Rangefinder camera As camera lens technology developed and wide aperture lenses became more common, rangefinder cameras were introduced to make focusing more precise. Early rangefinders had two separate viewfinder windows, one of which is linked to the focusing mechanisms and moved right or left as the focusing ring is turned. The two separate images are brought together on a ground glass viewing screen. When vertical lines in the object being photographed meet exactly in the combined image, the object is in focus. A normal composition viewfinder is also provided. Later the viewfinder and rangefinder were combined. Many rangefinder cameras had interchangeable lenses, each lens requiring its range- and viewfinder linkages. Rangefinder cameras were produced in half- and full-frame 35 mm and roll film (medium format). Motion picture cameras A movie camera or a video camera operates similarly to a still camera, except it records a series of static images in rapid succession, commonly at a rate of 24 frames per second. When the images are combined and displayed in order, the illusion of motion is achieved. Cameras that capture many images in sequence are known as movie cameras or as cine cameras in Europe; those designed for single images are still cameras. However, these categories overlap as still cameras are often used to capture moving images in special effects work and many modern cameras can quickly switch between still and motion recording modes. A ciné camera or movie camera takes a rapid sequence of photographs on an image sensor or strips of film. In contrast to a still camera, which captures a single snapshot at a time, the ciné camera takes a series of images, each called a frame, through the use of an intermittent mechanism. The frames are later played back in a ciné projector at a specific speed, called the frame rate (number of frames per second). While viewing, a person's visual system merge the separate pictures to create the illusion of motion. The first ciné camera was built around 1888 and by 1890 several types were being manufactured. The standard film size for ciné cameras was quickly established as 35mm film and this remained in use until the transition to digital cinematography. Other professional standard formats include 70 mm film and 16 mm film whilst amateur filmmakers used 9.5 mm film, 8 mm film, or Standard 8 and Super 8 before the move into digital format. The size and complexity of ciné cameras vary greatly depending on the uses required of the camera. Some professional equipment is very large and too heavy to be handheld whilst some amateur cameras were designed to be very small and light for single-handed operation. Professional video camera A professional video camera (often called a television camera even though the use has spread beyond television) is a high-end device for creating electronic moving images (as opposed to a movie camera, that earlier recorded the images on film). Originally developed for use in television studios, they are now also used for music videos, direct-to-video movies, corporate and educational videos, marriage videos, etc. These cameras earlier used vacuum tubes and later electronic image sensors. Camcorders A camcorder is an electronic device combining a video camera and a video recorder. Although marketing materials may use the colloquial term "camcorder", the name on the package and manual is often "video camera recorder". Most devices capable of recording video are camera phones and digital cameras primarily intended for still pictures; the term "camcorder" is used to describe a portable, self-contained device, with video capture and recording its primary function. Digital camera A digital camera (or digicam) is a camera that encodes digital images and videos and stores them for later reproduction. They typically use semiconductor image sensors. Most cameras sold today are digital, and they are incorporated into many devices ranging from mobile phones (called camera phones) to vehicles. Digital and film cameras share an optical system, typically using a lens of variable aperture to focus light onto an image pickup device. The aperture and shutter admit the correct amount of light to the imager, just as with film but the image pickup device is electronic rather than chemical. However, unlike film cameras, digital cameras can display images on a screen immediately after being captured or recorded, and store and delete images from memory. Most digital cameras can also record moving videos with sound. Some digital cameras can crop and stitch pictures & perform other elementary image editing. Consumers adopted digital cameras in the 1990s. Professional video cameras transitioned to digital around the 2000s–2010s. Finally, movie cameras transitioned to digital in the 2010s. The first camera using digital electronics to capture and store images was developed by Kodak engineer Steven Sasson in 1975. He used a charge-coupled device (CCD) provided by Fairchild Semiconductor, which provided only 0.01 megapixels to capture images. Sasson combined the CCD device with movie camera parts to create a digital camera that saved black and white images onto a cassette tape.The images were then read from the cassette and viewed on a TV monitor. Later, cassette tapes were replaced by flash memory. In 1986, Japanese company Nikon introduced an analog-recording electronic single-lens reflex camera, the Nikon SVC. The first full-frame digital SLR cameras were developed in Japan from around 2000 to 2002: the MZ-D by Pentax, the N Digital by Contax's Japanese R6D team, and the EOS-1Ds by Canon. Gradually in the 2000s, the full-frame DSLR became the dominant camera type for professional photography. On most digital cameras a display, often a liquid crystal display (LCD), permits the user to view the scene to be recorded and settings such as ISO speed, exposure, and shutter speed. Camera phone In 2000, Sharp introduced the world's first digital camera phone, the J-SH04 J-Phone, in Japan. By the mid-2000s, higher-end cell phones had an integrated digital camera, and by the beginning of the 2010s, almost all smartphones had an integrated digital camera. See also Camera matrix History of the camera List of camera types List of digital camera brands Footnotes References Further reading External links How cameras works at How stuff works. Photography equipment Optical devices	Camera	[ "Materials_science", "Technology", "Engineering" ]	6,761	[ "Glass engineering and science", "Recording devices", "Optical devices", "Cameras" ]
52,671	https://en.wikipedia.org/wiki/Psychosomatic%20medicine	Psychosomatic medicine is an interdisciplinary medical field exploring the relationships among social, psychological, behavioral factors on bodily processes and quality of life in humans and animals. The academic forebearer of the modern field of behavioral medicine and a part of the practice of consultation-liaison psychiatry, psychosomatic medicine integrates interdisciplinary evaluation and management involving diverse specialties including psychiatry, psychology, neurology, psychoanalysis, internal medicine, pediatrics, surgery, allergy, dermatology, and psychoneuroimmunology. Clinical situations where mental processes act as a major factor affecting medical outcomes are areas where psychosomatic medicine has competence. Psychosomatic disorders Some physical diseases are believed to have a mental component derived from stresses and strains of everyday living. This has been suggested, for example, of lower back pain and high blood pressure, which some researchers have suggested may be related to stresses in everyday life. The psychosomatic framework additionally sees mental and emotional states as capable of significantly influencing the course of any physical illness. Psychiatry traditionally distinguishes between psychosomatic disorders, disorders in which mental factors play a significant role in the development, expression, or resolution of a physical illness, and somatoform disorders, disorders in which mental factors are the sole cause of a physical illness. It is difficult to establish for certain whether an illness has a psychosomatic component. A psychosomatic component is often inferred when there are some aspects of the patient's presentation that are unaccounted for by biological factors, or some cases where there is no biological explanation at all. For instance, Helicobacter pylori causes 80% of peptic ulcers. However, most people living with Helicobacter pylori do not develop ulcers, and 20% of patients with ulcers have no H. pylori infection. Therefore, in these cases, psychological factors could still play some role. Similarly, in irritable bowel syndrome (IBS), there are abnormalities in the behavior of the gut. However, there are no actual structural changes in the gut, so stress and emotions might still play a role. The strongest perspective on psychosomatic disorders is that attempting to distinguish between purely physical and mixed psychosomatic disorders is obsolete as almost all physical illness have mental factors that determine their onset, presentation, maintenance, susceptibility to treatment, and resolution. According to this view, even the course of serious illnesses, such as cancer, can potentially be influenced by a person's thoughts, feelings and general state of mental health. Addressing such factors is the remit of the applied field of behavioral medicine. In modern society, psychosomatic aspects of illness are often attributed to stress making the remediation of stress one important factor in the development, treatment, and prevention of psychosomatic illness. Connotations of the term "psychosomatic illness" The term psychosomatic disease was most likely first used by Paul D. MacLean in his 1949 seminal paper ‘Psychosomatic disease and the “visceral brain”; recent developments bearing on the Papez theory of emotions.’ In the field of psychosomatic medicine, the phrase "psychosomatic illness" is used more narrowly than it is within the general population. For example, in lay language, the term often encompasses illnesses with no physical basis at all, and even illnesses that are faked (malingering). In contrast, in contemporary psychosomatic medicine, the term is normally restricted to those illnesses that do have a clear physical basis, but where it is believed that psychological and mental factors also play a role. Some researchers within the field believe that this overly broad interpretation of the term may have caused the discipline to fall into disrepute clinically. For this reason, among others, the field of behavioral medicine has taken over much of the remit of psychosomatic medicine in practice and there exist large areas of overlap in the scientific research. Criticism Studies have yielded mixed evidence regarding the impact of psychosomatic factors in illnesses. Early evidence suggested that patients with advanced-stage cancer may be able to survive longer if provided with psychotherapy to improve their social support and outlook. However, a major review published in 2007, which evaluated the evidence for these benefits, concluded that no studies meeting the minimum quality standards required in this field have demonstrated such a benefit. The review further argues that unsubstantiated claims that "positive outlook" or "fighting spirit" can help slow cancer may be harmful to the patients themselves if they come to believe that their poor progress results from "not having the right attitude". Treatment While in the U.S., psychosomatic medicine is considered a subspecialty of the fields of psychiatry and neurology, in Germany and other European countries it is considered a subspecialty of internal medicine. Thure von Uexküll and contemporary physicians following his thoughts regard the psychosomatic approach as a core attitude of medical doctors, thereby declaring it not as a subspecialty, but rather an integrated part of every specialty. Medical treatments and psychotherapy are used to treat illnesses believed to have a psychosomatic component. History In the medieval Islamic world the Persian psychologist-physicians Ahmed ibn Sahl al-Balkhi (d. 934) and Haly Abbas (d. 994) developed an early model of illness that emphasized the interaction of the mind and the body. He proposed that a patient's physiology and psychology can influence one another. Contrary to Hippocrates and Galen, Ahmed ibn Sahl al-Balkhi did not believe that mere regulation and modulation of the body tempers and medication would remedy mental disorders because words play a vital and necessary role in emotional regulation. To change such behaviors, he used techniques, such as belief altering, regular musing, rehearsals of experiences, and imagination. In the beginnings of the 20th century, there was a renewed interest in psychosomatic concepts. Psychoanalyst Franz Alexander had a deep interest in understanding the dynamic interrelation between mind and body. Sigmund Freud pursued a deep interest in psychosomatic illnesses following his correspondence with Georg Groddeck who was, at the time, researching the possibility of treating physical disorders through psychological processes. Hélène Michel-Wolfromm applied psychosomatic medicine to the field of gynecology and sexual problems experienced by women. In the 1970s, Thure von Uexküll and his colleagues in Germany and elsewhere proposed a biosemiotic theory (the umwelt concept) that was widely influential as a theoretical framework for conceptualizing mind-body relations. This model shows that life is a meaning or functional system. Farzad Goli further explains in Biosemiotic Medicine (2016), how signs in the form of matter (e.g., atoms, molecules, cells), energy (e.g., electrical signals in nervous system), symbols (e.g., words, images, machine codes), and reflections (e.g., mindful moments, metacognition) can be interpreted and translated into each other. Henri Laborit, one of the founders of modern neuropsychopharmacology, carried out experiments in the 1970s that showed that illness quickly occurred when there was inhibition of action in rats. Rats in exactly the same stressful situations but whom were not inhibited in their behavior (those who could flee or fight—even if fighting is completely ineffective) had no negative health consequences. He proposed that psychosomatic illnesses in humans largely have their source in the constraints that society puts on individuals in order to maintain hierarchical structures of dominance. The film My American Uncle, directed by Alain Resnais and influenced by Laborit, explores the relationship between self and society and the effects of the inhibition of action. In February 2005, the Boston Syndromic Surveillance System detected an increase in young men seeking medical treatment for stroke. Most of them did not actually experience a stroke, but the largest number presented a day after Tedy Bruschi, a local sports figure, was hospitalized for a stroke. Presumably they began misinterpreting their own harmless symptoms, a group phenomenon now known as Tedy Bruschi syndrome. Robert Adler is credited with coining the term Psychoneuroimmunology (PNI) to categorize a new field of study also known as mind-body medicine. The principles of mind-body medicine suggest that our mind and the emotional thoughts we produce have an incredible impact on our physiology, either positive or negative. PNI integrates the mental/psychological, nervous, and immune system, and these systems are further linked together by ligands, which are hormones, neurotransmitters and peptides. PNI studies how every single cell in our body is in constant communication—how they are literally having a conversation and are responsible for 98% of all data transferred between the body and the brain. Dr. Candace Pert, a professor and neuroscientist who discovered the opiate receptor, called this communication between our cells the ‘Molecules of Emotion' because they produce the feelings of bliss, hunger, anger, relaxation, or satiety. Dr. Pert maintains that our body is our subconscious mind, so what is going on in the subconscious mind is being played out by our body. See also , also known as "somatoform disorder" References External links Mind-Body Medicine: An Overview, US National Institutes of Health, Center for Complementary and Integrative Health NIH Academy of Psychosomatic Medicine Psychosomatics, journal of the Academy of Psychosomatic Medicine American Psychosomatic Society Psychosomatic Medicine, journal of the American Psychosomatic Society Medical specialties Mind–body interventions Stress (biological and psychological) Anxiety disorder treatment Immune system Somatic psychology	Psychosomatic medicine	[ "Biology" ]	2,007	[ "Immune system", "Organ systems" ]
52,675	https://en.wikipedia.org/wiki/Strouhal%20number	In dimensional analysis, the Strouhal number (St, or sometimes Sr to avoid the conflict with the Stanton number) is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics. The Strouhal number is often given as where f is the frequency of vortex shedding in Hertz, L is the characteristic length (for example, hydraulic diameter or the airfoil thickness) and U is the flow velocity. In certain cases, like heaving (plunging) flight, this characteristic length is the amplitude of oscillation. This selection of characteristic length can be used to present a distinction between Strouhal number and reduced frequency: where k is the reduced frequency, and A is amplitude of the heaving oscillation. For large Strouhal numbers (order of 1), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid "plug". For low Strouhal numbers (order of 10−4 and below), the high-speed, quasi-steady-state portion of the movement dominates the oscillation. Oscillation at intermediate Strouhal numbers is characterized by the buildup and rapidly subsequent shedding of vortices. For spheres in uniform flow in the Reynolds number range of 8×102 < Re < 2×105 there co-exist two values of the Strouhal number. The lower frequency is attributed to the large-scale instability of the wake, is independent of the Reynolds number Re and is approximately equal to 0.2. The higher-frequency Strouhal number is caused by small-scale instabilities from the separation of the shear layer. Derivation Knowing Newton’s Second Law stating force is equivalent to mass times acceleration, or , and that acceleration is the derivative of velocity, or (characteristic speed/time) in the case of fluid mechanics, we see , Since characteristic speed can be represented as length per unit time, , we get , where, m = mass, U = characteristic speed, L = characteristic length. Dividing both sides by , we get ⇒ , where, m = mass, U = characteristic speed, F = net external forces, L = characteristic length. This provides a dimensionless basis for a relationship between mass, characteristic speed, net external forces, and length (size) which can be used to analyze the effects of fluid mechanics on a body with mass. If the net external forces are predominantly elastic, we can use Hooke’s Law to see , where, k = spring constant (stiffness of elastic element), ΔL = deformation (change in length). Assuming , then . With the natural resonant frequency of the elastic system, , being equal to , we get , where, m = mass, U = characteristic speed, = natural resonant frequency, ΔL = deformation (change in length). Given that cyclic motion frequency can be represented by we get, , where, f = frequency, L = characteristic length, U = characteristic speed. Applications Micro/Nanorobotics In the field of micro and nanorobotics, the Strouhal number is used alongside the Reynolds number in analyzing the impact of an external oscillatory fluidic flow on the body of a microrobot. When considering a microrobot with cyclic motion, the Strouhal number can be evaluated as , where, f = cyclic motion frequency, L = characteristic length of robot, U = characteristic speed. The analysis of a microrobot using the Strouhal number allows one to assess the impact that the motion of the fluid it is in has on its motion in relation to the inertial forces acting on the robot–regardless of the dominant forces being elastic or not. Medical In the medical field, microrobots that use swimming motions to move may make micromanipulations in unreachable environments. The equation used for a blood vessel: , where, f = oscillation frequency of the microbot swimming motion D = blood vessel diameter V = unsteady viscoelastic flow The Strouhal number is used as a ratio of the Deborah number (De) and Weissenberg number (Wi): . The Strouhal number may also be used to obtain the Womersley number (Wo). The case for blood flow can be categorized as an unsteady viscoelastic flow, therefore the Womersley number is , Or considering both equations, . Metrology In metrology, specifically axial-flow turbine meters, the Strouhal number is used in combination with the Roshko number to give a correlation between flow rate and frequency. The advantage of this method over the frequency/viscosity versus K-factor method is that it takes into account temperature effects on the meter. where, f = meter frequency, U = flow rate, C = linear coefficient of expansion for the meter housing material. This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C3, resulting in units of pulses/volume (same as K-factor). This relationship between flow and frequency can also be found in the aeronautical field. Considering pulsating methane-air coflow jet diffusion flames, we get , where, a = fuel jet radius w = the modulation frequency U = exit velocity of the fuel jet For a small Strouhal number (St=0.1) the modulation forms a deviation in the flow that travels very far downstream. As the Strouhal number grows, the non-dimensional frequency approaches the natural frequency of a flickering flame, and eventually will have greater pulsation than the flame. Animal locomotion In swimming or flying animals, Strouhal number is defined as where, f = oscillation frequency (tail-beat, wing-flapping, etc.), U = flow rate, A = peak-to-peak oscillation amplitude. In animal flight or swimming, propulsive efficiency is high over a narrow range of Strouhal constants, generally peaking in the 0.2 < St < 0.4 range. This range is used in the swimming of dolphins, sharks, and bony fish, and in the cruising flight of birds, bats and insects. However, in other forms of flight other values are found. Intuitively the ratio measures the steepness of the strokes, viewed from the side (e.g., assuming movement through a stationary fluid) – f is the stroke frequency, A is the amplitude, so the numerator fA is half the vertical speed of the wing tip, while the denominator V is the horizontal speed. Thus the graph of the wing tip forms an approximate sinusoid with aspect (maximal slope) twice the Strouhal constant. Efficient motion The Strouhal number is most commonly used for assessing oscillating flow as a result of an object's motion through a fluid. The Strouhal number reflects the difficulty for animals to travel efficiently through a fluid with their cyclic propelling motions. The number relates to propulsive efficiency, which peaks between when within the optimal Strouhal number range of . Through the use of factors such as the stroke frequency, the amplitude of each stroke, and velocity, the Strouhal number is able to analyze the efficiency and impact of an animal's propulsive forces through a fluid, such as those from swimming or flying. For instance, the value represents the constraints to achieve greater propulsive efficiency, which affects motion when cruising and aerodynamic forces when hovering. Greater reactive forces and properties that act against the object, such as viscosity and density, reduce the ability of an animal's motion to fall within the ideal Strouhal number range when swimming. Through the assessment of different species that fly or swim, it was found that the motion of many species of birds and fish falls within the optimal Strouhal range. However, the Strouhal number varies more within the same species than other species based on the method of how they move in a constrained manner in response to aerodynamic forces. Example: Alcid The Strouhal number has significant importance in analyzing the flight of animals since it is based on the streamlines and the animal's velocity as it travels through the fluid. Its significance is demonstrated through the motion of alcids as it passes through different mediums (air to water). The assessment of alcids determined the peculiarity of being able to fly under the efficient Strouhal number range in air and water despite a high mass relative to their wing area. The alcid’s efficient dual-medium motion developed through natural selection where the environment played a role in the evolution of animals over time to fall under a certain efficient range. The dual-medium motion demonstrates how alcids had two different flight patterns based on the stroke velocities as it moved through each fluid. However, as the bird travels through a different medium, it has to face the influence of the fluid’s density and viscosity. Furthermore, the alcid also has to resist the upward-acting buoyancy as it moves horizontally. Scaling of the Strouhal number Scale Analysis In order to determine significance of the Strouhal number at varying scales, one may perform scale analysis–a simplification method to analyze the impact of factors as they change with respect to some scale. When considered in the context of microrobotics and nanorobotics, size is the factor of interest when performing scale analysis. Scale analysis of the Strouhal number allows for analysis of the relationship between mass and inertial forces as both change with respect to size. Taking its original underived form, , we can then relate each term to size and see how the ratio changes as size changes. Given where m is mass, V is volume, and is density, we can see mass is directly related to size as volume scales with length (L). Taking the volume to be , we can directly relate mass and size as . Characteristic speed (U) is in terms of , and relative distance scales with size, therefore . The net external forces (F) scales in relation to mass and acceleration, given by . Acceleration is in terms of , therefore . The mass-size relationship was established to be , so considering all three relationships, we get . Length (L) already denotes size and remains L. Taking all of this together, we get . With the Strouhal number relating the mass to inertial forces, this can be expected as these two factors will scale proportionately with size and neither will increase nor decrease in significance with respect to their contribution to the body’s behavior in the cyclic motion of the fluid. Relationship with the Richardson number The scaling relationship between the Richardson number and the Strouhal number is represented by the equation: , where a and b are constants depending on the condition. For round helium buoyant jets and plumes: . When , . When , . For planar buoyant jets and plumes: . For shape-independent scaling: Relationship with Reynolds number The Strouhal number and Reynolds number must be considered when addressing the ideal method to develop a body made to move through a fluid. Furthermore, the relationship for these values is expressed through Lighthill's elongated-body theory, which relates the reactive forces experienced by a body moving through a fluid with its inertial forces. The Strouhal number was determined to depend upon the dimensionless Lighthill number, which in turn relates to the Reynolds number. The value of the Strouhal number can then be seen to decrease with an increasing Reynolds number, and to increase with an increasing Lighthill number. See also References External links Vincenc Strouhal, Ueber eine besondere Art der Tonerregung Dimensionless numbers of fluid mechanics Fluid dynamics	Strouhal number	[ "Chemistry", "Engineering" ]	2,442	[ "Piping", "Chemical engineering", "Fluid dynamics" ]
52,684	https://en.wikipedia.org/wiki/Ancient%20Greek%20architecture	Ancient Greek architecture came from the Greeks, or Hellenes, whose culture flourished on the Greek mainland, the Peloponnese, the Aegean Islands, and in colonies in Anatolia and Italy for a period from about 900 BC until the 1st century AD, with the earliest remaining architectural works dating from around 600 BC. Ancient Greek architecture is best known for its temples, many of which are found throughout the region, with the Parthenon regarded, now as in ancient times, as the prime example. Most remains are very incomplete ruins, but a number survive substantially intact, mostly outside modern Greece. The second important type of building that survives all over the Hellenic world is the open-air theatre, with the earliest dating from around 525–480 BC. Other architectural forms that are still in evidence are the processional gateway (propylon), the public square (agora) surrounded by storied colonnade (stoa), the town council building (bouleuterion), the public monument, the monumental tomb (mausoleum) and the stadium. Ancient Greek architecture is distinguished by its highly formalised characteristics, both of structure and decoration. This is particularly so in the case of temples where each building appears to have been conceived as a sculptural entity within the landscape, most often raised on high ground so that the elegance of its proportions and the effects of light on its surfaces might be viewed from all angles. Nikolaus Pevsner refers to "the plastic shape of the [Greek] temple [...] placed before us with a physical presence more intense, more alive than that of any later building". The formal vocabulary of ancient Greek architecture, in particular the division of architectural style into three defined orders: the Doric Order, the Ionic Order and the Corinthian Order, was to have a profound effect on Western architecture of later periods. The architecture of ancient Rome grew out of that of Greece and maintained its influence in Italy unbroken until the present day. From the Renaissance, revivals of Classicism have kept alive not only the precise forms and ordered details of Greek architecture, but also its concept of architectural beauty based on balance and proportion. The successive styles of Neoclassical architecture and Greek Revival architecture followed and adapted ancient Greek styles closely. Influences Geography The mainland and islands of Greece are very rocky, with deeply indented coastline, and rugged mountain ranges with few substantial forests. The most freely available building material is stone. Limestone was readily available and easily worked. There is an abundance of high quality white marble both on the mainland and islands, particularly Paros and Naxos. This finely grained material was a major contributing factor to precision of detail, both architectural and sculptural, that adorned ancient Greek architecture. Deposits of high-quality potter's clay were found throughout Greece and the Islands, with major deposits near Athens. It was used not only for pottery vessels but also roof tiles and architectural decoration. The climate of Greece is maritime, with both the coldness of winter and the heat of summer tempered by sea breezes. This led to a lifestyle where many activities took place outdoors. Hence temples were placed on hilltops, their exteriors designed as a visual focus of gatherings and processions, while theatres were often an enhancement of a naturally occurring sloping site where people could sit, rather than a containing structure. Colonnades encircling buildings, or surrounding courtyards provided shelter from the sun and from sudden winter storms. The light of Greece may be another important factor in the development of the particular character of ancient Greek architecture. The light is often extremely bright, with both the sky and the sea vividly blue. The clear light and sharp shadows give a precision to the details of the landscape, pale rocky outcrops and seashore. This clarity is alternated with periods of haze that varies in colour to the light on it. In this characteristic environment, the ancient Greek architects constructed buildings that were marked by the precision of detail. The gleaming marble surfaces were smooth, curved, fluted, or ornately sculpted to reflect the sun, cast graded shadows and change in colour with the ever-changing light of day. History Historians divide ancient Greek civilization into two eras, the Hellenic period (from around 900 BC to the death of Alexander the Great in 323 BC), and the Hellenistic period (323 BC – 30 AD). During the earlier Hellenic period, substantial works of architecture began to appear around 600 BC. During the later (Hellenistic) period, Greek culture spread as a result of Alexander's conquest of other lands, and later as a result of the rise of the Roman Empire, which adopted much of Greek culture. Before the Hellenic era, two major cultures had dominated the region: the Minoan (), and the Mycenaean (c. 1500–1100 BC). Minoan is the name given by modern historians to the culture of the people of ancient Crete, known for its elaborate and richly decorated Minoan palaces, and for its pottery, the most famous of which painted with floral and motifs of sea life. The Mycenaean culture, which flourished on the Peloponnesus, was different in character. Its people built citadels, fortifications and tombs, and decorated their pottery with bands of marching soldiers rather than octopus and seaweed. Both these civilizations came to an end around 1100 BC, that of Crete possibly because of volcanic devastation, and that of Mycenae because of an invasion by the Dorian people who lived on the Greek mainland. Following these events, there was a period from which only a village level of culture seems to have existed. This period is thus often referred to as the Greek Dark Age. Art The art history of the Hellenic era is generally subdivided into four periods: the Protogeometric (1100–900 BC), the Geometric (900–700 BC), the Archaic (700–500 BC) and the Classical (500–323 BC) with sculpture being further divided into Severe Classical, High Classical and Late Classical. The first signs of the particular artistic character that defines ancient Greek architecture are to be seen in the pottery of the Dorian Greeks from the 10th century BC. Already at this period it is created with a sense of proportion, symmetry and balance not apparent in similar pottery from Crete and Mycenae. The decoration is precisely geometric, and ordered neatly into zones on defined areas of each vessel. These qualities were to manifest themselves not only through a millennium of Greek pottery making, but also in the architecture that was to emerge in the 6th century. The major development that occurred was in the growing use of the human figure as the major decorative motif, and the increasing surety with which humanity, its mythology, activities and passions were depicted. The development in the depiction of the human form in pottery was accompanied by a similar development in sculpture. The tiny stylised bronzes of the Geometric period gave way to life-sized highly formalised monolithic representation in the Archaic period. The Classical period was marked by a rapid development towards idealised but increasingly lifelike depictions of gods in human form. This development had a direct effect on the sculptural decoration of temples, as many of the greatest extant works of ancient Greek sculpture once adorned temples, and many of the largest recorded statues of the age, such as the lost chryselephantine statues of Zeus at the Temple of Zeus at Olympia and Athena at the Parthenon, Athens, both over 40 feet high, were once housed in them. Religion and philosophy The religion of ancient Greece was a form of nature worship that grew out of the beliefs of earlier cultures. However, unlike earlier cultures, man was no longer perceived as being threatened by nature, but as its sublime product. The natural elements were personified as gods of the complete human form, and very human behaviour. The home of the gods was thought to be Olympus, the highest mountain in Greece. The most important deities were: Zeus, the supreme god and ruler of the sky; Hera, his wife and goddess of marriage; Athena, goddess of wisdom; Poseidon, the god of the sea; Demeter, goddess of the harvest; Apollo, the god of the sun, law, healing, plague, reason, music and poetry; Artemis, goddess of chastity, the hunt and the wilderness; Aphrodite, goddess of love; Ares, God of war; Hermes, the god of commerce and travellers, Hephaestus, the god of fire and metalwork; and Dionysus, the god of wine and fruit-bearing plants. Worship, like many other activities, was done in the community, in the open. However, by 600 BC, the gods were often represented by large statues and it was necessary to provide a building in which each of these could be housed. This led to the development of temples. The ancient Greeks perceived order in the universe, and in turn, applied order and reason to their creations. Their humanist philosophy put mankind at the centre of things and promoted well-ordered societies and the development of democracy. At the same time, the respect for human intellect demanded a reason, and promoted a passion for enquiry, logic, challenge, and problem-solving. The architecture of the ancient Greeks, and in particular, temple architecture, responds to these challenges with a passion for beauty, and for order and symmetry which is the product of a continual search for perfection, rather than a simple application of a set of working rules. Architectural character Early development There is a clear division between the architecture of the preceding Mycenaean and Minoan cultures and that of the ancient Greeks, with much of the techniques and an understanding of their style being lost when these civilisations fell. Mycenaean architecture is marked by massive fortifications, typically surrounding a citadel with a royal palace, much smaller than the rambling Minoan "palaces", and relatively few other buildings. The megaron, a rectangular hall with a hearth in the centre, was the largest room in the palaces, and also larger houses. Sun-dried brick above rubble bases were the usual materials, with wooden columns and roof-beams. Rows of ashlar stone orthostats lined the base of walls in some prominent locations. The Minoan architecture of Crete was of the trabeated form like that of ancient Greece. It employed wooden columns with capitals, but the wooden columns were of a very different form to Doric columns, being narrow at the base and splaying upward. The earliest forms of columns in Greece seem to have developed independently. As with Minoan architecture, ancient Greek domestic architecture centred on open spaces or courtyards surrounded by colonnades. This form was adapted to the construction of hypostyle halls within the larger temples. The evolution that occurred in architecture was towards the public building, first and foremost the temple, rather than towards grand domestic architecture such as had evolved in Crete, if the Cretan "palaces" were indeed domestic, which remains uncertain. Some Mycenaean tombs are marked by circular structures and tapered domes with flat-bedded, cantilevered courses. This architectural form did not carry over into the architecture of ancient Greece, but reappeared about 400 BC in the interior of large monumental tombs such as the Lion Tomb at Knidos (c. 350 BC). Types of buildings Domestic buildings The Greek word for the family or household, oikos, is also the name for the house. Houses followed several different types. It is probable that many of the earliest houses were simple structures of two rooms, with an open porch or pronaos, above which rose a low pitched gable or pediment. This form is thought to have contributed to temple architecture. The construction of many houses employed walls of sun-dried clay bricks or wooden framework filled with fibrous material such as straw or seaweed covered with clay or plaster, on a base of stone which protected the more vulnerable elements from damp. The roofs were probably of thatch with eaves which overhung the permeable walls. Many larger houses, such as those at Delos, were built of stone and plastered. The roofing material for the substantial house was tile. Houses of the wealthy had mosaic floors and demonstrated the Classical style. Many houses centred on a wide passage or "pasta" which ran the length of the house and opened at one side onto a small courtyard which admitted light and air. Larger houses had a fully developed peristyle (courtyard) at the centre, with the rooms arranged around it. Some houses had an upper floor which appears to have been reserved for the use of the women of the family. City houses were built with adjoining walls and were divided into small blocks by narrow streets. Shops were sometimes located in the rooms towards the street. City houses were inward-facing, with major openings looking onto the central courtyard, rather than the street. Public buildings The rectangular temple is the most common and best-known form of Greek public architecture. This rectilinear structure borrows from the Late Helladic, Mycenaean megaron, which contained a central throne room, vestibule, and porch. The temple did not serve the same function as a modern church, since the altar stood under the open sky in the temenos or sacred precinct, often directly before the temple. Temples served as the location of a cult image and as a storage place or strong room for the treasury associated with the cult of the god in question, and as a place for devotees of the god to leave their votive offerings, such as statues, helmets and weapons. Some Greek temples appear to have been oriented astronomically. The temple was generally part of a religious precinct known as the acropolis. According to Aristotle, "the site should be a spot seen far and wide, which gives good elevation to virtue and towers over the neighbourhood". Small circular temples, tholoi were also constructed, as well as small temple-like buildings that served as treasuries for specific groups of donors. During the late 5th and 4th centuries BC, town planning became an important consideration of Greek builders, with towns such as Paestum and Priene being laid out with a regular grid of paved streets and an agora or central market place surrounded by a colonnade or stoa. The completely restored Stoa of Attalos can be seen in Athens. Towns were also equipped with a public fountain where water could be collected for household use. The development of regular town plans is associated with Hippodamus of Miletus, a pupil of Pythagoras. Public buildings became "dignified and gracious structures", and were sited so that they related to each other architecturally. The propylon or porch, formed the entrance to temple sanctuaries and other significant sites with the best-surviving example being the Propylaea on the Acropolis of Athens. The bouleuterion was a large public building with a hypostyle hall that served as a court house and as a meeting place for the town council (boule). Remnants of bouleuterion survive at Athens, Olympia and Miletus, the latter having held up to 1,200 people. Every Greek town had an open-air theatre. These were used for both public meetings as well as dramatic performances. The theatre was usually set in a hillside outside the town, and had rows of tiered seating set in a semicircle around the central performance area, the orchestra. Behind the orchestra was a low building called the skênê, which served as a store-room, a dressing room, and also as a backdrop to the action taking place in the orchestra. A number of Greek theatres survive almost intact, the best known being at Epidaurus by the architect Polykleitos the Younger. Greek towns of substantial size also had a palaestra or a gymnasium, the social centre for male citizens which included spectator areas, baths, toilets and club rooms. Other buildings associated with sports include the hippodrome for horse racing, of which only remnants have survived, and the stadium for foot racing, 600 feet in length, of which examples exist at Olympia, Delphi, Epidaurus and Ephesus, while the Panathinaiko Stadium in Athens, which seats 45,000 people, was restored in the 19th century and was used in the 1896, 1906 and 2004 Olympic Games. Structure Post and lintel The architecture of ancient Greece is of a trabeated or "post and lintel" form, i.e. it is composed of upright beams (posts) supporting horizontal beams (lintels). Although the existent buildings of the era are constructed in stone, it is clear that the origin of the style lies in simple wooden structures, with vertical posts supporting beams which carried a ridged roof. The posts and beams divided the walls into regular compartments which could be left as openings, or filled with sun dried bricks, lathes or straw and covered with clay daub or plaster. Alternately, the spaces might be filled with rubble. It is likely that many early houses and temples were constructed with an open porch or "pronaos" above which rose a low pitched gable or pediment. The earliest temples, built to enshrine statues of deities, were probably of wooden construction, later replaced by the more durable stone temples many of which are still in evidence today. The signs of the original timber nature of the architecture were maintained in the stone buildings. A few of these temples are very large, with several, such as the Temple of Zeus Olympus and the Olympians at Athens being well over 300 feet in length, but most were less than half this size. It appears that some of the large temples began as wooden constructions in which the columns were replaced piecemeal as stone became available. This, at least was the interpretation of the historian Pausanias looking at the Temple of Hera at Olympia in the 2nd century AD. The stone columns are made of a series of solid stone cylinders or "drums" that rest on each other without mortar, but were sometimes centred with a bronze pin. The columns are wider at the base than at the top, tapering with an outward curve known as entasis. Each column has a capital of two parts, the upper, on which rests the lintels, being square and called the abacus. The part of the capital that rises from the column itself is called the echinus. It differs according to the order, being plain in the Doric order, fluted in the Ionic and foliate in the Corinthian. Doric and usually Ionic capitals are cut with vertical grooves known as fluting. This fluting or grooving of the columns is a retention of an element of the original wooden architecture. Entablature and pediment The columns of a temple support a structure that rises in two main stages, the entablature and the pediment. The entablature is the major horizontal structural element supporting the roof and encircling the entire building. It is composed of three parts. Resting on the columns is the architrave made of a series of stone "lintels" that spanned the space between the columns, and meet each other at a joint directly above the centre of each column. Above the architrave is a second horizontal stage called the frieze. The frieze is one of the major decorative elements of the building and carries a sculptured relief. In the case of Ionic and Corinthian architecture, the relief decoration runs in a continuous band, but in the Doric order, it is divided into sections called metopes, which fill the spaces between vertical rectangular blocks called triglyphs. The triglyphs are vertically grooved like the Doric columns, and retain the form of the wooden beams that would once have supported the roof. The upper band of the entablature is called the cornice, which is generally ornately decorated on its lower edge. The cornice retains the shape of the beams that would once have supported the wooden roof at each end of the building. At the front and rear of each temple, the entablature supports a triangular structure called the pediment. The tympanum is the triangular space framed by the cornices and the location of the most significant sculptural decoration on the exterior of the building. Masonry Every temple rested on a masonry base called the crepidoma, generally of three steps, of which the upper one which carried the columns was the stylobate. Masonry walls were employed for temples from about 600 BC onwards. Masonry of all types was used for ancient Greek buildings, including rubble, but the finest ashlar masonry was usually employed for temple walls, in regular courses and large sizes to minimise the joints. The blocks were rough hewn and hauled from quarries to be cut and bedded very precisely, with mortar hardly ever being used. Blocks, particularly those of columns and parts of the building bearing loads were sometimes fixed in place or reinforced with iron clamps, dowels and rods of wood, bronze or iron fixed in lead to minimise corrosion. Openings Door and window openings were spanned with a lintel, which in a stone building limited the possible width of the opening. The distance between columns was similarly affected by the nature of the lintel, columns on the exterior of buildings and carrying stone lintels being closer together than those on the interior, which carried wooden lintels. Door and window openings narrowed towards the top. Temples were constructed without windows, the light to the naos entering through the door. It has been suggested that some temples were lit from openings in the roof. A door of the Ionic Order at the Erechtheion (17 feet high and 7.5 feet wide at the top) retains many of its features intact, including mouldings, and an entablature supported on console brackets. (See Architectural Decoration, below) Roof The widest span of a temple roof was across the cella, or inner chamber. In a large building, this space contains columns to support the roof, the architectural form being known as hypostyle. It appears that, although the architecture of ancient Greece was initially of wooden construction, the early builders did not have the concept of the diagonal truss as a stabilising member. This is evidenced by the nature of temple construction in the 6th century BC, where the rows of columns supporting the roof of the cella rise higher than the outer walls, unnecessary if roof trusses are employed as an integral part of the wooden roof. The indication is that initially all the rafters were supported directly by the entablature, walls and hypostyle, rather than on a trussed wooden frame, which came into use in Greek architecture only in the 3rd century BC. Ancient Greek buildings of timber, clay and plaster construction were probably roofed with thatch. With the rise of stone architecture came the appearance of fired ceramic roof tiles. These early roof tiles showed an S-shape, with the pan and cover tile forming one piece. They were much larger than modern roof tiles, being up to long, wide, thick and weighing around apiece. Only stone walls, which were replacing the earlier mudbrick and wood walls, were strong enough to support the weight of a tiled roof. The earliest finds of roof tiles of the Archaic period in Greece are documented from a very restricted area around Corinth, where fired tiles began to replace thatched roofs at the temples of Apollo and Poseidon between 700 and 650 BC. Spreading rapidly, roof tiles were within fifty years in evidence for a large number of sites around the Eastern Mediterranean, including Mainland Greece, Western Asia Minor, Southern and Central Italy. Being more expensive and labour-intensive to produce than thatch, their introduction has been explained by the fact that their fireproof quality would have given desired protection to the costly temples. As a side-effect, it has been assumed that the new stone and tile construction also ushered in the end of overhanging eaves in Greek architecture, as they made the need for an extended roof as rain protection for the mudbrick walls obsolete. Vaults and arches were not generally used, but begin to appear in tombs (in a "beehive" or cantilevered form such as used in Mycenaea) and occasionally, as an external feature, exedrae of voussoired construction from the 5th century BC. The dome and vault never became significant structural features, as they were to become in ancient Roman architecture. Temple plans Most ancient Greek temples were rectangular, and were approximately twice as long as they were wide, with some notable exceptions such as the enormous Temple of Olympian Zeus, Athens with a length of nearly 2 times its width. A number of surviving temple-like structures are circular, and are referred to as tholos. The smallest temples are less than 25 metres (approx. 75 feet) in length, or in the case of the circular tholos, in diameter. The great majority of temples are between 30 and 60 metres (approx. 100–200 feet) in length. A small group of Doric temples, including the Parthenon, are between 60 and 80 metres (approx. 200–260 feet) in length. The largest temples, mainly Ionic and Corinthian, but including the Doric Temple of the Olympian Zeus, Agrigento, were between 90 and 120 metres (approx. 300–390 feet) in length. The temple rises from a stepped base or stylobate, which elevates the structure above the ground on which it stands. Early examples, such as the Temple of Zeus at Olympus, have two steps, but the majority, like the Parthenon, have three, with the exceptional example of the Temple of Apollo at Didyma having six. The core of the building is a masonry-built "naos" within which is a cella, a windowless room originally housing the statue of the god. The cella generally has a porch or "pronaos" before it, and perhaps a second chamber or "antenaos" serving as a treasury or repository for trophies and gifts. The chambers were lit by a single large doorway, fitted with a wrought iron grill. Some rooms appear to have been illuminated by skylights. On the stylobate, often completely surrounding the naos, stand rows of columns. Each temple is defined as being of a particular type, with two terms: one describing the number of columns across the entrance front, and the other defining their distribution. Examples: Distyle in antis describes a small temple with two columns at the front, which are set between the projecting walls of the pronaos or porch, like the Temple of Nemesis at Rhamnus. (see above, figure 1.) Amphiprostyle tetrastyle describes a small temple that has columns at both ends which stand clear of the naos. Tetrastyle indicates that the columns are four in number, like those of the Temple on the Ilissus in Athens. (figure 4.) Peripteral hexastyle describes a temple with a single row of peripheral columns around the naos, with six columns across the front, like the Theseion in Athens. (figure 7.) Peripteral octastyle describes a temple with a single row of columns around the naos, (figure 7.) with eight columns across the front, like the Parthenon, Athens. (figures 6 and 9.) Dipteral decastyle describes the huge temple of Apollo at Didyma, with the naos surrounded by a double row of columns, (figure 6.) with ten columns across the entrance front. The Temple of Zeus Olympius at Agrigentum, is termed Pseudo-periteral heptastyle, because its encircling colonnade has pseudo columns that are attached to the walls of the naos. (figure 8.) Heptastyle means that it has seven columns across the entrance front. Proportion and optical illusion The ideal of proportion that was used by ancient Greek architects in designing temples was not a simple mathematical progression using a square module. The math involved a more complex geometrical progression, the so-called golden mean. The ratio is similar to that of the growth patterns of many spiral forms that occur in nature such as rams' horns, nautilus shells, fern fronds, and vine tendrils and which were a source of decorative motifs employed by ancient Greek architects as particularly in evidence in the volutes of capitals of the Ionic and Corinthian Orders. The ancient Greek architects took a philosophic approach to the rules and proportions. The determining factor in the mathematics of any notable work of architecture was its ultimate appearance. The architects calculated for perspective, for the optical illusions that make edges of objects appear concave and for the fact that columns that are viewed against the sky look different from those adjacent that are viewed against a shadowed wall. Because of these factors, the architects adjusted the plans so that the major lines of any significant building are rarely straight. The most obvious adjustment is to the profile of columns, which narrow from base to top. However, the narrowing is not regular, but gently curved so that each column appears to have a slight swelling, called entasis below the middle. The entasis is never sufficiently pronounced as to make the swelling wider than the base; it is controlled by a slight reduction in the rate of decrease of diameter. The Parthenon, the Temple to the Goddess Athena on the Acropolis in Athens, is referred to by many as the pinnacle of ancient Greek architecture. Helen Gardner refers to its "unsurpassable excellence", to be surveyed, studied and emulated by architects of later ages. Yet, as Gardner points out, there is hardly a straight line in the building. Banister Fletcher calculated that the stylobate curves upward so that its centres at either end rise about above the outer corners, and on the longer sides. A slightly greater adjustment has been made to the entablature. The columns at the ends of the building are not vertical but are inclined towards the centre, with those at the corners being out of plumb by about . These outer columns are both slightly wider than their neighbours and are slightly closer than any of the others. Style Orders Ancient Greek architecture of the most formal type, for temples and other public buildings, is divided stylistically into three Classical orders, first described by the Roman architectural writer Vitruvius. These are: the Doric order, the Ionic order, and the Corinthian order, the names reflecting their regional origins within the Greek world. While the three orders are most easily recognizable by their capitals, they also governed the form, proportions, details and relationships of the columns, entablature, pediment, and the stylobate. The different orders were applied to the whole range of buildings and monuments. The Doric order developed on mainland Greece and spread to Magna Graecia (Italy). It was firmly established and well-defined in its characteristics by the time of the building of the Temple of Hera at Olympia, c. 600 BC. The Ionic order co-existed with the Doric, being favoured by the Greek cities of Ionia, in Asia Minor and the Aegean Islands. It did not reach a clearly defined form until the mid 5th century BC. The early Ionic temples of Asia Minor were particularly ambitious in scale, such as the Temple of Artemis at Ephesus. The Corinthian order was a highly decorative variant not developed until the Hellenistic period and retaining many characteristics of the Ionic. It was popularised by the Romans. Doric order The Doric order is recognised by its capital, of which the echinus is like a circular cushion rising from the top of the column to the square abacus on which rest the lintels. The echinus appears flat and splayed in early examples, deeper and with greater curve in later, more refined examples, and smaller and straight-sided in Hellenistic examples. A refinement of the Doric column is the entasis, a gentle convex swelling to the profile of the column, which prevents an optical illusion of concavity. This is more pronounced in earlier examples. Doric columns are almost always cut with grooves, known as "fluting", which run the length of the column and are usually 20 in number, although sometimes fewer. The flutes meet at sharp edges called arrises. At the top of the columns, slightly below the narrowest point, and crossing the terminating arrises, are three horizontal grooves known as the hypotrachelion. Doric columns have no bases, until a few examples in the Hellenistic period. The columns of an early Doric temple such as the Temple of Apollo at Syracuse, Sicily, may have a height to base diameter ratio of only 4:1 and a column height to entablature ratio of 2:1, with relatively crude details. A column height to diameter of 6:1 became more usual, while the column height to entablature ratio at the Parthenon is about 3:1. During the Hellenistic period, Doric conventions of solidity and masculinity dropped away, with the slender and unfluted columns reaching a height to diameter ratio of 7.5:1. The Doric entablature is in three parts, the architrave, the frieze and the cornice. The architrave is composed of the stone lintels which span the space between the columns, with a joint occurring above the centre of each abacus. On this rests the frieze, one of the major areas of sculptural decoration. The frieze is divided into triglyphs and metopes, the triglyphs, as stated elsewhere in this article, are a reminder of the timber history of the architectural style. Each triglyph has three vertical grooves, similar to the columnar fluting, and below them, seemingly connected, are guttae, small strips that appear to connect the triglyphs to the architrave below. A triglyph is located above the centre of each capital, and above the centre of each lintel. However, at the corners of the building, the triglyphs do not fall over the centre the column. The ancient architects took a pragmatic approach to the apparent "rules", simply extending the width of the last two metopes at each end of the building. The cornice is a narrow jutting band of complex molding, which overhangs and protects the ornamented frieze, like the edge of an overhanging wooden-framed roof. It is decorated on the underside with projecting blocks, mutules, further suggesting the wooden nature of the prototype. At either end of the building the pediment rises from the cornice, framed by moulding of similar form. The pediment is decorated with figures that are in relief in the earlier examples, though almost free-standing by the time of the sculpture on the Parthenon. Early architectural sculptors found difficulty in creating satisfactory sculptural compositions in the tapering triangular space. By the Early Classical period, with the decoration of the Temple of Zeus at Olympia (486–460 BC), the sculptors had solved the problem by having a standing central figure framed by rearing centaurs and fighting men who are falling, kneeling and lying in attitudes that fit the size and angle of each part of the space. The famous sculptor Phidias fills the space at the Parthenon (448–432 BC) with a complex array of draped and undraped figures of deities, who appear in attitudes of sublime relaxation and elegance. Ionic order The Ionic order is recognized by its voluted capital, in which a curved echinus of similar shape to that of the Doric order, but decorated with stylised ornament, is surmounted by a horizontal band that scrolls under to either side, forming spirals or volutes similar to those of the nautilus shell or ram's horn. In plan, the capital is rectangular. It is designed to be viewed frontally but the capitals at the corners of buildings are modified with an additional scroll so as to appear regular on two adjoining faces. In the Hellenistic period, four-fronted Ionic capitals became common. Like the Doric order, the Ionic order retains signs of having its origins in wooden architecture. The horizontal spread of a flat timber plate across the top of a column is a common device in wooden construction, giving a thin upright a wider area on which to bear the lintel, while at the same time reinforcing the load-bearing strength of the lintel itself. Likewise, the columns always have bases, a necessity in wooden architecture to spread the load and protect the base of a comparatively thin upright. The columns are fluted with narrow, shallow flutes that do not meet at a sharp edge but have a flat band or fillet between them. The usual number of flutes is twenty-four but there may be as many as forty-four. The base has two convex mouldings called torus, and from the late Hellenic period stood on a square plinth similar to the abacus. The architrave of the Ionic order is sometimes undecorated, but more often rises in three outwardly-stepped bands like overlapping timber planks. The frieze, which runs in a continuous band, is separated from the other members by rows of small projecting blocks. They are referred to as dentils, meaning "teeth", but their origin is clearly in narrow wooden slats which supported the roof of a timber structure. The Ionic order is altogether lighter in appearance than the Doric, with the columns, including base and capital, having a 9:1 ratio with the diameter, while the whole entablature was also much narrower and less heavy than the Doric entablature. There was some variation in the distribution of decoration. Formalised bands of motifs such as alternating forms known as egg-and-dart were a feature of the Ionic entablatures, along with the bands of dentils. The external frieze often contained a continuous band of figurative sculpture or ornament, but this was not always the case. Sometimes a decorative frieze occurred around the upper part of the naos rather than on the exterior of the building. These Ionic-style friezes around the naos are sometimes found on Doric buildings, notably the Parthenon. Some temples, like the Temple of Artemis at Ephesus, had friezes of figures around the lower drum of each column, separated from the fluted section by a bold moulding. Caryatids, draped female figures used as supporting members to carry the entablature, were a feature of the Ionic order, occurring at several buildings including the Siphnian Treasury at Delphi in 525 BC and at the Erechtheion, about 410 BC. Corinthian order The Corinthian order does not have its origin in wooden architecture. It grew directly out of the Ionic in the mid 5th century BC, and was initially of much the same style and proportion, but distinguished by its more ornate capitals. The capital was very much deeper than either the Doric or the Ionic capital, being shaped like a large krater, a bell-shaped mixing bowl, and being ornamented with a double row of acanthus leaves above which rose voluted tendrils, supporting the corners of the abacus, which, no longer perfectly square, splayed above them. According to Vitruvius, the capital was invented by a bronze founder, Callimachus of Corinth, who took his inspiration from a basket of offerings that had been placed on a grave, with a flat tile on top to protect the goods. The basket had been placed on the root of an acanthus plant which had grown up around it. The ratio of the column height to diameter is generally 10:1, with the capital taking up more than 1/10 of the height. The ratio of capital height to diameter is generally about 1.16:1. The Corinthian order was initially used internally, as at the Temple of Apollo Epicurius at Bassae (c. 450–425 BC). In 334 BC, it appeared as an external feature on the Choragic Monument of Lysicrates in Athens, and then on a huge scale at the Temple of Zeus Olympia in Athens (174 BC–132 AD). It was popularised by the Romans, who added a number of refinements and decorative details. During the Hellenistic period, Corinthian columns were sometimes built without fluting. Decoration Architectural ornament Early wooden structures, particularly temples, were ornamented and in part protected by fired and painted terracotta revetments in the form of rectangular panels, and ornamental discs. Many fragments of these have outlived the buildings that they decorated and demonstrate a wealth of formal border designs of geometric scrolls, overlapping patterns and foliate motifs. With the introduction of stone-built temples, the revetments no longer served a protective purpose and sculptured decoration became more common. The clay ornaments were limited to the roof of buildings, decorating the cornice, the corners and surmounting the pediment. At the corners of pediments they were called acroteria and along the sides of the building, antefixes. Early decorative elements were generally semi-circular, but later of roughly triangular shape with moulded ornament, often palmate. Ionic cornices were often set with a row of lion's masks, with open mouths that ejected rainwater. From the Late Classical period, acroteria were sometimes sculptured figures (see Architectural sculpture). In the three orders of ancient Greek architecture, the sculptural decoration, be it a simple half round astragal, a frieze of stylised foliage or the ornate sculpture of the pediment, is all essential to the architecture of which it is a part. In the Doric order, there is no variation in its placement. Reliefs never decorate walls in an arbitrary way. The sculpture is always located in several predetermined areas, the metopes and the pediment. In later Ionic architecture, there is greater diversity in the types and numbers of mouldings and decorations, particularly around doorways, where voluted brackets sometimes occur supporting an ornamental cornice over a door, such as that at the Erechtheion. A much applied narrow moulding is called "bead and reel" and is symmetrical, stemming from turned wooden prototypes. Wider mouldings include one with tongue-like or pointed leaf shapes, which are grooved and sometimes turned upward at the tip, and "egg and dart" moulding which alternates ovoid shapes with narrow pointed ones. Architectural sculpture Architectural sculpture showed a development from early Archaic examples through Severe Classical, High Classical, Late Classical and Hellenistic. Remnants of Archaic architectural sculpture (700–500 BC) exist from the early 6th century BC with the earliest surviving pedimental sculptures being fragments of a Gorgon flanked by heraldic panthers from the centre of the pediment of the Artemis Temple of Corfu. A metope from a temple known as "Temple C" at Selinus, Sicily, shows, in a better preserved state, Perseus slaying the Gorgon Medusa. Both images parallel the stylised depiction of the Gorgons on the black figure name vase decorated by the Nessos painter (c. 600 BC), with the face and shoulders turned frontally, and the legs in a running or kneeling position. At this date, images of terrifying monsters have predominance over the emphasis on the human figure that developed with Humanist philosophy. Early pedimental sculptures, and those on smaller temples, were usually in relief, and the late free-standing ones were often in terracotta, which has survived only in fragments. The sculptures were covered with a layer of stucco and painted or, if terracotta, painted with the more restrained fired colours of Greek pottery. The Severe Classical Style (500–450 BC) is represented by the pedimental sculptures of the Temple of Zeus at Olympia (470–456 BC). The eastern pediment shows a moment of stillness and "impending drama" before the beginning of a chariot race, the figures of Zeus and the competitors being severe and idealised representations of the human form. The western pediment has Apollo as the central figure, "majestic" and "remote", presiding over a battle of Lapiths and Centaurs, in strong contrast to that of the eastern pediment for its depiction of violent action, and described by Donald E. Strong as the "most powerful piece of illustration" for a hundred years. The reliefs and three-dimensional sculpture which adorned the frieze and pediments, respectively, of the Parthenon, are the lifelike products of the High Classical style (450–400 BC) and were created under the direction of the sculptor Phidias. The pedimental sculpture represents the Gods of Olympus, while the frieze shows the Panathenaic procession and ceremonial events that took place every four years to honour the titular Goddess of Athens. The frieze and remaining figures of the eastern pediment show a profound understanding of the human body, and how it varies depending upon its position and the stresses that action and emotion place upon it. Benjamin Robert Haydon described the reclining figure of Dionysus as "the most heroic style of art, combined with all the essential detail of actual life". The names of many famous sculptors are known from the Late Classical period (400–323 BC), including Timotheos, Praxiteles, Leochares and Skopas, but their works are known mainly from Roman copies. Little architectural sculpture of the period remains intact. The Temple of Asclepius at Epidauros had sculpture by Timotheos working with the architect Theodotos. Fragments of the eastern pediment survive, showing the Sack of Troy. The scene appears to have filled the space with figures carefully arranged to fit the slope and shape available, as with the earlier east pediment of the Temple of Zeus at Olympus. But the figures are more violent in action, the central space taken up, not with a commanding God, but with the dynamic figure of Neoptolemos as he seizes the aged king Priam and stabs him. The remaining fragments give the impression of a range of human emotions, fear, horror, cruelty and lust for conquest. The acroteria were sculptured by Timotheus, except for that at the centre of the east pediment which is the work of the architect. The palmate acroteria have been replaced here with small figures, the eastern pediment being surmounted by a winged Nike, poised against the wind. Hellenistic architectural sculpture (323–31 BC) was to become more flamboyant, both in the rendering of expression and motion, which is often emphasised by flowing draperies, the Nike Samothrace which decorated a monument in the shape of a ship being a well-known example. The Pergamon Altar (c. 180–160 BC) has a frieze (120 metres long by 2.3 metres high) of figures in very high relief. The frieze represents the battle for supremacy of Gods and Titans, and employs many dramatic devices: frenzy, pathos and triumph, to convey the sense of conflict. See also Ancient Greek art Ancient Roman architecture Byzantine architecture Classical architecture Greek culture Greek technology List of ancient architectural records List of ancient Greek temples Modern Greek architecture Outline of classical architecture References Citations Sources External links The Foundations of Classical Architecture Part Two: Greek Classicism – Free educational program by the ICAA (published August 29, 2018) Joseph Woods (1828), Letters of an Architect, From France, Italy, and Greece. Architectural history	Ancient Greek architecture	[ "Engineering" ]	9,830	[ "Architectural history", "Architecture" ]
52,685	https://en.wikipedia.org/wiki/Ancient%20Roman%20architecture	Ancient Roman architecture adopted the external language of classical ancient Greek architecture for the purposes of the ancient Romans, but was different from Greek buildings, becoming a new architectural style. The two styles are often considered one body of classical architecture. Roman architecture flourished in the Roman Republic and to an even greater extent under the Empire, when the great majority of surviving buildings were constructed. It used new materials, particularly Roman concrete, and newer technologies such as the arch and the dome to make buildings that were typically strong and well engineered. Large numbers remain in some form across the former empire, sometimes complete and still in use today. Roman architecture covers the period from the establishment of the Roman Republic in 509 BC to about the 4th century AD, after which it becomes reclassified as Late Antique or Byzantine architecture. Few substantial examples survive from before about 100 BC, and most of the major survivals are from the later empire, after about 100 AD. Roman architectural style continued to influence building in the former empire for many centuries, and the style used in Western Europe beginning about 1000 is called Romanesque architecture to reflect this dependence on basic Roman forms. The Romans only began to achieve significant originality in architecture around the beginning of the Imperial period, after they had combined aspects of their originally Etruscan architecture with others taken from Greece, including most elements of the style we now call classical architecture. They moved from trabeated construction mostly based on columns and lintels to one based on massive walls, punctuated by arches, and later domes, both of which greatly developed under the Romans. The classical orders now became largely decorative rather than structural, except in colonnades. Stylistic developments included the Tuscan and Composite orders; the first being a shortened, simplified variant on the Doric order and the Composite being a tall order with the floral decoration of the Corinthian and the scrolls of the Ionic. The period from roughly 40 BC to about 230 AD saw most of the greatest achievements, before the Crisis of the Third Century and later troubles reduced the wealth and organizing power of the central governments. The Romans produced massive public buildings and works of civil engineering, and were responsible for significant developments in housing and public hygiene, for example their public and private baths and latrines, under-floor heating in the form of the hypocaust, mica glazing (examples in Ostia Antica), and piped hot and cold water (examples in Pompeii and Ostia). Overview Despite the technical developments of the Romans, which took their buildings far away from the basic Greek conception where columns were needed to support heavy beams and roofs, they were reluctant to abandon the classical orders in formal public buildings, even though these had become essentially decorative. However, they did not feel entirely restricted by Greek aesthetic concerns and treated the orders with considerable freedom. Innovation started in the 3rd or 2nd century BC with the development of Roman concrete as a readily available adjunct to, or substitute for, stone and brick. More daring buildings soon followed, with great pillars supporting broad arches and domes. The freedom of concrete also inspired the colonnade screen, a row of purely decorative columns in front of a load-bearing wall. In smaller-scale architecture, concrete's strength freed the floor plan from rectangular cells to a more free-flowing environment. Factors such as wealth and high population densities in cities forced the ancient Romans to discover new architectural solutions of their own. The use of vaults and arches, together with a sound knowledge of building materials, enabled them to achieve unprecedented successes in the construction of imposing infrastructure for public use. Examples include the aqueducts of Rome, the Baths of Diocletian and the Baths of Caracalla, the basilicas and Colosseum. These were reproduced at a smaller scale in the most important towns and cities in the Empire. Some surviving structures are almost complete, such as the town walls of Lugo in Hispania Tarraconensis, now northern Spain. The administrative structure and wealth of the Empire made possible very large projects even in locations remote from the main centers, as did the use of slave labor, both skilled and unskilled. Especially under the empire, architecture often served a political function, demonstrating the power of the Roman state in general, and of specific individuals responsible for building. Roman architecture perhaps reached its peak in the reign of Hadrian, whose many achievements include rebuilding the Pantheon in its current form and leaving his mark on the landscape of northern Britain with Hadrian's Wall. Origins While borrowing much from the preceding Etruscan architecture, such as the use of hydraulics and the construction of arches, Roman prestige architecture remained firmly under the spell of ancient Greek architecture and the classical orders. This came initially from Magna Graecia, the Greek colonies in southern Italy, and indirectly from Greek influence on the Etruscans, but after the Roman conquest of Greece directly from the best classical and Hellenistic examples in the Greek world. The influence is evident in many ways; for example, in the introduction and use of the triclinium in Roman villas as a place and manner of dining. Roman builders employed Greeks in many capacities, especially in the great boom in construction in the early Empire. Roman architectural revolution The Roman architectural revolution, also known as the "concrete revolution", was the widespread use in Roman architecture of the previously little-used architectural forms of the arch, vault, and dome. For the first time in history, their potential was fully exploited in the construction of a wide range of civil engineering structures, public buildings, and military facilities. These included amphitheatres, aqueducts, baths, bridges, circuses, dams, domes, harbours, temples, and theatres. According to Gottfried Semper, Roman architecture was "the idea of world domination expressed in stone". A crucial factor in this development, which saw a trend toward monumental architecture, was the invention of Roman concrete (opus caementicium), which led to the liberation of shapes from the dictates of the traditional materials of stone and brick. These enabled the building of the many aqueducts throughout the Roman Empire, such as the Aqueduct of Segovia, the Pont du Gard, and the eleven aqueducts of Rome. The same concepts produced numerous bridges, some of which are still in daily use, for example, the Puente Romano at Mérida in Spain, and the Pont Julien and the bridge at Vaison-la-Romaine, both in Provence, France. The dome permitted the construction of vaulted ceilings without crossbeams and made possible large covered public spaces such as public baths and basilicas, such as Hadrian's Pantheon, the Baths of Diocletian and the Baths of Caracalla, all in Rome. The Romans first adopted the arch from the Etruscans and implemented it in their own building. The use of arches that spring directly from the tops of columns was a Roman development, seen from the 1st century AD, that was very widely adopted in medieval Western, Byzantine and Islamic architecture. Domes The Romans were the first builders in the history of architecture to realize the potential of domes for the creation of large and well-defined interior spaces. Domes were introduced in a number of Roman building types such as temples, thermae, palaces, mausolea and later also churches. Half-domes also became a favored architectural element and were adopted as apses in Christian sacred architecture. Monumental domes began to appear in the 1st century BC in Rome and the provinces around the Mediterranean Sea. Along with vaults, they gradually replaced the traditional post and lintel construction which makes use of the column and architrave. The construction of domes was greatly facilitated by the invention of concrete, a process which has been termed the Roman architectural revolution. Their enormous dimensions remained unsurpassed until the introduction of structural steel frames in the late 19th century (see List of the world's largest domes). Influence on later architecture Roman architecture supplied the basic vocabulary of Pre-Romanesque and Romanesque architecture, and spread across Christian Europe well beyond the old frontiers of the empire, to Ireland and Scandinavia for example. In the East, Byzantine architecture developed new styles of churches, but most other buildings remained very close to Late Roman forms. The same can be said in turn of Islamic architecture, where Roman forms long continued, especially in private buildings such as houses and the bathhouse, and civil engineering such as fortifications and bridges. In Europe the Italian Renaissance saw a conscious revival of correct classical styles, initially purely based on Roman examples. Vitruvius was respectfully reinterpreted by a series of architectural writers, and the Tuscan and Composite orders formalized for the first time, to give five rather than three orders. After the flamboyance of Baroque architecture, the Neoclassical architecture of the 18th century revived purer versions of classical style, and for the first time added direct influence from the Greek world. Numerous local classical styles developed, such as Palladian architecture, Georgian architecture and Regency architecture in the English-speaking world, Federal architecture in the United States, and later Stripped Classicism and PWA Moderne. Roman influences may be found around us today, in banks, government buildings, great houses, and even small houses, perhaps in the form of a porch with Doric columns and a pediment or in a fireplace or a mosaic shower floor derived from a Roman original, often from Pompeii or Herculaneum. The mighty pillars, domes and arches of Rome echo in the New World too, where in Washington, D.C. stand the Capitol building, the White House, the Lincoln Memorial, and other government buildings. All across the US the seats of regional government were normally built in the grand traditions of Rome, with vast flights of stone steps sweeping up to towering pillared porticoes, with huge domes gilded or decorated inside with the same or similar themes that were popular in Rome. In Britain, a similar enthusiasm has seen the construction of thousands of neoclassical buildings over the last five centuries, both civic and domestic, and many of the grandest country houses and mansions are purely Classical in style, an obvious example being Buckingham Palace. Materials Stone Marble is not found especially close to Rome, and was only rarely used there before Augustus, who famously boasted that he had found Rome made of brick and left it made of marble, though this was mainly as a facing for brick or concrete. The Temple of Hercules Victor of the late 2nd century BC is the earliest surviving exception in Rome. From Augustus' reign the quarries at Carrara were extensively developed for the capital, and other sources around the empire exploited, especially the prestigious Greek marbles like Parian. Travertine limestone was found much closer, around Tivoli, and was used from the end of the Republic; the Colosseum is mainly built of this stone, which has good load-bearing capacity, with a brick core. Other more or less local stones were used around the Empire. The Romans were fond of luxury imported coloured marbles with fancy veining, and the interiors of the most important buildings were often faced with slabs of these, which have usually now been removed even where the building survives. Imports from Greece for this purpose began in the 2nd century BC. Roman brick The Romans made fired clay bricks from about the beginning of the Empire, replacing earlier sun-dried mudbrick. Roman brick was almost invariably of a lesser height than modern brick, but was made in a variety of different shapes and sizes. Shapes included square, rectangular, triangular and round, and the largest bricks found have measured over three feet in length. Ancient Roman bricks had a general size of 1½ Roman feet by 1 Roman foot, but common variations up to 15 inches existed. Other brick sizes in ancient Rome included 24" x 12" x 4", and 15" x 8" x 10". Ancient Roman bricks found in France measured 8" x 8" x 3". The Constantine Basilica in Trier is constructed from Roman bricks 15" square by 1½" thick. There is often little obvious difference (particularly when only fragments survive) between Roman bricks used for walls on the one hand, and tiles used for roofing or flooring on the other, so archaeologists sometimes prefer to employ the generic term ceramic building material (or CBM). The Romans perfected brick-making during the first century of their empire and used it ubiquitously, in public and private construction alike. They took their brickmaking skills everywhere they went, introducing the craft to the local populations. The Roman legions, which operated their own kilns, introduced bricks to many parts of the Empire; bricks are often stamped with the mark of the legion that supervised their production. The use of bricks in southern and western Germany, for example, can be traced to traditions already described by the Roman architect Vitruvius. In the British Isles, the introduction of Roman brick by the ancient Romans was followed by a 600–700 year gap in major brick production. Roman concrete Concrete quickly supplanted brick as the primary building material, and more daring buildings soon followed, with great pillars supporting broad arches and domes rather than dense lines of columns suspending flat architraves. The freedom of concrete also inspired the colonnade screen, a row of purely decorative columns in front of a load-bearing wall. In smaller-scale architecture, concrete's strength freed the floor plan from rectangular cells to a more free-flowing environment. Most of these developments are described by Vitruvius, writing in the first century BC in his work De architectura. Although concrete had been used on a minor scale in Mesopotamia, Roman architects perfected Roman concrete and used it in buildings where it could stand on its own and support a great deal of weight. The first use of concrete by the Romans was in the town of Cosa sometime after 273 BC. Ancient Roman concrete was a mixture of lime mortar, aggregate, pozzolana, water, and stones, and was stronger than previously used concretes. The ancient builders placed these ingredients in wooden frames where they hardened and bonded to a facing of stones or (more frequently) bricks. The aggregates used were often much larger than in modern concrete, amounting to rubble. When the framework was removed, the new wall was very strong, with a rough surface of bricks or stones. This surface could be smoothed and faced with an attractive stucco or thin panels of marble or other coloured stones called a "revetment". Concrete construction proved to be more flexible and less costly than building solid stone buildings. The materials were readily available and not difficult to transport. The wooden frames could be used more than once, allowing builders to work quickly and efficiently. Concrete is arguably the Roman contribution most relevant to modern architecture. Building types Amphitheatre The amphitheatre was, with the triumphal arch and basilica, the only major new type of building developed by the Romans. Some of the most impressive secular buildings are the amphitheatres, over 200 being known and many of which are well preserved, such as that at Arles, as well as its progenitor, the Colosseum in Rome. They were used for gladiatorial contests, public displays, public meetings and bullfights, the tradition of which still survives in Spain and Portugal. Their typical shape, functions and name distinguish them from Roman theatres, which are more or less semicircular in shape; from the circuses (akin to hippodromes) whose much longer circuits were designed mainly for horse or chariot racing events; and from the smaller stadia, which were primarily designed for athletics and footraces. The earliest Roman amphitheatres date from the middle of the first century BC, but most were built under Imperial rule, from the Augustan period (27 BC–14 AD) onwards. Imperial amphitheatres were built throughout the Roman Empire; the largest could accommodate 40,000–60,000 spectators, and the most elaborate featured multi-storeyed, arcaded façades and were elaborately decorated with marble, stucco and statuary. After the end of gladiatorial games in the 5th century and of animal killings in the 6th, most amphitheatres fell into disrepair, and their materials were mined or recycled. Some were razed, and others converted into fortifications. A few continued as convenient open meeting places; in some of these, churches were sited. Architecturally, they are typically an example of the Roman use of the classical orders to decorate large concrete walls pierced at intervals, where the columns have nothing to support. Aesthetically, however, the formula is successful. Basilica The Roman basilica was a large public building where business or legal matters could be transacted. They were normally where the magistrates held court, and used for other official ceremonies, having many of the functions of the modern town hall. The first basilicas had no religious function. As early as the time of Augustus, a public basilica for transacting business had been part of any settlement that considered itself a city, used in the same way as the late medieval covered market houses of northern Europe, where the meeting room, for lack of urban space, was set above the arcades. Although their form was variable, basilicas often contained interior colonnades that divided the space, giving aisles or arcaded spaces on one or both sides, with an apse at one end (or less often at each end), where the magistrates sat, often on a slightly raised dais. The central aisle tended to be wide and was higher than the flanking aisles, so that light could penetrate through the clerestory windows. The oldest known basilica, the Basilica Porcia, was built in Rome in 184 BC by Cato the Elder during the time he was censor. Other early examples include the basilica at Pompeii (late 2nd century BC). After Christianity became the official religion, the basilica shape was found appropriate for the first large public churches, with the attraction of avoiding reminiscences of the Greco-Roman temple form. Circus The Roman circus was a large open-air venue used for public events in the ancient Roman Empire. The circuses were similar to the ancient Greek hippodromes, although circuses served varying purposes and differed in design and construction. Along with theatres and amphitheatres, circuses were one of the main entertainment sites of the time. Circuses were venues for chariot racing, horse races, and performances that commemorated important events of the Empire were performed there. For events that involved re-enactments of naval battles, the circus was flooded with water. The performance space of the Roman circus was normally, despite its name, an oblong rectangle of two linear sections of race track, separated by a median strip running along the length of about two thirds the track, joined at one end with a semicircular section and at the other end with an undivided section of track closed (in most cases) by a distinctive starting gate known as the carceres, thereby creating a circuit for the races. Forum During the years of the Republic, Augustus claimed he "found the city in brick and left it in marble". While chances are high that this was an exaggeration, there is something to be said for the influx of marble use in Roman Forum from 63 BC onwards. During Augustus' reign, the Forum was described to have been "a larger, freer space than was the Forum of Imperial times." The Forum began to take on even more changes upon the arrival of Julius Caesar, who drew out extensive plans for the market hub. While Caesar's death came prematurely, his ideas, as well as Augustus' in regards to the Forum proved to be the most influential for years to come. According to Walter Dennison's The Roman Forum As Cicero Saw It, the author writes that "the diverting of public business to the larger and splendid Imperial fora erected in the vicinity resulted in leaving the general design of the Forum Romanum". Every city had at least one forum of varying size. In addition to its standard function as a marketplace, a forum was a gathering place of great social significance, and often the scene of diverse activities, including political discussions and debates, rendezvous, meetings, etc. The best known example is the Roman Forum, the earliest of several in Rome. In new Roman towns the forum was usually located at, or just off, the intersection of the main north–south and east–west streets (the cardo and decumanus). All forums would have a Temple of Jupiter at the north end, and would also contain other temples, as well as the basilica; a public weights and measures table, so customers at the market could ensure they were not being sold short measures; and would often have the baths nearby. Horreum A horreum was a type of public warehouse used during the ancient Roman period. Although the Latin term is often used to refer to granaries, Roman horrea were used to store many other types of consumables; the giant Horrea Galbae in Rome were used not only to store grain but also olive oil, wine, foodstuffs, clothing and even marble. By the end of the Imperial period, the city of Rome had nearly 300 horrea to supply its demands. The biggest were enormous, even by modern standards; the Horrea Galbae contained 140 rooms on the ground floor alone, covering an area of some . The first horrea were built in Rome towards the end of the 2nd century BC, with the first known public horreum being constructed by the ill-fated tribune Gaius Gracchus in 123 BC. The word came to be applied to any place designated for the preservation of goods; thus, it was often used to refer to cellars (horrea subterranea), but it could also be applied to a place where artworks were stored, or even to a library. Some public horrea functioned somewhat like banks, where valuables could be stored, but the most important class of horrea were those where foodstuffs such as grain and olive oil were stored and distributed by the state. The word itself is thought to have linguist roots tied to the word hordeum, which in Latin means barley. In the Johns Hopkins University Press, The Classical Weekly states that "Pliny the Elder does indeed make a distinction between the two words. He describes the horreum as a structure made of brick, the walls of which were not less than three feet thick; it had no windows or openings for ventilation". Furthermore, the storehouses would also host oil and wine and also use large jars that could serve as cache's for large amounts of products. These storehouses were also used to keep large sums of money and were used much like personal storage units today are. "These horrea were divided and subdivided, so that one could hire only so much space as one wanted, a whole room (cella), a closet (armarium), or only a chest or strong box (arca, arcula, locus, loculus)." Insula Multi-story apartment blocks called insulae catered to a range of residential needs. The cheapest rooms were at the top owing to the inability to escape in the event of a fire and the lack of piped water. Windows were mostly small, facing the street, with iron security bars. Insulae were often dangerous, unhealthy, and prone to fires because of overcrowding and haphazard cooking arrangements. There are examples in the Roman port town of Ostia, that date to the reign of Trajan, but they seem to have been found mainly in Rome and a few other places. Elsewhere writers report them as something remarkable, but Livy and Vitruvius refer to them in Rome. External walls were in opus reticulatum and interiors in opus incertum, which would then be plastered and sometimes painted. To lighten up the small dark rooms, some tenants able to afford a degree of painted colourful murals on the walls. Examples have been found of jungle scenes with wild animals and exotic plants. Imitation windows (trompe-l'œil) were sometimes painted to make the rooms seem less confined. Ancient Rome had elaborate and luxurious houses owned by the elite. The average house, or in cities apartment, of a commoner or plebeius did not contain many luxuries. The domus, or single-family residence, was only for the well-off in Rome, with most having a layout of the closed unit, consisting of one or two rooms. Between 312 and 315 AD Rome had 1781 domus and 44,850 of insulae. Insulae have been the subject of debate for historians of Roman culture, defining the various meanings of the word. Insula was a word used to describe apartment buildings, or the apartments themselves, meaning apartment, or inhabitable room, demonstrating just how small apartments for plebeians were. Urban divisions were originally street blocks, and later began to divide into smaller divisions, the word insula referring to both blocks and smaller divisions. The insula contained cenacula, tabernae, storage rooms under the stairs, and lower floor shops. Another type of housing unit for plebs was a cenaculum, an apartment, divided into three individual rooms: cubiculum, exedra, and medianum. Common Roman apartments were mainly masses of smaller and larger structures, many with narrow balconies that present mysteries as to their use, having no doors to access them, and they lacked the excessive decoration and display of wealth that aristocrats' houses contained. Luxury in houses was not common, as the life of the average person did not consist of being in their houses, as they instead would go to public baths, and engage in other communal activities. Lighthouses Many lighthouses were built around the Mediterranean and the coasts of the empire, including the Tower of Hercules at A Coruña in northern Spain, a structure which survives to this day. A smaller lighthouse at Dover, England also exists as a ruin about half the height of the original. The light would have been provided by a fire at the top of the structure. Thermae All Roman cities had at least one thermae, a popular facility for public bathing, exercising and socializing. Exercise might include wrestling and weightlifting, as well as swimming. Bathing was an important part of the Roman day, where some hours might be spent, at a very low cost subsidized by the government. Wealthier Romans were often accompanied by one or more slaves, who performed any required tasks such as fetching refreshment, guarding valuables, providing towels, and at the end of the session, applying olive oil to their masters' bodies, which was then scraped off with a strigil, a scraper made of wood or bone. Roman bath-houses were also provided for private villas, town houses and forts. They were normally supplied with water from an adjacent river or stream, or by aqueduct. The design of thermae is discussed by Vitruvius in De architectura. Temples Roman temples were among the most important and richest buildings in Roman culture, though only a few survive in any sort of complete state. Their construction and maintenance was a major part of ancient Roman religion, and all towns of any importance had at least one main temple, as well as smaller shrines. The main room (cella) housed the cult image of the deity to whom the temple was dedicated, and often a small altar for incense or libations. Behind the cella was a room or rooms used by temple attendants for storage of equipment and offerings. Remains of many Roman temples survive, above all in Rome itself, but the relatively few near-complete examples were nearly all converted to Christian churches, usually a considerable time after the initial triumph of Christianity under Constantine. The decline of Roman religion was relatively slow, and the temples themselves were not appropriated by the government until a decree of the Emperor Honorius in 415. Some of the oldest surviving temples include the Temple of Hercules Victor (mid 2nd century BC) and Temple of Portunus (120–80 BC), both standing within the Forum Boarium. Original marble columns of the Temple of Janus in Rome's Forum Holitorium, dedicated by Gaius Duilius after his naval victory at the Battle of Mylae in 260 BC, still stand as a component of the exterior wall of the Renaissance era church of San Nicola in Carcere. The form of the Roman temple was mainly derived from the Etruscan model, but using Greek styles. Roman temples emphasised the front of the building, which followed Greek temple models and typically consisted of wide steps leading to a portico with columns, a pronaos, and usually a triangular pediment above, which was filled with statuary in the most grand examples; this was as often in terracotta as stone, and no examples have survived except as fragments. However, unlike the Greek models, which generally gave equal treatment to all sides of the temple, which could be viewed and approached from all directions, the sides and rear of Roman temples might be largely undecorated (as in the Pantheon, Rome and temple of Vic), inaccessible by steps (as in the Maison carrée and Vic), and even back on to other buildings. As in the Maison carrée, columns at the side might be engaged columns, emerging from ("engaged with" in architectural terminology) the wall. The platform on which the temple sat was typically raised higher in Roman examples than Greek, with up ten or twelve or more steps rather than the three typical in Greek temples; the Temple of Claudius was raised twenty steps. These steps were normally only at the front, and typically not the whole width of that. The Greek classical orders in all their details were closely followed in the façades of temples, as in other prestigious buildings. However, the idealized proportions between the different elements set out by the only significant Roman writer on architecture to survive, Vitruvius, and subsequent Italian Renaissance writers, do not reflect actual Roman practice, which could be very variable, though always aiming at balance and harmony. Following a Hellenistic trend, the Corinthian order and its variant the Composite order were most common in surviving Roman temples, but for small temples like that at Alcántara, a simple Tuscan order could be used. There was considerable local variation in style, as Roman architects often tried to incorporate elements the population expected in its sacred architecture. This was especially the case in Egypt and the Near East, where different traditions of large stone temples were already millennia old. The Romano-Celtic temple was a simple style for small temples found in the Western Empire, and by far the most common type in Roman Britain. It often lacked any of the distinctive classical features, and may have had considerable continuity with pre-Roman temples of the Celtic religion. Theatres Roman theatres were built in all areas of the Empire, from Spain to the Middle East. Because of the Romans' ability to influence local architecture, numerous theatres were built around the world with uniquely Roman attributes. These buildings were semi-circular and possessed certain inherent architectural structures, with minor differences depending on the region in which they were constructed. The scaenae frons was a high back wall of the stage floor, supported by columns. The proscaenium was a wall that supported the front edge of the stage with ornately decorated niches to the sides. The Hellenistic influence is seen through the use of the proscaenium. The Roman theatre also had a podium, which sometimes supported the columns of the scaenae frons. The scaenae was originally not part of the building itself, constructed only to provide sufficient background for the actors. Eventually, it became a part of the edifice itself, made out of concrete. The theatre itself was divided into the stage (orchestra) and the seating section (auditorium). Vomitoria or entrances and exits were made available to the audience. Villa A Roman villa was a country house built for the upper class, while a domus was a wealthy family's house in a town. The Empire contained many kinds of villas, not all of them lavishly appointed with mosaic floors and frescoes. In the provinces, any country house with some decorative features in the Roman style may be called a "villa" by modern scholars. Some, like Hadrian's Villa at Tivoli, were pleasure palaces such as those that were situated in the cool hills within easy reach of Rome or, like the Villa of the Papyri at Herculaneum, on picturesque sites overlooking the Bay of Naples. Some villas were more like the country houses of England, the visible seat of power of a local magnate, such as the famous palace rediscovered at Fishbourne in Sussex. Suburban villas on the edge of cities were also known, such as the Middle and Late Republican villas that encroached on the Campus Martius, at that time on the edge of Rome, and which can be also seen outside the city walls of Pompeii, including the Villa of the Mysteries, known for its frescos. These early suburban villas, such as the one at Rome's Auditorium site or at Grottarossa in Rome, demonstrate the antiquity and heritage of the villa suburbana in Central Italy. It is possible that these early, suburban villas were also in fact the seats of power (maybe even palaces) of regional strongmen or heads of important families (gentes). A third type of villa provided the organizational center of the large farming estates called latifundia; such villas might be lacking in luxuries. By the 4th century, villa could simply mean an agricultural estate or holding: Jerome translated the Gospel of Mark (xiv, 32) chorion, describing the olive grove of Gethsemane, with villa, without an inference that there were any dwellings there (Catholic Encyclopedia "Gethsemane"). With the colossal Diocletian's Palace, built in the countryside but later turned into a fortified city, a form of residential castle emerges, that anticipates the Middle Ages. Watermills The initial invention of the watermill appears to have occurred in the Hellenized eastern Mediterranean in the wake of the conquests of Alexander the Great and the rise of Hellenistic science and technology. In the subsequent Roman era, the use of water-power was diversified and different types of watermills were introduced. These include all three variants of the vertical water wheel as well as the horizontal water wheel. Apart from its main use in grinding flour, water-power was also applied to pounding grain, crushing ore, sawing stones and possibly fulling and bellows for iron furnaces. Decorative structures Monoliths In architecture, a monolith is a structure which has been excavated as a unit from a surrounding matrix or outcropping of rock. Monoliths are found in all types of Roman buildings. They were either: quarried without being moved; or quarried and moved; or quarried, moved and lifted clear off the ground into their position (e.g., architraves); or quarried, moved and erected in an upright position (e.g., columns). Transporting was done by land or water (or a combination of both), in the later case often by special-built ships such as obelisk carriers. For lifting operations, ancient cranes were employed since c. 515 BC, such as in the construction of Trajan's Column. Obelisks An obelisk is a tall, four-sided, narrow tapering monument which ends in a pyramid-like shape at the top. These were originally called "tekhenu" by the builders, the ancient Egyptians. The Greeks who saw them used the Greek 'obeliskos' to describe them, and this word passed into Latin and then English. The Romans commissioned obelisks in an ancient Egyptian style. Examples include: Arles, France – the Arles Obelisk, in Place de la République, a 4th-century obelisk of Roman origin Benevento, Italy – three Roman obelisks Munich – obelisk of Titus Sextius Africanus, Staatliches Museum Ägyptischer Kunst, Kunstareal, 1st century AD, 5.80 m Rome – there are five ancient Roman obelisks in Rome. Roman gardens Roman gardens were influenced by Egyptian, Persian, and Greek gardening techniques. In Ancient Latium, a garden was part of every farm. According to Cato the Elder, every garden should be close to the house and should have flower beds and ornamental trees. Horace wrote that during his time flower gardens became a national indulgence. Gardens were not reserved for the extremely wealthy. Excavations in Pompeii show that gardens attaching to residences were scaled down to meet the space constraints of the home of the average Roman. Modified versions of Roman garden designs were adopted in Roman settlements in Africa, Gaul, and Britannia. As town houses were replaced by tall insulae (apartment buildings), these urban gardens were replaced by window boxes or roof gardens. Triumphal arches A triumphal arch is a monumental structure in the shape of an archway with one or more arched passageways, often designed to span a road. The origins of the Roman triumphal arch are unclear, other than in the temporary structures, whose appearance is unknown, erected for Roman triumphs under the Roman Republic, and later. There were precursors to the permanent triumphal arch within the Roman world; in Italy, the Etruscans used elaborately decorated single bay arches as gates or portals to their cities. Surviving examples of Etruscan arches can still be seen at Perugia and Volterra. The two key elements of the triumphal arch – a round-topped arch and a square entablature – had long been in use as separate architectural elements in ancient Greece. The innovation of the Romans was to use these elements in a single free-standing structure. The columns became purely decorative elements on the outer face of the arch, while the entablature, liberated from its role as a building support, became the frame for the civic and religious messages that the arch builders wished to convey. Little is known about how the Romans viewed triumphal arches. Pliny the Elder, writing in the first century AD, was the only ancient author to discuss them. He wrote that they were intended to "elevate above the ordinary world" an image of an honoured person usually depicted in the form of a statue with a quadriga. The first recorded Roman triumphal arches were set up in the time of the Roman Republic. Generals who were granted a triumph were termed triumphators and would erect fornices or honorific arches bearing statues to commemorate their victories. Roman triumphal practices changed significantly at the start of the Imperial period, when the first Roman Emperor Augustus decreed that only emperors would be granted triumphs. The triumphal arch changed from being a personal monument to being an essentially propagandistic one, serving to announce and promote the presence of the ruler and the laws of the state. Arches were not necessarily built as entrances, but – unlike many modern triumphal arches – they were often erected across roads and were intended to be passed through, not round. Most Roman triumphal arches were built during the Imperial period. By the fourth century AD there were 36 such arches in Rome, of which three have survived – the Arch of Titus (AD 81), the Arch of Septimius Severus (203–205) and the Arch of Constantine (312). Numerous arches were built elsewhere in the Roman Empire. The single arch was the most common, but many triple arches were also built, of which the Triumphal Arch of Orange (c. AD 21) is the earliest surviving example. From the 2nd century AD, many examples of the arcus quadrifrons – a square triumphal arch erected over a crossroads, with arched openings on all four sides – were built, especially in North Africa. Arch-building in Rome and Italy diminished after the time of Trajan (AD 98–117) but remained widespread in the provinces during the 2nd and 3rd centuries AD; they were often erected to commemorate imperial visits. The ornamentation of an arch was intended to serve as a constant visual reminder of the triumph and triumphator. The façade was ornamented with marble columns, and the piers and attics with decorative cornices. Sculpted panels depicted victories and achievements, the deeds of the triumphator, the captured weapons of the enemy or the triumphal procession itself. The spandrels usually depicted flying Victories, while the attic was often inscribed with a dedicatory inscription naming and praising the triumphator. The piers and internal passageways were also decorated with reliefs and free-standing sculptures. The vault was ornamented with coffers. Some triumphal arches were surmounted by a statue or a currus triumphalis, a group of statues depicting the emperor or general in a quadriga. Inscriptions on Roman triumphal arches were works of art in themselves, with very finely cut, sometimes gilded letters. The form of each letter and the spacing between them was carefully designed for maximum clarity and simplicity, without any decorative flourishes, emphasizing the Roman taste for restraint and order. This conception of what later became the art of typography remains of fundamental importance to the present day. Victory columns Infrastructure Roads Roman roads were vital to the maintenance and development of the Roman state, and were built from about 500 BC through the expansion and consolidation of the Roman Republic and the Roman Empire. They provided efficient means for the overland movement of armies, officials and civilians, and the inland carriage of official communications and trade goods. At the peak of Rome's development, no fewer than 29 great military highways radiated from the capital, and the Late Empire's 113 provinces were interconnected by 372 great road links. Roman road builders aimed at a regulation width (see Laws and standards above), but actual widths have been measured at between and more than . Today, the concrete has worn from the spaces around the stones, giving the impression of a very bumpy road, but the original practice was to produce a surface that was much closer to being flat. Aqueduct The Romans constructed numerous aqueducts in order to bring water from distant sources into their cities and towns, supplying public baths, latrines, fountains and private households. Waste water was removed by complex sewage systems and released into nearby bodies of water, keeping the towns clean and free from effluent. Aqueducts also provided water for mining operations, milling, farms and gardens. Aqueducts moved water through gravity alone, being constructed along a slight downward gradient within conduits of stone, brick or concrete. Most were buried beneath the ground, and followed its contours; obstructing peaks were circumvented or, less often, tunnelled through. Where valleys or lowlands intervened, the conduit was carried on bridgework, or its contents fed into high-pressure lead, ceramic or stone pipes and siphoned across. Most aqueduct systems included sedimentation tanks, sluices and distribution tanks to regulate the supply as needed. Ancient Rome's first aqueduct – the Aqua Appia – supplied a water-fountain sited at the city's cattle market in the fourth century BC. By the third century AD, the city had eleven aqueducts, sustaining a population of over a million people in a water-extravagant economy; most of the water supplied the city's many public baths. Cities and municipalities throughout the Roman Empire emulated this model and funded aqueducts as objects of public interest and civic pride, "an expensive yet necessary luxury to which all could, and did, aspire." Most Roman aqueducts proved reliable, and durable; some were maintained into the early modern era, and a few are still partly in use. Methods of aqueduct surveying and construction are noted by Vitruvius in his work De architectura (1st century BC). The general Frontinus gives more detail in his official report on the problems, uses and abuses of Imperial Rome's public water supply. Notable examples of aqueduct architecture include the supporting piers of the Aqueduct of Segovia, and the aqueduct-fed cisterns of Constantinople. Bridges Roman bridges, built by ancient Romans, were the first large and lasting bridges built. Roman bridges were built with stone and had the arch as the basic structure. Most used concrete as well, which the Romans were the first to use for bridges. Roman arch bridges were usually semicircular, although a few were segmental (such as Alconétar Bridge). A segmental arch is an arch that is less than a semicircle. The advantages of the segmental arch bridge were that it allowed great amounts of flood water to pass under it, which would prevent the bridge from being swept away during floods and the bridge itself could be more lightweight. Generally, Roman bridges featured wedge-shaped primary arch stones (voussoirs) of the same in size and shape. The Romans built both single spans and lengthy multiple arch aqueducts, such as the Pont du Gard and Segovia Aqueduct. Their bridges featured from an early time onwards flood openings in the piers, e.g. in the Pons Fabricius in Rome (62 BC), one of the world's oldest major bridges still standing. Roman engineers were the first and until the Industrial Revolution the only ones to construct bridges with concrete, which they called opus caementicium. The outside was usually covered with brick or ashlar, as in the Alcántara bridge. The Romans also introduced segmental arch bridges into bridge construction. The 330 m long Limyra Bridge in southwestern Turkey features 26 segmental arches with an average span-to-rise ratio of 5.3:1, giving the bridge an unusually flat profile unsurpassed for more than a millennium. Trajan's bridge over the Danube featured open-spandrel segmental arches made of wood (standing on 40 m high concrete piers). This was to be the longest arch bridge for a thousand years both in terms of overall and individual span length, while the longest extant Roman bridge is the 790 m long Puente Romano at Mérida. Canals Roman canals were typically multi-purpose structures, intended for irrigation, drainage, land reclamation, flood control and navigation where feasible. Some navigational canals were recorded by ancient geographers and are still traceable by modern archaeology. Channels which served the needs of urban water supply are covered at the List of aqueducts in the Roman Empire. Cisterns Freshwater reservoirs were commonly set up at the termini of aqueducts and their branch lines, supplying urban households, agricultural estates, imperial palaces, thermae or naval bases of the Roman navy. Dams Roman dam construction began in earnest in the early imperial period. For the most part, it concentrated on the semi-arid fringe of the empire, namely the provinces of North Africa, the Near East, and Hispania. The relative abundance of Spanish dams below is due partly to more intensive field work there; for Italy only the Subiaco Dams, created by emperor Nero (54–68 AD) for recreational purposes, are attested. These dams are noteworthy, though, for their extraordinary height, which remained unsurpassed anywhere in the world until the Late Middle Ages. The most frequent dam types were earth- or rock-filled embankment dams and masonry gravity dams. These served a wide array of purposes, such as irrigation, flood control, river diversion, soil-retention, or a combination of these functions. The impermeability of Roman dams was increased by the introduction of waterproof hydraulic mortar and especially opus caementicium in the Concrete Revolution. These materials also allowed for bigger structures to be built, like the Lake Homs Dam, possibly the largest water barrier today, and the sturdy Harbaqa Dam, both of which consist of a concrete core. Roman builders were the first to realize the stabilizing effect of arches and buttresses, which they integrated into their dam designs. Previously unknown dam types introduced by the Romans include arch-gravity dams, arch dams, buttress dams, and multiple-arch buttress dams. Defensive walls The Romans generally fortified cities rather than fortresses, but there are some fortified camps such as the Saxon Shore forts like Porchester Castle in England. City walls were already significant in Etruscan architecture, and in the struggle for control of Italy under the early Republic many more were built, using different techniques. These included tightly fitting massive irregular polygonal blocks, shaped to fit exactly in a way reminiscent of later Inca work. The Romans called a simple rampart wall an agger; at this date great height was not necessary. The Servian Wall around Rome was an ambitious project of the early 4th century BC. The wall was up to in height in places, wide at its base, long, and is believed to have had 16 main gates, though many of these are mentioned only from writings, with no other known remains. Some of it had a fossa or ditch in front, and an agger behind, and it was enough to deter Hannibal. Later the Aurelian Wall replaced it, enclosing an expanded city, and using more sophisticated designs, with small forts at intervals. The Romans walled major cities and towns in areas they saw as vulnerable, and parts of many walls remain incorporated in later defensive fortifications, as at Córdoba (2nd century BC), Chester (earth and wood in the 70s AD, stone from ), and York (from 70s AD). Strategic walls across open country were far rarer, and Hadrian's Wall (from 122) and the Antonine Wall (from 142, abandoned only 8 years after completion) are the most significant examples, both on the Pictish frontier of Roman Britain. Architectural features Mosaics On his return from campaigns in Greece, the general Sulla brought back what is probably the best-known element of the early imperial period: the mosaic, a decoration made of colourful chips of stone inserted into cement. This tiling method took the empire by storm in the late first century and the second century and in the Roman home joined the well-known mural in decorating floors, walls, and grottoes with geometric and pictorial designs. There were two main techniques in Greco-Roman mosaic. Opus vermiculatum used tiny tesserae, typically cubes of 4 millimeters or less, and was produced in workshops in relatively small panels, which were transported to the site glued to some temporary support. The tiny tesserae allowed very fine detail and an approach to the illusionism of painting. Often small panels called emblemata were inserted into walls or as the highlights of larger floor-mosaics in coarser work. The normal technique, however, was opus tessellatum, using larger tesserae, which were laid on site. There was a distinct native Italian style using black on a white background, which was no doubt cheaper than fully coloured work. A specific genre of Roman mosaic obtained the name asaroton (Greek "unswept floor"). It represented an optical illusion of the leftovers from a feast on the floor of rich houses. Hypocaust A hypocaust was an ancient Roman system of underfloor heating, used to heat buildings with hot air. The Roman architect Vitruvius, writing about the end of the 1st century BC, attributes their invention to Sergius Orata. Many remains of Roman hypocausts have survived throughout Europe, western Asia, and northern Africa. The hypocaust was an invention which improved the hygiene and living conditions of citizens, and was a forerunner of modern central heating. Hypocausts were used for heating hot baths (thermae), houses and other buildings, whether public or private. The floor was raised above the ground by pillars, called pilae stacks, with a layer of tiles, then a layer of concrete, then another of tiles on top; and spaces were left inside the walls so that hot air and smoke from the furnace would pass through these enclosed areas and out of flues in the roof, thereby heating but not polluting the interior of the room. Roman roofs In Magna Graecia truss roofs presumably appeared as early as 550 BC. Their potential was fully realized in the Roman period, which saw trussed roofs over 30 meters wide spanning the rectangular spaces of monumental public buildings such as temples, basilicas, and later churches. Such spans were three times as wide as the widest prop-and-lintel roofs and only surpassed by the largest Roman domes. The largest truss roof by span of ancient Rome covered the Aula Regia (throne room) built for emperor Domitian (81–96 AD) on the Palatine Hill, Rome. The timber truss roof had a width of 31.67 m, slightly surpassing the postulated limit of 30 m for Roman roof constructions. Tie-beam trusses allowed for much larger spans than the older prop-and-lintel system and even concrete vaulting. Nine out of the ten largest rectangular spaces in Roman architecture were bridged this way, the only exception being the groin vaulted Basilica of Maxentius. Spiral stairs The spiral stair is a type of stairway which, due to its complex helical structure, was introduced relatively late into architecture. Although the oldest example dates to the 5th century BC, it was only in the wake of the influential design of Trajan's Column that this space-saving new type permanently caught hold in Roman architecture. Apart from the triumphal columns in the imperial cities of Rome and Constantinople, other types of buildings such as temples, thermae, basilicas and tombs were also fitted with spiral stairways. Their notable absence in the towers of the Aurelian Wall indicates that although used in medieval castles, they did not yet figure prominently in Roman military engineering. By late antiquity, separate stair towers were constructed adjacent to the main buildings, as in the Basilica of San Vitale. The construction of spiral stairs passed on both to Christian and Islamic architecture. City design The ancient Romans employed regular orthogonal structures on which they molded their colonies. They probably were inspired by Greek and Hellenic examples, as well as by regularly planned cities that were built by the Etruscans in Italy. (see Marzabotto) The Romans used a consolidated scheme for city planning, developed for military defense and civil convenience. The basic plan consisted of a central forum with city services, surrounded by a compact, rectilinear grid of streets, and wrapped in a wall for defense. To reduce travel times, two diagonal streets crossed the square grid, passing through the central square. A river usually flowed through the city, providing water, transport, and sewage disposal. Hundreds of towns and cities were built by the Romans throughout their Empire. Many European towns, such as Turin, preserve the remains of these schemes, which show the very logical way the Romans designed their cities. They would lay out the streets at right angles, in the form of a square grid. All roads were equal in width and length, except for two, which were slightly wider than the others. One of these ran east–west, the other, north–south, and they intersected in the middle to form the center of the grid. All roads were made of carefully fitted flagstones and filled in with smaller, hard-packed rocks and pebbles. Bridges were constructed where needed. Each square marked off by four roads was called an insula, the Roman equivalent of a modern city block. Each insula was square, with the land within it divided. As the city developed, each insula would eventually be filled with buildings of various shapes and sizes and crisscrossed with back roads and alleys. Most insulae were given to the first settlers of a Roman city, but each person had to pay to construct his own house. The city was surrounded by a wall to protect it from invaders and to mark the city limits. Areas outside city limits were left open as farmland. At the end of each main road was a large gateway with watchtowers. A portcullis covered the opening when the city was under siege, and additional watchtowers were constructed along the city walls. An aqueduct was built outside the city walls. The development of Greek and Roman urbanization is well-known, as there are relatively many written sources, and there has been much attention to the subject, since the Romans and Greeks are generally regarded as the main ancestors of modern Western culture. It should not be forgotten, though, that the Etruscans had many considerable towns and there were also other cultures with more or less urban settlements in Europe, primarily of Celtic origin. Significant buildings and areas Public buildings Baths of Trajan – these were a massive thermae, a bathing and leisure complex, built in ancient Rome starting from 104 AD and dedicated during the Kalends of July in 109. Baths of Diocletian – in ancient Rome, these were the grandest of the public baths (thermae), built by successive emperors Baths of Caracalla Colosseum Trajan's Column, in Rome Circus Maximus, in Rome Curia Hostilia (Senate House), in Rome Domus Aurea (former building) Forum of Augustus Hadrian's Villa Pantheon Tower of Hercules Tropaeum Traiani Verona Arena, in Verona Rotunda Church of St. George, Serdika, Sofia, Bulgaria Roman theatre of Philippopolis, Plovdiv, Bulgaria Roman Stadium, Philippopolis, Plovdiv, Bulgaria Roman baths, Odessos, Varna, Bulgaria Roman city walls of Diocletianopolis (Thrace), Hisarya, Bulgaria Roman tomb, Primorsko, Bulgaria Tholos Private architecture Alyscamps – a necropolis in Arles, France, one of the most famous necropolises of the ancient world Domus Catacombs of Rome Roman villa Villa rustica Pompeii Herculaneum Stabiae Civil engineering Roman engineering – Romans are famous for their advanced engineering accomplishments, although some of their own inventions were improvements on older ideas, concepts and inventions. Roman watermill Military engineering Castrum Antonine Wall Hadrian's Wall Limes Germanicus See also Outline of ancient Rome Outline of architecture Ancient Greek architecture Architecture of Mesopotamia Achaemenid architecture Roman technology Agriculture in ancient Rome References Footnotes Works cited Favro, Diane, et al. "Rome, ancient, Architecture." Grove Art Online. Oxford Art Online. Oxford University Press, accessed 26 March 2016, subscription required Henig, Martin (ed), A Handbook of Roman Art, Chapter 2 "Architecture" by Thomas Blagg, Phaidon, 1983, Lawrence, A. W., Greek Architecture, 1957, Penguin, Pelican history of art Semper, Gottfried, Style in the technical and tectonic arts, or, Practical aesthetics, 2004 translation of Der Stil in der technischen und tektonischen Künsten (1860-62), Getty Research Institute, ISBN 9780892365975, google books Summerson, John, The Classical Language of Architecture, 1980 edition, Thames and Hudson World of Art series, Yarwood, Doreen, The Architecture of Europe, 1987 (first edn. 1974), Spring Books, Further reading Adam, Jean Pierre. Roman Building: Materials and Techniques. Bloomington: Indiana University Press, 1994. Anderson, James C. Roman Architecture and Society. Baltimore: Johns Hopkins University Press, 1997. Boëthius, Axel. Etruscan and Early Roman Architecture. New Haven: Yale University Press, 1994. Fant, J. Clayton. "Quarrying and Stoneworking." In The Oxford Handbook of Engineering and Technology in the Classical World, edited by John P. Oleson, 121–135. Oxford: Oxford University Press, 2008. Hopkins, John North. The Genesis of Roman Architecture. New Haven: Yale University Press, 2016. Lancaster, Lynne C. Concrete Vaulted Construction In Imperial Rome: Innovations In Context. Cambridge: Cambridge University Press, 2005. --. "Roman Engineering and Construction." In The Oxford Handbook of Engineering and Technology in the Classical World, edited by John P. Oleson, 256–284. Oxford: Oxford University Press. 2008. MacDonald, William Lloyd. The Architecture of the Roman Empire. Rev. ed. New Haven, Connecticut: Yale University Press, 1982. Macready, Sarah, and F. H. Thompson. Roman architecture in the Greek world. London: Society of Antiquaries, 1987. Sear, Frank. Roman Architecture. Ithaca, New York: Cornell University Press, 1983. Thomas, Edmund V. Monumentality and the Roman Empire: Architecture in the Antonine age. Oxford: Oxford University Press, 2007. Ulrich, Roger B. Roman Woodworking. New Haven, Connecticut: Yale University Press, 2007. Ulrich, Roger B., and Caroline K Quenemoen. A Companion to Roman Architecture. Somerset: Wiley, 2013. External links Traianus – Technical investigation of Roman public works Housing and apartments in Rome – A look at various aspects of housing in ancient Rome, apartments and villas. Rome Reborn − A Video Tour through Ancient Rome based on a digital model. . —A virtual tour through Ancient Rome based on a digital model Culture of ancient Rome Architectural history	Ancient Roman architecture	[ "Engineering" ]	12,542	[ "Architectural history", "Architecture" ]
52,713	https://en.wikipedia.org/wiki/Binary%20star	A binary star or binary star system is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved as separate stars using a telescope, in which case they are called visual binaries. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known. They may also be detected by indirect techniques, such as spectroscopy (spectroscopic binaries) or astrometry (astrometric binaries). If a binary star happens to orbit in a plane along our line of sight, its components will eclipse and transit each other; these pairs are called eclipsing binaries, or, together with other binaries that change brightness as they orbit, photometric binaries. If components in binary star systems are close enough, they can gravitationally distort each other's outer stellar atmospheres. In some cases, these close binary systems can exchange mass, which may bring their evolution to stages that single stars cannot attain. Examples of binaries are Sirius, and Cygnus X-1 (Cygnus X-1 being a well-known black hole). Binary stars are also common as the nuclei of many planetary nebulae, and are the progenitors of both novae and type Ia supernovae. Discovery Double stars, a pair of stars that appear close to each other, have been observed since the invention of the telescope. Early examples include Mizar and Acrux. Mizar, in the Big Dipper (Ursa Major), was observed to be double by Giovanni Battista Riccioli in 1650 (and probably earlier by Benedetto Castelli and Galileo). The bright southern star Acrux, in the Southern Cross, was discovered to be double by Father Fontenay in 1685. Evidence that stars in pairs were more than just optical alignments came in 1767 when English natural philosopher and clergyman John Michell became the first person to apply the mathematics of statistics to the study of the stars, demonstrating in a paper that many more stars occur in pairs or groups than a perfectly random distribution and chance alignment could account for. He focused his investigation on the Pleiades cluster, and calculated that the likelihood of finding such a close grouping of stars was about one in half a million. He concluded that the stars in these double or multiple star systems might be drawn to one another by gravitational pull, thus providing the first evidence for the existence of binary stars and star clusters. William Herschel began observing double stars in 1779, hoping to find a near star paired with a distant star so he could measure the near star's changing position as the Earth orbited the Sun (measure its parallax), allowing him to calculate the distance to the near star. He would soon publish catalogs of about 700 double stars. By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, and concluded that, instead of showing parallax changes, they seemed to be orbiting each other in binary systems. The first orbit of a binary star was computed in 1827, when Félix Savary computed the orbit of Xi Ursae Majoris. Over the years, many more double stars have been catalogued and measured. As of June 2017, the Washington Double Star Catalog, a database of visual double stars compiled by the United States Naval Observatory, contains over 100,000 pairs of double stars, including optical doubles as well as binary stars. Orbits are known for only a few thousand of these double stars. Etymology The term binary was first used in this context by Sir William Herschel in 1802, when he wrote: By the modern definition, the term binary star is generally restricted to pairs of stars which revolve around a common center of mass. Binary stars which can be resolved with a telescope or interferometric methods are known as visual binaries. For most of the known visual binary stars one whole revolution has not been observed yet; rather, they are observed to have travelled along a curved path or a partial arc. The more general term double star is used for pairs of stars which are seen to be close together in the sky. This distinction is rarely made in languages other than English. Double stars may be binary systems or may be merely two stars that appear to be close together in the sky but have vastly different true distances from the Sun. The latter are termed optical doubles or optical pairs. Classifications Methods of observation Binary stars are classified into four types according to the way in which they are observed: visually, by observation; spectroscopically, by periodic changes in spectral lines; photometrically, by changes in brightness caused by an eclipse; or astrometrically, by measuring a deviation in a star's position caused by an unseen companion. Any binary star can belong to several of these classes; for example, several spectroscopic binaries are also eclipsing binaries. Visual binaries A visual binary star is a binary star for which the angular separation between the two components is great enough to permit them to be observed as a double star in a telescope, or even high-powered binoculars. The angular resolution of the telescope is an important factor in the detection of visual binaries, and as better angular resolutions are applied to binary star observations, an increasing number of visual binaries will be detected. The relative brightness of the two stars is also an important factor, as glare from a bright star may make it difficult to detect the presence of a fainter component. The brighter star of a visual binary is the primary star, and the dimmer is considered the secondary. In some publications (especially older ones), a faint secondary is called the comes (plural comites; companion). If the stars are the same brightness, the discoverer designation for the primary is customarily accepted. The position angle of the secondary with respect to the primary is measured, together with the angular distance between the two stars. The time of observation is also recorded. After a sufficient number of observations are recorded over a period of time, they are plotted in polar coordinates with the primary star at the origin, and the most probable ellipse is drawn through these points such that the Keplerian law of areas is satisfied. This ellipse is known as the apparent ellipse, and is the projection of the actual elliptical orbit of the secondary with respect to the primary on the plane of the sky. From this projected ellipse the complete elements of the orbit may be computed, where the semi-major axis can only be expressed in angular units unless the stellar parallax, and hence the distance, of the system is known. Spectroscopic binaries Sometimes, the only evidence of a binary star comes from the Doppler effect on its emitted light. In these cases, the binary consists of a pair of stars where the spectral lines in the light emitted from each star shifts first towards the blue, then towards the red, as each moves first towards us, and then away from us, during its motion about their common center of mass, with the period of their common orbit. In these systems, the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be perpendicular to the line of sight, the orbital velocities have components in the line of sight, and the observed radial velocity of the system varies periodically. Since radial velocity can be measured with a spectrometer by observing the Doppler shift of the stars' spectral lines, the binaries detected in this manner are known as spectroscopic binaries. Most of these cannot be resolved as a visual binary, even with telescopes of the highest existing resolving power. In some spectroscopic binaries, spectral lines from both stars are visible, and the lines are alternately double and single. Such a system is known as a double-lined spectroscopic binary (often denoted "SB2"). In other systems, the spectrum of only one of the stars is seen, and the lines in the spectrum shift periodically towards the blue, then towards red and back again. Such stars are known as single-lined spectroscopic binaries ("SB1"). The orbit of a spectroscopic binary is determined by making a long series of observations of the radial velocity of one or both components of the system. The observations are plotted against time, and from the resulting curve a period is determined. If the orbit is circular, then the curve is a sine curve. If the orbit is elliptical, the shape of the curve depends on the eccentricity of the ellipse and the orientation of the major axis with reference to the line of sight. It is impossible to determine individually the semi-major axis a and the inclination of the orbit plane i. However, the product of the semi-major axis and the sine of the inclination (i.e. ) may be determined directly in linear units (e.g. kilometres). If either a or i can be determined by other means, as in the case of eclipsing binaries, a complete solution for the orbit can be found. Binary stars that are both visual and spectroscopic binaries are rare and are a valuable source of information when found. About 40 are known. Visual binary stars often have large true separations, with periods measured in decades to centuries; consequently, they usually have orbital speeds too small to be measured spectroscopically. Conversely, spectroscopic binary stars move fast in their orbits because they are close together, usually too close to be detected as visual binaries. Binaries that are found to be both visual and spectroscopic thus must be relatively close to Earth. Eclipsing binaries An eclipsing binary star is a binary star system in which the orbital plane of the two stars lies so nearly in the line of sight of the observer that the components undergo mutual eclipses. In the case where the binary is also a spectroscopic binary and the parallax of the system is known, the binary is quite valuable for stellar analysis. Algol, a triple star system in the constellation Perseus, contains the best-known example of an eclipsing binary. Eclipsing binaries are variable stars, not because the light of the individual components vary but because of the eclipses. The light curve of an eclipsing binary is characterized by periods of practically constant light, with periodic drops in intensity when one star passes in front of the other. The brightness may drop twice during the orbit, once when the secondary passes in front of the primary and once when the primary passes in front of the secondary. The deeper of the two eclipses is called the primary regardless of which star is being occulted, and if a shallow second eclipse also occurs it is called the secondary eclipse. The size of the brightness drops depends on the relative brightness of the two stars, the proportion of the occulted star that is hidden, and the surface brightness (i.e. effective temperature) of the stars. Typically the occultation of the hotter star causes the primary eclipse. An eclipsing binary's period of orbit may be determined from a study of its light curve, and the relative sizes of the individual stars can be determined in terms of the radius of the orbit, by observing how quickly the brightness changes as the disc of the nearest star slides over the disc of the other star. If it is also a spectroscopic binary, the orbital elements can also be determined, and the mass of the stars can be determined relatively easily, which means that the relative densities of the stars can be determined in this case. Since about 1995, measurement of extragalactic eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them to directly measure the distances to external galaxies, a process that is more accurate than using standard candles. By 2006, they had been used to give direct distance estimates to the LMC, SMC, Andromeda Galaxy, and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to an improved 5% level of accuracy. Non-eclipsing binaries that can be detected through photometry Nearby non-eclipsing binaries can also be photometrically detected by observing how the stars affect each other in three ways. The first is by observing extra light which the stars reflect from their companion. Second is by observing ellipsoidal light variations which are caused by deformation of the star's shape by their companions. The third method is by looking at how relativistic beaming affects the apparent magnitude of the stars. Detecting binaries with these methods requires accurate photometry. Astrometric binaries Astronomers have discovered some stars that seemingly orbit around an empty space. Astrometric binaries are relatively nearby stars which can be seen to wobble around a point in space, with no visible companion. The same mathematics used for ordinary binaries can be applied to infer the mass of the missing companion. The companion could be very dim, so that it is currently undetectable or masked by the glare of its primary, or it could be an object that emits little or no electromagnetic radiation, for example a neutron star. The visible star's position is carefully measured and detected to vary, due to the gravitational influence from its counterpart. The position of the star is repeatedly measured relative to more distant stars, and then checked for periodic shifts in position. Typically this type of measurement can only be performed on nearby stars, such as those within 10 parsecs. Nearby stars often have a relatively high proper motion, so astrometric binaries will appear to follow a wobbly path across the sky. If the companion is sufficiently massive to cause an observable shift in position of the star, then its presence can be deduced. From precise astrometric measurements of the movement of the visible star over a sufficiently long period of time, information about the mass of the companion and its orbital period can be determined. Even though the companion is not visible, the characteristics of the system can be determined from the observations using Kepler's laws. This method of detecting binaries is also used to locate extrasolar planets orbiting a star. However, the requirements to perform this measurement are very exacting, due to the great difference in the mass ratio, and the typically long period of the planet's orbit. Detection of position shifts of a star is a very exacting science, and it is difficult to achieve the necessary precision. Space telescopes can avoid the blurring effect of Earth's atmosphere, resulting in more precise resolution. Configuration of the system Another classification is based on the distance between the stars, relative to their sizes: Detached binaries are binary stars where each component is within its Roche lobe, i.e. the area where the gravitational pull of the star itself is larger than that of the other component. While on the main sequence the stars have no major effect on each other, and essentially evolve separately. Most binaries belong to this class. Semidetached binary stars are binary stars where one of the components fills the binary star's Roche lobe and the other does not. In this interacting binary star, gas from the surface of the Roche-lobe-filling component (donor) is transferred to the other, accreting star. The mass transfer dominates the evolution of the system. In many cases, the inflowing gas forms an accretion disc around the accretor. A contact binary is a type of binary star in which both components of the binary fill their Roche lobes. The uppermost part of the stellar atmospheres forms a common envelope that surrounds both stars. As the friction of the envelope brakes the orbital motion, the stars may eventually merge. W Ursae Majoris is an example. Cataclysmic variables and X-ray binaries When a binary system contains a compact object such as a white dwarf, neutron star or black hole, gas from the other (donor) star can accrete onto the compact object. This releases gravitational potential energy, causing the gas to become hotter and emit radiation. Cataclysmic variable stars, where the compact object is a white dwarf, are examples of such systems. In X-ray binaries, the compact object can be either a neutron star or a black hole. These binaries are classified as low-mass or high-mass according to the mass of the donor star. High-mass X-ray binaries contain a young, early-type, high-mass donor star which transfers mass by its stellar wind, while low-mass X-ray binaries are semidetached binaries in which gas from a late-type donor star or a white dwarf overflows the Roche lobe and falls towards the neutron star or black hole. Probably the best known example of an X-ray binary is the high-mass X-ray binary Cygnus X-1. In Cygnus X-1, the mass of the unseen companion is estimated to be about nine times that of the Sun, far exceeding the Tolman–Oppenheimer–Volkoff limit for the maximum theoretical mass of a neutron star. It is therefore believed to be a black hole; it was the first object for which this was widely believed. Orbital period Orbital periods can be less than an hour (for AM CVn stars), or a few days (components of Beta Lyrae), but also hundreds of thousands of years (Proxima Centauri around Alpha Centauri AB). Variations in period The Applegate mechanism explains long term orbital period variations seen in certain eclipsing binaries. As a main-sequence star goes through an activity cycle, the outer layers of the star are subject to a magnetic torque changing the distribution of angular momentum, resulting in a change in the star's oblateness. The orbit of the stars in the binary pair is gravitationally coupled to their shape changes, so that the period shows modulations (typically on the order of ∆P/P ~ 10−5) on the same time scale as the activity cycles (typically on the order of decades). Another phenomenon observed in some Algol binaries has been monotonic period increases. This is quite distinct from the far more common observations of alternating period increases and decreases explained by the Applegate mechanism. Monotonic period increases have been attributed to mass transfer, usually (but not always) from the less massive to the more massive star Designations A and B The components of binary stars are denoted by the suffixes A and B appended to the system's designation, A denoting the primary and B the secondary. The suffix AB may be used to denote the pair (for example, the binary star α Centauri AB consists of the stars α Centauri A and α Centauri B.) Additional letters, such as C, D, etc., may be used for systems with more than two stars. In cases where the binary star has a Bayer designation and is widely separated, it is possible that the members of the pair will be designated with superscripts; an example is Zeta Reticuli, whose components are ζ1 Reticuli and ζ2 Reticuli. Discoverer designations Double stars are also designated by an abbreviation giving the discoverer together with an index number. α Centauri, for example, was found to be double by Father Richaud in 1689, and so is designated RHD 1. These discoverer codes can be found in the Washington Double Star Catalog. Hot and cold The secondary star in a binary star system may be designated as the hot companion or cool companion, depending on its temperature relative to the primary star. Examples: Antares (Alpha Scorpii) is a red supergiant star in a binary system with a hotter blue main-sequence star Antares B. Antares B can therefore be termed a hot companion of the cool supergiant. Symbiotic stars, such as R Aquarii, are binary star systems composed of a late-type giant star and a hotter companion object. Since the nature of the companion is not well-established in all cases, it may be termed a "hot companion". The luminous blue variable Eta Carinae has been determined to be a binary star system. The secondary appears to have a higher temperature than the primary and has therefore been described as being the "hot companion" star. It may be a Wolf–Rayet star. NASA's Kepler mission has discovered examples of eclipsing binary stars where the secondary is the hotter component. KOI-74b is a 12,000 K white dwarf companion of KOI-74 (), a 9,400 K early A-type main-sequence star. KOI-81b is a 13,000 K white dwarf companion of KOI-81 (), a 10,000 K late B-type main-sequence star. Evolution Formation While it is not impossible that some binaries might be created through gravitational capture between two single stars, given the very low likelihood of such an event (three objects being actually required, as conservation of energy rules out a single gravitating body capturing another) and the high number of binaries currently in existence, this cannot be the primary formation process. The observation of binaries consisting of stars not yet on the main sequence supports the theory that binaries develop during star formation. Fragmentation of the molecular cloud during the formation of protostars is an acceptable explanation for the formation of a binary or multiple star system. The outcome of the three-body problem, in which the three stars are of comparable mass, is that eventually one of the three stars will be ejected from the system and, assuming no significant further perturbations, the remaining two will form a stable binary system. Mass transfer and accretion As a main-sequence star increases in size during its evolution, it may at some point exceed its Roche lobe, meaning that some of its matter ventures into a region where the gravitational pull of its companion star is larger than its own. The result is that matter will transfer from one star to another through a process known as Roche lobe overflow (RLOF), either being absorbed by direct impact or through an accretion disc. The mathematical point through which this transfer happens is called the first Lagrangian point. It is not uncommon that the accretion disc is the brightest (and thus sometimes the only visible) element of a binary star. If a star grows outside of its Roche lobe too fast for all abundant matter to be transferred to the other component, it is also possible that matter will leave the system through other Lagrange points or as stellar wind, thus being effectively lost to both components. Since the evolution of a star is determined by its mass, the process influences the evolution of both companions, and creates stages that cannot be attained by single stars. Studies of the eclipsing ternary Algol led to the Algol paradox in the theory of stellar evolution: although components of a binary star form at the same time, and massive stars evolve much faster than the less massive ones, it was observed that the more massive component Algol A is still in the main sequence, while the less massive Algol B is a subgiant at a later evolutionary stage. The paradox can be solved by mass transfer: when the more massive star became a subgiant, it filled its Roche lobe, and most of the mass was transferred to the other star, which is still in the main sequence. In some binaries similar to Algol, a gas flow can actually be seen. Runaways and novae It is also possible for widely separated binaries to lose gravitational contact with each other during their lifetime, as a result of external perturbations. The components will then move on to evolve as single stars. A close encounter between two binary systems can also result in the gravitational disruption of both systems, with some of the stars being ejected at high velocities, leading to runaway stars. If a white dwarf has a close companion star that overflows its Roche lobe, the white dwarf will steadily accrete gases from the star's outer atmosphere. These are compacted on the white dwarf's surface by its intense gravity, compressed and heated to very high temperatures as additional material is drawn in. The white dwarf consists of degenerate matter and so is largely unresponsive to heat, while the accreted hydrogen is not. Hydrogen fusion can occur in a stable manner on the surface through the CNO cycle, causing the enormous amount of energy liberated by this process to blow the remaining gases away from the white dwarf's surface. The result is an extremely bright outburst of light, known as a nova. In extreme cases this event can cause the white dwarf to exceed the Chandrasekhar limit and trigger a supernova that destroys the entire star, another possible cause for runaways. An example of such an event is the supernova SN 1572, which was observed by Tycho Brahe. The Hubble Space Telescope recently took a picture of the remnants of this event. Astrophysics Binaries provide the best method for astronomers to determine the mass of a distant star. The gravitational pull between them causes them to orbit around their common center of mass. From the orbital pattern of a visual binary, or the time variation of the spectrum of a spectroscopic binary, the mass of its stars can be determined, for example with the binary mass function. In this way, the relation between a star's appearance (temperature and radius) and its mass can be found, which allows for the determination of the mass of non-binaries. Because a large proportion of stars exist in binary systems, binaries are particularly important to our understanding of the processes by which stars form. In particular, the period and masses of the binary tell us about the amount of angular momentum in the system. Because this is a conserved quantity in physics, binaries give us important clues about the conditions under which the stars were formed. Calculating the center of mass in binary stars In a simple binary case, the distance r1 from the center of the first star to the center of mass or barycenter is given by where a is the distance between the two stellar centers, and m1 and m2 are the masses of the two stars. If a is taken to be the semimajor axis of the orbit of one body around the other, then r1 is the semimajor axis of the first body's orbit around the center of mass or barycenter, and is the semimajor axis of the second body's orbit. When the center of mass is located within the more massive body, that body appears to wobble rather than following a discernible orbit. Center-of-mass animations The red cross marks the center of mass of the system. These images do not represent any specific real system. Research findings It is estimated that approximately one third of the star systems in the Milky Way are binary or multiple, with the remaining two thirds being single stars. The overall multiplicity frequency of ordinary stars is a monotonically increasing function of stellar mass. That is, the likelihood of being in a binary or a multi-star system steadily increases as the masses of the components increase. There is a direct correlation between the period of revolution of a binary star and the eccentricity of its orbit, with systems of short period having smaller eccentricity. Binary stars may be found with any conceivable separation, from pairs orbiting so closely that they are practically in contact with each other, to pairs so distantly separated that their connection is indicated only by their common proper motion through space. Among gravitationally bound binary star systems, there exists a so-called log normal distribution of periods, with the majority of these systems orbiting with a period of about 100 years. This is supporting evidence for the theory that binary systems are formed during star formation. In pairs where the two stars are of equal brightness, they are also of the same spectral type. In systems where the brightnesses are different, the fainter star is bluer if the brighter star is a giant star, and redder if the brighter star belongs to the main sequence. The mass of a star can be directly determined only from its gravitational attraction. Apart from the Sun and stars which act as gravitational lenses, this can be done only in binary and multiple star systems, making the binary stars an important class of stars. In the case of a visual binary star, after the orbit and the stellar parallax of the system has been determined, the combined mass of the two stars may be obtained by a direct application of the Keplerian harmonic law. Unfortunately, it is impossible to obtain the complete orbit of a spectroscopic binary unless it is also a visual or an eclipsing binary, so from these objects only a determination of the joint product of mass and the sine of the angle of inclination relative to the line of sight is possible. In the case of eclipsing binaries which are also spectroscopic binaries, it is possible to find a complete solution for the specifications (mass, density, size, luminosity, and approximate shape) of both members of the system. Planets While a number of binary star systems have been found to harbor extrasolar planets, such systems are comparatively rare compared to single star systems. Observations by the Kepler space telescope have shown that most single stars of the same type as the Sun have plenty of planets, but only one-third of binary stars do. According to theoretical simulations, even widely separated binary stars often disrupt the discs of rocky grains from which protoplanets form. On the other hand, other simulations suggest that the presence of a binary companion can actually improve the rate of planet formation within stable orbital zones by "stirring up" the protoplanetary disk, increasing the accretion rate of the protoplanets within. Detecting planets in multiple star systems introduces additional technical difficulties, which may be why they are only rarely found. Examples include the white dwarf-pulsar binary PSR B1620-26, the subgiant-red dwarf binary Gamma Cephei, and the white dwarf-red dwarf binary NN Serpentis, among others. A study of fourteen previously known planetary systems found three of these systems to be binary systems. All planets were found to be in S-type orbits around the primary star. In these three cases the secondary star was much dimmer than the primary and so was not previously detected. This discovery resulted in a recalculation of parameters for both the planet and the primary star. Science fiction has often featured planets of binary or ternary stars as a setting, for example, George Lucas' Tatooine from Star Wars, and one notable story, "Nightfall", even takes this to a six-star system. In reality, some orbital ranges are impossible for dynamical reasons (the planet would be expelled from its orbit relatively quickly, being either ejected from the system altogether or transferred to a more inner or outer orbital range), whilst other orbits present serious challenges for eventual biospheres because of likely extreme variations in surface temperature during different parts of the orbit. Planets that orbit just one star in a binary system are said to have "S-type" orbits, whereas those that orbit around both stars have "P-type" or "circumbinary" orbits. It is estimated that 50–60% of binary systems are capable of supporting habitable terrestrial planets within stable orbital ranges. Examples The large distance between the components, as well as their difference in color, make Albireo one of the easiest observable visual binaries. The brightest member, which is the third-brightest star in the constellation Cygnus, is actually a close binary itself. Also in the Cygnus constellation is Cygnus X-1, an X-ray source considered to be a black hole. It is a high-mass X-ray binary, with the optical counterpart being a variable star. Sirius is another binary and the brightest star in the night time sky, with a visual apparent magnitude of −1.46. It is located in the constellation Canis Major. In 1844 Friedrich Bessel deduced that Sirius was a binary. In 1862 Alvan Graham Clark discovered the companion (Sirius B; the visible star is Sirius A). In 1915 astronomers at the Mount Wilson Observatory determined that Sirius B was a white dwarf, the first to be discovered. In 2005, using the Hubble Space Telescope, astronomers determined Sirius B to be in diameter, with a mass that is 98% of the Sun. An example of an eclipsing binary is Epsilon Aurigae in the constellation Auriga. The visible component belongs to the spectral class F0, the other (eclipsing) component is not visible. The last such eclipse occurred from 2009 to 2011, and it is hoped that the extensive observations that will likely be carried out may yield further insights into the nature of this system. Another eclipsing binary is Beta Lyrae, which is a semidetached binary star system in the constellation of Lyra. Other interesting binaries include 61 Cygni (a binary in the constellation Cygnus, composed of two K class (orange) main-sequence stars, 61 Cygni A and 61 Cygni B, which is known for its large proper motion), Procyon (the brightest star in the constellation Canis Minor and the eighth-brightest star in the night time sky, which is a binary consisting of the main star with a faint white dwarf companion), SS Lacertae (an eclipsing binary which stopped eclipsing), V907 Sco (an eclipsing binary which stopped, restarted, then stopped again), BG Geminorum (an eclipsing binary which is thought to contain a black hole with a K0 star in orbit around it), and 2MASS J18082002−5104378 (a binary in the "thin disk" of the Milky Way, and containing one of the oldest known stars). Multiple-star examples Systems with more than two stars are termed multiple stars. Algol is the most noted ternary (long thought to be a binary), located in the constellation Perseus. Two components of the system eclipse each other, the variation in the intensity of Algol first being recorded in 1670 by Geminiano Montanari. The name Algol means "demon star" (from al-ghūl), which was probably given due to its peculiar behavior. Another visible ternary is Alpha Centauri, in the southern constellation of Centaurus, which contains the third-brightest star in the night sky, with an apparent visual magnitude of −0.01. This system also underscores the fact that no search for habitable planets is complete if binaries are discounted. Alpha Centauri A and B have an 11 AU distance at closest approach, and both should have stable habitable zones. There are also examples of systems beyond ternaries: Castor is a sextuple star system, which is the second-brightest star in the constellation Gemini and one of the brightest stars in the nighttime sky. Astronomically, Castor was discovered to be a visual binary in 1719. Each of the components of Castor is itself a spectroscopic binary. Castor also has a faint and widely separated companion, which is also a spectroscopic binary. The Alcor–Mizar visual binary in Ursa Majoris also consists of six stars: four comprising Mizar and two comprising Alcor. QZ Carinae is a complex multiple star system made up of at least nine individual stars. See also 104 Aquarii, possible binary 107 Aquarii, "double star", about 240 light-years from Earth Beta Centauri Binary black hole Binary brown dwarfs Circumbinary planet Habitability of binary star systems HD 30453, a spectroscopic binary with a 3rd component Hills mechanism Heartbeat star, a type of binary star system Rotational Brownian motion (astronomy) Two-body problem in general relativity Notes and references External links IAU Commission G1: Binary and Multiple Star Systems List of the best visual binaries for amateurs, with orbital elements Pictures and news of binaries at Hubblesite.org Chandra X-ray Observatory Selected visual double stars and their relative position as a function of time AAVSO Eclipsing Binaries section OGLE Atlas of Variable Star Light Curves - Eclipsing binaries Star types Articles containing video clips	Binary star	[ "Astronomy" ]	7,481	[ "Star types", "Astronomical classification systems" ]
52,716	https://en.wikipedia.org/wiki/Microsoft%20SharePoint%20Workspace	Microsoft SharePoint Workspace (formerly Microsoft Office Groove) is a discontinued desktop application designed for document collaboration in teams with members who are regularly off-line or who do not share the same network security clearance. It is no longer included with Microsoft Office 2013. It has been replaced by a web-based service called OneDrive for Business. Groove's uses have included coordination between emergency relief agencies, where different organizations do not share a common security infrastructure and where offline access is important, and amongst teams of knowledge workers, such as consultants who need to work securely on client sites. It is also used as a staging system for documents in development, where content can be developed then transferred to a portal when complete. Groove was initially developed by Lotus Notes creator Ray Ozzie, and developed by Groove Networks of Beverly, Massachusetts, until Microsoft's acquisition of Groove Networks in March 2005. Collaboration tools Groove's basic set of services (including always-on security, persistent chat, store-and-forward messaging delivery, firewall/NAT transparency, ad-hoc group formation, and change notification) may be customized with tools. Tools are mini-applications that rely on Groove's underlying functionality to disseminate and synchronize their contents with other members' copies of the workspace. Groove provides various tools that can be added to (and removed from) a workspace to customize the functionality of each space (for example a calendar, discussion, file sharing, an outliner, pictures, notepad, sketchpad, web browser, etc.). Tools that members use in a workspace often drive the nature of the person-to-person collaboration that ensues. In Groove 2007, the SharePoint Files tools can be used to take SharePoint 2007 document libraries offline. Groove 2007 includes a presence subsystem, which keeps track of which users in the contact store are online, and presents the information in the launchbar. If Groove server is used, a user is considered online when they log on to the server. In absence of a server, the Device Presence Protocol (which comes in different variants for LANs and WANs) is used. Groove also allows sending instant messages to peers. All session and user information is stored by the Groove client at client side. Versions Groove Virtual Office 3.1 was the last version before Microsoft's acquisition of Groove Networks. The following versions have been released since: Groove 2007 (Included in Office 2007 Ultimate and Enterprise editions and also available as a separate product), released January 27, 2007. SharePoint Workspace 2010, released July 15, 2010. Microsoft claims the name change is a natural progression, since Groove is to SharePoint what Outlook is to Exchange. Microsoft asserts that features have been added to make it easier to deploy and manage, and claims that SharePoint Workspace will make it easier to access SharePoint content (or content from any server that implements the publicly documented protocols). Server application Microsoft Groove Server is a tool for centrally managing all deployments of Microsoft SharePoint Workspace in an enterprise. It enables using Active Directory for Groove user accounts, and create Groove Domains, with individual policy settings. See also Comparison of office suites Collaborative software References Further reading External links Groupware SharePoint Workspace Collaborative real-time editors Collaborative software	Microsoft SharePoint Workspace	[ "Technology" ]	668	[ "Collaborative real-time editors" ]
52,742	https://en.wikipedia.org/wiki/Desktop%20computer	A desktop computer, often abbreviated as desktop, is a personal computer designed for regular use at a stationary location on or near a desk (as opposed to a portable computer) due to its size and power requirements. The most common configuration has a case that houses the power supply, motherboard (a printed circuit board with a microprocessor as the central processing unit, memory, bus, certain peripherals and other electronic components), disk storage (usually one or more hard disk drives, solid-state drives, optical disc drives, and in early models floppy disk drives); a keyboard and mouse for input; and a monitor, speakers, and, often, a printer for output. The case may be oriented horizontally or vertically and placed either underneath, beside, or on top of a desk. Desktop computers with their cases oriented vertically are referred to as towers. As the majority of cases offered since the mid 1990s are in this form factor, the term desktop has been retronymically used to refer to modern cases offered in the traditional horizontal orientation. History Origins Prior to the widespread use of microprocessors, a computer that could fit on a desk was considered remarkably small; the type of computers most commonly used were minicomputers, which, despite the name, were rather large and were "mini" only compared to the so-called "big iron". Early computers, and later the general purpose high throughput "mainframes", took up the space of a whole room. Minicomputers, on the contrary, generally fit into one or a few refrigerator-sized racks, or, for the few smaller ones, built into a fairly large desk, not put on top of it. It was not until the 1970s when fully programmable computers appeared that could fit entirely on top of a desk. 1970 saw the introduction of the Datapoint 2200, a "smart" computer terminal complete with keyboard and monitor, was designed to connect with a mainframe computer but that did not stop owners from using its built-in computational abilities as a stand-alone desktop computer. The HP 9800 series, which started out as programmable calculators in 1971 but was programmable in BASIC by 1972, used a smaller version of a minicomputer design based on ROM memory and had small one-line LED alphanumeric displays and displayed graphics with a plotter. The Wang 2200 of 1973 had a full-size cathode-ray tube (CRT) and cassette tape storage. The IBM 5100 in 1975 had a small CRT display and could be programmed in BASIC and APL. These were generally expensive specialized computers sold for business or scientific uses. Growth and development Apple II, TRS-80 and Commodore PET were first generation personal home computers launched in 1977, which were aimed at the consumer market – rather than businessmen or computer hobbyists. Byte magazine referred to these three as the "1977 Trinity" of personal computing. Throughout the 1980s and 1990s, desktop computers became the predominant type, the most popular being the IBM PC and its clones, followed by the Apple Macintosh, with the third-placed Commodore Amiga having some success in the mid-1980s but declining by the early 1990s. Early personal computers, like the original IBM Personal Computer, were enclosed in a "desktop case", horizontally oriented to have the display screen placed on top, thus saving space on the user's actual desk, although these cases had to be sturdy enough to support the weight of CRT displays that were widespread at the time. Over the course of the 1990s, desktop cases gradually became less common than the more-accessible tower cases that may be located on the floor under or beside a desk rather than on a desk. Not only do these tower cases have more room for expansion, they have also freed up desk space for monitors which were becoming larger every year. Desktop cases, particularly the compact form factors, remain popular for corporate computing environments and kiosks. Some computer cases can be interchangeably positioned either horizontally (desktop) or upright (mini-tower). Influential games such as Doom and Quake during the 1990s had pushed gamers and enthusiasts to frequently upgrade to the latest CPUs and graphics cards (3dfx, ATI, and Nvidia) for their desktops (usually a tower case) in order to run these applications, though this has slowed since the late 2000s as the growing popularity of Intel integrated graphics forced game developers to scale back. Creative Technology's Sound Blaster series were a de facto standard for sound cards in desktop PCs during the 1990s until the early 2000s, when they were reduced to a niche product, as OEM desktop PCs came with sound boards integrated directly onto the motherboard. Decline While desktops have long been the most common configuration for PCs, by the mid-2000s the growth shifted from desktops to laptops. Notably, while desktops were mainly produced in the United States, laptops had long been produced by contract manufacturers based in Asia, such as Foxconn. This shift led to the closure of the many desktop assembly plants in the United States by 2010. Another trend around this time was the increasing proportion of inexpensive base-configuration desktops being sold, hurting PC manufacturers such as Dell whose build-to-order customization of desktops relied on upselling added features to buyers. Battery-powered portable computers had just a 2% worldwide market share in 1986. However, laptops have become increasingly popular, both for business and personal use. Around 109 million notebook PCs shipped worldwide in 2007, a growth of 33% compared to 2006. In 2008, it was estimated that 145.9 million notebooks were sold and that the number would grow in 2009 to 177.7 million. The third quarter of 2008 was the first time when worldwide notebook PC shipments exceeded desktops, with 38.6 million units versus 38.5 million units. The sales breakdown of the Apple Macintosh has seen sales of desktop Macs staying mostly constant while being surpassed by that of Mac notebooks whose sales rate has grown considerably; seven out of ten Macs sold were laptops in 2009, a ratio projected to rise to three out of four by 2010. The change in sales of form factors is due to the desktop iMac moving from affordable G3 to upscale G4 model and subsequent releases are considered premium all-in-ones. By contrast, the MSRP of the MacBook laptop lines have dropped through successive generations such that the MacBook Air and MacBook Pro constitute the lowest price of entry to a Mac, with the exception of the even more inexpensive Mac Mini (albeit without a monitor and keyboard), and the MacBooks are the top-selling form factors of the Macintosh platform today. The decades of development mean that most people already own desktop computers that meet their needs and have no need of buying a new one merely to keep pace with advancing technology. Notably, the successive release of new versions of Windows (Windows 95, 98, XP, Vista, 7, 8, 10 and so on) had been drivers for the replacement of PCs in the 1990s, but this slowed in the 2000s due to the poor reception of Windows Vista over Windows XP. IDC analyst Jay Chou suggested that Windows 8 actually hurt sales of PCs in 2012, as businesses decided to stick with Windows 7 rather than upgrade. Some suggested that Microsoft had acknowledged "implicitly ringing the desktop PC death knell" as Windows 8 offered little upgrade in desktop PC functionality over Windows 7; instead, Windows 8's innovations were mostly on the mobile side. The post-PC trend saw a decline in the sales of desktop and laptop PCs. The decline was attributed to increased power and applications of alternative computing devices, namely smartphones and tablet computers. Although most people exclusively use their smartphones and tablets for more basic tasks such as social media and casual gaming, these devices have in many instances replaced a second or third PC in the household that would have performed these tasks, though most families still retain a powerful PC for serious work. Among PC form factors, desktops remain a staple in the enterprise market but lost popularity among home buyers. PC makers and electronics retailers responded by investing their engineering and marketing resources towards laptops (initially netbooks in the late 2000s, and then the higher-performance Ultrabooks from 2011 onwards), which manufacturers believed had more potential to revive the PC market than desktops. In April 2017, StatCounter declared a "Milestone in technology history and end of an era" with the mobile Android operating system becoming more popular than Windows (the operating system that made desktops dominant over mainframe computers). Windows is still most popular on desktops (and laptops), while smartphones (and tablets) use Android or iOS. Resurgence Towards the middle of the 2010s, media sources began to question the existence of the post-PC trend, at least as conventionally defined, stating that the so-called post-PC devices are just other portable forms of PCs joining traditional desktop PCs which still have their own operation areas and evolve. Although for casual use traditional desktops and laptops have seen a decline in sales, in 2018, global PC sales experienced a resurgence, driven by the business market. Desktops remain a solid fixture in the commercial and educational sectors. According to the International Data Corporation (IDC), PC sales shot up 14.8% between 2020 and 2021 and desktop market grew faster than the laptop market in the second quarter of 2021. Total PC shipments during 2021 reached 348.8 million units, up 14.8% from 2020. This represents the highest level of shipments the PC market has seen since 2012. In addition, gaming desktops have seen a global revenue increase of 54% annually. For gaming the global market of gaming desktops, laptops, and monitors is expected to grow to 61.1 million shipments by the end of 2023, up from 42.1 million, with desktops growing from 15.1 million shipments to 19 million. PC gaming as a whole accounts for 28% of the total gaming market as of 2017. This is partially due to the increasing affordability of desktop PCs. Types By size Full-size Full-sized desktops are characterized by separate display and processing components. These components are connected to each other by cables or wireless connections. They often come in a tower form factor. These computers are easy to customize and upgrade per user requirements, e.g. by expansion card. Early extended-size (significantly larger than mainstream ATX case) tower computers sometimes were labeled as "deskside computers", but currently this naming is quite rare. Compact Compact desktops are reduced in physical proportions compared to full-sized desktops. They are typically small-sized, inexpensive, low-power computers designed for basic tasks such as web browsing, accessing web-based applications, document processing, and audio/video playback. Hardware specifications and processing power are usually reduced and hence make them less appropriate for running complex or resource-intensive applications. A nettop is a notable example of a compact desktop. A laptop without a screen can functionally be used as a compact desktop, sometimes called a "slabtop". Form factor All-in-one An all-in-one (AIO) desktop computer integrates the system's internal components into the same case as the display, thus occupying a smaller footprint (with fewer cables) than desktops that incorporate a tower. The All-in-one systems are rarely labeled as desktop computers. Tower In personal computing, a tower is a form factor of desktop computer case whose height is much greater than its width, thus having the appearance of an upstanding tower block. Pizza box form factor In computing, a pizza box enclosure is a design for desktop computers. Pizza box cases tend to be wide and flat, resembling pizza delivery boxes and thus the name. Cube Cube Workstations have a cube case enclosure to house the motherboard, PCI-E expansion cards, GPU, CPU, DRAM DIMM slots, computer cooling equipment, chipsets, I/O ports, hard disk drives, and solid-state drives. By usage Gaming computer Gaming computers are desktop computers with high performance CPU, GPU, and RAM optimized for playing video games at high resolution and frame rates. Gaming computer peripheries usually include mechanical keyboards for faster response time, and a gaming computer mouse which can track higher dots per inch movement. Home theater These desktops are connected to home entertainment systems and typically used for amusement purpose. They come with high definition display, video graphics, surround sound and TV tuner systems to complement typical PC features. Thin client / Internet appliance Over time some traditional desktop computers have been replaced with thin clients utilizing off-site computing solutions like the cloud. As more services and applications are served over the internet from off-site servers, local computing needs decrease, this drives desktop computers to be smaller, cheaper, and need less powerful hardware. More applications and in some cases entire virtual desktops are moved off-site and the desktop computer runs only an operating system or a shell application while the actual content is served from a server. Thin client computers may do almost all of their computing on a virtual machine in another site. Internal, hosted virtual desktops can offer users a completely consistent experience from anywhere. Workstation Workstations are advanced class of personal computers designed for a user and more powerful than a regular PC but less powerful than a server in regular computing. They are capable of high-resolution and three-dimensional interfaces, and typically used to perform scientific and engineering work. Like server computers, they are often connected with other workstations. The main form-factor for this class is a Tower case, but most vendors produce compact or all-in-one low-end workstations. Most tower workstations can be converted to a rack-mount version. Desktop server Oriented for small business class of servers; typically entry-level server machines, with similar to workstation/gaming PC computing powers and with some mainstream servers features, but with only basic graphic abilities; and some desktop servers can be converted to workstations. Comparison with laptops Desktops have an advantage over laptops in that the spare parts and extensions tend to be standardized, resulting in lower prices and greater availability. For example, the size and mounting of the motherboard are standardized into ATX, microATX, BTX or other form factors. Desktops have several standardized expansion slots, like conventional PCI or PCI Express, while laptops tend to have only one mini-PCI slot and one PC Card slot (or ExpressCard slot). Procedures for assembly and disassembly of desktops tend to be simple and standardized as well. This tends not to be the case for laptops, though adding or replacing some parts, like the optical drive, hard disk, or adding an extra memory module is often quite simple. This means that a desktop computer configuration, usually a tower case, can be customized and upgraded to a greater extent than laptops. This customization has kept tower cases popular among gamers and enthusiasts. Another advantage of the desktop is that (apart from environmental concerns) power consumption is not as critical as in laptop computers because the desktop is exclusively powered from the wall socket. Desktop computers also provide more space for cooling fans and vents to dissipate heat, allowing enthusiasts to overclock with less risk. The two large microprocessor manufacturers, Intel and AMD, have developed special CPUs for mobile computers (i.e. laptops) that consume less power and lower heat, but with lower performance levels. Laptop computers, conversely, offer portability that desktop systems (including small form factor and all-in-one desktops) cannot due to their compact size and clamshell design. The laptop's all-in-one design provides a built-in keyboard and a pointing device (such as a touchpad) for its user and can draw on power supplied by a rechargeable battery. Laptops also commonly integrate wireless technologies like Wi-Fi, Bluetooth, and 3G, giving them a broader range of options for connecting to the internet, though this trend is changing as newer desktop computers come integrated with one or more of these technologies. A desktop computer needs a UPS to handle electrical disturbances like short interruptions, blackouts, and spikes; achieving an on-battery time of more than 20–30 minutes for a desktop PC requires a large and expensive UPS. A laptop with a sufficiently charged battery can continue to be used for hours in case of a power outage and is not affected by short power interruptions and blackouts. A desktop computer often has the advantage over a comparable laptop in computational capacity. Overclocking is often more feasible on a desktop than on a laptop; similarly, hardware add-ons such as discrete graphics co-processors may be possible to install only in a desktop. See also Mobile workstation Gaming computer Home computer Legacy ports Operating system Single-board computer Software x86 and x86-64, the most common architecture in desktop computers, the latter has mostly taken over References External links Computer Tourof major components of a desktop computers at HowStuffWorks Classes of computers Personal computers Office equipment	Desktop computer	[ "Technology" ]	3,501	[ "Classes of computers", "Computers", "Computer systems" ]
52,747	https://en.wikipedia.org/wiki/Albireo	Albireo is a binary star designated Beta Cygni (β Cygni, abbreviated Beta Cyg, β Cyg). The International Astronomical Union uses the name "Albireo" specifically for the brightest star in the system. Although designated 'beta', it is fainter than Gamma Cygni, Delta Cygni, and Epsilon Cygni and is the fifth-brightest point of light in the constellation of Cygnus. Appearing to the naked eye to be a single star of magnitude 3, viewing through even a low-magnification telescope resolves it into its two components. The brighter yellow star, itself a very close trinary system, makes a striking colour contrast with its fainter blue companion. Nomenclature β Cygni (Latinised to Beta Cygni) is the system's Bayer designation. The brighter of the two components is designated β¹ Cygni or Beta Cygni A and the fainter β² Cygni or Beta Cygni B. The origin of the star system's traditional name Albireo is unclear. Christian Ludwig Ideler traced it to the heading for the constellation we call Cygnus in Ptolemy's star catalog, in the translation of the Almagest by Gerard of Cremona: "Stellatio Eurisim: et est volans; et jam vocatur gallina. et dicitur eurisim quasi redolens ut lilium ab ireo" ("Constellation Eurisim: and it is the Flyer, and it is also called the Hen, and it is called Eurisim as if redolent like the lily from the 'ireo'"). (The original Greek just calls the constellation "Ορνιθος αστερισμος", "the constellation of the Bird".) The word "ireo" is obscure as wellIdeler suggests that Gerard took "Eurisim" to mean the plant Erysimum, which is called irio in Latin, but the ablative case of that is not "ireo" but irione. In any case, Ideler proposed that (somehow) the phrase "ab ireo" was applied to the star at the head of the bird, and this became "Albireo" when an "l" was mistakenly inserted as though it was an Arabic name. Ideler also supposed that the name Eurisim was a mistaken transliteration of the Arabic name "Urnis" for Cygnus (from the Greek "Ορνις"). In 2016, the International Astronomical Union (IAU) organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016 included a table of the first two batches of names approved by the WGSN; which included Albireo for β¹ Cygni. It is now so entered in the IAU Catalog of Star Names. Medieval Arabic-speaking astronomers called Beta Cygni (English: the hen's beak). The term (منقار الدجاجة) or Menchir al Dedjadjet appeared in the catalogue of stars in the Calendarium of Al Achsasi Al Mouakket, which was translated into Latin as Rostrum Gallinae, meaning the hen's beak. Since Cygnus is the swan, and Beta Cygni is located at the head of the swan, it is sometimes called the "beak star". With Deneb, Gamma Cygni (Sadr), Delta Cygni, and Epsilon Cygni (Gienah), it forms the asterism called the Northern Cross. Properties Beta Cygni is about away from the Sun. When viewed with the naked eye, Albireo appears to be a single star. However, in a telescope it resolves into a double star consisting of β Cygni A (amber, apparent magnitude 3.1), and β Cygni B (blue-green, apparent magnitude 5.1). Separated by 35 seconds of arc, the two components provide one of the best contrasting double stars in the sky due to their different colors. It is not known whether the two components β Cygni A and B are orbiting around each other in a physical binary system, or if they are merely an optical double. If they are a physical binary, their orbital period is probably at least 100,000 years. Some experts, however, support the optical double argument, based on observations that suggest different proper motions for the components, which implies that they are unrelated. The primary and secondary also have different measured distances from the Hipparcos mission – for the primary and for the secondary. More recently the Gaia mission has measured distances of about 330–390 light years (100–120 parsecs) for both components, but noise in the astrometric measurements for the stars means that data from Gaia's second data release is not yet sufficient to determine whether the stars are physically associated. In around 3.87 million years, Albireo will become the brightest star in the night sky. It will peak in brightness with an apparent magnitude of –0.53 in 4.61 million years. There are a further 10 faint companions listed in the Washington Double Star catalogue, all fainter than magnitude 10. Only one is closer to the primary than Albireo B, with the others up to 142" away. Albireo A The spectrum of Beta Cygni A was found to be composite when it was observed as part of the Henry Draper Memorial project in the late 19th century, leading to the supposition that it was itself double. This was supported by observations from 1898 to 1918 which showed that it had a varying radial velocity. In 1923, the two components were identified in the Henry Draper Catalogue as HD 183912 and HD 183913. In 1978, speckle interferometry observations using the 1.93m telescope at the Haute-Provence Observatory resolved a companion at 0.125". This observation was published in 1980, and the companion is referred to as component Ab in the Washington Double Star Catalog. In 1976 speckle interferometry was used to resolve a companion using the 2.1-meter telescope at the Kitt Peak National Observatory. It was measured at a separation of 0.44", and it is noted that the observation was inconsistent with the Haute-Provence observations and hence not of the same star. Although these observations pre-dated those at Haute-Provence, they were not published until 1982 and this component is designated Ac in the Washington Double Star Catalog. It is designated as component C in the Catalog of Components of Double and Multiple Stars, not to be confused with component C in the Washington Double Star Catalog which is a faint optical companion. An orbit for the pair has since been computed using interferometric measurements, but as only approximately a quarter of the orbit has been observed, the orbital parameters must be regarded as preliminary. The period of this orbit is 214 years. The confirmed close pair are referred to as Aa and Ac in modern papers, with Ab being the unconfirmed third component. A 2022 study treats the existence of Albireo Ab as "very unlikely". In 2022, a third component was found to be orbiting Albireo Aa, named Albireo Ad. It is a very-low-mass star with around 8.5% the Sun's mass and an orbital period of 371 days. The diameter of the primary K-type giant star has been measured using interferometry from the Navy Precision Optical Interferometer. A limb-darkened angular diameter of was measured. At the parallax-derived distance of 111.4pc, a radius equivalent to is calculated. Albireo B β Cygni B is a fast-rotating Be star, with an equatorial rotational velocity of at least 250 kilometers per second. Its surface temperature has been spectroscopically estimated to be about 13,200 K. β Cygni B has been reported to be a very close double, but the observations appear to have been incorrect. Moving group Analysis of Gaia Data Release 2 astrometry suggests that four fainter stars may form a moving group along with the brighter visible components. Namesakes Albireo (AK-90) was a United States Navy Crater-class cargo ship named after the star. Notes References Further reading External links A picture of Albireo by Stefan Seip () Albireo at Pete Roberts' Fuzzy Blobs site About Cygnus, including more information about the origin of the name Albireo. B-type main-sequence stars Cygni, Beta Be stars Binary stars 7417 Cygnus (constellation) BD+27 3410 Cygni, 06 183912 095947 K-type bright giants Albireo Triple stars	Albireo	[ "Astronomy" ]	1,811	[ "Cygnus (constellation)", "Constellations" ]
52,797	https://en.wikipedia.org/wiki/Digital%20camera	A digital camera, also called a digicam, is a camera that captures photographs in digital memory. Most cameras produced today are digital, largely replacing those that capture images on photographic film or film stock. Digital cameras are now widely incorporated into mobile devices like smartphones with the same or more capabilities and features of dedicated cameras. High-end, high-definition dedicated cameras are still commonly used by professionals and those who desire to take higher-quality photographs. Digital and digital movie cameras share an optical system, typically using a lens with a variable diaphragm to focus light onto an image pickup device. The diaphragm and shutter admit a controlled amount of light to the image, just as with film, but the image pickup device is electronic rather than chemical. However, unlike film cameras, digital cameras can display images on a screen immediately after being recorded, and store and delete images from memory. Many digital cameras can also record moving videos with sound. Some digital cameras can crop and stitch pictures and perform other kinds of image editing. History The first semiconductor image sensor was the charge-coupled device (CCD), invented by Willard S. Boyle and George E. Smith at Bell Labs in 1969, based on MOS capacitor technology. The NMOS active-pixel sensor was later invented by Tsutomu Nakamura's team at Olympus in 1985, which led to the development of the CMOS active-pixel sensor (CMOS sensor) at the NASA Jet Propulsion Laboratory in 1993. In the 1960s, Eugene F. Lally of the Jet Propulsion Laboratory was thinking about how to use a mosaic photosensor to capture digital images. His idea was to take pictures of the planets and stars while travelling through space to give information about the astronauts' position. As with Texas Instruments employee Willis Adcock's filmless camera (US patent 4,057,830) in 1972, the technology had yet to catch up with the concept. In 1972, the Landsat 1 satellite's multispectral scanner (MSS) started taking digital images of Earth. The MSS, designed by Virginia Norwood at Hughes Aircraft Company starting in 1969, captured and transmitted image data from green, red, and two infrared bands with 6 bits per channel, using a mechanical rocking mirror and an array of 24 detectors. Operating for six years, it transmitted more than 300,000 digital photographs of Earth while orbiting the planet about 14 times per day. Also in 1972, Thomas McCord from MIT and James Westphal from Caltech together developed a digital camera for use with telescopes. Their 1972 "photometer-digitizer system" used an analog-to-digital converter and a digital frame memory to store 256 x 256-pixel images of planets and stars, which were then recorded on digital magnetic tape. CCD sensors were not yet commercially available, and the camera used a silicon diode vidicon tube detector, which was cooled using dry ice to reduce dark current, allowing exposure times of up to one hour. The Cromemco Cyclops was an all-digital camera introduced as a commercial product in 1975. Its design was published as a hobbyist construction project in the February 1975 issue of Popular Electronics magazine. It used a 32×32 metal–oxide–semiconductor (MOS) image sensor, which was a modified MOS dynamic RAM (DRAM) memory chip. Steven Sasson, an engineer at Eastman Kodak, built a self-contained electronic camera that used a monochrome Fairchild CCD image sensor in 1975. Around the same time, Fujifilm began developing CCD technology in the 1970s. Early uses were mainly military and scientific, followed by medical and news applications. The first filmless SLR (single lens reflex) camera was publicly demonstrated by Sony in August 1981. The Sony "Mavica" (magnetic still video camera) used a color-striped 2/3" format CCD sensor with 280K pixels, along with analogue video signal processing and recording. The Mavica electronic still camera recorded FM-modulated analog video signals on a newly developed 2" magnetic floppy disk, dubbed the "Mavipak". The disk format was later standardized as the "Still Video Floppy", or "SVF". The Canon RC-701, introduced in May 1986, was the first SVF camera (and the first electronic SLR camera) sold in the US. It employed an SLR viewfinder, included a 2/3" format color CCD sensor with 380K pixels, and was sold along with a removable 11-66mm and 50-150mm zoom lens. Over the next few years, many other companies began selling SVF cameras. These analog electronic cameras included the Nikon QV-1000C, which had an SLR viewfinder and a 2/3" format monochrome CCD sensor with 380K pixels and recorded analog black-and-white images on a Still Video Floppy. At Photokina 1988, Fujifilm introduced the FUJIX DS-1P, the first fully digital camera, which recorded digital images using a semiconductor memory card. The camera's memory card had a capacity of 2 MB of SRAM (static random-access memory) and could hold up to ten photographs. In 1989, Fujifilm released the FUJIX DS-X, the first fully digital camera to be commercially released. In 1996, Toshiba's 40 MB flash memory card was adopted for several digital cameras. The first commercial camera phone was the Kyocera Visual Phone VP-210, released in Japan in May 1999. It was called a "mobile videophone" at the time, and had a 110,000-pixel front-facing camera. It stored up to 20 JPEG digital images, which could be sent over e-mail, or the phone could send up to two images per second over Japan's Personal Handy-phone System (PHS) cellular network. The Samsung SCH-V200, released in South Korea in June 2000, was also one of the first phones with a built-in camera. It had a TFT liquid-crystal display (LCD) and stored up to 20 digital photos at 350,000-pixel resolution. However, it could not send the resulting image over the telephone function but required a computer connection to access photos. The first mass-market camera phone was the J-SH04, a Sharp J-Phone model sold in Japan in November 2000. It could instantly transmit pictures via cell phone telecommunication. By the mid-2000s, higher-end cell phones had an integrated digital camera, and by the early 2010s, almost all smartphones had an integrated digital camera. Image sensors The two major types of digital image sensors are CCD and CMOS. A CCD sensor has one amplifier for all the pixels, while each pixel in a CMOS active-pixel sensor has its own amplifier. Compared to CCDs, CMOS sensors use less power. Cameras with a small sensor use a back-side-illuminated CMOS (BSI-CMOS) sensor. The image processing capabilities of the camera determine the outcome of the final image quality much more than the sensor type. Sensor resolution The resolution of a digital camera is often limited by the image sensor that turns light into discrete signals. The brighter the image at a given point on the sensor, the larger the value that is read for that pixel. Depending on the physical structure of the sensor, a color filter array may be used, which requires demosaicing to recreate a full-color image. The number of pixels in the sensor determines the camera's "pixel count". In a typical sensor, the pixel count is the product of the number of rows and the number of columns. For example, a 1,000 by 1,000-pixel sensor would have 1,000,000 pixels, or 1 megapixel. Resolution options Firmwares' resolution selector allows the user to optionally lower the resolution to reduce the file size per picture and extend lossless digital zooming. The bottom resolution option is typically 640×480 pixels (0.3 megapixels). A lower resolution extends the number of remaining photos in free space, postponing the exhaustion of space storage, which is of use where no further data storage device is available and for captures of lower significance, where the benefit from less space storage consumption outweighs the disadvantage from reduced detail. Image sharpness An image's sharpness is presented through the crisp detail, defined lines, and its depicted contrast. Sharpness is a factor of multiple systems throughout the DSLR camera by its ISO, resolution, lens, and the lens settings, the environment of the image, and its post-processing. Images have a possibility of being too sharp, but they can never be too in focus. A digital camera resolution is determined by a digital sensor. The digital sensor indicates a high level of sharpness can be produced through the amount of noise and grain that is tolerated through the lens of the camera. Resolution within the field of digital stills and digital movies is indicated through the camera's ability to determine detail based on the distance, which is then measured by frame size, pixel type, number, and organization. Although some DSLR cameras have limited resolutions, it is almost impossible to not have the proper sharpness for an image. The ISO choice when taking a photo affects the quality of the image, as high ISO settings equate to an image that is less sharp due to the increased amount of noise allowed into the image, along with too little noise, which can also produce an image that is not sharp. Methods of image capture Since the first digital backs were introduced, there have been three main methods of capturing the image, each based on the hardware configuration of the sensor and color filters. Single-shot capture systems use either one sensor chip with a Bayer filter mosaic, or three separate image sensors (one each for the primary additive colors red, green, and blue) which are exposed to the same image via a beam splitter (see Three-CCD camera). Multi-shot exposes the sensor to the image in a sequence of three or more openings of the lens aperture. There are several methods of application of the multi-shot technique. The most common was originally to use a single image sensor with three filters passed in front of the sensor in sequence to obtain the additive color information. Another multiple-shot method is called microscanning. This method uses a single sensor chip with a Bayer filter and physically moves the sensor on the focus plane of the lens to construct a higher resolution image than the native resolution of the chip. A third version combines these two methods without a Bayer filter on the chip. The third method is called scanning because the sensor moves across the focal plane much like the sensor of an image scanner. The linear or tri-linear sensors in scanning cameras utilize only a single line of photosensors, or three lines for the three colors. Scanning may be accomplished by moving the sensor (for example, when using color co-site sampling) or by rotating the whole camera. A digital rotating line camera offers images consisting of a total resolution that is very high. The choice of method for a given capture is determined largely by the subject matter. It is usually inappropriate to attempt to capture a subject that moves with anything but a single-shot system. However, the higher color fidelity and larger file sizes and resolutions that are available with multi-shot and scanning backs make them more attractive for commercial photographers who are working with stationary subjects and large-format photographs. Improvements in single-shot cameras and image file processing at the beginning of the 21st century made single-shot cameras almost completely dominant, even in high-end commercial photography. Filter mosaics, interpolation, and aliasing Most current consumer digital cameras use a Bayer filter mosaic in combination with an optical anti-aliasing filter to reduce the aliasing due to the reduced sampling of the different primary-color images. A demosaicing algorithm is used to interpolate color information to create a full array of RGB image data. Cameras that use a beam-splitter single-shot 3CCD approach, three-filter multi-shot approach, color co-site sampling or Foveon X3 sensor do not use anti-aliasing filters, nor demosaicing. Firmware in the camera, or a software in a raw converter program such as Adobe Camera Raw, interprets the raw data from the sensor to obtain a full-color image, because the RGB color model requires three intensity values for each pixel: one each for the red, green, and blue (other color models, when used, also require three or more values per pixel). A single sensor element cannot simultaneously record these three intensities, so a color filter array (CFA) must be used to selectively filter a particular color for each pixel. The Bayer filter pattern is a repeating 2x2 mosaic pattern of light filters, with green ones at opposite corners and red and blue in the other two positions. The high proportion of green takes advantage of the properties of the human visual system, which determines brightness mostly from green and is far more sensitive to brightness than to hue or saturation. Sometimes a 4-color filter pattern is used, often involving two different hues of green. This provides potentially more accurate color, but requires a slightly more complicated interpolation process. The color intensity values not captured for each pixel can be interpolated from the values of adjacent pixels which represent the color being calculated. Sensor size and angle of view Cameras with digital image sensors that are smaller than the typical 35 mm film size have a smaller field or angle of view when used with a lens of the same focal length. This is because the angle of view is a function of both focal length and the sensor or film size used. The crop factor is relative to the 35mm film format. If a smaller sensor is used, as in most digicams, the field of view is cropped by the sensor to smaller than the 35 mm full-frame format's field of view. This narrowing of the field of view may be described as crop factor, a factor by which a longer focal length lens would be needed to get the same field of view on a 35 mm film camera. Full-frame digital SLRs utilize a sensor of the same size as a frame of 35 mm film. Common values for field of view crop in DSLRs using active pixel sensors include 1.3x for some Canon (APS-H) sensors, 1.5x for Sony APS-C sensors used by Nikon, Pentax and Konica Minolta and for Fujifilm sensors, 1.6 (APS-C) for most Canon sensors, ~1.7x for Sigma's Foveon sensors and 2x for Kodak and Panasonic 4/3-inch sensors currently used by Olympus and Panasonic. Crop factors for non-SLR consumer compact and bridge cameras are larger, frequently 4x or more. Sensor resolution The resolution of a digital camera is often limited by the image sensor that turns light into discrete signals. The brighter the image at a given point on the sensor, the larger the value that is read for that pixel. Depending on the physical structure of the sensor, a color filter array may be used, which requires demosaicing to recreate a full-color image. The number of pixels in the sensor determines the camera's "pixel count". In a typical sensor, the pixel count is the product of the number of rows and the number of columns. Pixels are square and is often equal to 1, for example, a 1,000 by 1,000-pixel sensor would have 1,000,000 pixels, or 1 megapixel. On full-frame sensors (i.e., 24 mm 36 mm), some cameras propose images with 20–25 million pixels that were captured by 7.5–m photosites, or a surface that is 50 times larger. Types of digital cameras Digital cameras come in a wide range of sizes, prices, and capabilities. In addition to general-purpose digital cameras, specialized cameras including multispectral imaging equipment and astrographs are used for scientific, military, medical, and other special purposes. Compacts Compact cameras are intended to be portable (pocketable) and are particularly suitable for casual "snapshots". Point-and-shoot cameras usually fall under this category. Many incorporate a retractable lens assembly that provides optical zoom. In most models, an auto-actuating lens cover protects the lens from elements. Most ruggedized or water-resistant models do not retract, and most with superzoom capability do not retract fully. Compact cameras are usually designed to be easy to use. Almost all include an automatic mode, or "auto mode", which automatically makes all camera settings for the user. Some also have manual controls. Compact digital cameras typically contain a small sensor that trades-off picture quality for compactness and simplicity; images can usually only be stored using lossy compression (JPEG). Most have a built-in flash usually of low power, sufficient for nearby subjects. A few high-end compact digital cameras have a hotshoe for connecting to an external flash. Live preview is almost always used to frame the photo on an integrated LCD. In addition to being able to take still photographs almost all compact cameras have the ability to record video. Compacts often have macro capability and zoom lenses, but the zoom range (up to 30x) is generally enough for candid photography but less than is available on bridge cameras (more than 60x), or the interchangeable lenses of DSLR cameras available at a much higher cost. Autofocus systems in compact digital cameras generally are based on a contrast-detection methodology using the image data from the live preview feed of the main imager. Some compact digital cameras use a hybrid autofocus system similar to what is commonly available on DSLRs. Typically, compact digital cameras incorporate a nearly silent leaf shutter into the lens but play a simulated camera sound for skeuomorphic purposes. For low cost and small size, these cameras typically use image sensor formats with a diagonal between 6 and 11 mm, corresponding to a crop factor between 7 and 4. This gives them weaker low-light performance, greater depth of field, generally closer focusing ability, and smaller components than cameras using larger sensors. Some cameras use a larger sensor including, at the high end, a pricey full-frame sensor compact camera, such as Sony Cyber-shot DSC-RX1, but have capability near that of a DSLR. A variety of additional features are available depending on the model of the camera. Such features include GPS, compass, barometers and altimeters. Starting in 2010, some compact digital cameras can take 3D still photos. These 3D compact stereo cameras can capture 3D panoramic photos with dual lens or even a single lens for playback on a 3D TV. In 2013, Sony released two add-on camera models without display, to be used with a smartphone or tablet, controlled by a mobile application via WiFi. Rugged compacts Rugged compact cameras typically include protection against submersion, hot and cold conditions, shock, and pressure. Terms used to describe such properties include waterproof, freeze-proof, heatproof, shockproof, and crushproof, respectively. Nearly all major camera manufacturers have at least one product in this category. Some are waterproof to a considerable depth up to 100 feet (30 m); others only 10 feet (3 m), but only a few will float. Ruggeds often lack some of the features of ordinary compact camera, but they have video capability and the majority can record sound. Most have image stabilization and built-in flash. Touchscreen LCD and GPS do not work underwater. Action cameras GoPro and other brands offer action cameras that are rugged, small, and can be easily attached to helmets, arms, bicycles, etc. Most have a wide angle and fixed focus and can take still pictures and video, typically with sound. 360-degree cameras The 360-degree camera can take picture or video 360 degrees using two lenses back-to-back and shooting at the same time. Some of the cameras are Ricoh Theta S, Nikon Keymission 360 and Samsung Gear 360. Nico360 was launched in 2016 and claimed as the world's smallest 360-degree camera with size 46 x 46 x 28 mm (1.8 x 1.8 x 1.1 in) and price less than $200. With virtual reality mode built-in stitching, Wifi, and Bluetooth, live streaming can be done. Due to it also being water resistant, the Nico360 can be used as action camera. There are tend that action cameras have capabilities to shoot 360 degrees with at least 4K resolution. Bridge cameras Bridge cameras physically resemble DSLRs, and are sometimes called DSLR-shape or DSLR-like. They provide some similar features but, like compacts, they use a fixed lens and a small sensor. Some compact cameras have also PSAM mode. Most use live preview to frame the image. Their usual autofocus is by the same contrast-detect mechanism as compacts, but many bridge cameras have a manual focus mode and some have a separate focus ring for greater control. The big physical size and small sensor allow superzoom and wide aperture. Bridge cameras generally include an image stabilization system to enable longer handheld exposures, sometimes better than DSLR for low light conditions. As of 2014, bridge cameras come in two principal classes in terms of sensor size, firstly the more traditional 1/2.3" sensor (as measured by image sensor format) which gives more flexibility in lens design and allows for handholdable zoom from 20 to 24 mm (35 mm equivalent) wide angle all the way up to over 1000 mm supertele, and secondly a 1" sensor that allows better image quality particularly in low light (higher ISO) but puts greater constraints on lens design, resulting in zoom lenses that stop at 200 mm (constant aperture, e.g. Sony RX10) or 400 mm (variable aperture, e.g. Panasonic Lumix FZ1000) equivalent, corresponding to an optical zoom factor of roughly 10 to 15. Some bridge cameras have a lens thread to attach accessories such as wide-angle or telephoto converters as well as filters such as UV or Circular Polarizing filter and lens hoods. The scene is composed by viewing the display or the electronic viewfinder (EVF). Most have a slightly longer shutter lag than a DSLR. Many of these cameras can store images in a raw format in addition to supporting JPEG. The majority have a built-in flash, but only a few have a hotshoe. In bright sun, the quality difference between a good compact camera and a digital SLR is minimal but bridge cameras are more portable, cost less and have a greater zoom ability. Thus a bridge camera may better suit outdoor daytime activities, except when seeking professional-quality photos. Mirrorless interchangeable-lens cameras In late 2008, a new type of camera emerged, called a mirrorless interchangeable-lens camera. It is technically a DSLR camera that does not require a reflex mirror, a key component of the former. While a typical DSLR has a mirror that reflects light from the lens up to the optical viewfinder, in a mirrorless camera, there is no optical viewfinder. The image sensor is exposed to light at all times, giving the user a digital preview of the image either on the built-in rear LCD screen or an electronic viewfinder (EVF). These are simpler and more compact than DSLRs due to not having a lens reflex system. MILCs, or mirrorless cameras for short, come with various sensor sizes depending on the brand and manufacturer, these include: a small 1/2.3 inch sensor, as is commonly used in bridge cameras such as the original Pentax Q (more recent Pentax Q versions have a slightly larger 1/1.7 inch sensor); a 1-inch sensor; a Micro Four Thirds sensor; an APS-C sensor found in Sony NEX series and α "DSLR-likes", Fujifilm X series, Pentax K-01, and Canon EOS M; and some, such as the Sony α7, use a full frame (35 mm) sensor, with the Hasselblad X1D being the first medium format mirrorless camera. Some MILCs have a separate electronic viewfinder to compensate the lack of an optical one. In other cameras, the back display is used as the primary viewfinder in the same way as in compact cameras. One disadvantage of mirrorless cameras compared to a typical DSLR is its battery life due to the energy consumption of the electronic viewfinder, but this can be mitigated by a setting inside the camera in some models. Many mirrorless cameras have a hotshoe. Olympus and Panasonic released many Micro Four Thirds cameras with interchangeable lenses that are fully compatible with each other without any adapter, while others have proprietary mounts. In 2014, Kodak released its first Micro Four Third system camera. , mirrorless cameras are fast becoming appealing to both amateurs and professionals alike due to their simplicity, compatibility with some DSLR lenses, and features that match most DSLRs today. Modular cameras While most digital cameras with interchangeable lenses feature a lens-mount of some kind, there are also a number of modular cameras, where the shutter and sensor are incorporated into the lens module. The first such modular camera was the Minolta Dimâge V in 1996, followed by the Minolta Dimâge EX 1500 in 1998 and the Minolta MetaFlash 3D 1500 in 1999. In 2009, Ricoh released the Ricoh GXR modular camera. At CES 2013, Sakar International announced the Polaroid iM1836, an 18MP camera with 1"-sensor with interchangeable sensor-lens. An adapter for Micro Four Thirds, Nikon and K-mount lenses was planned to ship with the camera. There are also a number of add-on camera modules for smartphones, they are called lens-style cameras (lens camera or smart lens). They contain all the essential components of a digital camera inside a DSLR lens-shaped module, hence the name, but lack any sort of viewfinder and most controls of a regular camera. Instead, they are connected wirelessly and/or mounted to a smartphone to be used as its display output and operate the camera's various controls. Lens-style cameras include: Sony Cyber-shot QX series "Smart Lens" or "SmartShot" cameras, announced and released in mid 2013 with the Cyber-shot DSC-QX10. In January 2014, a firmware update was announced for the DSC-QX10 and DSC-QX100. In September 2014, Sony announced the Cyber-shot DSC-QX30 as well as the Alpha ILCE-QX1, the former an ultrazoom with a built-in 30x optical zoom lens, the latter opting for an interchangeable Sony E-mount instead of a built-in lens. Kodak PixPro smart lens camera series, announced in 2014. These include: the 5X optical zoom SL5, 10X optical zoom SL10, and the 25X optical zoom SL25; all featuring 16MP sensors and 1080p video recording, except for the SL5 which caps at 720p. ViviCam IU680 smart lens camera from Sakar-owned brand, Vivitar, announced in 2014. Olympus Air A01 lens camera, announced in 2014 and released in 2015, the lens camera is an open platform with an Android operating system and can detach into 2 parts (sensor module and lens), just like the Sony QX1, and all compatible Micro Four Thirds lenses can then be attached to the built-in lens mount of the camera's sensor module. Digital single-lens reflex cameras (DSLR) Digital single-lens reflex cameras (DSLR) is a camera with a digital sensor that utilizes a reflex mirror to split or direct light into the viewfinder to produce an image. The reflex mirror finds the image by blocking light to the camera's sensor and then reflecting it into the camera's pentaprism which allows it to be seen through the viewfinder. When the shutter release is fully pressed the reflex mirror pulls out horizontally below the pentaprism briefly darkening the viewfinder and then opening up the sensor for exposure which creates the photo. The digital image is produced by the sensor which is an array of photoreceptors on a microchip capable of recording light values. Many modern DSLRs offer the ability for "live view" or the framing of the subject emitted from the sensor onto a digital screen, and many have a hotshoe. The sensor also known as a full-frame sensor is much larger than the other types, typically 18mm to 36mm on the diagonal (crop factor 2, 1.6, or 1). The larger sensor permits more light to be received by each pixel; this, combined with the relatively large lenses provides superior low-light performance. For the same field of view and the same aperture, a larger sensor gives shallower focus. DSLRs can equip interchangeable lenses for versatility by removing it from the lens mount of the camera, typically a silver ring on the front side of DSLRs. These lenses work in tandem with the mechanics of the DSLR to adjust aperture and focus. Autofocus is accomplished using sensors in the mirror box and on most modern lenses can be activated from the lens itself which will trigger upon shutter release. Digital Still Cameras (DSC) Digital Still Camera (DSC), such as the Sony DSC cameras, is a type of camera that does not use a reflex mirror. DSCs are like point-and-shoot cameras and are the most common type of cameras, due to their comfortable price and its quality. Here are a list of DSCs: List of Sony Cyber-shot cameras Fixed-mirror DSLT cameras Cameras with fixed semi-transparent mirrors, also known as DSLT cameras, such as the Sony SLT cameras, are single-lens without a moving reflex mirror as in a conventional DSLR. A semi-transparent mirror transmits some of the light to the image sensor and reflects some of the light along the path to a pentaprism/pentamirror which then goes to an optical view finder (OVF) as is done with a reflex mirror in DSLR cameras. The total amount of light is not changed, just some of the light travels one path and some of it travels the other. The consequences are that DSLT cameras should shoot a half stop differently from DSLR. One advantage of using a DSLT camera is the blind moments a DSLR user experiences while the reflecting mirror is moved to send the light to the sensor instead of the viewfinder do not exist for DSLT cameras. Because there is no time at which light is not traveling along both paths, DSLT cameras get the benefit of continuous auto-focus tracking. This is especially beneficial for burst-mode shooting in low-light conditions and also for tracking when taking video. Digital rangefinders A rangefinder is a device to measure subject distance, with the intent to adjust the focus of a camera's objective lens accordingly (open-loop controller). The rangefinder and lens focusing mechanism may or may not be coupled. In common parlance, the term "rangefinder camera" is interpreted very narrowly to denote manual-focus cameras with a visually-read out optical rangefinder based on parallax. Most digital cameras achieve focus through analysis of the image captured by the objective lens and distance estimation, if it is provided at all, is only a byproduct of the focusing process (closed-loop controller). Line-scan camera systems A line-scan camera traditionally has a single row of pixel sensors, instead of a matrix of them. The lines are continuously fed to a computer that joins them to each other and makes an image. This is most commonly done by connecting the camera output to a frame grabber which resides in a PCI slot of an industrial computer. The frame grabber acts to buffer the image and sometimes provide some processing before delivering to the computer software for processing. Industrial processes often require height and width measurements performed by digital line-scan systems. Multiple rows of sensors may be used to make colored images, or to increase sensitivity by TDI (time delay and integration). Many industrial applications require a wide field of view. Traditionally maintaining consistent light over large 2D areas is quite difficult. With a line scan camera all that is necessary is to provide even illumination across the "line" currently being viewed by the camera. This makes sharp pictures of objects that pass the camera at high speed. Such cameras are also commonly used to make photo finishes, to determine the winner when multiple competitors cross the finishing line at nearly the same time. They can also be used as industrial instruments for analyzing fast processes. Line-scan cameras are also extensively used in imaging from satellites (see push broom scanner). In this case the row of sensors is perpendicular to the direction of satellite motion. Line-scan cameras are widely used in scanners. In this case, the camera moves horizontally. Superzoom cameras Digital superzoom cameras are digital cameras that can zoom in very far. These superzoom cameras are suitable for people who have nearsightedness. The HX series is a series containing Sony's superzoom cameras like HX20V, HX90V and the newest HX99. HX stands for HyperXoom. Light-field camera This type of digital camera captures information about the light field emanating from a scene; that is, the intensity of light in a scene, and also the direction that the light rays are traveling in space. This contrasts with a conventional digital camera, which records only light intensity. Event camera Instead of measuring the intensity of light over some predetermined time interval (the exposure time), event cameras detect when the intensity of light changes by some threshold for each pixel independently, usually with microsecond precision. Integration into other devices Many devices have a built-in digital camera, including, for example, smartphones, mobile phones, PDAs and laptop computers. Built-in cameras generally store the images in the JPEG file format, although cameras in Apple's iPhone line have used the HEIC format since 2017. Mobile phones incorporating digital cameras were introduced in Japan in 2001 by J-Phone. In 2003 camera phones outsold stand-alone digital cameras, and in 2006 they outsold film and digital stand-alone cameras. Five billion camera phones were sold in five years, and by 2007 more than half of the installed base of all mobile phones were camera phones. Sales of separate cameras peaked in 2008. Notable digital camera manufacturers There are many manufacturers that lead in the production of digital cameras (commonly DSLRs). Each brand embodies different mission statements that differ them from each other outside of the physical technology that they produce. While the majority of manufacturers share modern features amongst their production of cameras, some specialize in specific details either physically on camera or within the system and image quality. Market trends Sales of traditional digital cameras have declined due to the increasing use of smartphones for casual photography, which also enable easier manipulation and sharing of photos through the use of apps and web-based services. "Bridge cameras", in contrast, have held their ground with functionality that most smartphone cameras lack, such as optical zoom and other advanced features. DSLRs have also lost ground to Mirrorless interchangeable-lens camera (MILC)s offering the same sensor size in a smaller camera. A few expensive ones use a full-frame sensor, just like DSLR professional cameras. In response to the convenience and flexibility of smartphone cameras, some manufacturers produced "smart" digital cameras that combine features of traditional cameras with those of a smartphone. In 2012, Nikon and Samsung released the Coolpix S800c and Galaxy Camera, the first two digital cameras to run the Android operating system. Since this software platform is used in many smartphones, they can integrate with some of the same services (such as e-mail attachments, social networks and photo sharing sites) that smartphones do and use other Android-compatible software. In an inversion, some phone makers have introduced smartphones with cameras designed to resemble traditional digital cameras. Nokia released the 808 PureView and Lumia 1020 in 2012 and 2013; the two devices respectively run the Symbian and Windows Phone operating systems, and both include a 41-megapixel camera (along with a camera grip attachment for the latter). Similarly, Samsung introduced the Galaxy S4 Zoom, having a 16-megapixel camera and 10x optical zoom, combining traits from the Galaxy S4 Mini with the Galaxy Camera. Panasonic Lumix DMC-CM1 is an Android KitKat 4.4 smartphone with 20MP, 1" sensor, the largest sensor for a smartphone ever, with Leica fixed lens equivalent of 28 mm at F2.8, can take RAW image and 4K video, has 21 mm thickness. Furthermore, in 2018 Huawei P20 Pro is an android Oreo 8.1 has triple Leica lenses in the back of the smartphone with 40MP 1/1.7" RGB sensor as first lens, 20MP 1/2.7" monochrome sensor as second lens and 8MP 1/4" RGB sensor with 3x optical zoom as third lens. Combination of first lens and second lens will produce bokeh image with larger high dynamic range, whereas combination of mega pixel first lens and optical zoom will produce maximum 5x digital zoom without loss of quality by reducing the image size to 8MP. Light-field cameras were introduced in 2013 with one consumer product and several professional ones. After a big dip of sales in 2012, consumer digital camera sales declined again in 2013 by 36 percent. In 2011, compact digital cameras sold 10 million per month. In 2013, sales fell to about 4 million per month. DSLR and MILC sales also declined in 2013 by 10–15% after almost ten years of double digit growth. Worldwide unit sales of digital cameras is continuously declining from 148 million in 2011 to 58 million in 2015 and tends to decrease more in the following years. Film camera sales hit their peak at about 37 million units in 1997, while digital camera sales began in 1989. By 2008, the film camera market had died and digital camera sales hit their peak at 121 million units in 2010. In 2002, cell phones with an integrated camera had been introduced and in 2003 the cell phone with an integrated camera had sold 80 million units per year. By 2011, cell phones with an integrated camera were selling hundreds of millions per year, which were causing a decline in digital cameras. In 2015, digital camera sales were 35 million units or only less than a third of digital camera sales numbers at their peak and also slightly less than film camera sold number at their peak. Connectivity Transferring photos Many digital cameras can connect directly to a computer to transfer data:- Early cameras used the PC serial port. USB is now the most widely used method (most cameras are viewable as USB mass storage), though some have a FireWire port. Some cameras use USB PTP mode for connection instead of USB MSC; some offer both modes. Other cameras use wireless connections, via Bluetooth or IEEE 802.11 Wi-Fi, such as the Kodak EasyShare One. Wi-Fi integrated Memory cards (SDHC, SDXC) can transmit stored images, video and other files to computers or smartphones. Mobile operating systems such as Android allow automatic upload and backup or sharing of images over Wi-Fi to photo sharing and cloud services. Cameras with integrated Wi-Fi or specific Wi-Fi adapters mostly allow camera control, especially shutter release, exposure control and more (tethering) from computer or smartphone apps additionally to the transfer of media data. Cameraphones and some high-end stand-alone digital cameras also use cellular networks to connect for sharing images. The most common standard on cellular networks is the MMS Multimedia Messaging Service, commonly called "picture messaging". The second method with smartphones is to send a picture as an email attachment. Many old cameraphones, however, do not support email. A common alternative is the use of a card reader which may be capable of reading several types of storage media, as well as high speed transfer of data to the computer. Use of a card reader also avoids draining the camera battery during the download process. An external card reader allows convenient direct access to the images on a collection of storage media. But if only one storage card is in use, moving it back and forth between the camera and the reader can be inconvenient. Many computers have a card reader built in, at least for SD cards. Printing photos Many modern cameras support the PictBridge standard, which allows them to send data directly to a PictBridge-capable printer without the need for a computer. PictBridge uses PTP to transfer images and control information. Wireless connectivity can also provide for printing photos without a cable connection. An instant-print camera, is a digital camera with a built-in printer. This confers a similar functionality as an instant camera which uses instant film to quickly generate a physical photograph. Such non-digital cameras were popularized by Polaroid with the SX-70 in 1972. Displaying photos Many digital cameras include a video output port. Usually sVideo, it sends a standard-definition video signal to a television, allowing the user to show one picture at a time. Buttons or menus on the camera allow the user to select the photo, advance from one to another, or automatically send a "slide show" to the TV. HDMI has been adopted by many high-end digital camera makers, to show photos in their high-resolution quality on an HDTV. In January 2008, Silicon Image announced a new technology for sending video from mobile devices to a television in digital form. MHL sends pictures as a video stream, up to 1080p resolution, and is compatible with HDMI. Some DVD recorders and television sets can read memory cards used in cameras; alternatively several types of flash card readers have TV output capability. Weather-sealing and waterproofing Cameras can be equipped with a varying amount of environmental sealing to provide protection against splashing water, moisture (humidity and fog), dust and sand, or complete waterproofness to a certain depth and for a certain duration. The latter is one of the approaches to allow underwater photography, the other approach being the use of waterproof housings. Many waterproof digital cameras are also shockproof and resistant to low temperatures. Some waterproof cameras can be fitted with a waterproof housing to increase the operational depth range. The Olympus 'Tough' range of compact cameras is an example. Modes Many digital cameras have preset modes for different applications. Within the constraints of correct exposure various parameters can be changed, including exposure, aperture, focusing, light metering, white balance, and equivalent sensitivity. For example, a portrait might use a wider aperture to render the background out of focus, and would seek out and focus on a human face rather than other image content. Few cameras are equipped with a voice note (audio-only) recording feature. Scene modes Vendors implement a variety scene modes in cameras' firmwares for various purposes, such as a "landscape mode" which prevents focusing on rainy and/or stained window glass such as a windshield, and a "sports mode" which reduces motion blur of moving subjects by reducing exposure time with the help of increased light sensitivity. Firmwares may be equipped with the ability to select a suitable scene mode automatically through artificial intelligence. Image data storage Many camera phones and most stand alone digital cameras store image data in flash memory cards or other removable media. Most stand-alone cameras use SD format, while a few use CompactFlash, CFexpress or other types. In January 2012, a faster XQD card format was announced. In early 2014, some high end cameras have two hot-swappable memory slots. Photographers can swap one of the memory card with camera-on. Each memory slot can accept either Compact Flash or SD Card. All new Sony cameras also have two memory slots, one for its Memory Stick and one for SD Card, but not hot-swapable. The approximate count of remaining photos until space exhaustion is calculated by the firmware throughout use and indicated in the viewfinder, to prepare the user for an impending necessary hot swap of the memory card, and/or file offload. A few cameras used other removable storage such as Microdrives (very small hard disk drives), CD single (185 MB), and 3.5" floppy disks (e. g. Sony Mavica). Other unusual formats include: Onboard (internal) flash memory — Cheap cameras and cameras secondary to the device's main use (such as a camera phone). Some have small capacities such as 100 Megabytes and less, where intended use is buffer storage for uninterrupted operation during a memory card hot swap. SuperDisk (LS120) used in two Panasonic digital cameras, the PV-SD4090 and PV-SD5000, which allowed them to use both SuperDisk and 3.5" floppy disks PC Card hard drives — early professional cameras (discontinued) PC Card flash memory cards Thermal printer — known only in the Casio Petit Colle ZR-1 and ZR-10 which printed images immediately rather than storing Zink technology — printing images immediately rather than storing PocketZip — media used in the Agfa ePhoto CL30 Clik! Most manufacturers of digital cameras do not provide drivers and software to allow their cameras to work with Linux or other free software. Still, many cameras use the standard USB mass storage and/or Media Transfer Protocol, and are thus widely supported. Other cameras are supported by the gPhoto project, and many computers are equipped with a memory card reader. File formats The Joint Photography Experts Group standard (JPEG) is the most common file format for storing image data. Other file types include Tagged Image File Format (TIFF) and various Raw image formats. Many cameras, especially high-end ones, support a raw image format. A raw image is the unprocessed set of pixel data directly from the camera's sensor, often saved in a proprietary format. Adobe Systems has released the DNG format, a royalty-free raw image format used by at least 10 camera manufacturers. Raw files initially had to be processed in specialized image editing programs, but over time many mainstream editing programs, such as Google's Picasa, have added support for raw images. Rendering to standard images from raw sensor data allows more flexibility in making major adjustments without losing image quality or retaking the picture. Formats for movies are AVI, DV, MPEG, MOV (often containing motion JPEG), WMV, and ASF (basically the same as WMV). Recent formats include MP4, which is based on the QuickTime format and uses newer compression algorithms to allow longer recording times in the same space. Other formats that are used in cameras (but not for pictures) are the Design Rule for Camera Format (DCF), an ISO specification, used in almost all camera since 1998, which defines an internal file structure and naming. Also used is the Digital Print Order Format (DPOF), which dictates what order images are to be printed in and how many copies. The DCF 1998 defines a logical file system with 8.3 filenames and makes the usage of either FAT12, FAT16, FAT32 or exFAT mandatory for its physical layer in order to maximize platform interoperability. Most cameras include Exif data that provides metadata about the picture. Exif data may include aperture, exposure time, focal length, date and time taken. Some are able to tag the location. Directory and file structure In order to guarantee interoperability, DCF specifies the file system for image and sound files to be used on formatted DCF media (like removable or non-removable memory) as FAT12, FAT16, FAT32, or exFAT. Media with a capacity of more than 2 GB must be formatted using FAT32 or exFAT. The filesystem in a digital camera contains a DCIM (Digital Camera IMages) directory, which can contain multiple subdirectories with names such as "123ABCDE" that consist of a unique directory number (in the range 100...999) and five alphanumeric characters, which may be freely chosen and often refer to a camera maker. These directories contain files with names such as "ABCD1234.JPG" that consist of four alphanumeric characters (often "100_", "DSC0", "DSCF", "IMG_", "MOV_", or "P000"), followed by a number. Handling of directories with possibly user-created duplicate numbers may vary among camera firmwares. DCF 2.0 adds support for DCF optional files recorded in an optional color space (that is, Adobe RGB rather than sRGB). Such files must be indicated by a leading "_" (as in "_DSC" instead of "100_" or "DSC0"). Thumbnail files To enable loading many images in miniature view quickly and efficiently, and to retain meta data, some vendors' firmwares generate accompanying low-resolution thumbnail files for videos and raw photos. For example, those of Canon cameras end with .THM. JPEG can already store a thumbnail image standalone. Batteries Digital cameras have become smaller over time, resulting in an ongoing need to develop a battery small enough to fit in the camera and yet able to power it for a reasonable length of time. Digital cameras utilize either proprietary or standard consumer batteries. , most cameras use proprietary lithium-ion batteries while some use standard AA batteries or primarily use a proprietary Lithium-ion rechargeable battery pack but have an optional AA battery holder available. Proprietary The most common class of battery used in digital cameras is proprietary battery formats. These are built to a manufacturer's custom specifications. Almost all proprietary batteries are lithium-ion. In addition to being available from the OEM, aftermarket replacement batteries are commonly available for most camera models. Standard consumer batteries Digital cameras that utilize off-the-shelf batteries are typically designed to be able to use both single-use disposable and rechargeable batteries, but not with both types in use at the same time. The most common off-the-shelf battery size used is AA. CR2, CR-V3 batteries, and AAA batteries are also used in some cameras. The CR2 and CR-V3 batteries are lithium based, intended for a single use. Rechargeable RCR-V3 lithium-ion batteries are also available as an alternative to non-rechargeable CR-V3 batteries. Some battery grips for DSLRs come with a separate holder to accommodate AA cells as an external power source. Conversion of film cameras to digital When digital cameras became common, many photographers asked whether their film cameras could be converted to digital. The answer was not immediately clear, as it differed among models. For the majority of 35 mm film cameras the answer is no, the reworking and cost would be too great, especially as lenses have been evolving as well as cameras. For most a conversion to digital, to give enough space for the electronics and allow a liquid crystal display to preview, would require removing the back of the camera and replacing it with a custom built digital unit. Many early professional SLR cameras, such as the Kodak DCS series, were developed from 35 mm film cameras. The technology of the time, however, meant that rather than being digital "backs" the bodies of these cameras were mounted on large, bulky digital units, often bigger than the camera portion itself. These were factory built cameras, however, not aftermarket conversions. A notable exception is the Nikon E2 and Nikon E3, using additional optics to convert the 35 mm format to a 2/3 CCD-sensor. A few 35 mm cameras have had digital camera backs made by their manufacturer, Leica being a notable example with the Leica R8–R9. Medium format and large format cameras (those using film stock greater than 35 mm), have a low unit production, and typical digital backs for them cost over $10,000. These cameras also tend to be highly modular, with handgrips, film backs, winders, and lenses available separately to fit various needs. The very large sensor these backs use leads to enormous image sizes. For example, Phase One's P45 39 MP image back creates a single TIFF image of size up to 224.6 MB, and even greater pixel counts are available. Medium format digitals such as this are geared more towards studio and portrait photography than their smaller DSLR counterparts; the ISO speed in particular tends to have a maximum of 400, versus 6400 for some DSLR cameras. (Canon EOS-1D Mark IV and Nikon D3S have ISO 12800 plus Hi-3 ISO 102400 with the Canon EOS-1Dx's ISO of 204800). Digital camera backs In the industrial and high-end professional photography market, some camera systems use modular (removable) image sensors. For example, some medium format SLR cameras, such as the Mamiya 645D series, allow installation of either a digital camera back or a traditional photographic film back. Area array CCD CMOS Linear array CCD (monochrome) 3-strip CCD with color filters Linear array cameras are also called scan backs. Single-shot Multi-shot (three-shot, usually) Most earlier digital camera backs used linear array sensors, moving vertically to digitize the image. Many of them only capture grayscale images. The relatively long exposure times, in the range of seconds or even minutes generally limit scan backs to studio applications, where all aspects of the photographic scene are under the photographer's control. Some other camera backs use CCD arrays similar to typical cameras. These are called single-shot backs. Since it is much easier to manufacture a high-quality linear CCD array with only thousands of pixels than a CCD matrix with millions, very high resolution linear CCD camera backs were available much earlier than their CCD matrix counterparts. For example, you could buy an (albeit expensive) camera back with over 7,000 pixel horizontal resolution in the mid-1990s. However, , it is still difficult to buy a comparable CCD matrix camera of the same resolution. Rotating line cameras, with about 10,000 color pixels in its sensor line, are able, , to capture about 120,000 lines during one full 360 degree rotation, thereby creating a single digital image of 1,200 Megapixels. Most modern digital camera backs use CCD or CMOS matrix sensors. The matrix sensor captures the entire image frame at once, instead of incrementing scanning the frame area through the prolonged exposure. For example, Phase One produces a 39 million pixel digital camera back with a 49.1 x 36.8 mm CCD in 2008. This CCD array is a little smaller than a frame of 120 film and much larger than a 35 mm frame (36 x 24 mm). In comparison, consumer digital cameras use arrays ranging from 36 x 24 mm (full frame on high end consumer DSLRs) to 1.28 x 0.96 mm (on camera phones) CMOS sensor. See also List of digital camera brands Computational photography DigitaOS Magic Lantern (firmware) Pixel shift Smart camera Video camera Digital signal processor Vision processing unit Image sensor Notes References External links History of the digital camera and digital imaging, Digital Camera Museum American inventions Audiovisual introductions in 1975 1975 in the arts 1975 in technology Computer-related introductions in 1975 20th-century inventions	Digital camera	[ "Technology" ]	11,570	[ "Recording devices", "Cameras" ]
52,806	https://en.wikipedia.org/wiki/Trivial%20File%20Transfer%20Protocol	Trivial File Transfer Protocol (TFTP) is a simple lockstep File Transfer Protocol which allows a client to get a file from or put a file onto a remote host. One of its primary uses is in the early stages of nodes booting from a local area network. TFTP has been used for this application because it is very simple to implement. TFTP was first standardized in 1981 and the current specification for the protocol can be found in . Overview Due to its simple design, TFTP can be easily implemented by code with a small memory footprint. It is, therefore, the protocol of choice for the initial stages of any network booting strategy like BOOTP, PXE, BSDP, etc., when targeting from highly resourced computers to very low resourced Single-board computers (SBC) and System on a Chip (SoC). It is also used to transfer firmware images and configuration files to network appliances like routers, firewalls, IP phones, etc. Today, TFTP is virtually unused for Internet transfers. TFTP's design was influenced from the earlier protocol EFTP, which was part of the PARC Universal Packet protocol suite. TFTP was first defined in 1980 by IEN 133. In June 1981 The TFTP Protocol (Revision 2) was published as RFC 783 and later updated in July 1992 by RFC 1350 which fixed among other things the Sorcerer's Apprentice syndrome. In March 1995 the TFTP Option Extension RFC 1782 updated later in May 1998 by RFC 2347, defined the option negotiation mechanism which establishes the framework for file transfer options to be negotiated prior to the transfer using a mechanism that is consistent with TFTP's original specification. TFTP is a simple protocol for transferring files, implemented on top of the UDP/IP protocols using well-known port number 69. TFTP was designed to be small and easy to implement, and therefore it lacks most of the advanced features offered by more robust file transfer protocols. TFTP only reads and writes files from or to a remote server. It cannot list, delete, or rename files or directories and it has no provisions for user authentication. Today TFTP is generally only used on local area networks (LAN). Details In TFTP, a transfer is initiated by the client issuing a request to read or write a particular file on the server. The request can optionally include a set of negotiated transfer parameters proposed by the client under the terms specified by RFC 2347. If the server grants the request, the file is sent in fixed-length blocks of 512 bytes by default or the number specified in the blocksize negotiated option defined by RFC 2348. Each block of transferred data, which is usually carried within a single IP packet in order to avoid IP fragmentation, must be acknowledged by an acknowledgment packet before the next block can be sent. A data packet of less than 512 bytes or the agreed blocksize option signals the termination of a transfer. If a packet gets lost in the network, the intended recipient will timeout and may retransmit their last packet (which may be data or an acknowledgment), thus causing the sender of the lost packet to retransmit that lost packet. The sender has to keep just one packet on hand for retransmission since the lock step acknowledgment guarantees that all older packets have been correctly received. Notice that both devices involved in a transfer are considered senders and receivers. One sends data and receives acknowledgments, the other sends acknowledgments and receives data. TFTP defines three modes of transfer: netascii, octet, and mail. Netascii is a modified form of ASCII, defined in RFC 764. It consists of an 8-bit extension of the 7-bit ASCII character space from 0x20 to 0x7F (the printable characters and the space) and eight of the control characters. The allowed control characters include the null (0x00), the line feed (LF, 0x0A), and the carriage return (CR, 0x0D). Netascii also requires that the end of line marker on a host be translated to the character pair CR LF for transmission and that any CR must be followed by either a LF or the null. Octet allows for the transfer of arbitrary raw 8-bit bytes, with the received file resulting byte-per-byte identical to the one sent. More correctly, if a host receives an octet file and then returns it, the returned file must be identical to the original. Mail transfer mode uses Netascii transfer, but the file is sent to an email recipient by specifying that recipient's email address as the file name. RFC 1350 declared this mode of transfer obsolete. TFTP uses UDP as its transport protocol. A transfer request is always initiated targeting port 69, but the data transfer ports are chosen independently by the sender and receiver during the transfer initialization. The ports are chosen at random according to the parameters of the networking stack, typically from the range of ephemeral ports. The initiating host A sends an RRQ (read request) or WRQ (write request) packet to host S at port number 69, containing the filename, transfer mode, and optionally any negotiated option under the terms of RFC 2347. S replies with an option ACK if options were used, and an ACK (acknowledgment) packet to WRQ and directly with a DATA packet to RRQ. The packet is sent from a randomly allocated ephemeral port, and all future packets to host S should be directed to this port. The source host sends numbered DATA packets to the destination host, all but the last containing a full-sized block of data (512 bytes default). The destination host replies with numbered ACK packets for all DATA packets. The final DATA packet must contain less than a full-sized block of data to signal that it is the last. If the size of the transferred file is an exact multiple of the block size, the source sends a final DATA packet containing 0 bytes of data. Receiver responds to each DATA with associated numbered ACK. The sender responds to the first received ACK of a block with DATA of the next block. If an ACK is not eventually received, a retransmit timer re-sends DATA packet. TFTP has always been associated to network booting. One of the first attempts in this regard was the Bootstrap Loading using TFTP standard RFC 906, published in 1984, which established the 1981 published Trivial File Transfer Protocol standard RFC 783 to be used as the standard file transfer protocol for bootstrap loading. It was followed shortly after by the Bootstrap Protocol standard RFC 951 (BOOTP), published in 1985, which allowed a disk-less client machine to discover its own IP address, the address of a TFTP server, and the name of a Network Bootstrap Program (NBP) to be TFTP transferred, loaded into memory, and executed. Dynamic Host Configuration Protocol standard RFC 2131 (DHCP) published in 1997 improved BOOTP capabilities. Finally, the Preboot Execution Environment (PXE) version 2.0 was released in December 1998, and the update 2.1 was made public in September 1999 counting on TFTP as its file transfer protocol. Intel has recently decided to widely support PXE within the new UEFI specification extending the TFTP support to all EFI/UEFI environments. The original protocol has a transfer file size limit of 512 bytes/block x 65535 blocks = 32 MB. In 1998 this limit was extended to 65535 bytes/block x 65535 blocks = 4 GB by TFTP Blocksize Option RFC 2348. If the defined blocksize produces an IP packet size that exceeds the minimum MTU at any point of the network path, IP fragmentation and reassembly will occur not only adding more overhead but also leading to total transfer failure when the minimalist IP stack implementation in a host's BOOTP or PXE ROM does not (or fails to properly) implement IP fragmentation and reassembly. If TFTP packets should be kept within the standard Ethernet MTU (1500), the blocksize value is calculated as 1500 minus headers of TFTP (4 bytes), UDP (8 bytes) and IP (20 bytes) = 1468 bytes/block, this gives a limit of 1468 bytes/block x 65535 blocks = 92 MB. Today most servers and clients support block number roll-over (block counter going back to 0 or 1 after 65535) which gives an essentially unlimited transfer file size. Since TFTP utilizes UDP, it has to supply its own transport and session support. Each file transferred via TFTP constitutes an independent exchange. Classically, this transfer is performed in lock-step, with only one packet (either a block of data or an acknowledgment) alternatively in flight on the network at any time. Due to this single data block strategy instead of sending a larger amount of uninterrupted data blocks before pausing the transfer to wait for the corresponding acknowledge (windowing), TFTP provides low throughput especially over high latency links. Microsoft introduced windowed TFTP in Windows 2008 as part of their Windows Deployment Services (WDS), in January 2015 TFTP Windowsize Option RFC 7440 was published. This substantially improves performance for things like PXE booting without the IP fragmentation side effect sometimes observed on Blocksize Option RFC 2348 Security considerations TFTP includes no login or access control mechanisms. Care must be taken when using TFTP for file transfers where authentication, access control, confidentiality, or integrity checking are needed. Note that those security services could be supplied above or below the layer at which TFTP runs. Care must also be taken in the rights granted to a TFTP server process so as not to violate the security of the server's file system. TFTP is often installed with controls such that only files that have public read access are available via TFTP. Also listing, deleting, renaming, and writing files via TFTP are typically disallowed. TFTP file transfers are not recommended where the inherent protocol limitations could raise insurmountable liability concerns. IETF standards documentation See also Simple File Transfer Protocol References Networking standards Network protocols Network file transfer protocols Network booting	Trivial File Transfer Protocol	[ "Technology", "Engineering" ]	2,201	[ "Networking standards", "Computer standards", "Computer networks engineering" ]
52,812	https://en.wikipedia.org/wiki/Humidity	Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. Humidity depends on the temperature and pressure of the system of interest. The same amount of water vapor results in higher relative humidity in cool air than warm air. A related parameter is the dew point. The amount of water vapor needed to achieve saturation increases as the temperature increases. As the temperature of a parcel of air decreases it will eventually reach the saturation point without adding or losing water mass. The amount of water vapor contained within a parcel of air can vary significantly. For example, a parcel of air near saturation may contain 8 g of water per cubic metre of air at , and 28 g of water per cubic metre of air at Three primary measurements of humidity are widely employed: absolute, relative, and specific. Absolute humidity is expressed as either mass of water vapor per volume of moist air (in grams per cubic meter) or as mass of water vapor per mass of dry air (usually in grams per kilogram). Relative humidity, often expressed as a percentage, indicates a present state of absolute humidity relative to a maximum humidity given the same temperature. Specific humidity is the ratio of water vapor mass to total moist air parcel mass. Humidity plays an important role for surface life. For animal life dependent on perspiration (sweating) to regulate internal body temperature, high humidity impairs heat exchange efficiency by reducing the rate of moisture evaporation from skin surfaces. This effect can be calculated using a heat index table, or alternatively using a similar humidex. The notion of air "holding" water vapor or being "saturated" by it is often mentioned in connection with the concept of relative humidity. This, however, is misleading—the amount of water vapor that enters (or can enter) a given space at a given temperature is almost independent of the amount of air (nitrogen, oxygen, etc.) that is present. Indeed, a vacuum has approximately the same equilibrium capacity to hold water vapor as the same volume filled with air; both are given by the equilibrium vapor pressure of water at the given temperature. There is a very small difference described under "Enhancement factor" below, which can be neglected in many calculations unless great accuracy is required. Definitions Absolute humidity Absolute humidity is the total mass of water vapor (gas form of water) present in a given volume or mass of air. It does not take temperature into consideration. Absolute humidity in the atmosphere ranges from near zero to roughly per cubic metre when the air is saturated at . Air is a gas, and its volume varies with pressure and temperature, per Boyles law. Absolute humidity is defined as water mass per volume of air. A given mass of air will grow or shrink as the temperature or pressure varies. So the absolute humidity of a mass of air will vary due to changes in temperature or pressure, even when the proportion of water in that mass of air (its specific humidity) remains constant. This makes the term absolute humidity as defined not ideal for some situations. Absolute humidity is the mass of the water vapor , divided by the volume of the air and water vapor mixture , which can be expressed as: In the equation above, if the volume is not set, the absolute humidity varies with changes in air temperature or pressure. Because of this variability, use of the term absolute humidity as defined is inappropriate for computations in chemical engineering, such as drying, where temperature variations might be significant. As a result, absolute humidity in chemical engineering may refer to mass of water vapor per unit mass of dry air, also known as the humidity ratio or mass mixing ratio (see "specific humidity" below), which is better suited for heat and mass balance calculations. Mass of water per unit volume as in the equation above is also defined as volumetric humidity. Because of the potential confusion, British Standard BS 1339 suggests avoiding the term "absolute humidity". Units should always be carefully checked. Many humidity charts are given in g/kg or kg/kg, but any mass units may be used. Relative humidity Relative humidity is the ratio of how much water vapour is in the air to how much water vapour the air could potentially contain at a given temperature. It varies with the temperature of the air: colder air can contain less vapour, and water will tend to condense out of the air more at lower temperatures. So changing the temperature of air can change the relative humidity, even when the absolute humidity remains constant. Chilling air increases the relative humidity. If the relative humidity rises over 100% (the dew point) and there is an available surface or particle, the water vapour will condense into liquid or ice. Likewise, warming air decreases the relative humidity. Warming some air containing a fog may cause that fog to evaporate, as the droplets are prone to total evaporation due to the lowering partial pressure of water vapour in that air, as the temperature rises. Relative humidity only considers the invisible water vapour. Mists, clouds, fogs and aerosols of water do not count towards the measure of relative humidity of the air, although their presence is an indication that a body of air may be close to the dew point. Relative humidity is normally expressed as a percentage; a higher percentage means that the air–water mixture is more humid. At 100% relative humidity, the air is saturated and is at its dew point. In the absence of a foreign body on which droplets or crystals can nucleate, the relative humidity can exceed 100%, in which case the air is said to be supersaturated. Introduction of some particles or a surface to a body of air above 100% relative humidity will allow condensation or ice to form on those nuclei, thereby removing some of the vapour and lowering the humidity. In a scientific notion, the relative humidity ( or ) of an air-water mixture is defined as the ratio of the partial pressure of water vapor () in air to the saturation vapor pressure () of water at the same temperature, usually expressed as a percentage: Relative humidity is an important metric used in weather forecasts and reports, as it is an indicator of the likelihood of precipitation, dew, or fog. In hot summer weather, a rise in relative humidity increases the apparent temperature to humans (and other animals) by hindering the evaporation of perspiration from the skin. For example, according to the heat index, a relative humidity of 75% at air temperature of would feel like . Relative humidity is also a key metric used to evaluate when it is appropriate to install flooring over a concrete slab. Specific humidity Specific humidity (or moisture content) is the ratio of the mass of water vapor to the total mass of the air parcel. Specific humidity is approximately equal to the mixing ratio, which is defined as the ratio of the mass of water vapor in an air parcel to the mass of dry air for the same parcel. It is typically represented with the symbol ω, and is commonly used in HVAC system design. Related concepts The term relative humidity is reserved for systems of water vapor in air. The term relative saturation is used to describe the analogous property for systems consisting of a condensable phase other than water in a non-condensable phase other than air. Measurement A device used to measure humidity of air is called a psychrometer or hygrometer. A humidistat is a humidity-triggered switch, often used to control a humidifier or a dehumidifier. The humidity of an air and water vapor mixture is determined through the use of psychrometric charts if both the dry bulb temperature (T) and the wet bulb temperature (Tw) of the mixture are known. These quantities are readily estimated by using a sling psychrometer. There are several empirical formulas that can be used to estimate the equilibrium vapor pressure of water vapor as a function of temperature. The Antoine equation is among the least complex of these, having only three parameters (A, B, and C). Other formulas, such as the Goff–Gratch equation and the Magnus–Tetens approximation, are more complicated but yield better accuracy. The Arden Buck equation is commonly encountered in the literature regarding this topic: where is the dry-bulb temperature expressed in degrees Celsius (°C), is the absolute pressure expressed in millibars, and is the equilibrium vapor pressure expressed in millibars. Buck has reported that the maximal relative error is less than 0.20% between when this particular form of the generalized formula is used to estimate the equilibrium vapor pressure of water. There are various devices used to measure and regulate humidity. Calibration standards for the most accurate measurement include the gravimetric hygrometer, chilled mirror hygrometer, and electrolytic hygrometer. The gravimetric method, while the most accurate, is very cumbersome. For fast and very accurate measurement the chilled mirror method is effective. For process on-line measurements, the most commonly used sensors nowadays are based on capacitance measurements to measure relative humidity, frequently with internal conversions to display absolute humidity as well. These are cheap, simple, generally accurate and relatively robust. All humidity sensors face problems in measuring dust-laden gas, such as exhaust streams from clothes dryers. Humidity is also measured on a global scale using remotely placed satellites. These satellites are able to detect the concentration of water in the troposphere at altitudes between . Satellites that can measure water vapor have sensors that are sensitive to infrared radiation. Water vapor specifically absorbs and re-radiates radiation in this spectral band. Satellite water vapor imagery plays an important role in monitoring climate conditions (like the formation of thunderstorms) and in the development of weather forecasts. Air density and volume Humidity depends on water vaporization and condensation, which, in turn, mainly depends on temperature. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. However, some of the water will condense until returning to almost the same humidity as before, giving the resulting total volume deviating from what the ideal gas law predicted. Conversely, decreasing temperature would also make some water condense, again making the final volume deviate from predicted by the ideal gas law. Therefore, gas volume may alternatively be expressed as the dry volume, excluding the humidity content. This fraction more accurately follows the ideal gas law. On the contrary the saturated volume is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity). Humid air is less dense than dry air because a molecule of water () is less massive than either a molecule of nitrogen () or a molecule of oxygen (). About 78% of the molecules in dry air are nitrogen (N2). Another 21% of the molecules in dry air are oxygen (O2). The final 1% of dry air is a mixture of other gases. For any gas, at a given temperature and pressure, the number of molecules present in a particular volume is constant. Therefore, when some number N of water molecules (vapor) is introduced into a volume of dry air, the number of air molecules in that volume must decrease by the same number N for the pressure to remain constant without using a change in temperature. The numbers are exactly equal if we consider the gases as ideal. The addition of water molecules, or any other molecules, to a gas, without removal of an equal number of other molecules, will necessarily require a change in temperature, pressure, or total volume; that is, a change in at least one of these three parameters. If temperature and pressure remain constant, the volume increases, and the dry air molecules that were displaced will initially move out into the additional volume, after which the mixture will eventually become uniform through diffusion. Hence the mass per unit volume of the gas—its density—decreases. Isaac Newton discovered this phenomenon and wrote about it in his book Opticks. Pressure dependence The relative humidity of an air–water system is dependent not only on the temperature but also on the absolute pressure of the system of interest. This dependence is demonstrated by considering the air–water system shown below. The system is closed (i.e., no matter enters or leaves the system). If the system at State A is isobarically heated (heating with no change in system pressure), then the relative humidity of the system decreases because the equilibrium vapor pressure of water increases with increasing temperature. This is shown in State B. If the system at State A is isothermally compressed (compressed with no change in system temperature), then the relative humidity of the system increases because the partial pressure of water in the system increases with the volume reduction. This is shown in State C. Above 202.64 kPa, the RH would exceed 100% and water may begin to condense. If the pressure of State A was changed by simply adding more dry air, without changing the volume, the relative humidity would not change. Therefore, a change in relative humidity can be explained by a change in system temperature, a change in the volume of the system, or change in both of these system properties. Enhancement factor The enhancement factor is defined as the ratio of the saturated vapor pressure of water in moist air to the saturated vapor pressure of pure water: The enhancement factor is equal to unity for ideal gas systems. However, in real systems the interaction effects between gas molecules result in a small increase of the equilibrium vapor pressure of water in air relative to equilibrium vapor pressure of pure water vapor. Therefore, the enhancement factor is normally slightly greater than unity for real systems. The enhancement factor is commonly used to correct the equilibrium vapor pressure of water vapor when empirical relationships, such as those developed by Wexler, Goff, and Gratch, are used to estimate the properties of psychrometric systems. Buck has reported that, at sea level, the vapor pressure of water in saturated moist air amounts to an increase of approximately 0.5% over the equilibrium vapor pressure of pure water. Effects Climate control refers to the control of temperature and relative humidity in buildings, vehicles and other enclosed spaces for the purpose of providing for human comfort, health and safety, and of meeting environmental requirements of machines, sensitive materials (for example, historic) and technical processes. Climate While humidity itself is a climate variable, it also affects other climate variables. Environmental humidity is affected by winds and by rainfall. The most humid cities on Earth are generally located closer to the equator, near coastal regions. Cities in parts of Asia and Oceania are among the most humid. Bangkok, Ho Chi Minh City, Kuala Lumpur, Hong Kong, Manila, Jakarta, Naha, Singapore, Kaohsiung and Taipei have very high humidity most or all year round because of their proximity to water bodies and the equator and often overcast weather. Some places experience extreme humidity during their rainy seasons combined with warmth giving the feel of a lukewarm sauna, such as Kolkata, Chennai and Kochi in India, and Lahore in Pakistan. Sukkur city located on the Indus River in Pakistan has some of the highest and most uncomfortable dew points in the country, frequently exceeding in the monsoon season. High temperatures combine with the high dew point to create heat index in excess of . Darwin experiences an extremely humid wet season from December to April. Houston, Miami, San Diego, Osaka, Shanghai, Shenzhen and Tokyo also have an extreme humid period in their summer months. During the South-west and North-east Monsoon seasons (respectively, late May to September and November to March), expect heavy rains and a relatively high humidity post-rainfall. Outside the monsoon seasons, humidity is high (in comparison to countries further from the Equator), but completely sunny days abound. In cooler places such as Northern Tasmania, Australia, high humidity is experienced all year due to the ocean between mainland Australia and Tasmania. In the summer the hot dry air is absorbed by this ocean and the temperature rarely climbs above . Global climate Humidity affects the energy budget and thereby influences temperatures in two major ways. First, water vapor in the atmosphere contains "latent" energy. During transpiration or evaporation, this latent heat is removed from surface liquid, cooling the Earth's surface. This is the biggest non-radiative cooling effect at the surface. It compensates for roughly 70% of the average net radiative warming at the surface. Second, water vapor is the most abundant of all greenhouse gases. Water vapor, like a green lens that allows green light to pass through it but absorbs red light, is a "selective absorber". Like the other greenhouse gasses, water vapor is transparent to most solar energy. However, it absorbs the infrared energy emitted (radiated) upward by the Earth's surface, which is the reason that humid areas experience very little nocturnal cooling but dry desert regions cool considerably at night. This selective absorption causes the greenhouse effect. It raises the surface temperature substantially above its theoretical radiative equilibrium temperature with the sun, and water vapor is the cause of more of this warming than any other greenhouse gas. Unlike most other greenhouse gases, however, water is not merely below its boiling point in all regions of the Earth, but below its freezing point at many altitudes. As a condensible greenhouse gas, it precipitates, with a much lower scale height and shorter atmospheric lifetime — weeks instead of decades. Without other greenhouse gases, Earth's blackbody temperature, below the freezing point of water, would cause water vapor to be removed from the atmosphere. Water vapor is thus a "slave" to the non-condensible greenhouse gases. Animal and plant life Humidity is one of the fundamental abiotic factors that defines any habitat (the tundra, wetlands, and the desert are a few examples), and is a determinant of which animals and plants can thrive in a given environment. The human body dissipates heat through perspiration and its evaporation. Heat convection, to the surrounding air, and thermal radiation are the primary modes of heat transport from the body. Under conditions of high humidity, the rate of evaporation of sweat from the skin decreases. Also, if the atmosphere is as warm or warmer than the skin during times of high humidity, blood brought to the body surface cannot dissipate heat by conduction to the air. With so much blood going to the external surface of the body, less goes to the active muscles, the brain, and other internal organs. Physical strength declines, and fatigue occurs sooner than it would otherwise. Alertness and mental capacity also may be affected, resulting in heat stroke or hyperthermia. Domesticated plants and animals (e.g. lizards) require regular upkeep of humidity percent when grown in-home and container conditions, for optimal thriving environment. Human comfort Although humidity is an important factor for thermal comfort, humans are more sensitive to variations in temperature than they are to changes in relative humidity. Humidity has a small effect on thermal comfort outdoors when air temperatures are low, a slightly more pronounced effect at moderate air temperatures, and a much stronger influence at higher air temperatures. Humans are sensitive to humid air because the human body uses evaporative cooling as the primary mechanism to regulate temperature. Under humid conditions, the rate at which perspiration evaporates on the skin is lower than it would be under arid conditions. Because humans perceive the rate of heat transfer from the body rather than temperature itself, we feel warmer when the relative humidity is high than when it is low. Humans can be comfortable within a wide range of humidities depending on the temperature—from 30 to 70%—but ideally not above the Absolute (60 °F Dew Point), between 40% and 60%. In general, higher temperatures will require lower humidities to achieve thermal comfort compared to lower temperatures, with all other factors held constant. For example, with clothing level = 1, metabolic rate = 1.1, and air speed 0.1 m/s, a change in air temperature and mean radiant temperature from 20 °C to 24 °C would lower the maximum acceptable relative humidity from 100% to 65% to maintain thermal comfort conditions. The CBE Thermal Comfort Tool can be used to demonstrate the effect of relative humidity for specific thermal comfort conditions and it can be used to demonstrate compliance with ASHRAE Standard 55–2017. Some people experience difficulty breathing in humid environments. Some cases may possibly be related to respiratory conditions such as asthma, while others may be the product of anxiety. Affected people will often hyperventilate in response, causing sensations of numbness, faintness, and loss of concentration, among others. Very low humidity can create discomfort, respiratory problems, and aggravate allergies in some individuals. Low humidity causes tissue lining nasal passages to dry, crack and become more susceptible to penetration of rhinovirus cold viruses. Extremely low (below 20%) relative humidities may also cause eye irritation. The use of a humidifier in homes, especially bedrooms, can help with these symptoms. Indoor relative humidities kept above 30% reduce the likelihood of the occupant's nasal passages drying out, especially in winter. Air conditioning reduces discomfort by reducing not just temperature but humidity as well. Heating cold outdoor air can decrease relative humidity levels indoors to below 30%. According to ASHRAE Standard 55-2017: Thermal Environmental Conditions for Human Occupancy, indoor thermal comfort can be achieved through the PMV method with relative humidities ranging from 0% to 100%, depending on the levels of the other factors contributing to thermal comfort. However, the recommended range of indoor relative humidity in air conditioned buildings is generally 30–60%. Human health Higher humidity reduces the infectivity of aerosolized influenza virus. A study concluded, "Maintaining indoor relative humidity >40% will significantly reduce the infectivity of aerosolized virus." Excess moisture in buildings expose occupants to fungal spores, cell fragments, or mycotoxins. Infants in homes with mold have a much greater risk of developing asthma and allergic rhinitis. More than half of adult workers in moldy/humid buildings develop nasal or sinus symptoms due to mold exposure. Mucociliary clearance in the respiratory tract is also hindered by low humidity. One study in dogs found that mucus transport was lower at an absolute humidity of 9 g/m3 than at 30 g/m3. Increased humidity can also lead to changes in total body water that usually leads to moderate weight gain, especially if one is acclimated to working or exercising in hot and humid weather. Building construction Common construction methods often produce building enclosures with a poor thermal boundary, requiring an insulation and air barrier system designed to retain indoor environmental conditions while resisting external environmental conditions. The energy-efficient, heavily sealed architecture introduced in the 20th century also sealed off the movement of moisture, and this has resulted in a secondary problem of condensation forming in and around walls, which encourages the development of mold and mildew. Additionally, buildings with foundations not properly sealed will allow water to flow through the walls due to capillary action of pores found in masonry products. Solutions for energy-efficient buildings that avoid condensation are a current topic of architecture. For climate control in buildings using HVAC systems, the key is to maintain the relative humidity at a comfortable range—low enough to be comfortable but high enough to avoid problems associated with very dry air. When the temperature is high and the relative humidity is low, evaporation of water is rapid; soil dries, wet clothes hung on a line or rack dry quickly, and perspiration readily evaporates from the skin. Wooden furniture can shrink, causing the paint that covers these surfaces to fracture. When the temperature is low and the relative humidity is high, evaporation of water is slow. When relative humidity approaches 100%, condensation can occur on surfaces, leading to problems with mold, corrosion, decay, and other moisture-related deterioration. Condensation can pose a safety risk as it can promote the growth of mold and wood rot as well as possibly freezing emergency exits shut. Certain production and technical processes and treatments in factories, laboratories, hospitals, and other facilities require specific relative humidity levels to be maintained using humidifiers, dehumidifiers and associated control systems. Vehicles The basic principles for buildings, above, also apply to vehicles. In addition, there may be safety considerations. For instance, high humidity inside a vehicle can lead to problems of condensation, such as misting of windshields and shorting of electrical components. In vehicles and pressure vessels such as pressurized airliners, submersibles and spacecraft, these considerations may be critical to safety, and complex environmental control systems including equipment to maintain pressure are needed. Aviation Airliners operate with low internal relative humidity, often under 20%, especially on long flights. The low humidity is a consequence of drawing in the very cold air with a low absolute humidity, which is found at airliner cruising altitudes. Subsequent warming of this air lowers its relative humidity. This causes discomfort such as sore eyes, dry skin, and drying out of mucosa, but humidifiers are not employed to raise it to comfortable mid-range levels because the volume of water required to be carried on board can be a significant weight penalty. As airliners descend from colder altitudes into warmer air, perhaps even flying through clouds a few thousand feet above the ground, the ambient relative humidity can increase dramatically. Some of this moist air is usually drawn into the pressurized aircraft cabin and into other non-pressurized areas of the aircraft and condenses on the cold aircraft skin. Liquid water can usually be seen running along the aircraft skin, both on the inside and outside of the cabin. Because of the drastic changes in relative humidity inside the vehicle, components must be qualified to operate in those environments. The recommended environmental qualifications for most commercial aircraft components is listed in RTCA DO-160. Cold, humid air can promote the formation of ice, which is a danger to aircraft as it affects the wing profile and increases weight. Naturally aspirated internal combustion engines have a further danger of ice forming inside the carburetor. Aviation weather reports (METARs) therefore include an indication of relative humidity, usually in the form of the dew point. Pilots must take humidity into account when calculating takeoff distances, because high humidity requires longer runways and will decrease climb performance. Density altitude is the altitude relative to the standard atmosphere conditions (International Standard Atmosphere) at which the air density would be equal to the indicated air density at the place of observation, or, in other words, the height when measured in terms of the density of the air rather than the distance from the ground. "Density Altitude" is the pressure altitude adjusted for non-standard temperature. An increase in temperature, and, to a much lesser degree, humidity, will cause an increase in density altitude. Thus, in hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude. Electronics Electronic devices are often rated to operate only under certain humidity conditions (e.g., 10% to 90%). The optimal humidity for electronic devices is 30% to 65%. At the top end of the range, moisture may increase the conductivity of permeable insulators leading to malfunction. Too low humidity may make materials brittle. A particular danger to electronic items, regardless of the stated operating humidity range, is condensation. When an electronic item is moved from a cold place (e.g., garage, car, shed, air conditioned space in the tropics) to a warm humid place (house, outside tropics), condensation may coat circuit boards and other insulators, leading to short circuit inside the equipment. Such short circuits may cause substantial permanent damage if the equipment is powered on before the condensation has evaporated. A similar condensation effect can often be observed when a person wearing glasses comes in from the cold (i.e. the glasses become foggy). It is advisable to allow electronic equipment to acclimatise for several hours, after being brought in from the cold, before powering on. Some electronic devices can detect such a change and indicate, when plugged in and usually with a small droplet symbol, that they cannot be used until the risk from condensation has passed. In situations where time is critical, increasing air flow through the device's internals, such as removing the side panel from a PC case and directing a fan to blow into the case, will reduce significantly the time needed to acclimatise to the new environment. In contrast, a very low humidity level favors the build-up of static electricity, which may result in spontaneous shutdown of computers when discharges occur. Apart from spurious erratic function, electrostatic discharges can cause dielectric breakdown in solid-state devices, resulting in irreversible damage. Data centers often monitor relative humidity levels for these reasons. Industry High humidity can often have a negative effect on the capacity of chemical plants and refineries that use furnaces as part of a certain processes (e.g., steam reforming, wet sulfuric acid processes). For example, because humidity reduces ambient oxygen concentrations (dry air is typically 20.9% oxygen, but at 100% relative humidity the air is 20.4% oxygen), flue gas fans must intake air at a higher rate than would otherwise be required to maintain the same firing rate. Baking High humidity in the oven, represented by an elevated wet-bulb temperature, increases the thermal conductivity of the air around the baked item, leading to a quicker baking process or even burning. Conversely, low humidity slows the baking process down. Other important facts At 100% relative humidity, air is saturated and at its dew point: the water vapor pressure would permit neither evaporation of nearby liquid water nor condensation to grow the nearby water; neither sublimation of nearby ice nor deposition to grow the nearby ice. Relative humidity can exceed 100%, in which case the air is supersaturated. Cloud formation requires supersaturated air. Cloud condensation nuclei lower the level of supersaturation required to form fogs and clouds – in the absence of nuclei around which droplets or ice can form, a higher level of supersaturation is required for these droplets or ice crystals to form spontaneously. In the Wilson cloud chamber, which is used in nuclear physics experiments, a state of supersaturation is created within the chamber, and moving subatomic particles act as condensation nuclei so trails of fog show the paths of those particles. For a given dew point and its corresponding absolute humidity, the relative humidity will change inversely, albeit nonlinearly, with the temperature. This is because the vapor pressure of water increases with temperature—the operative principle behind everything from hair dryers to dehumidifiers. Due to the increasing potential for a higher water vapor partial pressure at higher air temperatures, the water content of air at sea level can get as high as 3% by mass at compared to no more than about 0.5% by mass at . This explains the low levels (in the absence of measures to add moisture) of humidity in heated structures during winter, resulting in dry skin, itchy eyes, and persistence of static electric charges. Even with saturation (100% relative humidity) outdoors, heating of infiltrated outside air that comes indoors raises its moisture capacity, which lowers relative humidity and increases evaporation rates from moist surfaces indoors, including human bodies and household plants. Similarly, during summer in humid climates a great deal of liquid water condenses from air cooled in air conditioners. Warmer air is cooled below its dew point, and the excess water vapor condenses. This phenomenon is the same as that which causes water droplets to form on the outside of a cup containing an ice-cold drink. A useful rule of thumb is that the maximum absolute humidity doubles for every increase in temperature. Thus, the relative humidity will drop by a factor of 2 for each increase in temperature, assuming conservation of absolute moisture. For example, in the range of normal temperatures, air at and 50% relative humidity will become saturated if cooled to , its dew point, and air at 80% relative humidity warmed to will have a relative humidity of only 29% and feel dry. By comparison, thermal comfort standard ASHRAE 55 requires systems designed to control humidity to maintain a dew point of though no lower humidity limit is established. Water vapor is a lighter gas than other gaseous components of air at the same temperature, so humid air will tend to rise by natural convection. This is a mechanism behind thunderstorms and other weather phenomena. Relative humidity is often mentioned in weather forecasts and reports, as it is an indicator of the likelihood of dew, or fog. In hot summer weather, it also increases the apparent temperature to humans (and other animals) by hindering the evaporation of perspiration from the skin as the relative humidity rises. This effect is calculated as the heat index or humidex. A device used to measure humidity is called a hygrometer; one used to regulate it is called a humidistat, or sometimes hygrostat. These are analogous to a thermometer and thermostat for temperature, respectively. The field concerned with the study of physical and thermodynamic properties of gas–vapor mixtures is named psychrometrics. Relationship between absolute humidity, relative humidity, and temperature References Citations General sources United States Environmental Protection Agency, "IAQ in Large Buildings" . Retrieved Jan. 9, 2006. Further reading External links Current map of global relative humidity Atmospheric thermodynamics Meteorological quantities Physical quantities Psychrometrics Climate	Humidity	[ "Physics", "Mathematics" ]	6,937	[ "Physical phenomena", "Physical quantities", "Quantity", "Meteorological quantities", "Physical properties" ]
52,820	https://en.wikipedia.org/wiki/Resident%20Evil	Resident Evil, known as in Japan, is a Japanese horror game series and media franchise created by Capcom. It consists of survival horror, third-person shooter and first-person shooter games, with players typically surviving in environments inhabited by zombies and other mutated creatures. The franchise has expanded into other media, including a live-action film series, animated films, television series, comic books, novels, audiobooks, and merchandise. Resident Evil is the highest-grossing horror franchise. The first Resident Evil game was created by Shinji Mikami and Tokuro Fujiwara for PlayStation, and released in 1996. It is credited for defining the survival horror genre and returning zombies to popular culture. With Resident Evil 4 (2005), the franchise shifted to more dynamic shooting action, popularizing the "over-the-shoulder" third-person view in action-adventure games. The franchise returned to survival horror with Resident Evil 7: Biohazard (2017) and Resident Evil Village (2021), which used a first-person perspective. Capcom has also released four Resident Evil remakes: Resident Evil (2002), Resident Evil 2 (2019), Resident Evil 3 (2020) and Resident Evil 4 (2023). Resident Evil is Capcom's best-selling franchise and the best-selling horror game series, with more than copies sold worldwide as of December 2024. The first Resident Evil film was released in 2002, starring Milla Jovovich, followed by five sequels and a reboot, Welcome to Raccoon City (2021). The films received mostly negative reviews, but have grossed more than $1.2 billion, making Resident Evil the third-highest-grossing video game film series. History The development of the first Resident Evil, released as Biohazard in Japan, began in 1993 when Capcom's Tokuro Fujiwara told Shinji Mikami and other co-workers to create a game using elements from Fujiwara's 1989 game Sweet Home on the Family Computer (Famicom) in Japan. When in late 1994 marketing executives were setting up to release Biohazard in the United States, it was pointed out that securing the rights to the name Biohazard would be very difficult as a DOS game had been registered under that name, as well as a New York hardcore punk band called Biohazard. A contest was held among company personnel to choose a new name; this competition turned up Resident Evil, the name under which it was released in the west. Resident Evil made its debut on the PlayStation in 1996 and was later ported to the Sega Saturn. The first entry in the series was the first game to be dubbed a "survival horror", a term coined for the new genre it initiated, and its critical and commercial success led to the production of two sequels, Resident Evil 2 in 1998 and Resident Evil 3: Nemesis in 1999, both for the PlayStation. A port of Resident Evil 2 was released for the Nintendo 64. In addition, ports of all three were released for Windows. The fourth game in the series, Resident Evil – Code: Veronica, was developed for the Dreamcast and released in 2000, followed by ports of Resident Evil 2 and Resident Evil 3: Nemesis. Resident Evil – Code: Veronica was later re-released for Dreamcast in Japan in an updated form as Code: Veronica Complete, which included slight changes, many of which revolved around story cutscenes. This updated version was later ported to the PlayStation 2 and GameCube as Code: Veronica X. Despite earlier announcements that the next game in the series would be released for the PlayStation 2, which resulted in the creation of an unrelated game, Devil May Cry, Mikami decided to make the series exclusively for the GameCube. The next three games in the series—a remake of the original Resident Evil and the prequel Resident Evil Zero, both released in 2002, as well as Resident Evil 4 (2005)—were all released initially as GameCube exclusives. Resident Evil 4 was later released for Windows, PlayStation 2, and Wii. A trilogy of GunCon-compatible light gun games known as the Gun Survivor series featured first-person gameplay. The first, Resident Evil Survivor, was released in 2000 for the PlayStation and PC but received mediocre reviews. The subsequent games, Resident Evil Survivor 2 – Code: Veronica and Resident Evil: Dead Aim, fared somewhat better. Dead Aim is the fourth Gun Survivor game in Japan, with Gun Survivor 3 being the Dino Crisis spin-off Dino Stalker. In a similar vein, the Chronicles series features first-person gameplay, albeit on an on-rails path. Resident Evil: The Umbrella Chronicles was released in 2007 for the Wii, with a sequel, Resident Evil: The Darkside Chronicles released in 2009 (both were later ported to the PlayStation 3 in 2012). Resident Evil Outbreak is an online game for the PlayStation 2, released in 2003, depicting a series of episodic storylines in Raccoon City set during the same period as Resident Evil 2 and Resident Evil 3: Nemesis. It was the first in the series and the first survival horror game to feature cooperative gameplay. It was followed by a sequel, Resident Evil Outbreak: File #2. Raccoon City is a metropolis located in the Arklay Mountains of the Midwestern United States that succumbed to the deadly T-virus outbreak and was consequently destroyed via a nuclear missile attack issued by the United States government. The town served as a critical junction for the series' progression as one of the main catalysts to Umbrella's downfall and the entry point for some of the series' most notable characters. Resident Evil Gaiden is an action-adventure game for the Game Boy Color featuring a role-playing-style combat system. There have been several downloadable mobile games based on the Resident Evil series in Japan. Some of these mobile games have been released in North America and Europe through T-Mobile. At the Sony press conference during E3 2009, Resident Evil Portable was announced for the PlayStation Portable, described as a new game being developed with "the PSP Go in mind" and "totally different for a Resident Evil game". No further announcements have been made, and the game is considered to have been canceled. In 2009, Resident Evil 5 was released for PlayStation 3, Windows and Xbox 360, becoming the best selling game of the franchise despite mixed fan reception. Capcom revealed the third-person shooter Resident Evil: Operation Raccoon City, which was developed by Slant Six Games for the PlayStation 3, Xbox 360 and Windows and released in March 2012. A survival horror game for the Nintendo 3DS, Resident Evil: Revelations, was released in February 2012. In October of the same year, the next numbered entry in the main series, Resident Evil 6, was released to mixed reviews, but enthusiastic pre-order sales. In 2013, producer Masachika Kawata said the Resident Evil franchise would return to focus on elements of horror and suspense over action, adding that "survival horror as a genre is never going to be on the same level, financially, as shooters and much more popular, mainstream games. At the same time, I think we need to have the confidence to put money behind these projects, and it doesn't mean we can't focus on what we need to do as a survival horror game to meet fan's needs." Resident Evil: Revelations 2, an episodic game set between Resident Evil 5 and Resident Evil 6, was released in March 2015. A series of team-based multiplayer games were developed beginning with the poorly received Umbrella Corps, which was released in June 2016. Resident Evil: Resistance was released in April 2020, followed by Resident Evil Re:Verse in October 2022, with both being available for free to those who bought Resident Evil 3 and Village respectively. Using the new RE Engine, which would develop the next generation of Resident Evil games, the series continued to shift back towards more horror elements. The next mainline game, Resident Evil 7: Biohazard was released for Windows, PlayStation 4 and Xbox One in January 2017. Set in a dilapidated mansion in Louisiana, the game uses a first-person perspective and emphasizes horror and exploration over action, unlike previous installments. The first-person perspective continued in the eighth mainline game Resident Evil Village. Released in May 2021, the game, set in a mysterious European village, is a direct sequel to Resident Evil 7: Biohazard although it incorporates more action elements inspired from Resident Evil 4. The game also marked the franchise's debut on PlayStation 5 and Xbox Series X/S A new generation of remakes of older entries began in 2019 with a remake of Resident Evil 2, being released for the PlayStation 4, Windows, and Xbox One. The remake outsold the original game within a year, selling over five million copies. Following in the success of the Resident Evil 2 remake, Capcom revealed a remake of Resident Evil 3: Nemesis in December 2019, known as Resident Evil 3. It was released in April 2020. In June 2022, a remake of Resident Evil 4 was announced, and released on March 24, 2023, for PlayStation 4, PlayStation 5, Xbox Series X/S, and PC. Story overview The early Resident Evil games focused on the Umbrella Corporation, an international pharmaceutical company that secretly develops mutagenic viruses to further their "bio-organic weapons" (BOW) research. The company's viruses can transform humans into mindless zombies while also mutating plants and animals into horrifying monstrosities. The Umbrella Corporation uses its vast resources to effectively control Raccoon City, a fictional midwestern American city. In the original Resident Evil, members of an elite police task force, Special Tactics and Rescue Service (STARS), are lured to a derelict mansion on the outskirts of Raccoon City. The STARS team is mostly decimated by zombies and other BOWs, leaving only a handful of survivors, including Chris Redfield, Jill Valentine, and Albert Wesker. Chris and Jill explore the zombie-infested mansion and uncover a secret underground Umbrella research facility. Wesker reveals himself to be a double agent for Umbrella and betrays his comrades. However, Wesker is seemingly murdered by a Tyrant, a special BOW that is the culmination of the Umbrella Corporation's research. Chris and Jill escape the mansion, but their testimony is ridiculed by Raccoon City's officials due to Umbrella's influence. Meanwhile, a separate viral outbreak occurs in another Umbrella research facility underneath Raccoon City. Most of the city's residents are infected and become zombies. Resident Evil 2 introduces two new protagonists, Leon S. Kennedy, a rookie police officer and Claire Redfield, the younger sister of Chris. Leon and Claire arrive in Raccoon City amidst the chaos of the viral outbreak. Leon is aided by Ada Wong, a corporate spy posing as an FBI agent, while Claire rescues Sherry Birkin, the daughter of two prominent Umbrella researchers. At the same time, Jill makes her escape from the city in Resident Evil 3: Nemesis. She is relentlessly pursued by a new Tyrant, Nemesis, who is deployed by Umbrella to eliminate all surviving STARS members. The U.S. Government destroys Raccoon City with a missile strike to sterilize the viral outbreak. Leon, Claire, Sherry, Ada, and Jill escape the city before its eradication. Claire continues to look for Chris, whereas Leon is recruited to work for the U.S. Government. Resident Evil – Code: Veronica follows Claire as she escapes from a prison camp in the Southern Ocean and later reunites with Chris at an Umbrella research facility in Antarctica. Resident Evil 4 is set six years after the Raccoon City incident and focuses on Leon as he tries to rescue the U.S. President's daughter from a cult in Spain. A government investigation into the Umbrella Corporation reveals its involvement in the Raccoon City disaster and leads to the company's dissolution. Despite the downfall of the Umbrella Corporation, the company's research and BOWs proliferate across the black market and lead to the rise of bioterrorism. Chris and Jill establish the Bioterrorism Security Assessment Alliance (BSAA) to combat these ever-growing threats on a global scale. Wesker is revealed to be alive and involved in the development of new potent viral agents and BOWs. In Resident Evil 5, Wesker seeks to unleash a highly mutagenic virus that will infect all of humanity. Chris and the BSAA confront and kill Wesker in Africa before he can fulfill his mission. Resident Evil 6 features Leon and Chris meeting for the first time in the video game series. The two work separately to triage bioterrorist attacks in the United States, Eastern Europe, and China. They are assisted by Sherry, Wesker's illegitimate son Jake Muller, Ada, and many members of the BSAA and U.S. government. Resident Evil 7: Biohazard and Resident Evil Village introduce a new protagonist, Ethan Winters, who becomes entangled in a bioterrorism incident while searching for his missing wife. He encounters Chris and the BSAA, who help him rescue his wife and defeat Eveline, a powerful BOW. Ethan, Mia, and their newborn daughter, Rosemary, are relocated to Eastern Europe but are abducted by a cult. Ethan ultimately sacrifices himself to destroy a fungal colony being weaponized by bioterrorists and save his family. Gameplay The Resident Evil franchise has had a variety of control schemes and gameplay mechanics throughout its history. Puzzle-solving has figured prominently throughout the series. Tank controls The first game introduced a control scheme that the player community has come to refer to as "tank controls" to the series. In a game with tank controls, players control movement relative to the position of the player character, rather than relative to the fixed virtual camera from which the player views the current scene. Pressing up (for example on a D-pad, analog stick, or cursor movement keys) on the game controller moves the character in the direction being faced, pressing down backpedals, and left and right rotates the character. This can feel counter-intuitive when the character is facing the camera, as the controls are essentially reversed in this state. This differs from many 3D games, in which characters move in the direction the player pushes the controls from the perspective of the camera. Some critics have posited that the control scheme is intentionally clumsy, meant to enhance stress and exacerbate difficulty. While the first three entries in the series featured this control scheme, the third, Resident Evil 3: Nemesis, saw some action-oriented additions. These included a 180 degree turn and dodge command that, according to GameSpot, "hinted at a new direction that the series would go in." Later games in the series, like Resident Evil 4, would feature a more fluid over-the-shoulder third-person camera instead of a fixed camera for each room, while Resident Evil 7 and Resident Evil Village are played from the first-person perspective. Third-person shooter gameplay Resident Evil 4 saw significant changes to the established gameplay, including switching from fixed camera perspectives to a tracking camera, and more action-oriented gameplay and mechanics. This was complemented by an abundance of ammunition and revised aiming and melee mechanics. Some critics claimed that this overhauled control scheme "made the game less scary." The next two games in the franchise furthered the action-oriented mechanics: Resident Evil 5 featured cooperative play and added strafing, while Resident Evil 6 allowed players to move while aiming and shooting for the first time, fully abandoning the series' signature tank controls. First-person shooter gameplay and VR Resident Evil 7 is the first main Resident Evil game to use the first-person perspective and to use virtual reality. It drew comparisons to modern survival horror games such as Outlast and PT. The eighth main-series game, Resident Evil Village, also features a first-person perspective. A VR version of Resident Evil 4 was released on the Oculus Quest 2 on October 21, 2021. Other media The Resident Evil franchise features video games and tie-in merchandise and products, including various live-action and animated films, comic books, and novels. Films Live-action films From 2002 to 2016, six live-action Resident Evil films were produced, all written and produced by Paul W. S. Anderson. The films do not follow the games' premise but feature some game characters. The series' protagonist is Alice, an original character created for the films portrayed by Milla Jovovich. Despite a negative reaction from critics, the live-action film series has made over $1 billion worldwide. They are, to date, the only video game adaptations to increase the amount of money made with each successive film. The series holds the record for the "Most Live-Action Film Adaptations of a Video Game" in the 2012 Guinness World Records Gamer's Edition, which also described it as "the most successful movie series to be based on a video game." A reboot, Resident Evil: Welcome to Raccoon City, was released on November 24, 2021, with Johannes Roberts as writer/director. Animated films The first computer animated film for the franchise was Biohazard 4D-Executer. It was a short 3D film produced for Japanese theme parks and did not feature any characters from the game. Starting in 2008, a series of feature-length computer-animated films have been released. These films take place in the same continuity with the games of the series, and feature characters such as Leon Kennedy, Claire Redfield, Ada Wong, Chris Redfield, Jill Valentine and Rebecca Chambers. Television Resident Evil: Infinite Darkness, a four-part CG anime series, premiered on July 8, 2021, on Netflix. Starring the Resident Evil 2 protagonists Leon S. Kennedy and Claire Redfield, the series features both uncovering a worldwide plot. The series released on July 8, 2021 on Netflix. Resident Evil premiered on July 14, 2022, on Netflix. An eight episode live-action series, two plotlines set in 2022 and 2036 follow Albert Wesker and his daughters navigating Umbrella's experiments in New Raccoon City. Merchandise Over the years, various toy companies have acquired the Resident Evil license, with each producing their own unique line of Resident Evil action figures or models. These include, but are not limited to, Toy Biz, Palisades Toys, NECA, and Hot Toys. Tokyo Marui also produced replicas of the guns used in the Resident Evil series in the form of gas blow-back airsoft guns. Some models included the STARS Beretta featured in Resident Evil 3, and the Desert Eagle in a limited edition that came with other memorabilia in a wooden case, along with the Gold Lugers from Code: Veronica and the "Samurai Edge" pistol from the Resident Evil remake. Other merchandise includes an energy drink called "T-virus Antidote". Resident Evil Archives is a reference guide of the Resident Evil series written by staff members of Capcom. It was translated into English and published by BradyGames. The guide describes and summarizes all of the key events that occur in Resident Evil Zero, Resident Evil, Resident Evil 2, Resident Evil 3: Nemesis, and Code: Veronica. The main plot analysis also contains character relationship charts, artwork, item descriptions, and file transcripts for all five games. A second Archives book was later released in December 2011 and covers Resident Evil 4, Resident Evil 5, the new scenarios detailed in Resident Evil: The Umbrella Chronicles and Resident Evil: The Darkside Chronicles, and the 2008 CGI movie, Resident Evil: Degeneration. The second Archives volume was also translated by Capcom and published by BradyGames. A Resident Evil theme restaurant called Biohazard Cafe & Grill S.T.A.R.S. opened in Tokyo in 2012. Halloween Horror Nights 2013, held at Universal Orlando, featured a haunted house titled Resident Evil: Escape from Raccoon City, based on Resident Evil 2 and Resident Evil 3: Nemesis. Novels The first Resident Evil novel was Hiroyuki Ariga's novella Biohazard: The Beginning, published in 1997 as a portion of the book The True Story of Biohazard, which was given away as a pre-order bonus with the Sega Saturn version of Biohazard. The story serves as a prelude to the original Resident Evil, in which Chris investigates the disappearance of his missing friend, Billy Rabbitson. S. D. Perry has written novelizations of the first five games, as well as two original novels taking place between games. The novels often take liberties with the games' plot by exploring events occurring outside and beyond the games. This often meant that the games would later contradict the books on a few occasions. One notable addition from the novels is the original character Trent, who often served as a mysterious behind-the-scenes string-puller who aided the main characters. Perry's novels were translated and released in Japan with new cover arts by Wolfina. Perry's novels, particularly The Umbrella Conspiracy, also alluded to events in Biohazard: The Beginning, such as the disappearance of Billy Rabbitson and Brian Irons' bid to run for Mayor. A reprinting of Perry's novels with new cover artwork began in 2012 to coincide with the release of Resident Evil: Retribution and its respective novelization. There are a trilogy of original Biohazard novels in Japan. was published in 1998 and was written by Kyū Asakura and the staff of Flagship. Two additional novels were published in 2002, To the Liberty by Sudan Kimura and Rose Blank by Tadashi Aizawa. While no official English translation of these novels has been published yet, the last two books were translated into German and published in 2006. Novelizations of the films Genesis, Apocalypse, and Extinction were written by Keith DeCandido. Afterlife did not receive a novelization due to Capcom's decision to discontinue working with Pocket Books, who had been their primary source of publishing books up to that point, Capcom would later make Titan Books their primary publisher going forth. Retribution was written by John Shirley, while The Final Chapter was written by Tim Waggoner. Genesis was published over two years after that film's release and coincided with the publication of Apocalypse, Genesis being marketed as a prequel to Apocalypse, while the Extinction novel was released in late July 2007, two months before the film's release. The Final Chapter was published in December 2016 alongside the film's theatrical release. There was also a Japanese novelization of the first film, unrelated to DeCandido's version, written by Osamu Makino. Makino also wrote two novels based on the game Resident Evil: The Umbrella Chronicles. The books are a two-part direct novelization of the game and are published in Japanese and German only. The first novel, titled Biohazard: The Umbrella Chronicles Side A in Japan and Resident Evil: The Umbrella Chronicles 1 in Germany, was released on December 22, 2007. The second novel, titled Biohazard: The Umbrella Chronicles Side B in Japan and Resident Evil: The Umbrella Chronicles 2 in Germany, was published in January 2008. Comics In 1997, Marvel Comics published a single-issue prologue comic based on the original Resident Evil, released through a promotional giveaway alongside the original PlayStation game. In 1998, WildStorm began producing a monthly comic book series based on the first two games, Resident Evil: The Official Comic Magazine, which lasted five issues. The first four issues were published by Image, while Wildstorm themselves published the fifth and final issue. Each issue was a compilation of short stories that were both adaptations of events from the games and related side stories. Like the Perry novels, the comics also explored events occurring beyond Resident Evil 2 (the latest game during the series' publication) and thus were contradicted by later games. Wildstorm also published a four-issue miniseries, Resident Evil: Fire & Ice, which depicted the ordeal of Charlie Team, a third STARS team created specifically for the comic. In 2009, Wildstorm reprinted Fire & Ice in a trade paperback collection. In Hong Kong, there has been officially licensed Biohazard manhua adaptations of Biohazard 0 by publisher Yulang Group, Biohazard 2 by Kings Fountain, Biohazard 3 Supplemental Edition by Cao Zhihao and, Biohazard 3 The Last Escape, and Biohazard Code: Veronica by Lee Chung Hing published by Tinhangse Publishing. The Code: Veronica manhua was translated into English, formatted to look like an American comic and distributed by WildStorm as a series of four graphic novel collections. In 2009, Wildstorm began publishing a Resident Evil comic book prequel to Resident Evil 5, which centers on two original members of the BSAA, Mina Gere and Holiday Sugarman. Written by Ricardo Sanchez and illustrated by Kevin Sharpe and Jim Clark, the first issue was published on March 11, 2009. On November 11, 2009, the third issue was released, and the fourth was released March 24, 2010. The sixth and final book was finally published in February 2011. Plays In the summer of 2000, Bioroid: Year Zero was performed in Japan. It was a musical horror-comedy but took the perspective of the infected. Super Eccentric Theater put on the production under the direction of Osamu Yagihashi. The stage play was performed from early July to late August. Biohazard The Stage was released in Japan in 2015. The play focused on iconic characters, Chris Redfield and Rebecca Chambers, as Philosophy University in Australia is experiencing a bioterrorist attack. The production was handled by Avex Live Creative and Ace Crew Entertainment, under supervision from Capcom. The following year, Musical Biohazard ~Voice of Gaia~ was released in September. It was produced by Umeda Arts Theater by director G2 and composer, Shunsuke Wada. Biohazard the Experience was the second Resident Evil play produced by Avex Live Creative and Ace Crew Entertainment. The story is set in 2015 and follows a cast of thirteen survivors who were abducted and woke up in a mansion during an outbreak. Reception and legacy Most of the games in the prominent Resident Evil series have been released to positive reviews. Some of the games, most notably Resident Evil, Resident Evil 2 and Resident Evil 4, have been bestowed with multiple Game of the Year honors and often placed on lists of the best video games ever made. In 1999, Next Generation listed the Resident Evil series as number 13 on their "Top 50 Games of All Time", commenting that, "Flawless graphics, excellent music, and a top-notch storyline all combined to make a game of unparalleled atmosphere and suspense." In 2012, Complex ranked Resident Evil at number 22 on the list of the best video game franchises. That same year, G4tv called it "one of the most successful series in gaming history." Commercial performance By December 2022, around 135 million Resident Evil games had been sold. The first two Resident Evil games had collectively sold approximately units worldwide by March 1999. By early 2001, the series had sold units worldwide, earning more than . By 2011, it had sold about copies and was estimated to have grossed at least . It is recognized by Guinness World Records as the best-selling survival horror series, with Resident Evil 2 remake being the best-selling survival horror game . Seven of the top ten best-selling horror games in North America are Resident Evil games. The 2023 Resident Evil 4 remake sold more than three million copies in its first two days of release. It sold four million copies in its first two weeks, making it one of the fastest-selling Resident Evil games. In Japan, it was the best-selling retail game in its first week, selling 89,662 copies on PlayStation 5 and 85,371 on PlayStation 4. The Resident Evil film series was the highest-grossing film series based on video games by 2012. By 2011, the films had grossed over at the box office, bringing the franchise's estimated revenue to at least more than in combined video game sales and box office gross up until then. , the films have grossed more than in box office and home video sales. The success of the video games and films have made Resident Evil the highest-grossing franchise in the horror and zombie genres. Cultural impact GameSpot listed the original Resident Evil as one of the fifteen most influential video games of all time. It is credited with defining and popularizing the survival horror genre of games. It is also credited with taking video games in a cinematic direction with its B-movie style cut-scenes, including live-action full-motion video (FMV) footage. Its live-action opening, however, was controversial; it became one of the first action games to receive the "Mature 17+" (M) rating from the Entertainment Software Rating Board (ESRB), despite the opening cutscene being censored in North America. The Resident Evil franchise is credited with sparking a revival of the zombie genre in popular culture, leading to a renewed interest in zombie films during the 2000s. Resident Evil also helped redefine the zombie genre, playing an important role in its shift from supernatural themes to scientific themes by using science to explain the origins of zombies. According to Kim Newman in the book Nightmare Movies (2011), "the zombie revival began in the Far East" mainly due to the 1996 Japanese zombie games Resident Evil and The House of the Dead. George A. Romero, in 2013, said it was the video games Resident Evil and House of the Dead "more than anything else" that popularised his zombie concept in early 21st-century popular culture. In a 2015 interview with Huffington Post, screenwriter-director Alex Garland credited the Resident Evil series as a primary influence on his script for the horror film 28 Days Later (2002), and credited the first Resident Evil game for revitalizing the zombie genre. Screenwriter Edgar Wright cited Resident Evil 2 as a primary influence on his zombie comedy film Shaun of the Dead (2004), with the film's star and co-writer Simon Pegg also crediting the first game with starting the zombie revival in popular culture. The Walking Dead comic book creator Robert Kirkman cited Resident Evil as his favorite zombie game, while The Walking Dead television series director Greg Nicotero credited Resident Evil and The House of the Dead with introducing the zombie genre "to a whole generation of younger people who didn't grow up watching Night of the Living Dead and Dawn of the Dead." The Resident Evil Apocalypse zombies were conceptualized and choreographed by Sharon B. Moore and Derek Aasland. Through script analysis and movement research a "scientific logic" was devised for the T-virus accounting for each Zombie behaviour envisioned in Paul W. S. Anderson's script. Sharon B. Moore and Derek Aasland then wrote the so-called Undead Bible - a Handbook for the Undead - used as the guide for the nearly 1000 cast under the choreographic department (stunt performers, actors, dancers, extras) to ensure the Undead physicality was performed in a unified way across the picture. The Stunt and Core teams participated in the "Undead Bootcamp". See also 2007 Documentary Undead Bootcamp starring producer Jeremy Bolt, director Alexander Witt, and choreographers Sharon B. Moore and Derek Aasland. On the DVD Featurette Resident Evil; Game Over Apocalypse director Alexander Witt said the zombies needed to be "more aggressive and more dangerous" than the original film, so they were created by the film's choreographers Sharon B. Moore and Derek Aasland as "liquid zombie[s]' in terms of their relentless forward motion: unstoppable, flowing around any kind of resistance, and then rushing in on the final attack. This is also detailed in the University of Liverpool book Biopunk Dystopias Genetic Engineering, Society, and Science Fiction (Lars Schmeink, 2016, p. 214). Additionally, the first Resident Evil film adaptation also contributed to the revival of zombie films, with the success of the film and the games resulting in zombies achieving greater mainstream prominence and several zombie films being greenlit, such as the video game film adaptation House of the Dead (2003), the remake Dawn of the Dead (2004) and Romero's Land of the Dead (2005). The Resident Evil films, 28 Days Later and the Dawn of the Dead remake all set box office records for the zombie genre, reaching levels of commercial success not seen since the original Dawn of the Dead (1978). They were followed by other zombie films such as 28 Weeks Later (2007), Zombieland (2009), Cockneys vs Zombies (2012), and World War Z (2013), as well as zombie-themed graphic novels and television shows such as The Walking Dead and The Returned, and books such as World War Z (2006), Pride and Prejudice and Zombies (2009) and Warm Bodies (2010). The zombie revival trend was popular across different media up until the mid-2010s. Since then, zombie films have declined in popularity during the late 2010s, but zombie video games have remained popular, as seen with the commercial success of the Resident Evil 2 remake and Days Gone in 2019. See also Genetic engineering in fiction List of fictional diseases List of zombie video games Dino Crisis, another horror series by Capcom Dead Rising, another zombie-themed series by Capcom Devil May Cry, another series by Capcom, initially conceived as a Resident Evil game Onimusha, another series by Capcom with similar gameplay, initially conceived as a Resident Evil game The Evil Within, other horror game made by Shinji Mikami References External links Undead Bootcamp - Resident Evil Apocalypse - (2007 - Documentary) Biopunk Capcom franchises Experimental medical treatments in fiction Fiction about genetic engineering Mythopoeia Video game franchises introduced in 1996 Human experimentation in fiction Mutants in fiction Fiction about bioterrorism Science fiction franchises	Resident Evil	[ "Engineering", "Biology" ]	6,914	[ "Genetic engineering", "Fiction about genetic engineering" ]
52,827	https://en.wikipedia.org/wiki/Volumetric%20heat%20capacity	The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K−1⋅m−3. The volumetric heat capacity can also be expressed as the specific heat capacity (heat capacity per unit of mass, in J⋅K−1⋅kg−1) times the density of the substance (in kg/L, or g/mL). It is defined to serve as an intensive property. This quantity may be convenient for materials that are commonly measured by volume rather than mass, as is often the case in engineering and other technical disciplines. The volumetric heat capacity often varies with temperature, and is different for each state of matter. While the substance is undergoing a phase transition, such as melting or boiling, its volumetric heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature. The volumetric heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (volumetric heat capacity at constant pressure) than when is heated in a closed vessel that prevents expansion (volumetric heat capacity at constant volume). If the amount of substance is taken to be the number of moles in the sample (as is sometimes done in chemistry), one gets the molar heat capacity (whose SI unit is joule per kelvin per mole, J⋅K−1⋅mol−1). Definition The volumetric heat capacity is defined as where is the volume of the sample at temperature , and is the amount of heat energy needed to raise the temperature of the sample from to . This parameter is an intensive property of the substance. Since both the heat capacity of an object and its volume may vary with temperature, in unrelated ways, the volumetric heat capacity is usually a function of temperature too. It is equal to the specific heat of the substance times its density (mass per volume) , both measured at the temperature . Its SI unit is joule per kelvin per cubic meter (J⋅K−1⋅m−3). This quantity is used almost exclusively for liquids and solids, since for gases it may be confused with the "specific heat capacity at constant volume", which generally has very different values. International standards now recommend that "specific heat capacity" always refer to capacity per unit of mass. Therefore, the word "volumetric" should always be used for this quantity. History Dulong and Petit predicted in 1818 that the product of solid substance density and specific heat capacity (ρcp) would be constant for all solids. This amounted to a prediction that volumetric heat capacity in solids would be constant. In 1819 they found that volumetric heat capacities were not quite constant, but that the most constant quantity was the heat capacity of solids adjusted by the presumed weight of the atoms of the substance, as defined by Dalton (the Dulong–Petit law). This quantity was proportional to the heat capacity per atomic weight (or per molar mass), which suggested that it is the heat capacity per atom (not per unit of volume) which is closest to being a constant in solids. Eventually it became clear that heat capacities per particle for all substances in all states are the same, to within a factor of two, so long as temperatures are not in the cryogenic range. Typical values The volumetric heat capacity of solid materials at room temperatures and above varies widely, from about 1.2 MJ⋅K−1⋅m−3 (for example bismuth) to 3.4 MJ⋅K−1⋅m−3 (for example iron). This is mostly due to differences in the physical size of atoms. Atoms vary greatly in density, with the heaviest often being more dense, and thus are closer to taking up the same average volume in solids than their mass alone would predict. If all atoms were the same size, molar and volumetric heat capacity would be proportional and differ by only a single constant reflecting ratios of the atomic molar volume of materials (their atomic density). An additional factor for all types of specific heat capacities (including molar specific heats) then further reflects degrees of freedom available to the atoms composing the substance, at various temperatures. For most liquids, the volumetric heat capacity is narrower, for example octane at 1.64 MJ⋅K−1⋅m−3 or ethanol at 1.9. This reflects the modest loss of degrees of freedom for particles in liquids as compared with solids. However, water has a very high volumetric heat capacity, at 4.18 MJ⋅K−1⋅m−3, and ammonia is also fairly high: 3.3 MJ⋅K−1⋅m−3. For gases at room temperature, the range of volumetric heat capacities per atom (not per molecule) only varies between different gases by a small factor less than two, because every ideal gas has the same molar volume. Thus, each gas molecule occupies the same mean volume in all ideal gases, regardless of the type of gas (see kinetic theory). This fact gives each gas molecule the same effective "volume" in all ideal gases (although this volume/molecule in gases is far larger than molecules occupy on average in solids or liquids). Thus, in the limit of ideal gas behavior (which many gases approximate except at low temperatures and/or extremes of pressure) this property reduces differences in gas volumetric heat capacity to simple differences in the heat capacities of individual molecules. As noted, these differ by a factor depending on the degrees of freedom available to particles within the molecules. Volumetric heat capacity of gases Large complex gas molecules may have high heat capacities per mole (of molecules), but their heat capacities per mole of atoms are very similar to those of liquids and solids, again differing by less than a factor of two per mole of atoms. This factor of two represents vibrational degrees of freedom available in solids vs. gas molecules of various complexities. In monatomic gases (like argon) at room temperature and constant volume, volumetric heat capacities are all very close to 0.5 kJ⋅K−1⋅m−3, which is the same as the theoretical value of RT per kelvin per mole of gas molecules (where R is the gas constant and T is temperature). As noted, the much lower values for gas heat capacity in terms of volume as compared with solids (although more comparable per mole, see below) results mostly from the fact that gases under standard conditions consist of mostly empty space (about 99.9% of volume), which is not filled by the atomic volumes of the atoms in the gas. Since the molar volume of gases is very roughly 1000 times that of solids and liquids, this results in a factor of about 1000 loss in volumetric heat capacity for gases, as compared with liquids and solids. Monatomic gas heat capacities per atom (not per molecule) are decreased by a factor of 2 with regard to solids, due to loss of half of the potential degrees of freedom per atom for storing energy in a monatomic gas, as compared with regard to an ideal solid. There is some difference in the heat capacity of monatomic vs. polyatomic gasses, and also gas heat capacity is temperature-dependent in many ranges for polyatomic gases; these factors act to modestly (up to the discussed factor of 2) increase heat capacity per atom in polyatomic gases, as compared with monatomic gases. Volumetric heat capacities in polyatomic gases vary widely, however, since they are dependent largely on the number of atoms per molecule in the gas, which in turn determines the total number of atoms per volume in the gas. The volumetric heat capacity is defined as having SI units of J/(m3⋅K). It can also be described in Imperial units of BTU/(ft3⋅°F). Volumetric heat capacity of solids Since the bulk density of a solid chemical element is strongly related to its molar mass (usually about 3R per mole, as noted above), there exists noticeable inverse correlation between a solid's density and its specific heat capacity on a per-mass basis. This is due to a very approximate tendency of atoms of most elements to be about the same size, despite much wider variations in density and atomic weight. These two factors (constancy of atomic volume and constancy of mole-specific heat capacity) result in a good correlation between the volume of any given solid chemical element and its total heat capacity. Another way of stating this, is that the volume-specific heat capacity (volumetric heat capacity) of solid elements is roughly a constant. The molar volume of solid elements is very roughly constant, and (even more reliably) so also is the molar heat capacity for most solid substances. These two factors determine the volumetric heat capacity, which as a bulk property may be striking in consistency. For example, the element uranium is a metal which has a density almost 36 times that of the metal lithium, but uranium's volumetric heat capacity is only about 20% larger than lithium's. Since the volume-specific corollary of the Dulong–Petit specific heat capacity relationship requires that atoms of all elements take up (on average) the same volume in solids, there are many departures from it, with most of these due to variations in atomic size. For instance, arsenic, which is only 14.5% less dense than antimony, has nearly 59% more specific heat capacity on a mass basis. In other words; even though an ingot of arsenic is only about 17% larger than an antimony one of the same mass, it absorbs about 59% more heat for a given temperature rise. The heat capacity ratios of the two substances closely follows the ratios of their molar volumes (the ratios of numbers of atoms in the same volume of each substance); the departure from the correlation to simple volumes in this case is due to lighter arsenic atoms being significantly more closely packed than antimony atoms, instead of similar size. In other words, similar-sized atoms would cause a mole of arsenic to be 63% larger than a mole of antimony, with a correspondingly lower density, allowing its volume to more closely mirror its heat capacity behavior. Volumetric heat capacity of liquids The volumetric heat capacity of liquids could be measured from the thermal conductivity and thermal diffusivity correlation. The volumetric heat capacity of liquids could be directly obtained during thermal conductivity analysis using thermal conductivity analyzers that use techniques like the transient plane source method. Constant volume and constant pressure For gases it is necessary to distinguish between volumetric heat capacity at constant volume and volumetric heat capacity at constant pressure, which is always larger due to the pressure–volume work done as a gas expands during heating at constant pressure (thus absorbing heat which is converted to work). The distinctions between constant-volume and constant-pressure heat capacities are also made in various types of specific heat capacity (the latter meaning either mass-specific or mole-specific heat capacity). Thermal inertia Thermal inertia is a term commonly used to describe the observed delays in a body's temperature response during heat transfers. The phenomenon exists because of a body's ability to both store and transport heat relative to its environment. Larger values of volumetric heat capacity, as may occur in association with thermal effusivity, typically yield slower temperature responses. See also Heat capacity Specific heat capacity Temperature Thermodynamic equations References Thermodynamic properties Physical quantities Volume Heat transfer	Volumetric heat capacity	[ "Physics", "Chemistry", "Mathematics" ]	2,408	[ "Transport phenomena", "Scalar physical quantities", "Physical phenomena", "Heat transfer", "Thermodynamic properties", "Physical quantities", "Quantity", "Size", "Extensive quantities", "Thermodynamics", "Volume", "Wikipedia categories named after physical quantities", "Physical properties"...
52,838	https://en.wikipedia.org/wiki/Charon%20%28moon%29	Charon ( or ), or (134340) Pluto I, is the largest of the five known natural satellites of the dwarf planet Pluto. It has a mean radius of . Charon is the sixth-largest known trans-Neptunian object after Pluto, Eris, Haumea, Makemake, and Gonggong. It was discovered in 1978 at the United States Naval Observatory in Washington, D.C., using photographic plates taken at the United States Naval Observatory Flagstaff Station (NOFS). With half the diameter and one-eighth the mass of Pluto, Charon is a very large moon in comparison to its parent body. Its gravitational influence is such that the barycenter of the Plutonian system lies outside Pluto, and the two bodies are tidally locked to each other. The dwarf planet systems Pluto–Charon and Eris–Dysnomia are the only known examples of mutual tidal locking in the Solar System, though it is likely that –Vanth is another. The reddish-brown cap of the north pole of Charon is composed of tholins, organic macromolecules that may be essential ingredients of life. These tholins were produced from methane, nitrogen, and related gases which may have been released by cryovolcanic eruptions on the moon, or may have been transferred over from the atmosphere of Pluto to the orbiting moon. The New Horizons spacecraft is the only probe that has visited the Pluto system. It approached Charon to within in 2015. Discovery Charon was discovered by United States Naval Observatory astronomer James Christy, using the telescope at United States Naval Observatory Flagstaff Station (NOFS). On June 22, 1978, he had been examining highly magnified images of Pluto on photographic plates taken with the telescope two months prior. Christy noticed that a slight elongation appeared periodically. The bulge was confirmed on plates dating back to April 29, 1965. Subsequent observations of Pluto determined that the bulge was due to a smaller accompanying body. The periodicity of the bulge corresponded to Pluto's rotation period, which was previously known from Pluto's light curve. This indicated a synchronous orbit, which strongly suggested that the bulge effect was real and not spurious. This resulted in reassessments of Pluto's size, mass, and other physical characteristics because the calculated mass and albedo of the Pluto–Charon system had previously been attributed to Pluto alone. The International Astronomical Union formally announced Christy's discovery to the world on July 7, 1978. Doubts about Charon's existence were erased when it and Pluto entered a five-year period of mutual eclipses and transits between 1985 and 1990. This occurs when the Pluto–Charon orbital plane is edge-on as seen from Earth, which only happens at two intervals in Pluto's 248-year orbital period. It was fortuitous that one of these intervals happened to occur soon after Charon's discovery. Name Charon was first given the temporary designation S/1978 P 1, after its discovery, following the then recently instituted convention. On June 24, 1978, Christy first suggested the name Charon as a scientific-sounding version of his wife Charlene's nickname, "Char". Although colleagues at the Naval Observatory proposed Persephone, Christy stuck with Charon after discovering that it was serendipitously the name of an appropriate mythological figure: Charon (; ) is the ferryman of the dead, closely associated with the god Pluto. The IAU officially adopted the name in late 1985, and it was announced on January 3, 1986. Coincidentally, nearly four decades before Charon's discovery, science fiction author Edmond Hamilton had invented three moons of Pluto for his 1940 novel Calling Captain Future and named them Charon, Styx, and Cerberus; Styx and Kerberos are the two smallest Plutonian moons, and were named in 2013. There is minor debate over the preferred pronunciation of the name. The mythological figure is pronounced with a sound, and this is often followed for the moon as well. However, Christy himself pronounced the initial as a sound, as he had named the moon after his wife Charlene. Many English-speaking astronomers follow the classical convention, but others follow Christy's, and that is the prescribed pronunciation at NASA and of the New Horizons team. Orbit Charon and Pluto orbit each other every 6.387 days. The two objects are gravitationally locked to one another, so each keeps the same face towards the other. This is a case of mutual tidal locking, as compared to that of the Earth and the Moon, where the Moon always shows the same face to Earth, but not vice versa. The average distance between Charon and Pluto is . The discovery of Charon allowed astronomers to calculate accurately the mass of the Plutonian system, and mutual occultations revealed their sizes. However, neither indicated the two bodies' individual masses. Those could only be estimated, until the discovery of Pluto's outer moons in late 2005. Details in the orbits of the outer moons then revealed that Charon has approximately 12% of the mass of Pluto. Formation Simulation work published in 2005 by Robin Canup suggested that Charon could have been formed by a collision around 4.5 billion years ago, much like Earth and the Moon. In this model, a large Kuiper belt object struck Pluto at high velocity, destroying itself and blasting off much of Pluto's outer mantle, and Charon coalesced from the debris. However, such an impact should result in an icier Charon and rockier Pluto than scientists have found. It is now thought that Pluto and Charon might have been two bodies that collided before going into orbit around each other. The collision would have been violent enough to boil off volatile ices like methane () but not violent enough to have destroyed either body. The very similar density of Pluto and Charon implies that the parent bodies were not fully differentiated when the impact occurred. The two bodies would have been stuck for a while, before separating from each other again, while remaining gravitationally bound. The internal heat in both bodies, created from both the collision and then the tidal friction as they separated, would have been sufficient to create Pluto's subsurface ocean without the need for radioactive elements. Physical characteristics Charon's diameter is , just over half that of Pluto. Larger than the dwarf planet Ceres, it is the twelfth-largest natural satellite in the Solar System. Charon is even similar in size to Uranus's moons Umbriel and Ariel. Charon's slow rotation means that there should be little flattening or tidal distortion if Charon is sufficiently massive to be in hydrostatic equilibrium. Any deviation from a perfect sphere is too small to have been detected by observations by the New Horizons mission. This is in contrast to Iapetus, a Saturnian moon similar in size to Charon but with a pronounced oblateness dating to early in its history. The lack of such oblateness in Charon could mean that it is currently in hydrostatic equilibrium, or simply that its orbit approached its current one early in its history, when it was still warm. Based on mass updates from observations made by New Horizons the mass ratio of Charon to Pluto is 0.1218:1. This is much larger than the Moon to the Earth: 0.0123:1. Because of the high mass ratio, the barycenter is outside of the radius of Pluto, and the Pluto–Charon system has been referred to as a dwarf double planet. With four smaller satellites in orbit about the two larger worlds, the Pluto–Charon system has been considered in studies of the orbital stability of circumbinary planets. Internal structure Charon's volume and mass allow calculation of its density, , from which it can be determined that Charon is slightly less dense than Pluto and suggesting a composition of 55% rock to 45% ice (± 5%), whereas Pluto is about 70% rock. The difference is considerably lower than that of most suspected collisional satellites. Following the New Horizons flyby, numerous discovered features on Charon's surface strongly indicated that Charon is differentiated, and may even have had a subsurface ocean early in its history. The past resurfacing observed on Charon's surface indicated that Charon's ancient subsurface ocean may have fed large-scale cryoeruptions on the surface, erasing many older features. As a result, two broad competing views on the nature of Charon's interior arose: the so-called hot start model, where Charon's formation is rapid and involves a violent impact with Pluto, and the cold start model, where Charon's formation is more gradual and involves a less violent impact with Pluto. According to the hot start model, Charon accreted rapidly (within ~ years) from the circumplanetary disc, resulting from a highly-disruptive giant impact scenario. This rapid time scale prevents the heat from accretion from radiating away during the formation process, leading to the partial melting of Charon's outer layers. However, Charon's crust failed to reach a melt fraction where complete differentiation occurs, leading to the crust retaining part of its silicate content upon freezing. A liquid subsurface ocean forms during or soon after Charon's accretion and persists for approximately 2 billion years before freezing, possibly driving cryovolcanic resurfacing of Vulcan Planitia. Radiogenic heat from Charon's core could then melt a second subsurface ocean composed of a eutectic water-ammonia mixture before it too freezes, possibly driving the formation of Kubrick Mons and other similar features. These freezing cycles could increase Charon's size by >20 km, leading to the formation of the complex tectonic features observed in Serenity Chasma and Oz Terra. In contrast, the cold start model argues that a large subsurface ocean early in Charon's history is not necessary to explain Charon's surface features, and instead proposes that Charon may have been homogeneous and more porous at formation. According to the cold start model, as Charon's interior begins to warm due to radiogenic heating and heating from serpentinization, a phase of contraction begins, largely driven by compaction in Charon's interior. Approximately 100-200 million years after formation, enough heat builds up to where a subsurface ocean melts, leading to rapid differentiation, further contraction, and the hydration of core rocks. Despite this melting, a pristine crust of amorphous water ice on Charon remains. After this period, differentiation continues, but the core can no longer absorb more water, and thus freezing at the base of Charon's mantle begins. This freezing drives a period of expansion until Charon's core becomes warm enough to begin compaction, starting a final period of contraction. Serenity Chasma may have formed from the expansion episode, whilst the final contraction episode may have given rise to the arcuate ridges observed in Mordor Macula. Surface Unlike Pluto's surface, which is composed of nitrogen and methane ices, Charon's surface appears to be dominated by the less volatile water ice. In 2007, observations by the Gemini Observatory detected patches of ammonia hydrates and water crystals on the surface of Charon that suggested the presence of active cryogeysers and cryovolcanoes. The fact that the ice was still in crystalline form suggested it may have been deposited recently, as it was expected that solar radiation would have degraded it to an amorphous state after roughly thirty thousand years. However, following new data from the New Horizons flyby, no active cryovolcanoes or geysers were detected. Later research has also called into question the cryovolcanic origin for the crystalline water ice and ammonia features, with some researchers instead proposing that ammonia may be replenished passively from underground material. Photometric mapping of Charon's surface shows a latitudinal trend in albedo, with a bright equatorial band and darker poles. The north polar region is dominated by a very large dark area informally dubbed "Mordor" by the New Horizons team. The favored explanation for this feature is that it is formed by condensation of gases that escaped from Pluto's atmosphere. In winter, the temperature is −258 °C, and these gases, which include nitrogen, carbon monoxide, and methane, condense into their solid forms; when these ices are subjected to solar radiation, they chemically react to form various reddish tholins. Later, when the area is again heated by the Sun as Charon's seasons change, the temperature at the pole rises to −213 °C, resulting in the volatiles sublimating and escaping Charon, leaving only the tholins behind. Over millions of years, the residual tholin builds up thick layers, obscuring the icy crust. In addition to Mordor, New Horizons found evidence of extensive past geology that suggests that Charon is probably differentiated; in particular, the southern hemisphere has fewer craters than the northern and is considerably less rugged, suggesting that a massive resurfacing event—perhaps prompted by the partial or complete freezing of an internal ocean—occurred at some point in the past and removed many of the earlier craters. Charon has a system of extensive grabens and scarps, such as Serenity Chasma, which extend as an equatorial belt for at least . Argo Chasma potentially reaches as deep as , with cliffs that may rival Verona Rupes on Miranda for the title of the tallest cliff in the Solar System. Hypothesized exosphere In contrast to Pluto, Charon has no significant atmosphere. There has been speculation about an extremely thin exosphere surrounding the moon contributing to the formation of dark regions such as Mordor Macula. The strong seasons experienced by Pluto and Charon could provide brief periods of exosphere formation as methane sublimates on Charon, interspersed by centuries of dormancy. Pluto does have a thin but significant atmosphere, which Charon's gravitation might pull toward Charon's surface. The gas, specifically nitrogen, is mostly caught in the combined center of gravity between the two bodies before reaching Charon, but any gas that does reach Charon is held closely against the surface. The gas is mostly made up of ions of nitrogen, but the amounts are negligible compared to the total of Pluto's atmosphere. The many spectral signatures of ice formations on the surface of Charon have led some to believe that the ice formations could supply an atmosphere, but atmosphere supplying formations have not been confirmed yet. Many scientists theorize that these ice formations could be concealed out of direct sight, either in deep craters or beneath Charon's surface. Charon's relatively low gravity, due to its low mass, causes any atmosphere that might be present to rapidly escape the surface into space. Even through stellar occultation, which is used to probe the atmosphere of stellar bodies, scientists cannot confirm an existing atmosphere; this was tested in 1986 while attempting to perform stellar occultation testing on Pluto. Charon also acts as a protector for Pluto's atmosphere, blocking the solar wind that would normally collide with Pluto and damage its atmosphere. Since Charon blocks these solar winds, its own atmosphere is diminished, instead of Pluto's. This effect is also a potential explanation for Charon's lack of atmosphere; the solar winds remove gases faster than they can accumulate. It is still possible for Charon to have an atmosphere, as Pluto transfers some of its atmospheric gas to Charon, from where it tends to escape into space. Assuming Charon's density is 1.71 g/cm3, it would have a surface gravity of 0.6 of Pluto's. It also has a higher mean molecular weight than Pluto and a lower exobase surface temperature, so that the gases in its atmosphere would not escape as rapidly from Charon as they do from Pluto. There has been significant proof of CO2 gas and H2O vapor on the surface of Charon, but these vapors are not sufficient for a viable atmosphere due to their low vapor pressures. Pluto's surface has abundant ice formations, but these are volatile, as they are made up of volatile substances like methane. These volatile ice structures cause a good deal of geological activity, keeping its atmosphere constant, while Charon's ice structures are mainly made up of water and carbon dioxide, much less volatile substances that can stay dormant and not affect the atmosphere much. Observation and exploration Since the first blurred images of the moon (1), images showing Pluto and Charon resolved into separate disks were taken for the first time by the Hubble Space Telescope in the 1990s (2). The telescope was responsible for the best, yet low-quality images of the moon. In 1994, the clearest picture of the Pluto–Charon system showed two distinct and well-defined disks (3). The image was taken by Hubble's Faint Object Camera (FOC) when the system was 4.4 billion kilometers (2.6 billion miles) away from Earth Later, the development of adaptive optics made it possible to resolve Pluto and Charon into separate disks using ground-based telescopes. Although ground-based observation is very challenging, a group of amateur astronomers in Italy used a 14-inch telescope in 2008 to successfully resolve Charon in an image of Pluto. In June 2015, the New Horizons spacecraft captured consecutive images of the Pluto–Charon system as it approached it. The images were put together in an animation. It was the best image of Charon to that date (4). In July 2015, the New Horizons spacecraft made its closest approach to the Pluto system. It is the only spacecraft to date to have visited and studied Charon. Charon's discoverer James Christy and the children of Clyde Tombaugh were guests at the Johns Hopkins Applied Physics Laboratory during the New Horizons closest approach. Classification The center of mass (barycenter) of the Pluto–Charon system lies outside either body. Because neither object truly orbits the other, and Charon has 12.2% of the mass of Pluto, it has been argued that Charon should be considered to be part of a binary planet with Pluto. The International Astronomical Union (IAU) states that Charon is a satellite of Pluto, but the idea that Charon might be classified as a dwarf planet in its own right may be considered at a later date. In a draft proposal for the 2006 redefinition of the term, the IAU proposed that a planet is defined as a body that orbits the Sun that is large enough for gravitational forces to render the object (nearly) spherical. Under this proposal, Charon would have been classified as a planet, because the draft explicitly defined a planetary satellite as one in which the barycenter lies within the major body. In the final definition, Pluto was reclassified as a dwarf planet, but a formal definition of a planetary satellite was not decided upon. Charon is not in the list of dwarf planets currently recognized by the IAU. Had the draft proposal been accepted, even the Moon would hypothetically be classified as a planet in billions of years when the tidal acceleration that is gradually moving the Moon away from Earth takes it far enough away that the center of mass of the system no longer lies within Earth. The other moons of Pluto Nix, Hydra, Kerberos, and Styx orbit the same barycenter but they are not large enough to be spherical and they are simply considered to be satellites of Pluto (or of Pluto–Charon). See also List of natural satellites Notes References External links Charon Profile at NASA's Solar System Exploration site Hubble reveals new map of Pluto, BBC News, September 12, 2005 Cryovolcanism on Charon and other Kuiper Belt Objects New Horizons Camera Spots Pluto's Largest Moon – July 10, 2013 40th anniversary NASA video describing the discovery and naming of Charon (June 22, 2018) NASA CGI video of Charon flyover (July 14, 2017) CGI video simulation of rotating Charon by Seán Doran (see album for more) Google Charon 3D, interactive map of the moon Interactive 3D gravity simulation of Pluto and Charon in addition to Pluto's four other moons Styx, Kerberos, Hydra and Nix Moons of Pluto Trans-Neptunian satellites Articles containing video clips M Planetary-mass satellites Moons with a prograde orbit Possible dwarf planets	Charon (moon)	[ "Physics", "Astronomy" ]	4,218	[ "Concepts in astronomy", "Unsolved problems in astronomy", "Possible dwarf planets" ]
52,842	https://en.wikipedia.org/wiki/Valve%20Corporation	Valve Corporation, also known as Valve Software, is an American video game developer, publisher, and digital distribution company headquartered in Bellevue, Washington. It is the developer of the software distribution platform Steam and the game franchises Half-Life, Counter-Strike, Portal, Day of Defeat, Team Fortress, Left 4 Dead and Dota. Valve was founded in 1996 by the former Microsoft employees Gabe Newell and Mike Harrington. Their debut game, the first-person shooter (FPS) Half-Life (1998), was a critical and commercial success and had a lasting influence on the FPS genre. Harrington left in 2000. In 2003, Valve launched Steam, followed by Half-Life 2 (2004), the episodic sequels Half-Life 2: Episode One (2006) and Episode Two (2007), the multiplayer games Team Fortress 2 (2007) and Left 4 Dead (2008), the puzzle games Portal (2007) and Portal 2 (2011) and the multiplayer online battle arena game Dota 2 (2013). In the 2010s, Valve released fewer games and experimented with hardware and virtual reality (VR). They entered the hardware market in 2015 with the Steam Machine, a line of gaming computers, which sold poorly, and released the HTC Vive and Valve Index VR headsets. They returned to the Half-Life series in 2020 with Half-Life: Alyx, their flagship VR game. In 2022, Valve released the Steam Deck, a portable gaming system. Valve uses a flat structure, whereby employees decide what to work on themselves. They develop games through playtesting and iteration, describing game design as a kind of experimental psychology. By 2012, Valve employed around 250 people and was reportedly worth over US$3 billion. Most of Valve's revenue comes from Steam, which controlled over half of the digital PC games market in 2011 and generated an estimated $3.4 billion in 2017. History Founding and Half-Life (1996–2003) Valve was founded in 1996 by former Microsoft employees Gabe Newell and Mike Harrington. Newell had spent the prior 13 years at Microsoft developing Windows, including the Windows 95 port of Doom. Wanting to move onto a new venture using their shared wealth, Newell and Harrington founded Valve, L.L.C. in Kirkland, Washington, about five miles from the Microsoft campus in Redmond, on August 24, 1996, Newell's wedding day. In a break from industry style of the time, Newell did not want a company name that suggested "testosterone-gorged muscles and the 'extreme' of anything". Alternative names considered by Newell and Harrington include Hollow Box, Fruitfly Ensemble and Rhino Scar. Valve's first game was Half-Life, a first-person shooter (FPS) with elements of horror. The development was aided by access to the Quake engine by id Software; Valve modified this engine into their GoldSrc engine. After struggling to find a publisher, Valve eventually signed with Sierra On-Line. Half-Life was released in November 1998 and was a critical and commercial success. With its realism, scripted sequences and seamless narrative, it had a lasting influence; according to IGN in 2014, the history of the FPS genre "breaks down pretty cleanly into pre-Half-Life and post-Half-Life eras". Valve enlisted Gearbox Software to develop three expansions for Half-Life: Opposing Force (1999), Blue Shift (2001) and Decay (2001). In 1998, Valve acquired TF Software, a group that had made the popular Team Fortress mod for Quake, and remade it for GoldSrc as Team Fortress Classic in 1999. Valve released the software development kit (SDK) for the GoldSrc engine, facilitating numerous user-created mods. They acquired the developers of one popular mod, Counter-Strike, to create a standalone Counter-Strike game. Happy with Valve's success, Harrington sold his stake in Valve to Newell in 2000. Valve's publishing agreement meant Sierra owned the Half-Life intellectual property and held exclusive publishing rights to future Valve games. In 2001, Valve renegotiated by threatening to cease future game development and develop other software, using an offer of a partnership from Amazon to create a digital storefront as a bargaining chip. After the agreement with Sierra was amended, Valve gained the Half-Life intellectual property and online distribution rights for its games. Source, Steam, and Half-Life 2 (2003–2010) In 2003, Valve moved to Bellevue, Washington, and reincorporated as Valve Corporation. In 2010, the office moved to a larger location in Bellevue. In 2016, Valve signed a nine-floor lease in the Lincoln Square complex in downtown Bellevue, doubling the size of its offices. Valve began developing Half-Life 2 six months after the release of the first Half-Life, using its new in-house engine, Source. With advanced physics systems and an increased focus on story and characters, it received critical acclaim upon its release in 2004. By 2011, it had sold 12 million copies. In 2002, Valve launched Steam, a digital storefront and delivery platform. Steam initially offered only Valve games, and was mandatory to install Half-Life 2, but became a publisher of third-party games. As Valve became its own publisher via Steam, it transitioned to a flat organization. Outside of executive management, Valve does not have bosses and uses an open allocation system, allowing employees to move between departments at will. After having taken five years to develop Half-Life 2, Valve moved to episodic development, planning to release shorter games more frequently. Half-Life 2: Episode One, the first in a planned trilogy of episodic Half-Life 2 sequels, was released in 2006. Episode Two followed in 2007, alongside the multiplayer game Team Fortress 2 and the puzzle game Portal, developed from the student project Narbacular Drop. In January 2008, Valve announced the acquisition of Turtle Rock Studios, which was renamed Valve South. Turtle Rock developed Left 4 Dead and Left 4 Dead 2 while associated with Valve. Turtle Rock Studios spun out of Valve again in March 2010. Forbes estimated that Valve had grossed $70 million in 2005. Transition to services (2010–2014) In 2009, Valve hired IceFrog, the developer of Defense of the Ancients, a Warcraft III mod. IceFrog led the development of a sequel not associated with the Warcraft elements, Dota 2, released in 2013. Alongside Dota 2 in 2011, Valve started the International, an annual esports tournament for Dota 2 with a prize pool supported by Valve and funds from microtransactions from battle passes purchased by players. Valve released Portal 2 in April 2011. As with the original Portal, Valve employed a Digipen student team to help develop it; the team behind Tag: The Power of Paint implemented the new gel gameplay. The Screen Digest analyst Ed Barton estimated Valve's 2010 revenue to be in the "high hundreds of millions of dollars". As of 2011, Valve had an estimated worth of $2 to 4 billion and employed 250 people; according to Newell, this made it more profitable per employee than Google or Apple. Most of Valve's revenue came from Steam, which controlled 50 to 70% of the market for downloaded PC games in 2011. By 2011, Valve had replaced episodic development with a platform-oriented approach, whereby games such as Left 4 Dead 2 and Team Fortress 2 were continually updated through Steam updates. Valve hired the economist Yanis Varoufakis to study the online economies of their games in June 2012. That December, Valve acquired Star Filled Studios, a two-person studio, to open a San Francisco office. Valve closed the office in August 2013 when they decided it had little benefit. At the 2013 D.I.C.E. Summit, Newell announced that he and the film director J. J. Abrams were collaborating to produce a Half-Life or Portal film, as well as a possible game. In the 2010s, Valve released fewer games and invested in hardware development. Newell intended to make Valve more like Nintendo, which develops games in tandem with hardware, allowing them to create innovative games such as Super Mario 64. Valve initially focused on augmented reality, but in 2013 Newell laid off many staff to focus on virtual reality (VR). In 2015, Valve released the Steam Machine, a line of gaming computers, which sold poorly. Media commentators speculated that Valve's transition to service provider with Steam, which generated an estimated $3.4 billion in 2017, had driven it away from game development. Valve canceled games including numerous Half-Life projects (including Episode Three), Left 4 Dead 3, a Soulslike game, and a voxel-based game, A.R.T.I. Additional VR projects included SimTrek, developed by members of the Kerbal Space Program development team, and a new VR device, Vader, that was determined to be too costly for consumers. According to the designer Robin Walker, the abundance of projects that failed to gain traction, with no shared vision, damaged morale. Many players grew frustrated in anticipation of a new Half-Life game. Source 2, virtual reality and Half-Life: Alyx (2015–present) Valve announced the Source 2 engine in March 2015 and ported Dota 2 to it that September. That year, Valve collaborated with the electronics company HTC to develop the HTC Vive, a VR headset released in 2016. Valve experimented with VR games, and in 2016 released The Lab, a collection of VR minigames. Valve recognized that many players wanted a more ambitious VR AAA game, and began exploring the development of a major VR game. They developed several prototypes, with three further VR projects under development by 2017. Finding that the portal systems of their puzzle series Portal were disorienting in VR, they settled on Half-Life. Walker said that Half-Life 3 had been a "terrifyingly daunting prospect", and the team saw VR as a way to return to the series. Full development of a VR Half-Life game started around late 2016, with the largest team in Valve's history. Valve acquired the 3D audio software developer Impulsonic in January 2017. In April 2018, Valve acquired the independent developer Campo Santo, known for the 2016 adventure game Firewatch. Campo Santo planned to develop its own games under Valve, though they initially helped develop Half-Life: Alyx. In November 2018, Valve released Artifact, a digital collectible card game based on Dota 2, with design by Richard Garfield, the creator of Magic: The Gathering. Artifact had unusual pay-for mechanics to acquire new cards, and did not draw a large playerbase, losing 95% of players months after release. In April 2021, Valve abandoned efforts to reboot the project, saying they had not found enough interested players to justify development. In June 2019, Valve released its second-generation VR hardware, the Valve Index. They also released Dota Underlords into early access, an auto battler based on a Dota 2 community-created mode Dota Auto Chess. In March 2020, Valve released Half-Life: Alyx, a VR game. It received acclaim and was described as VR's first killer app. Newell said in January 2021 that the success of Alyx created desire within the company to develop more games, and that several were under development. Valve collaborated with Netflix for Dota: Dragon's Blood, an animated television series based on Dota, which premiered in March 2021. In February 2022, Valve released the Steam Deck, a portable game system that runs on SteamOS. In September 2023, Valve released Counter-Strike 2. It received generally favorable reviews, but player reception was mixed. In 2024, Valve began beta-testing a new multiplayer game, Deadlock, a combination of a hero shooter and MOBA. In September, staff members from Hopoo Games, developers of Risk of Rain, announced that they had been employed at Valve. According to a report by Forbes Australia published in December 2024, Valve had an annual revenue of $5 billion by 2023, with a 40% profit margin. Steam accounted for around 60% of this revenue, double that of 2019. Structure Initially, Valve used a hierarchical structure more typical of other development firms, driven by the nature of physical game releases through publishers that required tasks to be completed by deadlines. However, as Valve became its own publisher via Steam, it found the hierarchical structure was hindering progress. After completing Half-Life 2, Valve transitioned to a flat organization; outside of executive management, Valve does not have bosses, and uses an open allocation system. Valve's marketing manager, Doug Lombardi, said: "Nobody writes a design doc and hands it to somebody and says, 'you go build this'. It's the teams that are coming up with the ideas and pushing in the directions that they want to take the product." This approach allows employees to work on whatever interests them, but requires them to take ownership of their product and mistakes they may make, according to Newell. Newell recognized that this structure works well for some but that "there are plenty of great developers for whom this is a terrible place to work". Following the difficult development of Half-Life 2, Newell said he became "obsessed" with improving Valve's work-life balance. Although Valve has no bosses, some employees hold more influence due to seniority or relationships. De facto project leads became "centralized conduits" for organization and sharing information, and decisions are made collectively. Valve uses a process named Overwatch to gather feedback from senior members, which teams may use or ignore. The success of Steam means that Valve is not dependent on the success of its games. The lack of organization structure has led to project cancellations, as it can be difficult to convince other employees to work on them. In 2020, Valve acknowledged that this made it difficult to gather momentum and had slowed their output during the 2010s. Their VR projects and Half-Life: Alyx became a turning point, setting short-term studio-wide goals to focus the company. According to Walker, "We sort of had to collectively admit we were wrong on the premise that you will be happiest if you work on something you personally want to work on the most." In January 2023, People Make Games released a report on Valve's corporate structure and culture, based on interviews with several current and former employees. They found that Valve's flat structure and stack-ranking compensation system created a poor release record and a lack of employee diversity. In 2024, Forbes estimated that Newell owned 50.1% of Valve, with the rest owned by employees. As part of Wolfire Games' lawsuit over Steam policies, case documents revealed details related to Valve's employee structure. Starting with 60 employees in 2003, Valve grew to around 350 employees around 2012 and remained around this number through 2021. Up through 2010, the employees were categorized in three areas, administration, game development, and Steam development; in 2011, a hardware development category was added. Valve time Valve time is an industry term used jokingly with game releases from Valve, used to acknowledge the difference between the "promised" date for released content stated by Valve and to the "actual" release date; "Valve Time" includes delays but also includes some content that was released earlier than expected. Valve has acknowledged the term, including tracking known discrepancies between ideal and actual releases on their public development wiki and using it in announcements about such delays. Valve ascribes delays to their mentality of team-driven initiatives over corporate deadlines. Playtesting Valve playtests its games extensively from the beginning of development, and iterates based on the results. Its website states: "We believe that all game designers are, in a sense, experimental psychologists." The Valve writer Chet Faliszek said he initially blamed testers when they failed to engage with designs as expected, but changed his mind when multiple testers had the same problem: "By the third or fourth time, all of a sudden you're realizing, 'I'm an idiot. This is pretty obvious this doesn't work. It's not their fault, it's our fault.'" He gave an example from the development of Left 4 Dead, wherein a texture change caused every tester to miss a ladder and become stuck. Walker said playtesting helped Valve maximize the experience for players. For example, when something exciting occurs by chance during a playtest, the developers attempt to have it occur for every player. Newell contrasted this approach to that of Warren Spector, whose open-ended games are designed to be replayed with different outcomes: "You spend all of this time to build stuff that most players will never ever ever see ... If only one per cent of your customers see this cool thing that takes five per cent of your development budget, that's not a good use of resources." Technology Products Games Valve is the main developer and publisher of the single-player Half-Life and Portal games and the multiplayer games Counter-Strike, Team Fortress 2, Dota 2, Day of Defeat, and Artifact. Valve also published the multiplayer game Left 4 Dead and developed and published Left 4 Dead 2. Unreleased and canceled Valve games include the fantasy role-playing game Prospero and numerous Half-Life projects, including Episode Three. Valve worked with Arkane Studios on The Crossing, which was canceled in May 2009. Steam Valve announced Steam, its digital distribution service, at the 2002 Game Developers Conference. It was launched in September 2003 and was first used to deliver patches and other updates to Valve's online games. On August 1, 2012, Valve announced revisions to the Steam Subscriber Agreement (SSA) to prohibit class action lawsuits by users against the service provider. By July 2014, there were over 3,400 games available on Steam, with over 150 million registered accounts by January 2018. Alongside these changes to the SSA, the company also declared publicly the incorporation of Valve S.a.r.l., a subsidiary based in Luxembourg. Valve set up a physical office in Kirchberg, Luxembourg. According to Valve's project manager Mike Dunkle, the location was chosen for eCommerce capabilities and infrastructure, talent acquisition, tax advantages and central geographic location – most major partners are accessible, 50% within driving distance. Valve S.a.r.l. was used to sell games to UK users to avoid paying the full 20% value-added tax (VAT). The tax loophole was expected to close on January 1, 2015. In December 2015, the French consumer group UFC Que Choisir initiated a lawsuit against Valve for several of their Steam policies that conflict or run afoul of French law. One of the reasons was for using the tax loophole. Valve S.a.r.l. ceased business on January 1, 2017, with the main company taking over EU sales again. In August 2017, Valve announced that Steam had reached over 67 million monthly and 33 million daily active users on the platform. Steam Machine Newell has been critical of the direction that Microsoft has taken with making Windows a closed architecture similar to Apple's products, and has stated that he believes that the changes made in Windows 8 are "a catastrophe for everyone in the [personal computer] space". Newell identified the open-source Linux platform as an ideal platform for Steam and said the only thing holding back its adoption is the lack of games. In 2012, Valve announced that they were working on a console-PC hybrid for the living room, dubbed by media as the "Steam Box". A precursor to such a unit is SteamOS, a freely available Linux-based operating system that builds upon the Steam client functionality that includes media services, live streaming across home networks, game sharing within families, and parental controls. SteamOS was officially announced in September 2013 as the first of several announcements related to the Steam Machine platform as well as their unique game controller. In May 2014, Valve announced that the company's own SteamOS-powered Steam Machine would be delayed until 2015 due to problems with the game controller. In 2015, Alienware, ZOTAC, and CyberPowerPC launched their versions of the Steam Machine. By June 2016, fewer than half a million had been sold. While the Steam Machine line has been effectively canceled, Valve continued to manufacture and sell Steam Controllers until late November 2019, and publishes both mobile apps and software for the Steam Link, allowing in-home streaming. Valve Index and virtual reality At the Game Developers Conference in March 2015, Valve and Taiwanese electronics company HTC unveiled SteamVR and the HTC Vive—a virtual reality platform and a virtual reality headset. The platform would be distinguished by its "Lighthouse" motion tracking system, where sensors on the headset and its included motion controllers read the position of two base station devices mounted in the play area. This would allow for "room-scale" VR experiences, where the player would not be required to remain in a stationary position in front of a camera and would be able to freely walk around the space. In November 2017, Microsoft added beta support for the SteamVR service for Windows Mixed Reality headsets. In June 2019, Valve released their own VR headset, known as the Valve Index, positioned as a higher-end device with wider field of view and higher refresh rate. They were accompanied by updated motion controllers, which are strapped against the user's palms and have sensors for detecting input pressure and individual fingers. Steam Deck Announced in July 2021, the Steam Deck is a hybrid game console similar to the Nintendo Switch. It is primarily a handheld device that supports playing of Steam games, but through a separate dock unit, the console can output to an external monitor and use external power, networking, and USB accessories connected to the dock. The hardware is based on customized AMD Zen 2 and RDNA 2 chipsets. Units started shipping in February 2022. Other projects PowerPlay PowerPlay was a technological initiative headed by Valve and Cisco Systems to decrease the latency for online games, announced in January 2000. It was described as a set of protocols and deployment standards at the router level to improve performance. It was claimed that a player with 1000 ms ping was able to play against another player on a LAN connection with no noticeable disadvantage. Initially the protocol was to be released with PowerPlay 1.0 focusing on quality of service (QoS) and later a revision, PowerPlay 2.0 that would focus on functionality. Cisco and Valve intended to deliver a single dial-up service in Q1 2000 in the United States with a 30-day free trial with a bundled copy of Team Fortress modified to support PowerPlay. The standard was to involve purchasing PowerPlay approved Cisco hardware and infrastructure that had adequate bandwidth and QoS standards that prioritize PowerPlay gaming packets at all others' expense. Newell conceded that Internet service providers (ISPs) would bear the brunt of this expense: "The ISPs are going to need to spend a fair amount of money to be compliant with PowerPlay. But how they get that back is up to them. Some will have a tiered service, and some will just try to recoup their investment through reduced customer churn and customer acquisition." Despite never deploying the dial-up plan featuring PowerPlay 1.0, Valve announced in January 2001 that the standard had indeed been finalized. 12 months after its announcement, PowerPlay was abandoned. Pipeline In July 2013, Valve announced Pipeline, an intern project consisting of ten high school students working together to learn how to create video game content. Pipeline serves to discuss and answer questions that teenagers often ask about the video game industry, and see if it is possible to train a group of teenagers with minimal work experience to work for a company like Valve. The latter purpose breaks Valve's tradition of employing experienced developers, as the company is not good at "teaching people straight out of school". Legal disputes Valve Corporation v. Vivendi Universal Games Between 2002 and 2005, Valve was involved in a complex legal dispute with its publisher, Vivendi Universal Games (under Vivendi's brand Sierra Entertainment). Valve had entered into a publishing agreement with Sierra to release Half-Life and subsequent games in 1997, with the contract giving Sierra some intellectual property (IP) rights to Valve's games. After Valve began development of Half-Life 2, it agreed a new contract with Sierra in 2001, removing these rights from Sierra and giving Valve some rights for digital distribution. Internally, Valve started work on Steam as a means to digitally distribute these games, and first revealed this project at the March 2002 Game Developers Conference. By August 2002, Valve had found that Sierra was distributing copies of their games to Internet cafes against the terms of their contracts and filed a lawsuit against Sierra and Vivendi. In addition to claims of copyright infringement, Valve asserted that Sierra breached contract by withholding royalties and delaying the release of Counter-Strike: Condition Zero until after the holiday season. Vivendi and Sierra countersued, stating that Valve had misrepresented their position in the revised 2001 contract since they had been working on Steam at that point as a means to circumvent the publishing agreement. Vivendi sought intellectual property rights to Half-Life and a ruling preventing Valve from using Steam to distribute Half-Life 2. On November 29, 2004, Judge Thomas Samuel Zilly of the U.S. District Court for the Western District of Washington ruled in favor of Valve. The ruling stated that Vivendi Universal and its affiliates (including Sierra) were not authorized to distribute Valve games, either directly or indirectly, through cyber cafés to end users for pay-to-play activities pursuant to the parties' publishing agreement. In addition, Judge Zilly ruled that Valve could recover copyright damages for infringements without regard to the publishing agreement's limitation of liability clause. Valve posted on the Steam website that the companies had come to a settlement in court on April 29, 2005. Electronic Arts announced on July 18, 2005, that they would partner with Valve in a multi-year deal to distribute their games, replacing Vivendi Universal. As a result of the trial, the arbitrator also awarded Valve $2,391,932. Valve Corporation v. Activision Blizzard In April 2009, Valve sued Activision Blizzard, which acquired Sierra Entertainment after a merger with its parent company, Vivendi Universal Games. Activision had allegedly refused to honor the Valve v. Vivendi arbitration agreement. Activision had only paid Valve $1,967,796 of the $2,391,932 award, refusing to pay the remaining $424,136, claiming it had overpaid that sum in the past years. Dota intellectual property ownership Defense of the Ancients (DotA) was a landmark mod first released in 2003 that created the basis of the genre of multiplayer online battle arena (MOBA). It was originally developed by Kyle Sommer (who goes by the alias Eul) within Blizzard Entertainment's Warcraft III: Reign of Chaos via its world editor, and spawned several similar efforts, notably DotA-Allstars. While there had been several that contributed to DotA-Allstars, the project was managed primarily by Steve "Guinsoo" Feak, and later by "IceFrog". IceFrog was eventually hired by Valve in 2009, with the rights to the DotA intellectual property being sold to Valve the following year. Eul was also hired into Valve by 2010. Valve then subsequently filed trademarks towards a sequel to DotA, titled Dota 2. DotA-Allstars, LLC, a group of former contributors to the DotA-Allstars project, filed an opposing trademark in August 2010 to contest Valve's claim it owned the property rights. DotA-Allstars, LLC was eventually acquired by Blizzard to start development of Blizzard All-Stars. Blizzard took over the trademark challenge. The United States Patent & Trademark Office initially ruled in Valve's favor. By this point, Riot Games had hired Guinsoo to help develop their own MOBA, League of Legends. As with IceFrog, Feak transferred his rights to the Dota property to Riot, who in turn sold those to Blizzard. Blizzard filed a lawsuit against Valve to challenge Valve's ownership, pitting the rights assigned through IceFrog to Guinsoo at odds. The case Blizzard Entertainment v. Valve Corporation was settled out of court in May 2012; Valve retained the right to use Dota commercially, while Blizzard reserved the right for fans to use Dota non-commercially. Blizzard changed the names of its own projects to remove the Dota term, and renamed Blizzard All-Stars as Heroes of the Storm. Valve's Dota 2 was released in 2013. In 2014, mobile developers Lilith and released their games Dota Legends and Heroes Charge, respectively. Both were influenced by Dota and the sequels. In 2017, Valve and Blizzard took joint action against these companies, citing copyright issues related to the Dota names. argued that the Dota games were a collective work and could not be copyrighted by anyone in particular, but the presiding judge, Charles R. Breyer, felt that, due to the trio's actions as maintainers of the Dota mods, they had a rightful copyright claim to this. Separately, Lilith and argued that Eul had, in a forum post from September 2004, assigned an open-source copyright license to Dota, which would make Valve and Blizzard's copyright claims void. The case was later heard by a jury. ACCC v. Valve Corporation The Australian Competition & Consumer Commission (ACCC) announced it was taking action against Valve in 2014. On March 29, 2016, Valve was found guilty of breaching Australian consumer law because: Valve claimed consumers were not entitled to a refund for digitally downloaded games purchased from Valve via the Steam website or Steam Client (in any circumstances); Valve had excluded statutory guarantees and/or warranties that goods would be of acceptable quality; and Valve had restricted or modified statutory guarantees and/or warranties of acceptable quality. During the prosecution of this case, Valve implemented a refund policy for Steam purchases, but the case still reviewed Valve's actions prior to the onset of the lawsuit. The court overseeing the case sided with the ACCC in assigning a (about ) fine against Valve in December 2016, as well as requiring Valve to inform Australian consumers of their rights when purchasing games from Steam. Valve appealed the court's determination that it "engaged in misleading or deceptive conduct and made false or misleading representations about consumer guarantees", as well as seeking to appeal the fine, but the Australian higher courts rejected the appeals in December 2017. In January 2018, Valve filed for a "special leave" of the court's decision, appealing to the High Court of Australia. The High Court dismissed this claim in April 2018, asserting that Valve still was liable under Australian law since it sold products directly to its citizens. UFC Que Choisir v. Valve Corporation Consumer rights group UFC Que Choisir, based in France, filed a lawsuit against Valve in December 2015, claiming users should be able to resell their software. The High Court of Paris ruled in favor of UFC Que Choisir in September 2019, stating that Valve must allow the resale of Steam games. Valve stated it will appeal the decision. Skins gambling Valve was named as a defendant in two lawsuits in June and July 2016 related to third-party gambling sites that use the Steamworks API to allow betting with the virtual currency of cosmetic weapon replacement textures, better known as "skins", from Counter-Strike: Global Offensive, which through these sites can be converted from or to real-world money. Both suits assert Valve aiding in underaged gambling. Valve subsequently stated it has no commercial ties with these sites, and that it would demand these sites cease their use of the Steamworks API as they violate the authorized use policies. In October 2016, the Washington State Gambling Commission required Valve to stop the use of virtual skins for gambling on Steam, stating they would face legal repercussions if they failed to co-operate. On October 17, 2016, Valve sent a letter to the Washington State Gambling Commission stating that they had "no business relationship with such gambling sites", asserting that they come into existence, operate, and go out of existence without their knowledge and consent, adding that they were not aware of any such law that Steam or any of their games were violating. Anti-competitive practices In February 2017, the European Commission began investigating Valve and five other publishers—Bandai Namco Entertainment, Capcom, Focus Home Interactive, Koch Media and ZeniMax Media—for anti-competitive practices, specifically the use of geo-blocking through the Steam storefront and Steam product keys to prevent access to software to citizens of certain countries. Such practices would be against the Digital Single Market initiative by the European Union. While the other five companies named are in stages of settling with the EU as of August 2019, Valve has stated it plans to fight the charges, asserting that geo-blocking affects less than 3% of its games, and that it had turned off such geo-blocking within the EU in 2015. In January 2021, five gamers filed a proposed class-action antitrust lawsuit in California against Valve, alleging that the company "abuses the Steam platform's market power" by requiring game developers and publishers to enter into a 'most favored nation' agreement with Valve, restricting their ability to sell games for less on other platforms and thereby preventing price competition. In May 2021, Wolfire Games filed a proposed class-action antitrust lawsuit against Valve, alleging that the company exerts monopoly power over the PC gaming market and uses its "gatekeeper role" to "wield extreme power over publishers of PC Desktop Games" and to extract "an extraordinarily high cut from nearly every sale that passes through its store." Although a motion by Valve to dismiss the original lawsuit was granted in November 2021, Wolfire was allowed to file a revised complaint, and in May 2022 US District Court Judge John C. Coughenour ruled that that lawsuit could proceed, finding that Wolfire's allegations were "sufficient to plausibly allege unlawful conduct." Wolfire's suit was consolidated with a similar lawsuit from another developer. In November 2024, it was affirmed into a class-action lawsuit, with any developer affected by Valve's revenue cut able to be part of the class. In June 2024, Vicki Shotbolt, a children's digital rights activist, filed a lawsuit with the Competition Appeal Tribunal in the UK that accuses Valve of "rigging the market" for PC games, alleging that Valve used its market dominance to overcharge 14 million people in the UK and seeking damages of £22 to £44 per affected customer, or £656 million in total. Valve Corporation v. Zaiger, LLC In 2023, Valve sued a law firm, Zaiger, alleging that it attempted to extort settlements from Valve by threatening to bring numerous antitrust arbitration cases on behalf of Steam customers, a tactic referred to as "mass arbitration". Valve also brought suit against a litigation financier for Zaiger over the funding of a social media campaign to recruit Steam users as clients. Valve alleged that they improperly interfered with its contracts with Steam customers and abused the arbitration process by signing up clients with the intent of obtaining settlements slightly lower than the cost of arbitration filing fees, rather than arbitrating their claims. Valve said that it was targeted due to the terms of the Steam Subscriber Agreement, in which Valve would be responsible for the fees and costs associated with arbitration. The lawsuit was dismissed without prejudice by the US District Court for the Western District of Washington in 2024 due to personal jurisdiction issues. In September 2024, Valve changed its Steam Subscriber Agreement to require disputes to proceed in court, with no option of arbitration. References External links 1996 establishments in Washington (state) Companies based in Bellevue, Washington Linux game porters Video game companies established in 1996 Video game companies of the United States Video game development companies Video game publishers Computer companies of the United States Computer hardware companies Computer systems companies	Valve Corporation	[ "Technology" ]	7,421	[ "Computer hardware companies", "Computer systems companies", "Computers", "Computer systems" ]
52,853	https://en.wikipedia.org/wiki/Alice%27s%20Adventures%20in%20Wonderland	Alice's Adventures in Wonderland (also known as Alice in Wonderland) is an 1865 English children's novel by Lewis Carroll, a mathematics don at the University of Oxford. It details the story of a girl named Alice who falls through a rabbit hole into a fantasy world of anthropomorphic creatures. It is seen as an example of the literary nonsense genre. The artist John Tenniel provided 42 wood-engraved illustrations for the book. It received positive reviews upon release and is now one of the best-known works of Victorian literature; its narrative, structure, characters and imagery have had a widespread influence on popular culture and literature, especially in the fantasy genre. It is credited as helping end an era of didacticism in children's literature, inaugurating an era in which writing for children aimed to "delight or entertain". The tale plays with logic, giving the story lasting popularity with adults as well as with children. The titular character Alice shares her name with Alice Liddell, a girl Carroll knew—scholars disagree about the extent to which the character was based upon her. The book has never been out of print and has been translated into 174 languages. Its legacy includes adaptations to screen, radio, visual art, ballet, opera, and musical theatre, as well as theme parks, board games and video games. Carroll published a sequel in 1871 entitled Through the Looking-Glass and a shortened version for young children, The Nursery "Alice", in 1890. Background "All in the golden afternoon..." Alice's Adventures in Wonderland was conceived on 4 July 1862, when Lewis Carroll and Reverend Robinson Duckworth rowed up the river Isis with the three young daughters of Carroll's friend Henry Liddell: Lorina Charlotte (aged 13; "Prima" in the book's prefatory verse); Alice Pleasance (aged 10; "Secunda" in the verse); and Edith Mary (aged 8; "Tertia" in the verse). The journey began at Folly Bridge, Oxford, and ended upstream at Godstow, Oxfordshire. During the trip, Carroll told the girls a story that he described in his diary as "Alice's Adventures Under Ground", which his journal says he "undertook to write out for Alice". Alice Liddell recalled that she asked Carroll to write it down: unlike other stories he had told her, this one she wanted to preserve. She finally received the manuscript more than two years later. 4 July was known as the "golden afternoon", prefaced in the novel as a poem. In fact, the weather around Oxford on 4 July was "cool and rather wet", although at least one scholar has disputed this claim. Scholars debate whether Carroll in fact came up with Alice during the "golden afternoon" or whether the story was developed over a longer period. Carroll had known the Liddell children since around March 1856, when he befriended Harry Liddell. He had met Lorina by early March as well. In June 1856, he took the children out on the river. Robert Douglas-Fairhurst, who wrote a literary biography of Carroll, suggests that Carroll favoured Alice Pleasance Liddell in particular because her name was ripe for allusion. "Pleasance" means pleasure and the name "Alice" appeared in contemporary works, including the poem "Alice Gray" by William Mee, of which Carroll wrote a parody; Alice is a character in "Dream-Children: A Reverie", a prose piece by Charles Lamb. Carroll, an amateur photographer by the late 1850s, produced many photographic portraits of the Liddell children – and especially of Alice, of which 20 survive. Manuscript: Alice's Adventures Under Ground Carroll began writing the manuscript of the story the next day, although that earliest version is lost. The girls and Carroll took another boat trip a month later, when he elaborated the plot of the story to Alice, and in November, he began working on the manuscript in earnest. To add the finishing touches, he researched natural history in connection with the animals presented in the book and then had the book examined by other children—particularly those of George MacDonald. Though Carroll did add his own illustrations to the original copy, on publication he was advised to find a professional illustrator so that the pictures were more appealing to his audience. He subsequently approached John Tenniel to reinterpret his visions through his own artistic eye, telling him that the story had been well-liked by the children. Carroll began planning a print edition of the Alice story in 1863. He wrote on 9 May 1863 that MacDonald's family had suggested he publish Alice. A diary entry for 2 July says that he received a specimen page of the print edition around that date. On 26 November 1864, Carroll gave Alice the manuscript of Alice's Adventures Under Ground, with illustrations by Carroll, dedicating it as "A Christmas Gift to a Dear Child in Memory of a Summer's Day". The published version of Alice's Adventures in Wonderland is about twice the length of Alice's Adventures Under Ground and includes episodes, such as the Mad Hatter's Tea-Party (or Mad Tea Party), that do not appear in the manuscript. The only known manuscript copy of Under Ground is held in the British Library. Macmillan published a facsimile of the manuscript in 1886. Plot Alice, a young girl, sits bored by a riverbank and spots a White Rabbit with a pocket watch and waistcoat lamenting that he is late. Surprised, Alice follows him down a rabbit hole, which sends her into a lengthy plummet but to a safe landing. Inside a room with a table, she finds a key to a tiny door, beyond which is a garden. While pondering how to fit through the door, she discovers a bottle labelled "Drink me". Alice drinks some of the bottle's contents, and to her astonishment, she shrinks small enough to enter the door. However, she had left the key upon the table and cannot reach it. Alice then discovers and eats a cake labelled "Eat me", which causes her to grow to a tremendous size. Unhappy, Alice bursts into tears, and the passing White Rabbit flees in a panic, dropping a fan and two gloves. Alice uses the fan for herself, which causes her to shrink once more and leaves her swimming in a pool of her own tears. Within the pool, Alice meets various animals and birds, who convene on a bank and engage in a "Caucus Race" to dry themselves. Following the end of the race, Alice inadvertently frightens the animals away by discussing her cat. The White Rabbit appears looking for the gloves and fan. Mistaking Alice for his maidservant, he orders her to go to his house and retrieve them. Alice finds another bottle and drinks from it, which causes her to grow to such an extent that she gets stuck in the house. Attempting to extract her, the White Rabbit and his neighbours eventually take to hurling pebbles that turn into small cakes. Alice eats one and shrinks herself, allowing her to flee into the forest. She meets a Caterpillar seated on a mushroom and smoking a hookah. During the Caterpillar's questioning, Alice begins to admit to her current identity crisis, compounded by her inability to remember a poem. Before crawling away, the Caterpillar says that a bite of one side of the mushroom will make her larger, while a bite from the other side will make her smaller. During a period of trial and error, Alice's neck extends between the treetops, frightening a pigeon who mistakes her for a serpent. After shrinking to an appropriate height, Alice arrives at the home of a Duchess, who owns a perpetually grinning Cheshire Cat. The Duchess's baby, whom she hands to Alice, transforms into a piglet, which Alice releases into the woods. The Cheshire Cat appears to Alice and directs her toward the Hatter and March Hare before disappearing, leaving his grin behind. Alice finds the Hatter, March Hare, and a sleepy Dormouse in the midst of a tea party. The Hatter explains that it is always 6 p.m. (tea time), claiming that time is standing still as punishment for the Hatter trying to "kill it". A conversation ensues around the table, and the riddle "Why is a raven like a writing desk?" is brought up. Alice impatiently decides to leave, calling the party stupid. Noticing a door on a tree, Alice passes through and finds herself back in the room from the beginning of her journey. She takes the key and uses it to open the door to the garden, which turns out to be the croquet court of the Queen of Hearts, whose guard consists of living playing cards. Alice participates in a croquet game, in which hedgehogs are used as balls, flamingos are used as mallets, and soldiers act as hoops. The Queen is short-tempered and constantly orders beheadings. When the Cheshire Cat appears as only a head, the Queen orders his beheading, only to be told that such an act is impossible. Because the cat belongs to the Duchess, Alice prompts the Queen to release the Duchess from prison to resolve the matter. When the Duchess ruminates on finding morals in everything around her, the Queen dismisses her on the threat of execution. Alice then meets a Gryphon and a Mock Turtle, who dance to the Lobster Quadrille while Alice recites (rather incorrectly) a poem. The Mock Turtle sings them "Beautiful Soup", during which the Gryphon drags Alice away for a trial, in which the Knave of Hearts stands accused of stealing the Queen's tarts. The trial is conducted by the King of Hearts, and the jury is composed of animals that Alice previously met. Alice gradually grows in size and confidence, allowing herself increasingly frequent remarks on the irrationality of the proceedings. The Queen eventually commands Alice's beheading, but Alice scoffs that the Queen's guard is only a pack of cards. Although Alice holds her own for a time, the guards soon gang up and start to swarm all over her. Alice's sister wakes her up from a dream, brushing what turns out to be leaves from Alice's face. Alice leaves her sister on the bank to imagine all the curious happenings for herself. Characters The main characters in Alice's Adventures in Wonderland are the following: Character allusions In The Annotated Alice, Martin Gardner provides background information for the characters. The members of the boating party that first heard Carroll's tale show up in chapter 3 ("A Caucus-Race and a Long Tale"). Alice Liddell is there, while Carroll is caricatured as the Dodo (Lewis Carroll was a pen name for Charles Lutwidge Dodgson; because he stuttered when he spoke, he sometimes pronounced his last name as "Dodo-Dodgson"). The Duck refers to Robinson Duckworth, and the Lory and Eaglet to Alice Liddell's sisters Lorina and Edith. Bill the Lizard may be a play on the name of British Prime Minister Benjamin Disraeli. One of Tenniel's illustrations in Through the Looking-Glass— the 1871 sequel to Alice— depicts the character referred to as the "Man in White Paper" (whom Alice meets on a train) as a caricature of Disraeli, wearing a paper hat. The illustrations of the Lion and the Unicorn (also in Looking-Glass) look like Tenniel's Punch illustrations of William Ewart Gladstone and Disraeli, although Gardner says there is "no proof" that they were intended to represent these politicians. Gardner has suggested that the Hatter is a reference to Theophilus Carter, an Oxford furniture dealer, and that Tenniel apparently drew the Hatter to resemble Carter, on a suggestion of Carroll's. The Dormouse tells a story about three little sisters named Elsie, Lacie, and Tillie. These are the Liddell sisters: Elsie is L.C. (Lorina Charlotte); Tillie is Edith (her family nickname is Matilda); and Lacie is an anagram of Alice. The Mock Turtle speaks of a drawling-master, "an old conger eel", who came once a week to teach "Drawling, Stretching, and Fainting in Coils". This is a reference to the art critic John Ruskin, who came once a week to the Liddell house to teach the children to draw, sketch, and paint in oils. The Mock Turtle sings "Turtle Soup", which is a parody of a song called "Star of the Evening, Beautiful Star", which the Liddells sang for Carroll. Poems and songs Carroll wrote multiple poems and songs for Alice's Adventures in Wonderland, including: "All in the golden afternoon..."—the prefatory verse to the book, an original poem by Carroll that recalls the rowing expedition on which he first told the story of Alice's adventures underground "How Doth the Little Crocodile"—a parody of Isaac Watts's nursery rhyme, "Against Idleness and Mischief" "The Mouse's Tale"—an example of concrete poetry "You Are Old, Father William"—a parody of Robert Southey's "The Old Man's Comforts and How He Gained Them" The Duchess's lullaby, "Speak roughly to your little boy..."—a parody of David Bates' "Speak Gently" "Twinkle, Twinkle, Little Bat"—a parody of Jane Taylor's "Twinkle Twinkle Little Star" "The Lobster Quadrille"—a parody of Mary Botham Howitt's "The Spider and the Fly" "'Tis the Voice of the Lobster"—a parody of Isaac Watts's "The Sluggard" "Beautiful Soup"—a parody of James M. Sayles's "Star of the Evening, Beautiful Star" "The Queen of Hearts"—an actual nursery rhyme "They told me you had been to her..."—White Rabbit's evidence Writing style and themes Symbolism Carroll's biographer Morton N. Cohen reads Alice as a roman à clef populated with real figures from Carroll's life. Alice is based on Alice Liddell; the Dodo is Carroll; Wonderland is Oxford; even the Mad Hatter's Tea Party, according to Cohen, is a send-up of Alice's own birthday party. The critic Jan Susina rejects Cohen's account, arguing that Alice the character bears a tenuous relationship with Alice Liddell. Beyond its refashioning of Carroll's everyday life, Cohen argues, Alice critiques Victorian ideals of childhood. It is an account of "the child's plight in Victorian upper-class society", in which Alice's mistreatment by the creatures of Wonderland reflects Carroll's own mistreatment by older people as a child. In the eighth chapter, three cards are painting the roses on a rose tree red, because they had accidentally planted a white-rose tree that the Queen of Hearts hates. According to Wilfrid Scott-Giles, the rose motif in Alice alludes to the English Wars of the Roses: red roses symbolised the House of Lancaster, and white roses the rival House of York. Language Alice is full of linguistic play, puns, and parodies. According to Gillian Beer, Carroll's play with language evokes the feeling of words for new readers: they "still have insecure edges and a nimbus of nonsense blurs the sharp focus of terms". The literary scholar Jessica Straley, in a work about the role of evolutionary theory in Victorian children's literature, argues that Carroll's focus on language prioritises humanism over scientism by emphasising language's role in human self-conception. Pat's "Digging for apples" is a cross-language pun, as pomme de terre (literally; "apple of the earth") means potato and pomme means apple. In the second chapter, Alice initially addresses the mouse as "O Mouse", based on her memory of the noun declensions "in her brother's Latin Grammar, 'A mouse – of a mouse – to a mouse – a mouse – O mouse! These words correspond to the first five of Latin's six cases, in a traditional order established by medieval grammarians: mus (nominative), muris (genitive), muri (dative), murem (accusative), (O) mus (vocative). The sixth case, mure (ablative) is absent from Alice's recitation. Nilson suggests that Alice's missing ablative is a pun on her father Henry Liddell's work on the standard A Greek-English Lexicon, since ancient Greek does not have an ablative case. Further, mousa (μούσα, meaning muse) was a standard model noun in Greek textbooks of the time in paradigms of the first declension, short-alpha noun. Mathematics Mathematics and logic are central to Alice. As Carroll was a mathematician at Christ Church, it has been suggested that there are many references and mathematical concepts in both this story and Through the Looking-Glass. Literary scholar Melanie Bayley asserts in the New Scientist magazine that Carroll wrote Alice in Wonderland in its final form as a satire on mid-19th century mathematics. Eating and devouring Carina Garland notes how the world is "expressed via representations of food and appetite", naming Alice's frequent desire for consumption (of both food and words), her 'Curious Appetites'. Often, the idea of eating coincides to make gruesome images. After the riddle "Why is a raven like a writing-desk?", the Hatter claims that Alice might as well say, "I see what I eat…I eat what I see" and so the riddle's solution, put forward by Boe Birns, could be that "A raven eats worms; a writing desk is worm-eaten"; this idea of food encapsulates idea of life feeding on life itself, for the worm is being eaten and then becomes the eater—a horrific image of mortality. Nina Auerbach discusses how the novel revolves around eating and drinking which "motivates much of her [Alice's] behaviour", for the story is essentially about things "entering and leaving her mouth." The animals of Wonderland are of particular interest, for Alice's relation to them shifts constantly because, as Lovell-Smith states, Alice's changes in size continually reposition her in the food chain, serving as a way to make her acutely aware of the 'eat or be eaten' attitude that permeates Wonderland. Nonsense Alice is an example of the literary nonsense genre. According to Humphrey Carpenter, Alice brand of nonsense embraces the nihilistic and existential. Characters in nonsensical episodes such as the Mad Hatter's Tea Party, in which it is always the same time, go on posing paradoxes that are never resolved. Rules and games Wonderland is a rule-bound world, but its rules are not those of our world. The literary scholar Daniel Bivona writes that Alice is characterised by "gamelike social structures." She trusts in instructions from the beginning, drinking from the bottle labelled "drink me" after recalling, during her descent, that children who do not follow the rules often meet terrible fates. Unlike the creatures of Wonderland, who approach their world's wonders uncritically, Alice continues to look for rules as the story progresses. Gillian Beer suggests that Alice looks for rules to soothe her anxiety, while Carroll may have hunted for rules because he struggled with the implications of the non-Euclidean geometry then in development. Illustrations The manuscript was illustrated by Carroll, who added 37 illustrations—printed in a facsimile edition in 1887. John Tenniel provided 42 wood-engraved illustrations for the published version of the book. The first print run was destroyed (or sold in the US) at Carroll's request because Tenniel was dissatisfied with the printing quality. There are only 22 known first edition copies in existence. The book was reprinted and published in 1866. Tenniel's detailed black-and-white drawings remain the definitive depiction of the characters. Tenniel's illustrations of Alice do not portray the real Alice Liddell, who had dark hair and a short fringe. Alice has provided a challenge for other illustrators, including those of 1907 by Charles Pears and the full series of colour plates and line-drawings by Harry Rountree published in the (inter-War) Children's Press (Glasgow) edition. Other significant illustrators include: Arthur Rackham (1907), Willy Pogany (1929), Mervyn Peake (1946), Ralph Steadman (1967), Salvador Dalí (1969), Graham Overden (1969), Max Ernst (1970), Peter Blake (1970), Tove Jansson (1977), Anthony Browne (1988), Helen Oxenbury (1999), and Lisbeth Zwerger (1999). Publication history Carroll first met Alexander Macmillan, a high-powered London publisher, on 19 October 1863. His firm, Macmillan Publishers, agreed to publish Alice's Adventures in Wonderland by sometime in 1864. Carroll financed the initial print run, possibly because it gave him more editorial authority than other financing methods. He managed publication details such as typesetting and engaged illustrators and translators. Macmillan had published The Water-Babies, also a children's fantasy, in 1863, and suggested its design as a basis for Alice. Carroll saw a specimen copy in May 1865. 2,000 copies were printed by July, but Tenniel objected to their quality, and Carroll instructed Macmillan to halt publication so they could be reprinted. In August, he engaged Richard Clay as an alternative printer for a new run of 2,000. The reprint cost £600, paid entirely by Carroll. He received the first copy of Clay's edition on 9 November 1865. Macmillan finally published the new edition, printed by Richard Clay, in November 1865. Carroll requested a red binding, deeming it appealing to young readers. A new edition, released in December 1865 for the Christmas market but carrying an 1866 date, was quickly printed. The text blocks of the original edition were removed from the binding and sold with Carroll's permission to the New York publishing house of D. Appleton & Company. The binding for the Appleton Alice was identical to the 1866 Macmillan Alice, except for the publisher's name at the foot of the spine. The title page of the Appleton Alice was an insert cancelling the original Macmillan title page of 1865 and bearing the New York publisher's imprint and the date 1866. The entire print run sold out quickly. Alice was a publishing sensation, beloved by children and adults alike. Oscar Wilde was a fan; Queen Victoria was also an avid reader of the book. She reportedly enjoyed Alice enough that she asked for Carroll's next book, which turned out to be a mathematical treatise; Carroll denied this. The book has never been out of print. Alice's Adventures in Wonderland has been translated into 174 languages. Publication timeline The following list is a timeline of major publication events related to Alice's Adventures in Wonderland: 1869: Published in German as Alice's Abenteuer im Wunderland, translated by Antonie Zimmermann. 1869: Published in French as Aventures d'Alice au pays des merveilles, translated by Henri Bué. 1870: Published in Swedish as Alice's Äventyr i Sagolandet, translated by Emily Nonnen. 1871: Carroll meets another Alice, Alice Raikes, during his time in London. He talks with her about her reflection in a mirror, leading to the sequel, Through the Looking-Glass, and What Alice Found There, which sells even better. 1872: Published in Italian as Le Avventure di Alice nel Paese delle Meraviglie, translated by Teodorico Pietrocòla Rossetti. 1886: Carroll publishes a facsimile of the earlier Alice's Adventures Under Ground manuscript. 1890: Carroll publishes The Nursery "Alice", an abridged version, around Easter. 1905: Mrs J. C. Gorham publishes Alice's Adventures in Wonderland Retold in Words of One Syllable in a series of such books published by A. L. Burt Company, aimed at young readers. 1906: Published in Finnish as Liisan seikkailut ihmemaailmassa, translated by Anni Swan. 1907: Copyright on Alice's Adventures in Wonderland expires in the UK, entering the tale into the public domain, 42 years after its publication, some nine years after Carroll's death in January 1898. 1910: Published in Esperanto as La Aventuroj de Alicio en Mirlando, translated by E. L. Kearney. 1915: Alice Gerstenberg's stage adaptation premieres. 1928: The manuscript of Alice's Adventures Under Ground written and illustrated by Carroll, which he had given to Alice Liddell, was sold at Sotheby's in London on 3 April. It was sold to Philip Rosenbach of Philadelphia for , a world record for the sale of a manuscript at the time; the buyer later presented it to the British Library (where the manuscript remains) as an appreciation for Britain's part in two World Wars. 1960: American writer Martin Gardner publishes a special edition, The Annotated Alice. 1988: Lewis Carroll and Anthony Browne, illustrator of an edition from Julia MacRae Books, win the Kurt Maschler Award. 1998: Carroll's own copy of Alice, one of only six surviving copies of the 1865 first edition, is sold at an auction for US$1.54 million to an anonymous American buyer, becoming the most expensive children's book (or 19th-century work of literature) ever sold to that point. 1999: Lewis Carroll and Helen Oxenbury, illustrators of an edition from Walker Books, win the Kurt Maschler Award for integrated writing and illustration. 2008: Folio publishes Alice's Adventures Under Ground facsimile edition (limited to 3,750 copies, boxed with The Original Alice pamphlet). 2009: Children's book collector and former American football player Pat McInally reportedly sold Alice Liddell's own copy at auction for US$115,000. Reception Alice was published to critical praise. One magazine declared it "exquisitely wild, fantastic, [and] impossible". In the late 19th century, Walter Besant wrote that Alice in Wonderland "was a book of that extremely rare kind which will belong to all the generations to come until the language becomes obsolete". F. J. Harvey Darton argued in a 1932 book that Alice ended an era of didacticism in children's literature, inaugurating a new era in which writing for children aimed to "delight or entertain". In 2014, Robert McCrum named Alice "one of the best loved in the English canon" and called it "perhaps the greatest, possibly most influential, and certainly the most world-famous Victorian English fiction". A 2020 review in Time states: "The book changed young people's literature. It helped to replace stiff Victorian didacticism with a looser, sillier, nonsense style that reverberated through the works of language-loving 20th-century authors as different as James Joyce, Douglas Adams and Dr. Seuss." The protagonist of the story, Alice, has been recognised as a cultural icon. In 2006, Alice in Wonderland was named among the icons of England in a public vote. Adaptations and influence Books for children in the Alice mould emerged as early as 1869 and continued to appear throughout the late 19th century. Released in 1903, the British silent film Alice in Wonderland was the first screen adaptation of the book. In 2015, Robert Douglas-Fairhurst wrote in the Guardian, Labelled "a dauntless, no-nonsense heroine" by the Guardian, the character of the plucky, yet proper, Alice has proven immensely popular and inspired similar heroines in literature and pop culture, many also named Alice in homage. The book has inspired numerous film and television adaptations, which have multiplied, as the original work is now in the public domain in all jurisdictions. Musical works inspired by Alice include the Beatles's song "Lucy in the Sky with Diamonds", with songwriter John Lennon attributing the song's fantastical imagery to his reading of Carroll's books. A popular figure in Japan since the country opened up to the West in the late 19th century, Alice has been a popular subject for writers of manga and a source of inspiration for Japanese fashion, in particular Lolita fashion. Live performance The first full major production was Alice in Wonderland, a musical play in London's West End by Henry Savile Clarke and Walter Slaughter, which premiered at the Prince of Wales Theatre in 1886. Twelve-year-old actress Phoebe Carlo (the first to play Alice) was personally selected by Carroll for the role. Carroll attended a performance on 30 December 1886, writing in his diary that he enjoyed it. The musical was frequently revived during West End Christmas seasons during the four decades after its premiere, including a London production at the Globe Theatre in 1888, with Isa Bowman as Alice. As the book and its sequel are Carroll's most widely recognised works, they have also inspired numerous live performances, including plays, operas, ballets, and traditional English pantomimes. These works range from fairly faithful adaptations to those that use the story as a basis for new works. Eva Le Gallienne's stage adaptation of the Alice books premiered on 12 December 1932 and ended its run in May 1933. The production was revived in New York in 1947 and 1982. A community theatre production of Alice was Olivia de Havilland's first foray onto the stage. Joseph Papp staged Alice in Concert at the Public Theater in New York City in 1980. Elizabeth Swados wrote the book, lyrics, and music based on both Alice's Adventures in Wonderland and Through the Looking-Glass. Papp and Swados had previously produced a version of it at the New York Shakespeare Festival. Meryl Streep played Alice, the White Queen, and Humpty Dumpty. The cast also included Debbie Allen, Michael Jeter, and Mark Linn-Baker. Performed on a bare stage with the actors in modern dress, the play is a loose adaptation, with song styles ranging the globe. The 1992 musical theatre production Alice used both books as its inspiration. It also employs scenes with Carroll, a young Alice Liddell, and an adult Alice Liddell, to frame the story. Paul Schmidt wrote the play, with Tom Waits and Kathleen Brennan writing the music. Although the original production in Hamburg, Germany, received only a small audience, Tom Waits released the songs as the album Alice in 2002. The English composer Joseph Horovitz composed an Alice in Wonderland ballet commissioned by the London Festival Ballet in 1953. It was performed frequently in England and the US. A ballet by Christopher Wheeldon and Nicholas Wright commissioned for the Royal Ballet entitled Alice's Adventures in Wonderland premiered in February 2011 at the Royal Opera House in London. The ballet was based on the novel Wheeldon grew up reading as a child and is generally faithful to the original story, although some critics claimed it may have been too faithful. Unsuk Chin's opera Alice in Wonderland premiered in 2007 at the Bavarian State Opera and was hailed as World Premiere of the Year by the German opera magazine Opernwelt. Gerald Barry's 2016 one-act opera, Alice's Adventures Under Ground, first staged in 2020 at the Royal Opera House, is a conflation of the two Alice books. In 2022, the Opéra national du Rhin performed the ballet Alice, with a score by Philip Glass, in Mulhouse, France. Commemoration Characters from the book are depicted in the stained glass windows of Carroll's hometown church, All Saints', in Daresbury, Cheshire. Another commemoration of Carroll's work in his home county of Cheshire is the granite sculpture The Mad Hatter's Tea Party, located in Warrington. International works based on the book include the Alice in Wonderland statue in Central Park, New York, and the Alice statue in Rymill Park, Adelaide, Australia. In 2015, Alice characters were featured on a series of UK postage stamps issued by the Royal Mail to mark the 150th anniversary of the publication of the book. See also Down the rabbit hole Translations of Alice's Adventures in Wonderland Translations of Through the Looking-Glass References Works cited External links Text Alice's Adventures in Wonderland (1866) (with forty-two illustrations by John Tenniel) full color scan from University of Southern California Digital Library Audio Archival materials Cassady Lewis Carroll Collection from University of Southern California Digital Library To all child-readers of "Alice's adventures in Wonderland" (Christmas 1871) Alice in Wonderland: coloured lantern slides, 1910-1919 "3 square blue boxes, each with 8 glass lantern slides and leaflet with abridged excerpt from 'Alice', 24 slides & 3 leaflets all" 1865 British novels 1865 fantasy novels British children's novels British children's books Children's books set in subterranea Children's fantasy novels English fantasy novels High fantasy novels Surreal comedy Victorian novels Series of children's books Alice in Wonderland Cultural depictions of Benjamin Disraeli British novels adapted into films British novels adapted into plays Novels adapted into video games Books about rabbits and hares Novels about dreams Fiction about size change Fictional fungi Novels set in fictional countries Novels set in one day Works by Lewis Carroll Books illustrated by John Tenniel Books illustrated by Arthur Rackham Macmillan Publishers books D. Appleton & Company books Children's books set in fictional countries	Alice's Adventures in Wonderland	[ "Physics", "Mathematics" ]	6,969	[ "Fiction about size change", "Quantity", "Physical quantities", "Size" ]
52,883	https://en.wikipedia.org/wiki/Lavon%20Affair	The Lavon affair was a failed Israeli covert operation, codenamed Operation Susannah, conducted in Egypt in the summer of 1954. As part of a false flag operation, a group of Egyptian Jews were recruited by Israeli military intelligence to plant bombs inside Egyptian-, American-, and British-owned civilian targets: cinemas, libraries, and American educational centers. The bombs were timed to detonate several hours after closing time. The attacks were to be blamed on the Muslim Brotherhood, Egyptian communists, "unspecified malcontents", or "local nationalists" with the aim of creating a climate of sufficient violence and instability to induce the British government to retain its occupying troops in Egypt's Suez Canal zone. The operation caused no casualties among the population, but resulted in the deaths of four operatives. The overseer of the operation allegedly informed the Egyptians, after which 11 suspected operatives were arrested. Two died by suicide after being captured, two were executed by the Egyptian authorities, two of them were acquitted at trial, and the remaining five received prison terms ranging from 7 years to life in prison. The operation ultimately became known as the "Lavon affair" after the Israeli defense minister Pinhas Lavon, who was forced to resign as a consequence of the incident. Before Lavon's resignation, the incident had been euphemistically referred to in Israel as the "Unfortunate Affair" or "The Bad Business" (, HaEsek HaBish). Israel publicly denied any involvement in the incident until 2005, when the surviving agents were awarded certificates of appreciation by Israeli President Moshe Katsav. Operation Susannah Aim In the early 1950s, the United States initiated a more activist policy of support for Egyptian nationalism; this aim was often in contrast with Britain's policy of maintaining its regional hegemony. Israel feared that the US policy, which encouraged Britain to withdraw its military forces from the Suez Canal, would embolden the military ambitions towards Israel of Gamal Abdel Nasser, the President of Egypt. Israel at first sought to influence this policy through diplomatic means, but was frustrated. In the summer of 1954, Colonel Binyamin Gibli, the chief of Israel's military intelligence directorate Aman, initiated 'Operation Susannah' in order to reverse that decision. The goal of the Operation was to carry out bombings and other acts of sabotage in Egypt, with the aim of creating an atmosphere in which the British and American opponents of British withdrawal from Egypt would be able to gain the upper hand and block the British withdrawal from Egypt. According to historian Shabtai Teveth, who wrote one of the more detailed accounts, the assignment was "To undermine Western confidence in the existing Egyptian regime by generating public insecurity and actions to bring about arrests, demonstrations, and acts of revenge, while totally concealing the Israeli factor. The team was accordingly urged to avoid detection, so that suspicion would fall on the Muslim Brotherhood, the Communists, 'unspecified malcontents' or 'local nationalists'." Secret cell The top-secret cell, Unit 131, which was to carry out the operation, had existed since 1948 and under Aman since 1950. At the time of Operation Susannah, Unit 131 was the subject of a bitter dispute between Aman (military intelligence) and Mossad (national intelligence agency) over who should control it. Unit 131 operatives had been recruited several years earlier, when the Israeli intelligence officer Avraham Dar arrived in Cairo under the cover of a British citizen from Gibraltar named John Darling. He had recruited several Egyptian Jews, known as sayanim (), who had also previously been active in helping Jews flee to Israel, activities that Egypt deemed illegal, and trained them for covert operations. Operation commenced Aman decided to activate the network in the spring of 1954. On 2 July, the cell detonated bombs at a post office in Alexandria, and on 14 July, it bombed the libraries of the U.S. Information Agency in Alexandria and Cairo, and a British-owned theater. The homemade bombs, consisting of bags containing acid placed over nitroglycerine, were inserted into books and placed on the shelves of the libraries just before closing time. Several hours later, as the acid ate through the bags, the bombs would explode. They did little damage to the targets and caused no injuries or deaths. Before the group began the operation, Israeli agent Avri Elad (Avraham Seidenberg) was sent to oversee the operations. Elad assumed the identity of Paul Frank, a former SS officer with Nazi underground connections. Avri Elad allegedly informed the Egyptians, resulting in the Egyptian intelligence agency following a suspect to his target, the Rio Theatre, where a fire engine was standing by. Egyptian authorities arrested this suspect, Philip Natanson, when his bomb accidentally ignited prematurely in his pocket. Having searched his apartment, they found incriminating evidence and names of accomplices to the operation. Eleven suspects were arrested, including Egyptian Jews and undercover Israelis. Elad and Colonel Dar managed to escape. Two suspects, Yosef Carmon and Israeli Meir Max Bineth, died by suicide in prison. Trials and jail The Egyptian trial began on 11 December and lasted until 27 January 1955; two of the accused (Moshe Marzouk and ) were sentenced to death by hanging, two were acquitted, and the rest received lengthy prison terms ranging from 7 years to life in prison. In 1954, on behalf of both Winston Churchill and the World Jewish Congress, Maurice Orbach went to Cairo to intercede for the lives of those sentenced to death. Later, he said that Egypt's president, Nasser, had agreed to spare their lives but then reneged on this, balancing their deaths with those of members of the Muslim Brotherhood. The trial was criticised in Israel as a show trial, although strict Israeli military censorship of the press at the time meant that the Israeli public was kept in the dark about the facts of the case, and in fact were led to believe that the defendants were innocent. There were allegations that evidence had been extracted by torture. After serving seven-year jail sentences, two of the imprisoned operatives (Meir Meyuhas and Meir Za'afran) were released in 1962. The rest were eventually freed in February 1968, including Marcelle Ninio, in a secret addendum to a prisoner-of-war exchange. Soon after the affair, Mossad chief Isser Harel expressed suspicion to Aman concerning the integrity of Avri Elad. Despite his concerns, Aman continued using Elad for intelligence operations until 1956, when he was caught trying to sell Israeli documents to the Egyptians. Elad was tried in Israel and sentenced to 10 years imprisonment. During his imprisonment in Ayalon Prison, the media were only able to refer to him as the "Third Man" or "X" due to government censorship. In 1976, while living in Los Angeles, Elad publicly identified himself as the "Third Man" from the Lavon Affair. In 1980, Harel publicly revealed evidence that Elad had been turned by the Egyptians even before Operation Susannah. Political aftermath Denial and first inquiry In meetings with the prime minister Moshe Sharett, minister of defense Pinhas Lavon denied any knowledge of the operation. When intelligence chief Gibli contradicted Lavon, Sharett commissioned a board of inquiry consisting of Israeli Supreme Court Justice Isaac Olshan and the first chief of staff of the Israel Defense Forces, Yaakov Dori that was unable to find conclusive evidence that Lavon had authorized the operation. Lavon tried to fix the blame on Shimon Peres, who was the secretary general of the defense ministry, and on Gibli for insubordination and criminal negligence. Sharett resolved the dilemma by siding with Peres (who had, along with Moshe Dayan, testified against Lavon), after which Lavon resigned on 17 February 1955. Former prime minister David Ben-Gurion succeeded Lavon as minister of defense. On 3 November 1955, Sharett (who had not known about the operation in advance, and had therefore strongly denied Israel's involvement) resigned as Prime Minister and was replaced by Ben-Gurion. Subsequent revelations and inquiries In April 1960, a review of minutes from the inquiry found inconsistencies and possibly a fraudulent document in Gibli's original testimony that seemed to support Lavon's account of events. During this time it came to light that Elad (the Israeli agent running Operation Susannah in Egypt) had committed perjury during the original inquiry. Elad was also suspected of betraying the group to Egyptian authorities, though the charges were never proven. He was eventually sentenced to a jail term of 10 years for trying to sell Israeli documents to the Egyptians in an unrelated matter. Ben-Gurion scheduled closed hearings with a new board of inquiry chaired by Haim Cohn, a Supreme Court justice. This inquiry found that the perjury indeed had been committed, and that Lavon had not authorized the operation. Sharett and Levi Eshkol tried to issue a statement that would placate both Lavon and those who had opposed him. Ben-Gurion refused to accept the compromise, and viewed it as a divisive play within the Mapai party. Another investigative committee took up the matter and sided with the Cohn inquiry. Ben-Gurion then resigned from his post as defense minister. This led to the expulsion of Lavon from the Histadrut labor union and an early call for new elections, the results of which changed the political structure in Israel. The specifics of Operation Susannah were kept secret from the Israeli public at the time of the political upheaval. Public debate Due to Israel's military censorship the details of the affair could originally not be openly discussed in the media. Despite this, debate occurred but with the use of code words such as the "Senior Officer", to refer to Gibli, and the "unfortunate business" to refer to the Egyptian operation. Legacy Operation Susannah and the Lavon Affair turned out to be disastrous for Israel in several ways: Israel lost significant standing and credibility in its relations with the United Kingdom and the United States, that took years to repair. The aftermath saw considerable political turmoil in Israel, which affected the influence of its government. Israel publicly honored the surviving spies on March 30, 2005; President Moshe Katsav presented each with a certificate of appreciation for their efforts on behalf of the state, ending decades of official denial by Israel. References Further reading Aviezer Golan, Ninio Marcelle, Victor Levy, Robert Dassa and Philip Natanson (As told to Aviezer Golan) (Translated from Hebrew by Peretz Kidron) (Fwd by Golda Meir): Operation Susannah, Harper & Row, NYC, 1978 Joel Beinin: Nazis and Spies The Discourse of Operation Susannah, ch 4 in The Dispersion Of Egyptian Jewry Culture, Politics, And The Formation Of A Modern Diaspora Berkeley: University of California Press, c1998. Amer Univ in Cairo Pr, 2005, Joel Beinin: Egyptian Jewish Identities. Communitarianisms, nationalisms, nostalgias Stanford Humanities Review, 1996 External links The Lavon Affair by Doron Geller, JUICE, The Jewish Agency for Israel, Education Department The Lavon Affair by David Hirst, Excerpts from his book: The Gun and the Olive Branch, 1977, 1984, Futura Publications List of books about the Lavon Affair Egypt in the Arab–Israeli conflict False flag operations Jewish Egyptian history 1954 in Israel 1954 in Egypt 1960 in Israel 1960 in Egypt Political scandals in Israel Espionage scandals and incidents Military scandals Secret military programs Diplomatic incidents Military Intelligence Directorate (Israel) Terrorism committed by Israel Terrorism in Egypt Anti-communist terrorism Military history of Alexandria Military history of Cairo Jewish extremist terrorism Zionist political violence	Lavon Affair	[ "Engineering" ]	2,408	[ "Military projects", "Secret military programs" ]
52,888	https://en.wikipedia.org/wiki/Logo	A logo (abbreviation of logotype; ) is a graphic mark, emblem, or symbol used to aid and promote public identification and recognition. It may be of an abstract or figurative design or include the text of the name that it represents, as in a wordmark. In the days of hot metal typesetting, a logotype was one word cast as a single piece of type (e.g. "The" in ATF Garamond), as opposed to a ligature, which is two or more letters joined, but not forming a word. By extension, the term was also used for a uniquely set and arranged typeface or colophon. At the level of mass communication and in common usage, a company's logo is today often synonymous with its trademark or brand. Etymology Douglas Harper's Online Etymology Dictionary states that the first surviving written record of the term 'logo' dates back to 1937, and that the term was "probably a shortening of logogram". History Numerous inventions and techniques have contributed to the contemporary logo, including cylinder seals (), coins (), trans-cultural diffusion of logographic languages, coats of arms, watermarks, silver hallmarks, and the development of printing technology. As the Industrial Revolution converted western societies from agrarian to industrial in the 18th and 19th centuries, photography and lithography contributed to the boom of an advertising industry that integrated typography and imagery together on the page. Simultaneously, typography itself was undergoing a revolution of form and expression that expanded beyond the modest, serif typefaces used in books, to bold, ornamental typefaces used on broadsheet posters. The arts were expanding in purpose—from expression and decoration of an artistic, storytelling nature, to a differentiation of brands and products that the growing middle classes were consuming. Consultancies and trades-groups in the commercial arts were growing and organizing; by 1890, the US had 700 lithographic printing firms employing more than 8,000 people. Artistic credit tended to be assigned to the lithographic company, as opposed to the individual artists who usually performed less important jobs. Innovators in the visual arts and lithographic process—such as French printing firm Rouchon in the 1840s, Joseph Morse of New York in the 1850s, Frederick Walker of England in the 1870s, and Jules Chéret of France in the 1870s—developed an illustrative style that went beyond tonal, representational art to figurative imagery with sections of bright, flat colors. Playful children's books, authoritative newspapers, and conversational periodicals developed their own visual and editorial styles for unique, expanding audiences. As printing costs decreased, literacy rates increased, and visual styles changed, the Victorian decorative arts led to an expansion of typographic styles and methods of representing businesses. The Arts and Crafts Movement of late-19th century, partially in response to the excesses of Victorian typography, aimed to restore an honest sense of craftsmanship to the mass-produced goods of the era. A renewal of interest in craftsmanship and quality also provided the artists and companies with a greater interest in credit, leading to the creation of unique logos and marks. By the 1950s, Modernism had shed its roots as an avant-garde artistic movement in Europe to become an international, commercialized movement with adherents in the United States and elsewhere. The visual simplicity and conceptual clarity that were the hallmarks of Modernism as an artistic movement formed a powerful toolset for a new generation of graphic designers whose logos embodied Ludwig Mies van der Rohe's dictum, "Less is more." Modernist-inspired logos proved successful in the era of mass visual communication ushered in by television, improvements in printing technology, and digital innovations. Contemporary logos The current era of logo design began in the 1870s with the first abstract logo, the Bass red triangle. , many corporations, products, brands, services, agencies, and other entities use an ideogram (sign, icon) or an emblem (symbol) or a combination of sign and emblem as a logo. As a result, only a few of the thousands of ideograms in circulation are recognizable without a name. An effective logo may consist of both an ideogram and the company name (logotype) to emphasize the name over the graphic, and employ a unique design via the use of letters, colors, and additional graphic elements. Ideograms and symbols may be more effective than written names (logotypes), especially for logos translated into many alphabets in increasingly globalized markets. For instance, a name written in Arabic script might have little resonance in most European markets. By contrast, ideograms keep the general proprietary nature of a product in both markets. In non-profit areas, the Red Cross (varied as the Red Crescent in Muslim countries and as the Red Star of David in Israel) exemplifies a well-known emblem that does not need an accompanying name. The red cross and red crescent are among the best-recognized symbols in the world. National Red Cross and Red Crescent Societies and their Federation as well as the International Committee of the Red Cross include these symbols in their logos. Branding can aim to facilitate cross-language marketing. Consumers and potential consumers can identify the Coca-Cola name written in different alphabets because of the standard color and "ribbon wave" design of its logo. The text was written in Spencerian Script, which was a popular writing style when the Coca-Cola Logo was being designed. Logo design Since a logo is the visual entity signifying an organization, logo design is an important area of graphic design. A logo is the central element of a complex identification system that must be functionally extended to all communications of an organization. Therefore, the design of logos and their incorporation in a visual identity system is one of the most difficult and important areas of graphic design. Logos fall into three classifications (which can be combined). Ideographs, such as Chase Bank, are completely abstract forms; pictographs are iconic, representational designs; logotypes (or wordmarks) depict the name or company initials. These elements can be combined in a set position and relative size in a logo lock-up, so named because elements are "locked" together and should not be broken apart or resized individually. Because logos are meant to represent companies' brands or corporate identities and foster their immediate customer recognition, it is counterproductive to frequently redesign logos. The logo design profession has substantially increased in numbers over the years since the rise of the Modernist movement in the United States in the 1950s. Three designers are widely considered the pioneers of that movement and of logo and corporate identity design: The first is Chermayeff & Geismar, which is the firm responsible for many iconic logos, such as Chase Bank (1964), Mobil Oil (1965), PBS (1984), NBC (1986), National Geographic (2003), and others. Due to the simplicity and boldness of their designs, many of their earlier logos are still in use today. The firm recently designed logos for the Library of Congress and the fashion brand Armani Exchange. Another pioneer of corporate identity design is Paul Rand, who was one of the originators of the Swiss Style of graphic design. He designed many posters and corporate identities, including the famous logos for IBM, UPS, and ABC. The third pioneer of corporate identity design is Saul Bass. Bass was responsible for several recognizable logos in North America, including both the Bell Telephone logo (1969) and successor AT&T Corporation globe (1983). Other well-known designs were Continental Airlines (1968), Dixie (1969), and United Way (1972). Later, he would produce logos for a number of Japanese companies as well. An important development in the documentation of logo design is the study of French trademarks by historian Edith Amiot and philosopher Jean Louis Azizollah. Logo color Color is a key element in logo design and plays an important and potentially vital role in brand differentiation. Colors can have immense consequences on our moods. They are remarkably dominant to the point that they can psychologically manipulate perspectives, emotions, and reactions. The importance of color in this context is due to the mechanics of human visual perception wherein color and contrast play critical roles in visual detail detection. In addition, we tend to acquire various color connotations and color associations through social and cultural conditioning, and these play a role in how we decipher and evaluate logo color. While color is considered important to brand recognition and logo design, it should not conflict with logo functionality, and it needs to be remembered that color connotations and associations are not consistent across all social and cultural groups. For example, in the United States, red, white, and blue are often used in logos for companies that want to project patriotic feelings but other countries will have different sets of colors that evoke national pride. Choosing an organisation's logo color is an important decision because of its long term implications and its role in creating differentiation among competitors' logos. A methodology for identifying potential logo colors within an industry sector is color mapping, whereby existing logo colors are systematically identified, mapped, and evaluated (O'Connor, 2011). Logo design process Designing a good logo often requires involvement from a marketing team teaming with the graphic design studio. Before a logo is designed, there must be a clear definition of the concept and values of the brand as well as understanding of the consumer or target group. Broad steps in the logo design process include research, conceptualization, investigation of alternative candidates, refinement of a chosen design, testing across products, and finally adoption and production of the chosen mark. Dynamic logos In 1898, the French tire manufacturer Michelin introduced the Michelin Man, a cartoon figure presented in many different contexts, such as eating, drinking, and playing sports. By the early 21st century, large corporations such as MTV, Nickelodeon, Google, Morton Salt, and Saks Fifth Avenue had adopted dynamic logos that change over time from setting to setting. Internet-compatible logos A company that uses logotypes (wordmarks) may desire a logo that matches the firm's Internet address. For short logotypes consisting of two or three characters, multiple companies are found to employ the same letters. A "CA" logo, for example, is used by the French bank Credit Agricole, the Dutch clothing retailer C&A, and the US software corporation CA Technologies, but only one can have the Internet domain name CA.com. In today's digital interface adaptive world, a logo will be formatted and re-formatted from large monitors to small handheld devices. With the constant size change and re-formatting, logo designers are shifting to a more bold and simple approach, with heavy lines and shapes, and solid colors. This reduces the confusion when mingled with other logos in tight spaces and when scaled between media. Social networks like Twitter, Facebook, LinkedIn, and Google+ use such logos. Design protection Logos and their design may be protected by copyright, via various intellectual property organisations worldwide which make available application procedures to register a design to give it protection at law. For example, in the UK, the Intellectual Property Office (United Kingdom) govern registered designs, patents, and trademarks. Ordinarily, the trademark registration will not 'make claim' to colors used, meaning it is the visual design that will be protected, even if it is reproduced in a variety of other colors or backgrounds. In some countries, especially civil law countries, the threshold of originality required for copyright protection can be quite high, so a logo that contains simple geometric shapes or text might not be eligible for copyright protection although it can be protected as a trademark. Sports For many teams, a logo or "crest" is an important way to recognize a team's history and can intimidate opponents. For certain teams, the logo and color scheme are synonymous with the team's players. For example, Manchester United, the Toronto Maple Leafs, or New York Yankees all have a recognizable logo that can be identified by any fan of the respective sport. See also Graphic design Heraldry Icon Logogram Monogram, a motif made by overlapping or combining two or more letters or other graphemes to form one symbol Seal (emblem) Slogan Sound trademark Swiss Style (design) Letter symbolism References Sources External links Communication design	Logo	[ "Engineering" ]	2,511	[ "Design", "Communication design" ]
52,897	https://en.wikipedia.org/wiki/Stone%E2%80%93%C4%8Cech%20compactification	In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX. The Stone–Čech compactification βX of a topological space X is the largest, most general compact Hausdorff space "generated" by X, in the sense that any continuous map from X to a compact Hausdorff space factors through βX (in a unique way). If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X can be thought of as a (dense) subspace of βX; every other compact Hausdorff space that densely contains X is a quotient of βX. For general topological spaces X, the map from X to βX need not be injective. A form of the axiom of choice is required to prove that every topological space has a Stone–Čech compactification. Even for quite simple spaces X, an accessible concrete description of βX often remains elusive. In particular, proofs that βX \ X is nonempty do not give an explicit description of any particular point in βX \ X. The Stone–Čech compactification occurs implicitly in a paper by and was given explicitly by and . History Andrey Nikolayevich Tikhonov introduced completely regular spaces in 1930 in order to avoid the pathological situation of Hausdorff spaces whose only continuous real-valued functions are constant maps. In the same 1930 article where Tychonoff defined completely regular spaces, he also proved that every Tychonoff space (i.e. Hausdorff completely regular space) has a Hausdorff compactification (in this same article, he also proved Tychonoff's theorem). In 1937, Čech extended Tychonoff's technique and introduced the notation βX for this compactification. Stone also constructed βX in a 1937 article, although using a very different method. Despite Tychonoff's article being the first work on the subject of the Stone–Čech compactification and despite Tychonoff's article being referenced by both Stone and Čech, Tychonoff's name is rarely associated with βX. Universal property and functoriality The Stone–Čech compactification of the topological space X is a compact Hausdorff space βX together with a continuous map iX : X → βX that has the following universal property: any continuous map f : X → K, where K is a compact Hausdorff space, extends uniquely to a continuous map βf : βX → K, i.e. (βf)iX = f. As is usual for universal properties, this universal property characterizes βX up to homeomorphism. As is outlined in , below, one can prove (using the axiom of choice) that such a Stone–Čech compactification iX : X → βX exists for every topological space X. Furthermore, the image iX(X) is dense in βX. Some authors add the assumption that the starting space X be Tychonoff (or even locally compact Hausdorff), for the following reasons: The map from X to its image in βX is a homeomorphism if and only if X is Tychonoff. The map from X to its image in βX is a homeomorphism to an open subspace if and only if X is locally compact Hausdorff. The Stone–Čech construction can be performed for more general spaces X, but in that case the map X → βX need not be a homeomorphism to the image of X (and sometimes is not even injective). As is usual for universal constructions like this, the extension property makes β a functor from Top (the category of topological spaces) to CHaus (the category of compact Hausdorff spaces). Further, if we let U be the inclusion functor from CHaus into Top, maps from βX to K (for K in CHaus) correspond bijectively to maps from X to UK (by considering their restriction to X and using the universal property of βX). i.e. Hom(βX, K) ≅ Hom(X, UK), which means that β is left adjoint to U. This implies that CHaus is a reflective subcategory of Top with reflector β. Examples If X is a compact Hausdorff space, then it coincides with its Stone–Čech compactification. The Stone–Čech compactification of the first uncountable ordinal , with the order topology, is the ordinal . The Stone–Čech compactification of the deleted Tychonoff plank is the Tychonoff plank. Constructions Construction using products One attempt to construct the Stone–Čech compactification of X is to take the closure of the image of X in where the product is over all maps from X to compact Hausdorff spaces K (or, equivalently, the image of X by the right Kan extension of the identity functor of the category CHaus of compact Hausdorff spaces along the inclusion functor of CHaus into the category Top of general topological spaces). By Tychonoff's theorem this product of compact spaces is compact, and the closure of X in this space is therefore also compact. This works intuitively but fails for the technical reason that the collection of all such maps is a proper class rather than a set. There are several ways to modify this idea to make it work; for example, one can restrict the compact Hausdorff spaces K to have underlying set P(P(X)) (the power set of the power set of X), which is sufficiently large that it has cardinality at least equal to that of every compact Hausdorff space to which X can be mapped with dense image. Construction using the unit interval One way of constructing βX is to let C be the set of all continuous functions from X into [0, 1] and consider the map where This may be seen to be a continuous map onto its image, if [0, 1]C is given the product topology. By Tychonoff's theorem we have that [0, 1]C is compact since [0, 1] is. Consequently, the closure of X in [0, 1]C is a compactification of X. In fact, this closure is the Stone–Čech compactification. To verify this, we just need to verify that the closure satisfies the appropriate universal property. We do this first for K = [0, 1], where the desired extension of f : X → [0, 1] is just the projection onto the f coordinate in [0, 1]C. In order to then get this for general compact Hausdorff K we use the above to note that K can be embedded in some cube, extend each of the coordinate functions and then take the product of these extensions. The special property of the unit interval needed for this construction to work is that it is a cogenerator of the category of compact Hausdorff spaces: this means that if A and B are compact Hausdorff spaces, and f and g are distinct maps from A to B, then there is a map h : B → [0, 1] such that hf and hg are distinct. Any other cogenerator (or cogenerating set) can be used in this construction. Construction using ultrafilters Alternatively, if is discrete, then it is possible to construct as the set of all ultrafilters on with the elements of corresponding to the principal ultrafilters. The topology on the set of ultrafilters, known as the , is generated by sets of the form for a subset of Again we verify the universal property: For with compact Hausdorff and an ultrafilter on we have an ultrafilter base on the pushforward of This has a unique limit because is compact Hausdorff, say and we define This may be verified to be a continuous extension of Equivalently, one can take the Stone space of the complete Boolean algebra of all subsets of as the Stone–Čech compactification. This is really the same construction, as the Stone space of this Boolean algebra is the set of ultrafilters (or equivalently prime ideals, or homomorphisms to the 2-element Boolean algebra) of the Boolean algebra, which is the same as the set of ultrafilters on The construction can be generalized to arbitrary Tychonoff spaces by using maximal filters of zero sets instead of ultrafilters. (Filters of closed sets suffice if the space is normal.) Construction using C-algebras The Stone–Čech compactification is naturally homeomorphic to the spectrum of Cb(X). Here Cb(X) denotes the C-algebra of all continuous bounded complex-valued functions on X with sup-norm. Notice that Cb(X) is canonically isomorphic to the multiplier algebra of C0(X). The Stone–Čech compactification of the natural numbers In the case where X is locally compact, e.g. N or R, the image of X forms an open subset of βX, or indeed of any compactification, (this is also a necessary condition, as an open subset of a compact Hausdorff space is locally compact). In this case one often studies the remainder of the space, βX \ X. This is a closed subset of βX, and so is compact. We consider N with its discrete topology and write βN \ N = N* (but this does not appear to be standard notation for general X). As explained above, one can view βN as the set of ultrafilters on N, with the topology generated by sets of the form for U a subset of N. The set N corresponds to the set of principal ultrafilters, and the set N* to the set of free ultrafilters. The study of βN, and in particular N, is a major area of modern set-theoretic topology. The major results motivating this are Parovicenko's theorems, essentially characterising its behaviour under the assumption of the continuum hypothesis. These state: Every compact Hausdorff space of weight at most (see Aleph number) is the continuous image of N (this does not need the continuum hypothesis, but is less interesting in its absence). If the continuum hypothesis holds then N* is the unique Parovicenko space, up to isomorphism. These were originally proved by considering Boolean algebras and applying Stone duality. Jan van Mill has described βN as a "three headed monster"—the three heads being a smiling and friendly head (the behaviour under the assumption of the continuum hypothesis), the ugly head of independence which constantly tries to confuse you (determining what behaviour is possible in different models of set theory), and the third head is the smallest of all (what you can prove about it in ZFC). It has relatively recently been observed that this characterisation isn't quite right—there is in fact a fourth head of βN, in which forcing axioms and Ramsey type axioms give properties of βN almost diametrically opposed to those under the continuum hypothesis, giving very few maps from N* indeed. Examples of these axioms include the combination of Martin's axiom and the Open colouring axiom which, for example, prove that (N)2 ≠ N, while the continuum hypothesis implies the opposite. An application: the dual space of the space of bounded sequences of reals The Stone–Čech compactification βN can be used to characterize (the Banach space of all bounded sequences in the scalar field R or C, with supremum norm) and its dual space. Given a bounded sequence there exists a closed ball B in the scalar field that contains the image of . is then a function from N to B. Since N is discrete and B is compact and Hausdorff, a is continuous. According to the universal property, there exists a unique extension βa : βN → B. This extension does not depend on the ball B we consider. We have defined an extension map from the space of bounded scalar valued sequences to the space of continuous functions over βN. This map is bijective since every function in C(βN) must be bounded and can then be restricted to a bounded scalar sequence. If we further consider both spaces with the sup norm the extension map becomes an isometry. Indeed, if in the construction above we take the smallest possible ball B, we see that the sup norm of the extended sequence does not grow (although the image of the extended function can be bigger). Thus, can be identified with C(βN). This allows us to use the Riesz representation theorem and find that the dual space of can be identified with the space of finite Borel measures on βN. Finally, it should be noticed that this technique generalizes to the L∞ space of an arbitrary measure space X. However, instead of simply considering the space βX of ultrafilters on X, the right way to generalize this construction is to consider the Stone space Y of the measure algebra of X: the spaces C(Y) and L∞(X) are isomorphic as C*-algebras as long as X satisfies a reasonable finiteness condition (that any set of positive measure contains a subset of finite positive measure). A monoid operation on the Stone–Čech compactification of the naturals The natural numbers form a monoid under addition. It turns out that this operation can be extended (generally in more than one way, but uniquely under a further condition) to βN, turning this space also into a monoid, though rather surprisingly a non-commutative one. For any subset, A, of N and a positive integer n in N, we define Given two ultrafilters F and G on N, we define their sum by it can be checked that this is again an ultrafilter, and that the operation + is associative (but not commutative) on βN and extends the addition on N; 0 serves as a neutral element for the operation + on βN. The operation is also right-continuous, in the sense that for every ultrafilter F, the map is continuous. More generally, if S is a semigroup with the discrete topology, the operation of S can be extended to βS, getting a right-continuous associative operation. See also Notes References External links Stone-Čech Compactification at Planet Math Dror Bar-Natan, Ultrafilters, Compactness, and the Stone–Čech compactification General topology Compactification (mathematics)	Stone–Čech compactification	[ "Mathematics" ]	3,091	[ "General topology", "Topology", "Compactification (mathematics)" ]
52,940	https://en.wikipedia.org/wiki/Marcus%20Manilius	Marcus Manilius () originally hailing from Syria, was a Roman poet, astrologer, and author of a poem in five books called Astronomica. The Astronomica The author of Astronomica is neither quoted nor mentioned by any ancient writer. Even his name is uncertain, but it was probably Marcus Manilius; in the earlier books the author is anonymous, the later give Manilius, Manlius, Mallius. The poem itself implies that the writer lived under Augustus or Tiberius, and that he was a citizen of and resident in Rome, suggesting that Manilius wrote the work during the 20s CE. According to the early 18th-century classicist Richard Bentley, he was an Asiatic Greek; according to the 19th-century classicist Fridericus Jacob, an African. His work is one of great learning; he had studied his subject in the best writers, and generally represents the most advanced views of the ancients?????? on astronomy (or rather astrology). Manilius frequently imitates Lucretius. Although his diction presents some peculiarities, the style is metrically correct, and he could write neat and witty hexameters. The astrological systems of houses, linking human affairs with the circuit of the zodiac, have evolved over the centuries, but they make their first appearance in Astronomica. The earliest datable surviving horoscope that uses houses in its interpretation is slightly earlier, . Claudius Ptolemy (100–170 CE) almost completely ignored houses (templa as Manilius calls them) in his astrological text, Tetrabiblos. A. E. Housman edition The work is also known for being the subject of the most salient of A. E. Housman's scholarly endeavours; his annotated edition he considered his magnum opus, and when the fifth and final volume was published in 1930, 27 years after the first, he remarked he would now "do nothing forever and ever." He nonetheless also thought that it was an obscure pursuit; to an American correspondent he wrote, "I do not send you a copy, as it would shock you very much; it is so dull that few professed scholars can read it, probably not one in the whole United States." It remains a source of bafflement to many that Housman should have elected to abandon (as they thought) a poet like Propertius in favour of Manilius. For example, the critic Edmund Wilson pondered the countless hours Housman devoted to Manilius and concluded, "Certainly it is the spectacle of a mind of remarkable penetration and vigor, of uncommon sensibility and intensity, condemning itself to duties which prevent it from rising to its full height." This is, however, to misunderstand the technical task of editing a classical text. In the same vein, Harry Eyres interpreted it as "what you could see as an act of self-punishment" that so many years were devoted to "a minor Roman versifier whose long didactic poem on astrology must rank as one of the most obscure in the entire annals of poetry". Honors An impact crater on the Moon is named after him: Manilius is located in the Mare Vaporum. References Editions J. R. Bram (ed.), Ancient Astrology: Theory and Practice. Matheseos Libri VIII by Firmicus Maternus (Park Ridge, 1975). Manilio Il poema degli astri (Astronomica), testo critico a cura di E. Flores, traduzione di Ricardo Scarcia, commento a cura di S. Feraboli e R. Scarcia, 2 vols. (Milano, 1996–2001). Wolfgang Hübner (ed.), Manilius, Astronomica, Buch V (2 Bde) (Berlin/New York: De Gruyter, 2010) (Sammlung wissenschaftlicher Commentare). Further reading Colborn, Robert. 2013. "Solving Problems With Acrostics: Manilius Dates Germanicus." Classical Quarterly 63.1: 450–452. Fratantuono, Lee Michael. 2012. "Andromeda, Perseus, and the End of the Astronomica." Maia: rivista di letterature classiche 64.2: 305–315. Glauthier, Patrick. 2017. "Repurposing the Stars: Manilius, Astronomica 1, and the Aratean Tradition." American Journal of Philology 138.2: 267–303. Goold, G. P. 1961. "A Greek Professorial Circle at Rome." Transactions and Proceedings of the American Philological Association 92: 168–192. Green, Steven J. 2014. Disclosure and Discretion in Roman Astrology: Manilius and his Augustan Contemporaries. Oxford; New York: Oxford University Press. Green, Steven J., and Katharina Volk, eds. 2011. Forgotten Stars: Rediscovering Manilius’ Astronomica. Oxford: Oxford Univ. Press. Habinek, Thomas N. 2007. "Probing the Entrails of the Universe: Astrology as Bodily Knowledge in Manilius’ Astronomica." In Ordering Knowledge in the Roman Empire. Edited by Jason König and Tim Whitmarsh, 229–240. Cambridge, UK: Cambridge Univ. Press. Komorowska, Joanna. 2016. "Ad Duo Templa Precor: Poetry, Astronomy, and the Authorial Persona in Manilius' Astronomica, I." Eirene 52: 341–358. Lapidge, Michael. 1989. "Stoic Cosmology and Roman Literature, First to Third Centuries A.D." Aufstieg und Niedergang der römischen Welt. Edited by Hildegard Temporini and Wolfgang Haase, 1379–1429. Berlin: de Gruyter. MacGregor, Alexander. 2004. "Which Art in Heaven: The Sphere of Manilius." Illinois Classical Studies 29: 143–157. Neuburg, Matt. 1993. "Hitch Your Wagon to a Star: Manilius and His Two Addressees." In Mega nepios: Il destinatario nell'epos didascalico/The Addressee in Didactic Epic. Edited by Alessandro Schiesaro, Philip Mitsis, and Jenny Strauss Clay, 243–282. Materiali e Discussioni per l'Analisi dei Testi Classici 31. Pisa: Giardini. Volk, Katharina. 2009. Manilius and His Intellectual Background. Oxford: Oxford Univ. Press. Volk, Katharina. 2002. The Poetics of Latin Didactic: Lucretius, Vergil, Ovid, Manilius. Oxford: Oxford Univ. Press. External links The Astronomica of Manilius at The Latin Library Die Astronomica of Manilius at Opolska Biblioteka Cyfrowa A. E. Housman's introduction M. Manilii astronomicon, 5 vols., A. E. Housman (ed.), Londinii, apud Grant Richards, 1903–30, vol. 1, vol. 2, vol. 3, vol. 4, vol. 5. Year of birth unknown Year of death unknown Ancient Roman astrologers Silver Age Latin writers 1st-century Roman poets 1st-century Syrian people Syrian poets Astrologers Syrian writers Manilii	Marcus Manilius	[ "Astronomy" ]	1,568	[ "People associated with astronomy", "Astrologers" ]
52,991	https://en.wikipedia.org/wiki/Pressure%20cooker	A pressure cooker is a sealed vessel for cooking food with the use of high pressure steam and water or a water-based liquid, a process called pressure cooking. The high pressure limits boiling and creates higher temperatures not possible at lower pressures, allowing food to be cooked faster than at normal pressure. The prototype of the modern pressure cooker was the steam digester invented in the seventeenth century by the physicist Denis Papin. It works by expelling air from the vessel and trapping steam produced from the boiling liquid. This is used to raise the internal pressure up to one atmosphere above ambient and gives higher cooking temperatures between . Together with high thermal heat transfer from steam it permits cooking in between a half and a quarter the time of conventional boiling as well as saving considerable energy. Almost any food that can be cooked in steam or water-based liquids can be cooked in a pressure cooker. Modern pressure cookers have many safety features to prevent the pressure cooker from holding too much pressure causing an explosion. After cooking, the steam pressure is lowered back to ambient atmospheric pressure so that the vessel can be opened. On all modern devices, a safety lock prevents opening while under pressure. According to the New York Times Magazine, 37% of U.S. households owned at least one pressure cooker in 1950. By 2011, that rate dropped to only 20%. Part of the decline has been attributed to fear of explosion (although this is extremely rare with modern pressure cookers) along with competition from other fast cooking devices such as the microwave oven. However, third-generation pressure cookers have many more safety features and digital temperature control, do not vent steam during cooking, and are quieter and more efficient, and these conveniences have helped make pressure cooking more popular. History In 1679, French physicist Denis Papin, better known for his studies on steam, invented the steam digester in an attempt to reduce the cooking time of food. His airtight cooker used steam pressure to raise the water's boiling point, thus cooking food more quickly. In 1681 Papin presented his invention to the Royal Society of London as a scientific study; he was later elected as a member. In 1864, Georg Gutbrod of Stuttgart began manufacturing pressure cookers made of tinned cast iron. Although the concept of cooking with pressurized steam had been known for two centuries, the term “pressure cooker” was not commonly used until the early 20th century. The earliest citation of the phrase given in the Oxford English Dictionary is from a Lincoln, Nebraska, newspaper in 1914. However, the Dictionary editors apparently overlooked or did not have access to certain Colorado newspapers from a few years earlier than that. As early as 1910, the inventor Zeno E. Crook founded a business called “The Pressure Cooker Company” in Denver, Colorado. Crook had developed an aluminum cooker of a size practical for home use, and soon began marketing it to communities in the high country of Colorado, where the device proved to be well suited for use in high-altitude cooking. In many of these communities, Crook's pressure cooker was hailed as a marvelous new invention, until 1918, when Popular Science Monthly broke the news that this “invention” was actually more than 200 years old. In 1918, Spain granted a patent for the pressure cooker to José Alix Martínez from Zaragoza. Martínez named it the olla exprés, literally "express cooking pot", under patent number 71143 in the Boletín Oficial de la Propiedad Industrial. In 1924, the first pressure cooking pot recipe book was published, written by José Alix and titled "360 fórmulas de cocina Para guisar con la 'olla expres'", or 360 recipes for cooking with a pressure cooker. In 1935, the Automa pressure cooker was introduced. Mountaineers attempting to climb Mount Everest took it along with them to cook in higher altitudes. In 1938, Alfred Vischer presented his invention, the Flex-Seal Speed Cooker, in New York City. Vischer's pressure cooker quickly gained popularity, and its success led to competition among American and European manufacturers. At the 1939 New York World's Fair, the National Pressure Cooker Company, later renamed National Presto Industries, introduced its own pressure cooker. First generation Also known as "old type" pressure cookers, these operate with a weight-modified or "jiggler" valve, which releases pressure during operation. Some people consider them loud because the valve rattles as excess steam is released. Older pressure cookers typically offered only one pressure level, but from the 1960s onwards some allow the operator to change the weight of the valve, thus changing the pressure. Today most pressure cookers are variations on the first-generation cookers, with the addition of new safety features such as a mechanism that prevents the cooker from being opened until it is entirely depressurized. Second generation These operate with a spring-loaded valve that is often hidden from view in a proprietary mechanism. This generation is characterized by two or more pressure settings. Some of these pressure cookers do not release any steam during operation (non-venting) and instead use a rising indicator with markings to show the pressure level. These only release steam when the pan is opened, or as a safety precaution if the heat source is not reduced enough when the pan reaches the required cooking pressure. Others use a dial that the operator can advance by a few clicks (which alters the spring tension) to change the pressure setting or release pressure; these release steam during operation (venting). Third generation "electric pressure cookers" After the stove-top pressure cookers came the electric pressure cookers in 1991, called the "third generation" pressure cookers. These include an electric heat source that is automatically regulated to maintain the operating temperature and pressure. They also include a spring-loaded valve (as described above) and are typically non venting during cooking. An electric pressure cooker integrates a timer. Depending on cooking control capability, there are three generations of electric pressure cookers: First-generation electric, with mechanical timer. There is no delayed cooking capability. Second-generation electric, with digital controller. Delayed cooking becomes possible and the controller shows a countdown timer when working pressure is reached. Third-generation electric, with smart programming, which includes pre-set cooking times and settings based on heating intensity, temperature, pressure and duration. Some pressure cookers are multifunctional (multicookers): pressure cooker, saute/browning, slow cooker, rice cooker, egg cooker, yogurt maker, steamer, sous vide, canner, and stockpot warmer that can also be used to keep cooked food warm. Since 2018, with the release of the Ninja Foodi pressure cooker, which was the first pressure cooker that could also air fry, several other pressure cooker manufacturers, including Instant Pot, have come out with their own pressure cookers that can air fry, which are now known as air fryer pressure cookers. Air fryer pressure cookers generally have two separate lids, one for pressure cooking, and one for air frying. Theory At standard pressure the boiling point of water is . With any food containing or cooked with water, once the temperature reaches the boiling point, any excess heat causes some of the water to vaporize into steam efficiently carrying away heat keeping the food temperature at 100 °C. In a sealed pressure cooker, as the water boils, the steam is trapped in the cooker which raises the pressure. However, the boiling point of water increases with pressure resulting in superheated water. The equation for the pressure, temperature and volume of the steam is given by the ideal gas law: or where , and are the pressure, volume and temperature; is the amount of substance; and is the ideal gas constant. In a sealed pressure cooker the volume and amount of steam is fixed, so the temperature can be controlled either directly or by setting the pressure, such as with a pressure release valve. For example, if the pressure reaches 1 bar or above the existing atmospheric pressure, the water will have reached a temperature of approximately which cooks the food much faster. Pressure cookers also use steam and water to rapidly transfer the heat to the food and all parts of the vessel. While compared to an oven, a pressure cooker's 120 °C is not particularly high, ovens contain air which is subject to thermal boundary layer effects which greatly slows heating, whereas pressure cookers flush air from the cooking vessel during warm up and replace it with hot steam. For items not placed within the liquid, as this steam condenses on the food it transfers water's latent heat of vaporization, which is extremely large (2.275 kJ/g), to the surface, rapidly bringing the surface of the food up to cooking temperature. Because the steam condenses and drips away, no significant boundary layer forms and heat transfer is exceptionally efficient, and food heats much faster and more evenly. However some recipes require browning to develop flavors as during roasting or frying. Higher temperatures are attainable with conventional cooking where the surface of the food can dry out. Such browning occurs via the Maillard reaction, at temperatures higher than the roughly achieved in pressure cooking. Because those temperatures are not reached in pressure cooking, foods are generally browned by searing them, either in the open pressure cooker or another pan beforehand. High altitudes A pressure cooker can be used to compensate for lower atmospheric pressure at high elevations. The boiling point of water drops by approximately 1 °C per every 294 metres of altitude (see: High-altitude cooking), causing the boiling point of water to be significantly below the at standard pressure. This is problematic because temperatures above roughly 90 °C are necessary to cook many common vegetables in a reasonable time. For example, on the summit of Everest (), the boiling point of water would be only . Without the use of a pressure cooker, many boiled foods may remain undercooked, as described in Charles Darwin's The Voyage of the Beagle (chapter XV, March 20, 1835): When pressure cooking at high altitudes, cooking times need to be increased by approximately 5% for every above elevation. Since the regulators work off the pressure differential between interior and ambient pressure, the absolute pressure in the interior of a pressure cooker will always be lower at higher altitudes. Weight is a concern with backpackers, so mountaineering pressure cookers are designed to operate at a lower differential pressure than stove-top units. This enables them to use thinner, and therefore lighter materials. Generally, the goal is to raise the cooking temperature enough to make cooking possible and to conserve fuel by reducing heat lost through boiling. Lightweight pressure cookers as small as weighing are available for mountain climbers. Sherpas often use pressure cookers in base camp. Health benefits Some food toxins can be reduced by pressure cooking. A Korean study of aflatoxins in rice (associated with Aspergillus fungus) showed that pressure cooking was capable of reducing aflatoxin concentrations to 32% of the amount in the uncooked rice, compared to 77% from ordinary cooking. Design Pressure cookers employ one or more regulators to control the pressure/temperature. All types have a calibrated pressure relief valve, as well as one or more emergency valves. With the simplest types, once the desired pressure is reached, the valve opens, and steam escapes cooling the vessel and limiting the temperature. More advanced stovetop models have pressure indicators that permit the user to adjust the heat to prevent the steam from escaping. Third generation types automatically measure the state of the vessel and control the power so as to not release steam in operation. Capacity Pressure cookers are available in different capacities for cooking larger or smaller amounts, with 6 litres' capacity being common. The maximum capacity of food is less than the advertised capacity because pressure cookers can only be filled up to 2/3 full, depending on ingredients and liquid (see Safety features section). Pan Metal pan body Pan handles, usually one each on opposite ends, for carrying the cooker with both hands Because of the forces that pressure cookers must withstand, they are usually heavier than conventional pots of similar size. The increased weight of conventional pressure cookers makes them unsuitable for applications in which saving weight is a priority, such as camping. Nonetheless, small, lightweight pressure cookers are available for mountain climbers (see High altitudes). Lid Lids usually have a number of features: Lid handle, usually with a locking device button or slider that "clicks" shut and prevents removal while cooking Gasket (also known as a "sealing ring") that seals the cooker airtight Steam vent with a pressure regulator on top (either a weight or spring device) that maintains the pressure level in the pan Pressure indicator pin, for showing the presence or absence of any pressure, however slight Safety devices on the lid (typically over-pressure and/or over-temperature pressure release valves) Gasket A gasket or sealing ring, made from either rubber or silicone, forms a gas-tight seal that does not allow air or steam to escape between the lid and pan. Normally, the only way steam can escape is through a regulator on the lid while the cooker is pressurized. If the regulator becomes blocked, a safety valve provides a backup escape route for steam. To seal the gasket there are several main methods used. Each determines the design of the pressure cooker: The twist-on design has slots on the lid engaging with flanges on the body, similar to a lid on a glass jar, that works by placing the lid on the pot and twisting it about 30° to lock it in place. A common modern design, it has easily implemented locking features that prevent the removal of the lid while under pressure. The center screw design has a bar that is slotted in place over the lid and a screw tightened downward to hold the lid on. Though an older design, it is still produced due to its ease of construction and simplicity. The bolt-down design has flanges on both its lid and its body for bolts to be passed through, and usually uses wingnuts that hinge on the body and so are never fully removed from the cooker; this sealing design is typically used for larger units such as canning retorts and autoclaves. It is very simple to produce, and it can seal with simple and inexpensive gaskets. The internally fitted lid design employs an oval lid that is placed inside and presses outward; the user inserts the lid at an angle, then turns the lid to align it with the pot opening on top because the lid is larger than the opening. A spring arrangement holds the lid in place until the pressure forms and holds the lid tightly against the body, preventing removal until the pressure is released. Gaskets (sealing rings) require special care when cleaning (e.g., not washed with kitchen knives), unlike a standard lid for a saucepan. Food debris, fats, and oils must be cleaned from the gasket after every use. Gasket/sealing rings need replacing with a new one about once a year (or sooner if it is damaged e.g. a small split). A very dry gasket can make it difficult or impossible to close the lid. Smearing the gasket sparingly with vegetable oil alleviates this problem (using too much vegetable oil can make the gasket swell and prevent it sealing properly). A gasket that has lost its flexibility makes bringing the cooker up to pressure difficult as steam can escape before sufficient pressure is generated to provide an adequate seal; this is usually a sign that the gasket needs replacing with a new one. Oiling the gasket with vegetable oil may alleviate the problem temporarily, but a new gasket is often required. Pressure cooker manufacturers sell replacement gaskets and recommend their replacement at regular intervals e.g. annually. If the pressure cooker has not been used for a long time, the gasket and other rubber or silicone parts will dry out and will likely need replacing. Safety features Early pressure cookers equipped with only a primary safety valve risked explosion from food blocking the release valve. On modern pressure cookers, food residues blocking the steam vent or the liquid boiling dry will trigger additional safety devices. Modern pressure cookers sold from reputable manufacturers have sufficient safety features to prevent the pressure cooker itself from exploding. When excess pressure is released by a safety mechanism, debris of food being cooked may also be ejected with the steam, which is loud and forceful. This can be avoided if the pressure cooker is regularly cleaned and maintained in accordance with the manufacturer's instructions and never overfilled with food and/or liquid. Modern pressure cookers typically have two or three redundant safety valves and additional safety features, such as an interlock lid that prevents the user from opening the lid when the internal pressure exceeds atmospheric pressure, preventing accidents from a sudden release of hot liquid, steam and food. If safety mechanisms are not correctly in place, the cooker will not pressurize the contents. Pressure cookers should be operated only after reading the instruction manual, to ensure correct usage. Pressure cooker failure is dangerous: a large quantity of scalding steam and water will be forcefully ejected and if the lid separates it may be propelled with considerable force. Some cookers with an internally fitted lid may be particularly dangerous upon failure as the lid fits tighter with increasing pressure, preventing the lid from deforming and venting around the edges. Due to these dangers pressure cookers are generally over-engineered in a safety regard and some countries even have regulations to prevent the sale of non-compliant cookers. For first generation pressure cookers with a weighted valve or "jiggler", the primary safety valve or regulator is usually a weighted stopper, commonly called "the rocker" or "vent weight". This weighted stopper is lifted by the steam pressure, allowing excess pressure to be released. There is a backup pressure release mechanism that releases pressure quickly if the primary pressure release mechanism fails (e.g., food jams the steam discharge path). One such method is a hole in the lid that is blocked by a low melting point alloy plug and another is a rubber grommet with a metal insert at the center. At a sufficiently high pressure, the grommet will distort and the insert will blow out of its mounting hole to release pressure. If the pressure continues to increase, the grommet itself will blow out to release pressure. These safety devices usually require replacement when activated by excess pressure. Newer pressure cookers may have a self-resettable spring device, fixed onto the lid, that releases excess pressure. On second generation pressure cookers, a common safety feature is the gasket, which expands to release excess pressure downward between the lid and the pot. This release of excess pressure is forceful and sufficient to extinguish the flame of a gas stove. Pressure cookers sold in the European Union (EU) must comply with the Pressure Equipment Directive. Maximum fill levels The recommended maximum fill levels of food/liquid avoids blockage of the steam valve or developing excess pressure: two-thirds full with solid food, half full for liquids and foods that foam and froth (e.g., rice, pasta; adding a tablespoon of cooking oil minimizes foaming), and no more than one-third full for pulses (e.g., lentils). Accessories Steamer basket Trivet for keeping the steamer basket above liquid Metal divider, for separating different foods in the steamer basket e.g. vegetables Inner pot, for pot-in-pot pressure steaming Materials Pressure cookers are typically made of aluminum (aluminium) or stainless steel. Aluminum pressure cookers may be stamped, polished, or anodized, but all are unsuitable for the dishwasher. They are cheaper, but the aluminum is reactive to acidic foods, whose flavors are changed in the reactions, and are less durable than stainless steel pressure cookers. Some aluminum pressure cookers from Afghanistan are known to be contaminated with lead and imported pots were responsible for the lead poisoning of Afghani refugees in Washington state in 2019. Higher-quality stainless steel pressure cookers are made with heavy, three-layer, or copper-clad bottoms (heat spreader) for uniform heating because stainless steel has lower thermal conductivity. Most modern stainless steel cookers are dishwasher safe, although some manufacturers may recommend washing by hand. Some pressure cookers have a non-stick interior. Operation Liquid Pressure cooking always requires a water-based liquid to generate the steam to raise the pressure within the cooker. Pressure cooking cannot be used for cooking methods that produce little steam such as roasting, pan frying, or deep frying. A minimum quantity of liquid is required to create and maintain pressure, as indicated in the manufacturer's instruction manual. For venting cookers more liquid is required for longer cooking times. This is not desirable for food requiring much less liquid, but recipes and books for pressure cookers take this into account. Assembling Food is placed inside the pressure cooker with a small amount of water or other liquid such as stock. Food is either cooked in the liquid or above the liquid for steaming; the latter method prevents the transfer of flavors from the liquid. Sauces which contain starch thickeners can tend to burn onto the interior base of the pressure cooker which may prevent the cooker from reaching operating pressure. Because of this issue, sauces may require thickening or reduction after pressure cooking. With pot in pot pressure cooking, some or all of the food is placed in an elevated pot on a trivet above water or another food item which generates the steam. This permits the cooking of multiple foods separately, and allows for minimal water mixed with the food, and thicker sauces, which would otherwise scorch onto the bottom of the pan. Bringing to pressure The lid is closed, the pressure setting is chosen and the pressure cooker is heated to boil the liquid. The cooker fills with steam and vents air. As the internal temperature rises, the pressure rises until it reaches the desired gauge pressure. It usually takes several minutes for the pressure cooker to reach the selected pressure level. It can take 10 minutes or longer depending on the quantity of food, the temperature of the food (cold or frozen food delays pressurization), the amount of liquid, the power of the heat source, and the size of the pressure cooker. There is typically a pop-up indicator that shows that the cooker has pressure inside, but it does not reliably signal that the cooker has reached the selected pressure. The pop-up indicator shows the state of the interlock which prevents the lid from being opened while there is any internal pressure. Manufacturers may use their own terminology for this, such as calling it a "locking indicator." Timing the recipe begins when the selected pressure/pressure is reached. Once the cooker reaches full pressure, the heat is lowered to maintain the pressure. With pressure cookers accurate timing is essential using an audible timer. With first generation designs, the pressure regulator weight begins levitating above its nozzle, allowing excess steam to escape. In second generation pressure cookers, either a relief valve subsequently opens, releasing steam to prevent the pressure from rising any further or a rod rises with markers to indicate the pressure level, without constantly venting steam. At this stage, the heat source is reduced to the lowest possible heat that still maintains pressure, as extra heat wastes energy and increases liquid loss. In third generation pressure cookers, the device will detect the vessel has reached the required cooking temperature/pressure and will maintain it for the programmed time, generally without further loss of steam. Recipes for foods using raising agents such as steamed puddings call for gentle pre-steaming, without pressure, in order to activate the raising agents prior to cooking and achieve a light, fluffy texture. Food containers Small containers such as plastic pudding containers can be used in a pressure cooker, if the containers (and any covering used) can withstand temperatures of and are not placed directly on the interior base. The containers can be used for cooking foods that are prone to burning on the base of the pressure cooker. A lid for the container may be used if the lid allows some steam to come into contact with the food and the lid is securely fitted; an example is foil or greaseproof paper, pleated in the center and tied securely with string. Containers that are cracked or have otherwise sustained damage are not suitable. Cooking time is longer when using covered containers because the food is not in direct contact with the steam. Since non-metal containers are poorer heat conductors, the type of container material stated in the recipe cannot be substituted without affecting the outcome. For example, if the recipe time is calculated using a stainless steel container and a plastic container is used instead, the recipe will be undercooked, unless the cooking time is increased. Containers with thicker sides, e.g., oven-proof glass or ceramic containers, which are slower to conduct heat, will add about 10 minutes to the cooking time. Liquid can be added inside the container when pressure cooking foods such as rice, which need to absorb liquid in order to cook properly. Pre-frying ingredients The flavor of some foods, such as meat and onions, can be improved by gently cooking with a little pre-heated cooking oil, butter or other fat in the open pressure cooker over medium heat for stove-top models (unless the manufacturer advises against this) before pressure cooking, while avoiding overheating the empty pressure cooker not heating the empty cooker with the lid and gasket in place to avoid damage. Electric pressure cookers usually have a "saute" or "brown" option for frying ingredients. The pressure cooker needs to cool briefly before adding liquid; otherwise some of the liquid will evaporate instantly, possibly leaving insufficient liquid for the entire pressure cooking time; if deglazing the pan, more liquid may need to be added. Pressure release methods After cooking, there are three ways of releasing the pressure, either quickly or slowly, before the lid can be opened. Recipes for pressure cookers state which release method is required at the end of the cooking time for proper results. Failure to follow the recommendation may result in food that is under-cooked or over-cooked. To avoid opening the pressure cooker too often while cooking different vegetables with varying cooking times, the vegetables that take longer to cook can be cut into smaller pieces and vegetables that cook faster can be cut into larger pieces. To inspect the food, the pressure cooker needs to be opened, which halts the cooking process. With a conventional saucepan, this can be done in a matter of seconds by visually inspecting the food. Manual, normal, regular, or automatic release This method is sometimes called a quick release, not to be confused with the cold water release (mentioned below). It involves the quick release of vapor by gradually lifting (or removing) the valve, pushing a button, or turning a dial. It is most suitable to interrupt cooking to add food that cooks faster than what is already in the cooker. For example, since meat takes longer to cook than vegetables, it is necessary to add vegetables to stew later so that it will cook only for the last few minutes. Releasing the steam with care avoids the risk of being scalded by the rapid release of hot steam. This release method is not suitable for foods that foam and froth while cooking; the hot contents might spray outwards due to the pressure released from the steam vent. Pressure cookers should be operated with caution when releasing vapour through the valve, especially while cooking foamy foods and liquids (lentils, beans, grains, milk, gravy, etc.) This release method takes about two minutes to release the pressure before the lid can be opened. Natural release The natural release method allows the pressure to drop slowly. This is achieved by removing the pressure cooker from the heat source and allowing the pressure to lower without action. It takes approximately 10 to 15 minutes (possibly longer) for the pressure to disappear before the lid can be opened. On many pressure cookers, a coloured indicator pin will drop when the pressure has gone. This natural release method is recommended for foods that foam and froth during cooking, such as rice, legumes, or recipes with raising agents such as steamed puddings. The texture and tenderness of meat cooked in a pressure cooker can be improved by using the natural release method. The natural release method finishes cooking foods or recipes that have longer cooking times because the inside of the pressure cooker stays hot. This method is not recommended for foods that require very short cooking times, otherwise the food overcooks. Cold water quick release This method is the fastest way of releasing pressure with portable pressure cookers, but can be dangerous if performed incorrectly. Hence it is safer to release pressure by using the other methods. The manufacturer's instruction book may advise against the cold water release or require it to be performed differently. The cold water release method involves using slow running cold tap water, over the edge of the pressure cooker lid, being careful to avoid the steam vent or any other valves or outlets, and never immersing the pressure cooker under water, otherwise steam can be ejected from under the lid, which could cause scalding injury to the user; also the pressure cooker lid can be permanently damaged by an internal vacuum if water gets sucked into the pressure cooker, since the incoming water blocks the inrush of air. The cold water release is most suitable for foods with short cooking times. It takes about 20 seconds for the cooker to cool down enough to lower the pressure so that it can be safely opened. This method is not suitable for electric pressure cookers, as they are not immersible. This type of pressure cooker cannot be opened with a cold water quick-release method. The cold water release method is not recommended when cooking pulses e.g. red kidney beans, as the sudden release of pressure can cause the bean to burst its skin. Pressure settings Most pressure cookers have a cooking (operating) pressure setting between 0.8–1 bar (11.6–15 psi) (gauge) so the pressure cooker operates at 1.8 to 2.0 bar (absolute). The standard cooking pressure of 15 psi gauge was determined by the United States Department of Agriculture in 1917. At this pressure, water boils at (described in vapour pressure of water article). The higher temperature causes food to cook faster; cooking times can typically be reduced to one-third of the time for conventional cooking methods. The actual cooking time also depends on the pressure release method used after timing (see Pressure release methods for details) and the thickness and density of the food, since thicker (and denser) foods take longer to cook. Meat joints and some other foods like sponge puddings and Christmas puddings are typically timed according to their weight. Frozen foods need extra cooking time to allow for thawing. When pressure cooking at 1 bar/15 psi (gauge), approximate cooking times are one minute for shredded cabbage, seven minutes for boiled potatoes (if cut small, not diced) and three minutes for fresh green beans. If the pressure is released naturally after timing (see Pressure release methods for details), cooking times are even shorter. Food cooks more quickly when cut into smaller pieces. Some recipes may require cooking at lower than 1 bar/15 psi (gauge) e.g. fresh vegetables, as these can easily overcook. Many pressure cookers have 2 or more selectable pressure settings or weights. Some pressure cookers have a lower or higher maximum pressure than 1 bar/15 psi (gauge) or can be adjusted to different pressures for some recipes; cooking times will increase or decrease accordingly. This is typically done by having different regulator weights or different pressure or temperature settings. Some pressure cookers operate at lower pressures than others. If the recipe is devised for a higher pressure and the pressure cooker does not reach that pressure, the cooking time can be increased to compensate. Efficiency Pressure cookers are considerably more expensive than conventional saucepans of the same size. The minimum quantity of water or liquid that keeps pressure cooker filled with steam is sufficient, so pressure cookers can use much less liquid than the amount required for conventional cooking. When less water or liquid is heated, the food reaches its cooking temperature faster and less energy is required than that of boiling, steaming, or oven cooking. It is also not necessary to immerse food in water. Additionally, with non venting pressure cookers, steam isn't continually escaping, thus evaporation losses are non existent once it has reached pressure. Overall, energy used by third generation pressure cookers can be as much as 70% lower than conventional pan cooking. Effect on food Pressure cooking requires much less water than conventional boiling, so food can be ready sooner. Because of this, vitamins and minerals are not leached (dissolved) away by water, as they would be if food were boiled in large amounts of water. Due to the shorter cooking time, vitamins are preserved relatively well during pressure cooking. Several foods can be cooked together in the pressure cooker, either for the same amount of time or added later for different times. Manufacturers provide steamer baskets to allow more foods to be cooked together inside the pressure cooker. Not only is this steam energy transmitted quickly to food, it is also transmitted rapidly to any micro-organisms that are present, easily killing even the deadliest types that are able to survive at the boiling point. Because of this enhanced germ killing ability, a pressure cooker can be used as an effective sanitizer for jam pots, glass baby bottles, or for water while camping. Foods unsuitable for pressure cooking Some foods are not recommended for pressure cooking. Foods such as noodles, pasta, cranberries, cereals and oatmeal can expand too much, froth and sputter, potentially blocking the steam vent and creating an unsafe condition. Use as weapons The appliance has been adapted as a crude type of bomb, which has been used in terrorist attacks. 2006 Mumbai train bombings 2010 Stockholm bombings (failed to explode) 2010 Times Square car bombing attempt (failed to explode) 2013 Boston Marathon bombing 2016 New York and New Jersey bombings 2017 Manchester Arena bombing Pressure cookers are allowed on airplanes but may be better in your checked luggage. Related devices An autoclave () is a type of pressure cooker used by laboratories and hospitals to sterilize equipment. A stovetop autoclave is essentially a higher-pressure cooker with a gauge, used as an autoclave in poorer areas. Pressure canners are large pressure cookers which have the capacity to hold jars used in home canning. Pressure canners are specifically designed for canning, whereas ordinary pressure cookers are not recommended for canning due to the risk of botulism poisoning. Pressure canners hold heat () and pressure for much longer than ordinary pressure cookers; these factors are a critical part of the total processing time required to destroy harmful microbes such as bacterial spores. Pressure fryers are used for deep fat frying under pressure, because ordinary pressure cookers are not suitable for pressure frying. An air fryer pressure cooker (not to be confused with a pressure fryer) is a recent combination of a pressure cooker and an air fryer, with two separate lids, one for pressure cooking and one for air frying. The air frying lid has a convection fan inside that allows it to air fry foods, similar to an air fryer oven. This innovation was popularized by the Ninja Foodi Pressure Cooker, marketed as the first pressure cooker that can crisp and air fry. A pressure oven is a recent combination of an oven and pressure cooker, usually as a countertop convection oven. Pressure ovens operate at low pressures, , compared to other pressure cookers. Their main function is as an enhanced oven or broiler for meat and poultry, avoiding drying. As such, they often include a rotisserie. Although having insufficient pressure for most conventional pressure cooking functions, they do also have non-pressure oven modes. See also List of cooking appliances Explanatory notes References External links Cooking appliances Cooking techniques Cooking vessels Culinary terminology French inventions Pressure	Pressure cooker	[ "Physics" ]	7,456	[ "Scalar physical quantities", "Mechanical quantities", "Physical quantities", "Pressure", "Wikipedia categories named after physical quantities" ]
52,994	https://en.wikipedia.org/wiki/Barr%20body	A Barr body (named after discoverer Murray Barr) or X-chromatin is an inactive X chromosome. In species with XY sex-determination (including humans), females typically have two X chromosomes, and one is rendered inactive in a process called lyonization. Errors in chromosome separation can also result in male and female individuals with extra X chromosomes. The Lyon hypothesis states that in cells with multiple X chromosomes, all but one are inactivated early in embryonic development in mammals. The X chromosomes that become inactivated are chosen randomly, except in marsupials and in some extra-embryonic tissues of some placental mammals, in which the X chromosome from the sperm is always deactivated. In humans with euploidy, a genotypical female (46, XX karyotype) has one Barr body per somatic cell nucleus, while a genotypical male (46, XY) has none. The Barr body can be seen in the interphase nucleus as a darkly staining small mass in contact with the nucleus membrane. Barr bodies can be seen in neutrophils at the rim of the nucleus. In humans with more than one X chromosome, the number of Barr bodies visible at interphase is always one fewer than the total number of X chromosomes. For example, people with Klinefelter syndrome (47, XXY) have a single Barr body, and people with a 47, XXX karyotype have two Barr bodies. Mechanism Someone with two X chromosomes (such as the majority of human females) has only one Barr body per somatic cell, while someone with one X chromosome (such as most human males) has none. Mammalian X-chromosome inactivation is initiated from the X inactivation centre or Xic, usually found near the centromere. The center contains twelve genes, seven of which code for proteins, five for untranslated RNAs, of which only two are known to play an active role in the X inactivation process, Xist and Tsix. The centre also appears to be important in chromosome counting: ensuring that random inactivation only takes place when two or more X-chromosomes are present. The provision of an extra artificial Xic in early embryogenesis can induce inactivation of the single X found in male cells. The roles of Xist and Tsix appear to be antagonistic. The loss of Tsix expression on the future inactive X chromosome results in an increase in levels of Xist around the Xic. Meanwhile, on the future active X Tsix levels are maintained; thus the levels of Xist remain low. This shift allows Xist to begin coating the future inactive chromosome, spreading out from the Xic. In non-random inactivation this choice appears to be fixed and current evidence suggests that the maternally inherited gene may be imprinted. Variations in Xi frequency have been reported with age, pregnancy, the use of oral contraceptives, fluctuations in menstrual cycle and neoplasia. It is thought that this constitutes the mechanism of choice, and allows downstream processes to establish the compact state of the Barr body. These changes include histone modifications, such as histone H3 methylation (i.e. H3K27me3 by PRC2 which is recruited by Xist) and histone H2A ubiquitination, as well as direct modification of the DNA itself, via the methylation of CpG sites. These changes help inactivate gene expression on the inactive X-chromosome and to bring about its compaction to form the Barr body. Reactivation of a Barr body is also possible, and has been seen in breast cancer patients. One study showed that the frequency of Barr bodies in breast carcinoma were significantly lower than in healthy controls, indicating reactivation of these once inactivated X chromosomes. Uses Barr Bodies in Ancient Samples: Observation and Relevance in Gender Identification of Extinct Species Barr bodies are condensed, inactive X chromosomes found in the somatic cells of female mammals. Their detection in ancient samples provides a powerful tool for gender identification in extinct species, offering insights into population dynamics, biology, and evolution. Recent advancements in histological and genomic techniques have made it possible to observe Barr bodies in ancient remains, including fossilized bones and tissues: Histological Staining: Techniques like hematoxylin-eosin staining can highlight chromatin structures, including Barr bodies, in well-preserved osteocytes embedded within bone matrix. Fluorescence Microscopy: Fluorescent dyes can differentiate X-chromosome condensation patterns, aiding in the visualization of Barr bodies. Integration with Genomic Tools: Techniques such as PaleoHi-C enable the spatial reconstruction of chromosomal interactions, confirming the presence of inactivated X chromosomes in ancient samples. In a notable example, Barr bodies were detected in osteocytes from ancient mammalian remains, demonstrating the potential of this approach for studying gender in extinct populations. Relevance in Gender Identification Population Studies: Identifying sex ratios in extinct species sheds light on social structures, reproductive strategies, and extinction dynamics. Reconstruction of Lifeways: Understanding the distribution of genders within ancient populations allows bioarchaeologists to analyze sex-based differences in diet, health, and activity patterns. Preservation of Chromatin: The discovery of intact Barr bodies in fossils underscores the potential for studying chromosomal and epigenetic features in ancient samples Limitations and Challenges Degradation of Samples: The fragmentation and chemical damage of ancient DNA and chromatin often hinder Barr body detection. Sample Availability: Successful detection depends on the preservation of osteocytes or other cells within the sample matrix. Replicability: Variability in preservation conditions can limit the reproducibility of results across samples. Future Directions Further research into the detection of Barr bodies may enhance our ability to: Identify gender in a broader range of extinct species. Study X-chromosome inactivation patterns across evolutionary timescales. Integrate histological and genomic methods to reconstruct detailed population dynamics. See also X-inactivation Sex-determination system Nuclear sexing, a genetic sex determination technique Demethylation Acetylation Xist Tsix (gene) References Links to full text articles are provided where access is free, in other cases only the abstract has been linked. Further reading (Web Edition, Free access) Turnpenny & Ellard: Emery's Elements of Medical Genetics 13E (http://www.studentconsult.com/content/default.cfm?ISBN=9780702029172&ID=HC006029 ) Genetics	Barr body	[ "Biology" ]	1,346	[ "Genetics" ]
52,999	https://en.wikipedia.org/wiki/Phobos%20%28moon%29	Phobos (; systematic designation: ) is the innermost and larger of the two natural satellites of Mars, the other being Deimos. The two moons were discovered in 1877 by American astronomer Asaph Hall. Phobos is named after the Greek god of fear and panic, who is the son of Ares (Mars) and twin brother of Deimos. Phobos is a small, irregularly shaped object with a mean radius of . It orbits from the Martian surface, closer to its primary body than any other known natural satellite to a planet. It orbits Mars much faster than Mars rotates and completes an orbit in just 7 hours and 39 minutes. As a result, from the surface of Mars it appears to rise in the west, move across the sky in 4 hours and 15 minutes or less, and set in the east, twice each Martian day. Phobos is one of the least reflective bodies in the Solar System, with an albedo of 0.071. Surface temperatures range from about on the sunlit side to on the shadowed side. The notable surface feature is the large impact crater, Stickney, which takes up a substantial proportion of the moon's surface. The surface is also marked by many grooves, and there are numerous theories as to how these grooves were formed. Images and models indicate that Phobos may be a rubble pile held together by a thin crust that is being torn apart by tidal interactions. Phobos gets closer to Mars by about per year. Discovery Phobos was discovered by the American astronomer Asaph Hall on 18 August 1877 at the United States Naval Observatory in Washington, D.C., at about 09:14 Greenwich Mean Time. (Contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as 17 August at 16:06 Washington mean time, meaning 18 August 04:06 in the modern convention.) Hall had discovered Deimos, Mars' other moon, a few days earlier. The discoveries were made using the world's largest refracting telescope, the 26-inch "Great Equatorial". The names, originally spelled Phobus and Deimus respectively, were suggested by the British academic Henry Madan, a science master at Eton College, who based them on Greek mythology, in which Phobos is a companion to the god, Ares. Physical characteristics Phobos has dimensions of , and retains too little mass to be rounded under its own gravity. Phobos does not have an atmosphere due to its low mass and low gravity. It is one of the least reflective bodies in the Solar System, with an albedo of about 0.071. Infrared spectra show that it has carbon-rich material found in carbonaceous chondrites, and its composition shows similarities to that of Mars' surface. Phobos' density is too low to be solid rock, and it is known to have significant porosity. These results led to the suggestion that Phobos might contain a substantial reservoir of ice. Spectral observations indicate that the surface regolith layer lacks hydration, but ice below the regolith is not ruled out. Surface temperatures range from about on the sunlit side to on the shadowed side. Unlike Deimos, Phobos is heavily cratered, with one of the craters near the equator having a central peak despite the moon's small size. The most prominent of these is the crater Stickney, a large impact crater some in diameter, which takes up a substantial proportion of the moon's surface area. As with Mimas' crater Herschel, the impact that created Stickney must have nearly shattered Phobos. Many grooves and streaks also cover the oddly shaped surface. The grooves are typically less than deep, wide, and up to in length, and were originally assumed to have been the result of the same impact that created Stickney. Analysis of results from the Mars Express spacecraft, however, revealed that the grooves are not radial to Stickney, but are centered on the leading apex of Phobos in its orbit (which is not far from Stickney). Researchers suspect that they have been excavated by material ejected into space by impacts on the surface of Mars. The grooves thus formed as crater chains, and all of them fade away as the trailing apex of Phobos is approached. They have been grouped into 12 or more families of varying age, presumably representing at least 12 Martian impact events. However, in November 2018, following further computational probability analysis, astronomers concluded that the many grooves on Phobos were caused by boulders, ejected from the asteroid impact that created Stickney crater. These boulders rolled in a predictable pattern on the surface of the moon. Faint dust rings produced by Phobos and Deimos have long been predicted but attempts to observe these rings have, to date, failed. Recent images from Mars Global Surveyor indicate that Phobos is covered with a layer of fine-grained regolith at least 100 meters thick; it is hypothesized to have been created by impacts from other bodies, but it is not known how the material stuck to an object with almost no gravity. The unique Kaidun meteorite that fell on a Soviet military base in Yemen in 1980 has been hypothesized to be a piece of Phobos, but this couldn't be verified because little is known about the exact composition of Phobos. Shklovsky's "Hollow Phobos" hypothesis In the late 1950s and 1960s, the unusual orbital characteristics of Phobos led to speculations that it might be hollow. Around 1958, Russian astrophysicist Iosif Samuilovich Shklovsky, studying the secular acceleration of Phobos' orbital motion, suggested a "thin sheet metal" structure for Phobos, a suggestion which led to speculations that Phobos was of artificial origin. Shklovsky based his analysis on estimates of the upper Martian atmosphere's density, and deduced that for the weak braking effect to be able to account for the secular acceleration, Phobos had to be very light—one calculation yielded a hollow iron sphere across but less than thick. In a February 1960 letter to the journal Astronautics, Fred Singer, then science advisor to U.S. President Dwight D. Eisenhower, said of Shklovsky's theory: If the satellite is indeed spiraling inward as deduced from astronomical observation, then there is little alternative to the hypothesis that it is hollow and therefore Martian made. The big 'if' lies in the astronomical observations; they may well be in error. Since they are based on several independent sets of measurements taken decades apart by different observers with different instruments, systematic errors may have influenced them. Subsequently, the systematic data errors that Singer predicted were found to exist, the claim was called into doubt, and accurate measurements of the orbit available by 1969 showed that the discrepancy did not exist. Singer's critique was justified when earlier studies were discovered to have used an overestimated value of per year for the rate of altitude loss, which was later revised to per year. The secular acceleration is now attributed to tidal effects, which create drag on the moon and therefore cause it to spiral inward. The density of Phobos has now been directly measured by spacecraft to be . Current observations are consistent with Phobos being a rubble pile. In addition, images obtained by the Viking probes in the 1970s clearly showed a natural object, not an artificial one. Nevertheless, mapping by the Mars Express probe and subsequent volume calculations do suggest the presence of voids and indicate that it is not a solid chunk of rock but a porous body. The porosity of Phobos was calculated to be 30% ± 5%, or a quarter to a third being empty. Named geological features Geological features on Phobos are named after astronomers who studied Phobos and people and places from Jonathan Swift's Gulliver's Travels. Craters on Phobos A number of craters have been named, and are listed in the following map and table. Other named features There is one named regio, Laputa Regio, and one named planitia, Lagado Planitia; both are named after places in Gulliver's Travels (the fictional Laputa, a flying island, and Lagado, imaginary capital of the fictional nation Balnibarbi). The only named ridge on Phobos is Kepler Dorsum, named after the astronomer Johannes Kepler. Orbital characteristics The orbital motion of Phobos has been intensively studied, making it "the best studied natural satellite in the Solar System" in terms of orbits completed. Its close orbit around Mars produces some unusual effects. With an altitude of , Phobos orbits Mars below the synchronous orbit radius, meaning that it moves around Mars faster than Mars itself rotates. Therefore, from the point of view of an observer on the surface of Mars, it rises in the west, moves comparatively rapidly across the sky (in 4 h 15 min or less) and sets in the east, approximately twice each Martian day (every 11 h 6 min). Because it is close to the surface and in an equatorial orbit, it cannot be seen above the horizon from latitudes greater than 70.4°. Its orbit is so low that its angular diameter, as seen by an observer on Mars, varies visibly with its position in the sky. Seen at the horizon, Phobos is about 0.14° wide; at zenith, it is 0.20°, one-third as wide as the full Moon as seen from Earth. By comparison, the Sun has an apparent size of about 0.35° in the Martian sky. Phobos' phases, inasmuch as they can be observed from Mars, take 0.3191 days (Phobos' synodic period) to run their course, a mere 13 seconds longer than Phobos' sidereal period. Solar transits An observer situated on the Martian surface, in a position to observe Phobos, would see regular transits of Phobos across the Sun. Several of these transits have been photographed by the Mars Rover Opportunity. During the transits, Phobos casts a shadow on the surface of Mars; this event has been photographed by several spacecraft. Phobos is not large enough to cover the Sun's disk, and so cannot cause a total eclipse. Predicted destruction Tidal deceleration is gradually decreasing the orbital radius of Phobos by approximately every 100 years, and with decreasing orbital radius the likelihood of breakup due to tidal forces increases, estimated in approximately 30–50 million years, or about 43 million years in one study's estimate. Phobos' grooves were long thought to be fractures caused by the impact that formed the Stickney crater. Other modelling suggested since the 1970s support the idea that the grooves are more like "stretch marks" that occur when Phobos gets deformed by tidal forces, but in 2015 when the tidal forces were calculated and used in a new model, the stresses were too weak to fracture a solid moon of that size, unless Phobos is a rubble pile surrounded by a layer of powdery regolith about thick. Stress fractures calculated for this model line up with the grooves on Phobos. The model is supported with the discovery that some of the grooves are younger than others, implying that the process that produces the grooves is ongoing. Given Phobos' irregular shape and assuming that it is a pile of rubble (specifically a Mohr–Coulomb body), it will eventually break up due to tidal forces when it reaches approximately 2.1 Mars radii. When Phobos is broken up, it will form a planetary ring around Mars. This predicted ring may last from 1 million to 100 million years. The fraction of the mass of Phobos that will form the ring depends on the unknown internal structure of Phobos. Loose, weakly bound material will form the ring. Components of Phobos with strong cohesion will escape tidal breakup and will enter the Martian atmosphere. It is predicted that within 30 to 50 million years it will either collide with the planet or break up into a planetary ring. Origin The origin of the Martian moons has been disputed. Phobos and Deimos both have much in common with carbonaceous C-type asteroids, with spectra, albedo, and density very similar to those of C- or D-type asteroids. Based on their similarity, one hypothesis is that both moons may be captured main-belt asteroids. Both moons have very circular orbits which lie almost exactly in Mars' equatorial plane, and hence a capture origin requires a mechanism for circularizing the initially highly eccentric orbit, and adjusting its inclination into the equatorial plane, most probably by a combination of atmospheric drag and tidal forces, although it is not clear that sufficient time is available for this to occur for Deimos. Capture also requires dissipation of energy. The current Martian atmosphere is too thin to capture a Phobos-sized object by atmospheric braking. Geoffrey A. Landis has pointed out that the capture could have occurred if the original body was a binary asteroid that separated under tidal forces. Phobos could be a second-generation Solar System object that coalesced in orbit after Mars formed, rather than forming concurrently out of the same birth cloud as Mars. Another hypothesis is that Mars was once surrounded by many Phobos- and Deimos-sized bodies, perhaps ejected into orbit around it by a collision with a large planetesimal. The high porosity of the interior of Phobos (based on the density of 1.88 g/cm3, voids are estimated to comprise 25 to 35 percent of Phobos' volume) is inconsistent with an asteroidal origin. Observations of Phobos in the thermal infrared suggest a composition containing mainly phyllosilicates, which are well known from the surface of Mars. The spectra are distinct from those of all classes of chondrite meteorites, again pointing away from an asteroidal origin. Both sets of findings support an origin of Phobos from material ejected by an impact on Mars that reaccreted in Martian orbit, similar to the prevailing theory for the origin of Earth's moon. Some areas of the surface are reddish in color, while others are bluish. The hypothesis is that gravity pull from Mars makes the reddish regolith move over the surface, exposing relatively fresh, unweathered and bluish material from the moon, while the regolith covering it over time has been weathered due to exposure of solar radiation. Because the blue rock differs from known Martian rock, it could contradict the theory that the moon is formed from leftover planetary material after the impact of a large object. In February 2021, Amirhossein Bagheri (ETH Zurich), Amir Khan (ETH Zurich), Michael Efroimsky (US Naval Observatory) and their colleagues proposed a new hypothesis on the origin of the moons. By analyzing the seismic and orbital data from Mars InSight Mission and other missions, they proposed that the moons are born from disruption of a common parent body around 1 to 2.7 billion years ago. The common progenitor of Phobos and Deimos was most probably hit by another object and shattered to form both moons. Exploration Launched missions Phobos has been photographed in close-up by several spacecraft whose primary mission has been to photograph Mars. The first was Mariner 7 in 1969, followed by Mariner 9 in 1971, Viking 1 in 1977, Phobos 2 in 1989 Mars Global Surveyor in 1998 and 2003, Mars Express in 2004, 2008, 2010 and 2019, and Mars Reconnaissance Orbiter in 2007 and 2008. On 25 August 2005, the Spirit rover, with an excess of energy due to wind blowing dust off of its solar panels, took several short-exposure photographs of the night sky from the surface of Mars, and was able to successfully photograph both Phobos and Deimos. The Soviet Union undertook the Phobos program with two probes, both launched successfully in July 1988. Phobos 1 was accidentally shut down by an erroneous command from ground control issued in September 1988 and lost while the craft was still en route. Phobos 2 arrived at the Mars system in January 1989 and, after transmitting a small amount of data and imagery shortly before beginning its detailed examination of Phobos' surface, the probe abruptly ceased transmission due either to failure of the onboard computer or of the radio transmitter, already operating on backup power. Other Mars missions collected more data, but no dedicated sample return mission has been successfully performed. The Russian Space Agency launched a sample return mission to Phobos in November 2011, called Fobos-Grunt. The return capsule also included a life science experiment of The Planetary Society, called Living Interplanetary Flight Experiment, or LIFE. A second contributor to this mission was the China National Space Administration, which supplied a surveying satellite called "Yinghuo-1", which would have been released in the orbit of Mars, and a soil-grinding and sieving system for the scientific payload of the Phobos lander. However, after achieving Earth orbit, the Fobos-Grunt probe failed to initiate subsequent burns that would have sent it to Mars. Attempts to recover the probe were unsuccessful and it crashed back to Earth in January 2012. On 1 July 2020, the Mars orbiter of the Indian Space Research Organisation was able to capture photos of the body from 4,200 km away. Missions considered In 1997 and 1998, the Aladdin mission was selected as a finalist in the NASA Discovery Program. The plan was to visit both Phobos and Deimos, and launch projectiles at the satellites. The probe would collect the ejecta as it performed a slow flyby (~1 km/s). These samples would be returned to Earth for study three years later. The Principal Investigator was Dr. Carle Pieters of Brown University. The total mission cost, including launch vehicle and operations was $247.7 million. Ultimately, the mission chosen to fly was MESSENGER, a probe to Mercury. In 2007, the European aerospace subsidiary EADS Astrium was reported to have been developing a mission to Phobos as a technology demonstrator. Astrium was involved in developing a European Space Agency plan for a sample return mission to Mars, as part of the ESA's Aurora programme, and sending a mission to Phobos with its low gravity was seen as a good opportunity for testing and proving the technologies required for an eventual sample return mission to Mars. The mission was envisioned to start in 2016, was to last for three years. The company planned to use a "mothership", which would be propelled by an ion engine, releasing a lander to the surface of Phobos. The lander would perform some tests and experiments, gather samples in a capsule, then return to the mothership and head back to Earth where the samples would be jettisoned for recovery on the surface. Proposed missions In 2007, the Canadian Space Agency funded a study by Optech and the Mars Institute for an uncrewed mission to Phobos known as Phobos Reconnaissance and International Mars Exploration (PRIME). A proposed landing site for the PRIME spacecraft is at the "Phobos monolith", a prominent object near Stickney crater. The PRIME mission would be composed of an orbiter and lander, and each would carry 4 instruments designed to study various aspects of Phobos' geology. In 2008, NASA Glenn Research Center began studying a Phobos and Deimos sample return mission that would use solar electric propulsion. The study gave rise to the "Hall" mission concept, a New Frontiers-class mission under further study as of 2010. Another concept of a sample return mission from Phobos and Deimos is OSIRIS-REx II, which would use heritage technology from the first OSIRIS-REx mission. As of January 2013, a new Phobos Surveyor mission is currently under development by a collaboration of Stanford University, NASA's Jet Propulsion Laboratory, and the Massachusetts Institute of Technology. The mission is currently in the testing phases, and the team at Stanford plans to launch the mission between 2023 and 2033. In March 2014, a Discovery class mission was proposed to place an orbiter in Mars orbit by 2021 to study Phobos and Deimos through a series of close flybys. The mission is called Phobos And Deimos & Mars Environment (PADME). Two other Phobos missions that were proposed for the Discovery 13 selection included a mission called Merlin, which would flyby Deimos but actually orbit and land on Phobos, and another one is Pandora which would orbit both Deimos and Phobos. The Japanese Aerospace Exploration Agency (JAXA) unveiled on 9 June 2015 the Martian Moons Exploration (MMX), a sample return mission targeting Phobos. MMX will land and collect samples from Phobos multiple times, along with conducting Deimos flyby observations and monitoring Mars' climate. By using a corer sampling mechanism, the spacecraft aims to retrieve a minimum 10 g amount of samples. NASA, ESA, DLR, and CNES are also participating in the project, and will provide scientific instruments. The U.S. will contribute the Neutron and Gamma-Ray Spectrometer (NGRS), and France the Near IR Spectrometer (NIRS4/MacrOmega). Although the mission has been selected for implementation and is now beyond proposal stage, formal project approval by JAXA has been postponed following the Hitomi mishap. Development and testing of key components, including the sampler, is currently ongoing. , MMX is scheduled to be launched in 2026, and will return to Earth five years later. Russia plans to repeat Fobos-Grunt mission in the late 2020s, and the European Space Agency is assessing a sample-return mission for 2024 called Phootprint. Human missions Phobos has been proposed as an early target for a human mission to Mars. The teleoperation of robotic scouts on Mars by humans on Phobos could be conducted without significant time delay, and planetary protection concerns in early Mars exploration might be addressed by such an approach. A landing on Phobos would be considerably less difficult and expensive than a landing on the surface of Mars itself. A lander bound for Mars would need to be capable of atmospheric entry and subsequent return to orbit without any support facilities, or would require the creation of support facilities in-situ. A lander instead bound for Phobos could be based on equipment designed for lunar and asteroid landings. Furthermore, due to Phobos' very weak gravity, the delta-v required to land on Phobos and return is only 80% of that required for a trip to and from the surface of the Moon. It has been proposed that the sands of Phobos could serve as a valuable material for aerobraking during a Mars landing. A relatively small amount of chemical fuel brought from Earth could be used to lift a large amount of sand from the surface of Phobos to a transfer orbit. This sand could be released in front of a spacecraft during the descent maneuver causing a densification of the atmosphere just in front of the spacecraft. While human exploration of Phobos could serve as a catalyst for the human exploration of Mars, it could be scientifically valuable in its own right. Space elevator base First discussed in fiction in 1956 by Fontenay, Phobos has been proposed as a future site for space elevator construction. This would involve a pair of space elevators: one extending 6,000 km from the Mars-facing side to the edge of Mars' atmosphere, the other extending from the other side and away from Mars. A spacecraft launching from Mars' surface to the lower space elevator would only need a delta-v of , as opposed to the over needed to launch to low Mars orbit. The spacecraft could be lifted up using electrical power and then released from the upper space elevator with a hyperbolic velocity of , enough to reach Earth and a significant fraction of the velocity needed to reach the asteroid belt. The space elevators could also work in reverse to help spacecraft enter the Martian system. The great mass of Phobos means that any forces from space elevator operation would have minimal effect on its orbit. Additionally, materials from Phobos could be used for space industry. See also List of natural satellites List of missions to the moons of Mars Phobos monolith Transit of Phobos from Mars References External links Phobos Imaged by HiRISE from the University of Arizona Target: Phobos in the Gazetteer of Planetary Nomenclature (USGS) Flight around Phobos and High-Resolution Animation of Phobos (two animations from Views of the Solar System) Phobos cartography (MIIGAiK Extraterrestrial Laboratory) 18770812 Moons of Mars Articles containing video clips Moons with a prograde orbit Solar System	Phobos (moon)	[ "Astronomy" ]	5,119	[ "Outer space", "Solar System" ]
53,008	https://en.wikipedia.org/wiki/Iridium%20Communications	Iridium Communications Inc. (formerly Iridium Satellite LLC) is a publicly traded American company headquartered in McLean, Virginia, United States. Iridium operates the Iridium satellite constellation, a system of 80 satellites: 66 are active satellites and the remaining fourteen function as in-orbit spares. Iridium Satellites are used for worldwide voice and data communication from handheld satellite phones, satellite messenger communication devices and integrated transceivers, as well as for two-way satellite messaging service from supported conventional mobile phones. The nearly polar orbit and communication between satellites via inter-satellite links provide global service availability. History The Iridium communications service was launched on November 1, 1998, formerly known as Iridium SSC. The first Iridium call was made from Vice President of the United States Al Gore to Gilbert Grosvenor, the great-grandson of Alexander Graham Bell and chairman of the National Geographic Society. Motorola provided the technology and major financial backing. The logo of the company represents the Big Dipper. The company derives its name from the chemical element iridium, which has an atomic number of 77, equaling the initial number of satellites which were calculated to be required for global coverage. However, due to optimizations of orbit trajectories, technology updates and real-world conditions, only 66 are required for global coverage. A total of 95 satellites were launched in this constellation, with 66 active and the remaining 29 satellites operating as spares. On August 13, 1999, nine months after the launch of the organization, the founding company went into Chapter 11 bankruptcy. The handsets could not operate as promoted until the entire constellation of satellites was in place, requiring a massive initial capital cost of billions of dollars. The cost of service dissuaded many potential users. Reception indoors was difficult and the handheld devices, when compared to terrestrial cellular mobile phones were bulkier and more expensive, both of which discouraged adoption among potential users. Mismanagement is another major factor that was cited in the original program's failure. In 1999, CNN writer David Rohde detailed how he applied for Iridium service and was sent information kits, but was never contacted by a sales representative. He encountered programming problems on Iridium's website, and a "run-around" from the company's representatives. After Iridium filed bankruptcy, it cited "difficulty gaining subscribers." The initial commercial failure of Iridium had a damping effect on other proposed commercial satellite constellation projects, including Teledesic. Other schemes (Orbcomm, ICO Global Communications, and Globalstar) followed Iridium into bankruptcy protection, while a number of other proposed schemes were never even constructed. In August 2000, Motorola announced that the Iridium satellites would have to be deorbited. Despite this, they remained in orbit and operational. In December 2000, the US government stepped in to save Iridium by providing US$72 million in exchange for a two-year contract. They also approved the fire sale of the company from US bankruptcy court for $25 million in March 2001. This erased over $4 billion in debt. Iridium service was restarted in 2001, by the newly founded Iridium Satellite LLC, which was owned by a group of private investors. On February 10, 2009, the Iridium 33 satellite collided with a defunct Russian satellite, named Kosmos 2251, over Siberia. Two large debris clouds were created. Iridium NEXT launch campaign Iridium replaced its original constellation by sending 75 new Iridium satellites into space on SpaceX Falcon 9 rockets in a series of 8 launches. The campaign also consisted of upgrades to Iridium ground infrastructure. The Iridium NEXT launch campaign was announced in 2007. Within three years, Iridium completed financing and began work on launching new satellites. In June 2010, Iridium announced a fixed-price contract with Thales Alenia Space for the design and construction of the next-generation satellites for the upgraded constellation. Two weeks later, Iridium announced a $492 million contract designating the Falcon 9 as a major provider of launch services for the Iridium NEXT campaign, becoming the largest single commercial launch deal ever signed (simultaneously representing a benchmark in cost-effective satellite delivery to space). On January 14, 2017, 10 years after the campaign was first announced, the first of eight Iridium NEXT launches took place with SpaceX from Vandenberg Air Force Base in California. Over the next two years, Iridium sent an additional 65 satellites into low Earth orbit to completely replace the original satellite constellation. The final Iridium NEXT launch took place on January 11, 2019, less than two years after the first launch. The Iridium NEXT network covers the entire Earth, including poles, oceans and airways, with 66 satellites, with the remaining nine acting as active backups, for a total of 75 launched. Six remain on the ground as spares for a total of 81 built. Present status Iridium Satellite LLC merged with a special-purpose acquisition company (GHQ) created by the investment bank Greenhill & Co. in September 2009 to create Iridium Communications Inc. The public company trades on NASDAQ under the symbol "IRDM". The company surpassed one million subscribers in March 2018. Revenue for the full year 2018 was $523.0 million with operational EBITDA of $302.0 million, a 14% increase from $265.6 million in the prior year. Iridium manages several operations centers, including Tempe, Arizona and Leesburg, Virginia, United States. The system is being used by the U.S. Department of Defense. Matt Desch is the current CEO of Iridium LLC. Hosted Payload Alliance Iridium is a founding member of the Hosted Payload Alliance (HPA), a satellite industry alliance program. Membership in the HPA is open to satellite operators, satellite manufacturers, system integrators, and other interested parties. Air safety communications In July 2011, the Federal Aviation Administration (FAA) issued a ruling that approves the use of Iridium for Future Air Navigation System (FANS) data links, enabling satellite data links with air-traffic control for aircraft flying in the FANS environment, including areas not served by Inmarsat (above or below 70 degrees latitude) which includes polar routes. Global Maritime Distress and Safety System In January 2020, the Iridium constellation was certified for use in the Global Maritime Distress and Safety System (GMDSS). The certification ended a monopoly on the provision of maritime distress services that had previously been held by Inmarsat since the system became operational in 1999. Adoption of standard-based solutions for cellphones In 2023, Qualcomm and Iridium announced an agreement that was supposed to bring two-way satellite messaging service to Android smartphones. The service, called Snapdragon Satellite, should have been supported starting with devices that feature Snapdragon 8 Gen 2 chipsets, which was expected to be launched in the second half of 2023. The solution for smartphones was supposed to utilize Iridium's L Band spectrum for downlink and uplink. On November 9, 2023, Iridium announced that Qualcomm had notified them about the end of their partnership due to a lack of interest in Qualcomm's and Iridium's proprietary solution by smartphone manufacturers. A Qualcomm spokesman stated "Smartphone makers have indicated a preference towards standards-based solutions for satellite-to-phone connectivity. We expect to continue to collaborate with Iridium on standards-based solutions while discontinuing efforts on the proprietary solution that was introduced earlier this year." In 2024, Iridium introduceed Project Stardust, a 3GPP standard-based satellite-to-cellphone service focusing on messaging, emergency communications and IoT for devices like cars, smartphones, tablets and related consumer applications. The solution will be supported using a version of the NB-IoT standard for 5G non-terrestrial networks (NTN). Scheduled for launch in 2026, it won't replace the company’s proprietary solution for voice and high-speed data; instead it will co-exist with that offering on the Iridium's existing global low-earth orbit satellite network. Russo-Ukrainian War From 2015-2022, Iridium Satellite was selling navigation systems directly to its Russian subsidiary, Iridium Communications. In 2022, the Moscow-based subsidiary gave the National Guard of Russia access to the satellite constellation. Following the 2022 Russian invasion of Ukraine, Iridium structured their operations to comply with US sanctions and stopped shipment of end-user equipment to Russia. Despite this, In 2023, Iridium Communications, via some unknown intermediaries, imported machines made by the American parent company for receiving and converting voice and images. Iridium satellite constellation The Iridium system requires 66 active satellites in low Earth orbit to complete its constellation and 9 spare satellites are kept in-orbit to serve in case of failure. The satellites are in six polar orbital planes at a height of approximately . Satellites communicate with neighboring satellites via Ka band intersatellite links to relay communications to and from ground stations. The original constellation was launched in the late 1990s before the company went through bankruptcy. In January 2017, Iridium began to launch its next-generation satellites through its $3 billion launch campaign, Iridium NEXT. The new satellites were sent into space on SpaceX Falcon 9 launch vehicles from Vandenberg AFB Space Launch Complex 4 in California over the course of eight launches between January 2017 and January 2019. On January 14, 2017, SpaceX launched 10 of the new Iridium satellites into orbit. The second launch of Iridium NEXT satellites took place on June 25, 2017 on a SpaceX Falcon 9 rocket out of Vandenberg Air Force Base. This was the second of eight scheduled launches. The third launch of 10 NEXT satellites took place on October 9, 2017. On December 22, 2017, ten additional satellites were deployed after a successful launch on a SpaceX Falcon 9 rocket. On May 22, SpaceX successfully launched an additional five Iridium NEXT satellites from Vandenberg Air Force Base. On January 11, 2019, the final ten satellites were placed in orbit by SpaceX. Subscriber equipment Handsets Iridium offers four satellite handsets: the 9555, 9575A (which is only available to US government customers), the Extreme, and the Extreme PTT. Wi-Fi Hotspots In 2014, Iridium began to offer the Iridium Go! hotspot, which can also be used as a distress beacon under certain circumstances. As of September 2020, Iridium's manufacturing contractor, Beam Communications, had built 50,000 of these devices. One-way pagers Two pagers were made for the Iridium network – the Motorola 9501 and Kyocera SP-66K. These are one-way devices that could receive messages sent in the form of SMS. Messages are delivered to pre-selected "MDAs" which cover a certain geographic area. Three of these MDAs may be selected on a web-based portal or updated automatically if the paging service is bound to an Iridium phone. Each country has its own MDA based on its country code; some of the larger countries are divided into several MDAs, while separate MDAs exist for sections of ocean and common aeronautic routes. Pagers are assigned with telephone numbers in area code 480 and can also be contacted using email, SMS and the web-based interface used to send messages to Iridium phones. Two-way satellite messengers In 2017, Garmin announced inReach SE+ and inReach Explorer+ satellite communicators, which use Iridium satellite network for global coverage. Garmin inReach mini, a satellite messenger, was announced a year later. These devices can send and receive text messages with any cell phone number, email address or another inReach device, as well as to provide location sharing, navigation and direct communication options to emergency services. ZOLEO satellite communicator uses global Iridium network when cellular or Wi-Fi coverage is unavailable. It does so by means of Bluetooth connection to provide two-way messaging to connected smartphone or tablet devices. Other satellite phones Several other Iridium-based telephones exist, such as payphones, and equipment intended for installation on ships and aircraft. The DPL handset made by NAL Research combined with a 9522 transceiver is used for some of these products. This handset provides a user interface nearly identical to that of the 9505 series phones. Standalone transceiver units These can be used for data-logging applications in remote areas (as in data collection satellites). Some types of buoys, such as those used for the tsunami warning system, use Iridium satellites to communicate with their base. The remote device is programmed to call or send short burst data (SBD) messages to the base at specified intervals, or it can be set to accept calls in order for it to offload its collected data. The following transceivers have been released over the years: Iridium Core 9523 – Similar to the 9522B, a modular transceiver released in 2012 Iridium 9522B – A transceiver released in late 2008, is smaller than the 9522A and has similar features. It also supports Circuit-Switched Data (CSD), not just SBD. Iridium 9522A – Based on the 9522, some variants have built in GPS and autonomous reporting functions. Supports SBD. Motorola 9522 – Last Motorola transceiver, supports outgoing SMS but no SBD. Motorola 9520 – Original transceiver module, does not support outgoing SMS or SBD. Designed for use in vehicles with accompanying handset Short burst data modems These devices support only SBD for Internet of things (IoT) services and do not use a SIM card. Iridium 9601 – Supports only SBD, several tracking devices and other products have been built around this modem. It was an Iridium manufactured product designed as an OEM module for integration into applications that only use the Iridium Short Burst Data Service. Short Burst Data applications are supported through an RS-232 interface. Examples of these applications include maritime vessel tracking or automatic vehicle tracking. Iridium 9602 – Smaller, cheaper version of 9601 (released in 2010). Iridium 9603 – One-fourth the volume and half the footprint of 9602 Iridium OpenPort Iridium OpenPort is a broadband satellite voice and data communications system for maritime vessels. The system is used for crew calling and e-mail services on sea vessels such as merchant fleets, government and navy vessels, fishing fleets and personal yachts. Iridium operates at only 2.2 to 3.8 kbit/s, which requires very aggressive voice compression and decompression algorithms. (By comparison, AMR used in 3G phones requires a minimum of 4.75 kbit/s, G.729 requires 6.4 kbit/s, and iLBC requires 13.33 kbit/s.) Latency for data connections averages 1800 ms round-trip, with a mode of 1300 to 1400 ms and a minimum around 980 ms. Latency is highly variable depending on the path data takes through the satellite constellation as well the need for retransmissions due to errors, which may be around 2 to 3% for mobile originated packets under good conditions. Iridium Certus One of the Iridium NEXT services is Iridium Certus, a globally available satellite broadband which is capable of up to 704 Kbps of bandwidth across maritime, aviation, land mobile, government, and IoT applications. Terminals for the service are provided by Cobham, Intellian Technologies and Thales. Iridium STL Iridium is providing Satellite Time & Location (STL) service. It was developed by Satelles company, which was later acquired by Iridium Communications in April 2024. According to the company, it is the only LEO satellite based commercial positioning, navigation, and timing (PNT) service (as of April 2024). See also Mobile-satellite service Broadband Global Area Network DeLorme Globalsat Group Globalstar Gonets Inmarsat OneWeb O3b Networks SES Broadband Sky and Space Global Starlink (SpaceX) Thuraya Quake Global References External links Application of Iridium telecommunications to oceanographic and polar research Iridium Data Modem (PDF) Technical success and economic failure (PDF), MIT Companies that filed for Chapter 11 bankruptcy in 1999 2009 initial public offerings Satellite telephony Companies based in McLean, Virginia Communications satellite operators Mobile phone companies of the United States Companies listed on the Nasdaq Satellite Internet access Data collection satellites Companies in the S&P 400	Iridium Communications	[ "Technology" ]	3,412	[ "Satellite telephony", "Iridium Communications" ]
53,031	https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann%20law	The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically. For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature, : The constant of proportionality, , is called the Stefan–Boltzmann constant. It has the value In the general case, the Stefan–Boltzmann law for radiant exitance takes the form: where is the emissivity of the surface emitting the radiation. The emissivity is generally between zero and one. An emissivity of one corresponds to a black body. Detailed explanation The radiant exitance (previously called radiant emittance), , has dimensions of energy flux (energy per unit time per unit area), and the SI units of measure are joules per second per square metre (J⋅s⋅m), or equivalently, watts per square metre (W⋅m). The SI unit for absolute temperature, , is the kelvin (K). To find the total power, , radiated from an object, multiply the radiant exitance by the object's surface area, : Matter that does not absorb all incident radiation emits less total energy than a black body. Emissions are reduced by a factor , where the emissivity, , is a material property which, for most matter, satisfies . Emissivity can in general depend on wavelength, direction, and polarization. However, the emissivity which appears in the non-directional form of the Stefan–Boltzmann law is the hemispherical total emissivity, which reflects emissions as totaled over all wavelengths, directions, and polarizations. The form of the Stefan–Boltzmann law that includes emissivity is applicable to all matter, provided that matter is in a state of local thermodynamic equilibrium (LTE) so that its temperature is well-defined. (This is a trivial conclusion, since the emissivity, , is defined to be the quantity that makes this equation valid. What is non-trivial is the proposition that , which is a consequence of Kirchhoff's law of thermal radiation.) A so-called grey body is a body for which the spectral emissivity is independent of wavelength, so that the total emissivity, , is a constant. In the more general (and realistic) case, the spectral emissivity depends on wavelength. The total emissivity, as applicable to the Stefan–Boltzmann law, may be calculated as a weighted average of the spectral emissivity, with the blackbody emission spectrum serving as the weighting function. It follows that if the spectral emissivity depends on wavelength then the total emissivity depends on the temperature, i.e., . However, if the dependence on wavelength is small, then the dependence on temperature will be small as well. Wavelength- and subwavelength-scale particles, metamaterials, and other nanostructures are not subject to ray-optical limits and may be designed to have an emissivity greater than 1. In national and international standards documents, the symbol is recommended to denote radiant exitance; a superscript circle (°) indicates a term relate to a black body. (A subscript "e" is added when it is important to distinguish the energetic (radiometric) quantity radiant exitance, , from the analogous human vision (photometric) quantity, luminous exitance, denoted .) In common usage, the symbol used for radiant exitance (often called radiant emittance) varies among different texts and in different fields. The Stefan–Boltzmann law may be expressed as a formula for radiance as a function of temperature. Radiance is measured in watts per square metre per steradian (W⋅m⋅sr). The Stefan–Boltzmann law for the radiance of a black body is: The Stefan–Boltzmann law expressed as a formula for radiation energy density is: where is the speed of light. History In 1864, John Tyndall presented measurements of the infrared emission by a platinum filament and the corresponding color of the filament. The proportionality to the fourth power of the absolute temperature was deduced by Josef Stefan (1835–1893) in 1877 on the basis of Tyndall's experimental measurements, in the article Über die Beziehung zwischen der Wärmestrahlung und der Temperatur (On the relationship between thermal radiation and temperature) in the Bulletins from the sessions of the Vienna Academy of Sciences. A derivation of the law from theoretical considerations was presented by Ludwig Boltzmann (1844–1906) in 1884, drawing upon the work of Adolfo Bartoli. Bartoli in 1876 had derived the existence of radiation pressure from the principles of thermodynamics. Following Bartoli, Boltzmann considered an ideal heat engine using electromagnetic radiation instead of an ideal gas as working matter. The law was almost immediately experimentally verified. Heinrich Weber in 1888 pointed out deviations at higher temperatures, but perfect accuracy within measurement uncertainties was confirmed up to temperatures of 1535 K by 1897. The law, including the theoretical prediction of the Stefan–Boltzmann constant as a function of the speed of light, the Boltzmann constant and the Planck constant, is a direct consequence of Planck's law as formulated in 1900. Stefan–Boltzmann constant The Stefan–Boltzmann constant, , is derived from other known physical constants: where is the Boltzmann constant, the is the Planck constant, and is the speed of light in vacuum. As of the 2019 revision of the SI, which establishes exact fixed values for , , and , the Stefan–Boltzmann constant is exactly: Thus, Prior to this, the value of was calculated from the measured value of the gas constant. The numerical value of the Stefan–Boltzmann constant is different in other systems of units, as shown in the table below. Examples Temperature of the Sun With his law, Stefan also determined the temperature of the Sun's surface. He inferred from the data of Jacques-Louis Soret (1827–1890) that the energy flux density from the Sun is 29 times greater than the energy flux density of a certain warmed metal lamella (a thin plate). A round lamella was placed at such a distance from the measuring device that it would be seen at the same angular diameter as the Sun. Soret estimated the temperature of the lamella to be approximately 1900 °C to 2000 °C. Stefan surmised that 1/3 of the energy flux from the Sun is absorbed by the Earth's atmosphere, so he took for the correct Sun's energy flux a value 3/2 times greater than Soret's value, namely 29 × 3/2 = 43.5. Precise measurements of atmospheric absorption were not made until 1888 and 1904. The temperature Stefan obtained was a median value of previous ones, 1950 °C and the absolute thermodynamic one 2200 K. As 2.574 = 43.5, it follows from the law that the temperature of the Sun is 2.57 times greater than the temperature of the lamella, so Stefan got a value of 5430 °C or 5700 K. This was the first sensible value for the temperature of the Sun. Before this, values ranging from as low as 1800 °C to as high as were claimed. The lower value of 1800 °C was determined by Claude Pouillet (1790–1868) in 1838 using the Dulong–Petit law. Pouillet also took just half the value of the Sun's correct energy flux. Temperature of stars The temperature of stars other than the Sun can be approximated using a similar means by treating the emitted energy as a black body radiation. So: where is the luminosity, is the Stefan–Boltzmann constant, is the stellar radius and is the effective temperature. This formula can then be rearranged to calculate the temperature: or alternatively the radius: The same formulae can also be simplified to compute the parameters relative to the Sun: where is the solar radius, and so forth. They can also be rewritten in terms of the surface area A and radiant exitance : where and With the Stefan–Boltzmann law, astronomers can easily infer the radii of stars. The law is also met in the thermodynamics of black holes in so-called Hawking radiation. Effective temperature of the Earth Similarly we can calculate the effective temperature of the Earth T⊕ by equating the energy received from the Sun and the energy radiated by the Earth, under the black-body approximation (Earth's own production of energy being small enough to be negligible). The luminosity of the Sun, L⊙, is given by: At Earth, this energy is passing through a sphere with a radius of a0, the distance between the Earth and the Sun, and the irradiance (received power per unit area) is given by The Earth has a radius of R⊕, and therefore has a cross-section of . The radiant flux (i.e. solar power) absorbed by the Earth is thus given by: Because the Stefan–Boltzmann law uses a fourth power, it has a stabilizing effect on the exchange and the flux emitted by Earth tends to be equal to the flux absorbed, close to the steady state where: T⊕ can then be found: where T⊙ is the temperature of the Sun, R⊙ the radius of the Sun, and a0 is the distance between the Earth and the Sun. This gives an effective temperature of 6 °C on the surface of the Earth, assuming that it perfectly absorbs all emission falling on it and has no atmosphere. The Earth has an albedo of 0.3, meaning that 30% of the solar radiation that hits the planet gets scattered back into space without absorption. The effect of albedo on temperature can be approximated by assuming that the energy absorbed is multiplied by 0.7, but that the planet still radiates as a black body (the latter by definition of effective temperature, which is what we are calculating). This approximation reduces the temperature by a factor of 0.71/4, giving . The above temperature is Earth's as seen from space, not ground temperature but an average over all emitting bodies of Earth from surface to high altitude. Because of the greenhouse effect, the Earth's actual average surface temperature is about , which is higher than the effective temperature, and even higher than the temperature that a black body would have. In the above discussion, we have assumed that the whole surface of the earth is at one temperature. Another interesting question is to ask what the temperature of a blackbody surface on the earth would be assuming that it reaches equilibrium with the sunlight falling on it. This of course depends on the angle of the sun on the surface and on how much air the sunlight has gone through. When the sun is at the zenith and the surface is horizontal, the irradiance can be as high as 1120 W/m2. The Stefan–Boltzmann law then gives a temperature of or . (Above the atmosphere, the result is even higher: .) We can think of the earth's surface as "trying" to reach equilibrium temperature during the day, but being cooled by the atmosphere, and "trying" to reach equilibrium with starlight and possibly moonlight at night, but being warmed by the atmosphere. Origination Thermodynamic derivation of the energy density The fact that the energy density of the box containing radiation is proportional to can be derived using thermodynamics. This derivation uses the relation between the radiation pressure p and the internal energy density , a relation that can be shown using the form of the electromagnetic stress–energy tensor. This relation is: Now, from the fundamental thermodynamic relation we obtain the following expression, after dividing by and fixing : The last equality comes from the following Maxwell relation: From the definition of energy density it follows that where the energy density of radiation only depends on the temperature, therefore Now, the equality is after substitution of Meanwhile, the pressure is the rate of momentum change per unit area. Since the momentum of a photon is the same as the energy divided by the speed of light, where the factor 1/3 comes from the projection of the momentum transfer onto the normal to the wall of the container. Since the partial derivative can be expressed as a relationship between only and (if one isolates it on one side of the equality), the partial derivative can be replaced by the ordinary derivative. After separating the differentials the equality becomes which leads immediately to , with as some constant of integration. Derivation from Planck's law The law can be derived by considering a small flat black body surface radiating out into a half-sphere. This derivation uses spherical coordinates, with θ as the zenith angle and φ as the azimuthal angle; and the small flat blackbody surface lies on the xy-plane, where θ = /2. The intensity of the light emitted from the blackbody surface is given by Planck's law, where is the amount of power per unit surface area per unit solid angle per unit frequency emitted at a frequency by a black body at temperature T. is the Planck constant is the speed of light, and is the Boltzmann constant. The quantity is the power radiated by a surface of area A through a solid angle in the frequency range between and . The Stefan–Boltzmann law gives the power emitted per unit area of the emitting body, Note that the cosine appears because black bodies are Lambertian (i.e. they obey Lambert's cosine law), meaning that the intensity observed along the sphere will be the actual intensity times the cosine of the zenith angle. To derive the Stefan–Boltzmann law, we must integrate over the half-sphere and integrate from 0 to ∞. Then we plug in for I: To evaluate this integral, do a substitution, which gives: The integral on the right is standard and goes by many names: it is a particular case of a Bose–Einstein integral, the polylogarithm, or the Riemann zeta function . The value of the integral is (where is the Gamma function), giving the result that, for a perfect blackbody surface: Finally, this proof started out only considering a small flat surface. However, any differentiable surface can be approximated by a collection of small flat surfaces. So long as the geometry of the surface does not cause the blackbody to reabsorb its own radiation, the total energy radiated is just the sum of the energies radiated by each surface; and the total surface area is just the sum of the areas of each surface—so this law holds for all convex blackbodies, too, so long as the surface has the same temperature throughout. The law extends to radiation from non-convex bodies by using the fact that the convex hull of a black body radiates as though it were itself a black body. Energy density The total energy density U can be similarly calculated, except the integration is over the whole sphere and there is no cosine, and the energy flux (U c) should be divided by the velocity c to give the energy density U: Thus is replaced by , giving an extra factor of 4. Thus, in total: The product is sometimes known as the radiation constant or radiation density constant. Decomposition in terms of photons The Stephan–Boltzmann law can be expressed as where the flux of photons, , is given by and the average energy per photon,, is given by Marr and Wilkin (2012) recommend that students be taught about instead of being taught Wien's displacement law, and that the above decomposition be taught when the Stefan–Boltzmann law is taught. See also Black-body radiation Rayleigh–Jeans law Sakuma–Hattori equation Notes References Laws of thermodynamics Power laws Heat transfer Ludwig Boltzmann	Stefan–Boltzmann law	[ "Physics", "Chemistry" ]	3,358	[ "Transport phenomena", "Physical phenomena", "Heat transfer", "Thermodynamics", "Laws of thermodynamics" ]
53,033	https://en.wikipedia.org/wiki/Josef%20Stefan	Josef Stefan (; 24 March 1835 – 7 January 1893) was a Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire. Life and work Stefan was born in the village of St. Peter (Slovene: ) on the outskirts of Klagenfurt) to Aleš (Aleksander) Stefan (1805-1872) and Marija Startinik (1815-1863). His parents, both ethnic Slovenes, did not marry until Josef was eleven. The Stefans were of modest means; his father was a milling assistant and his mother served as a maidservant. Josef was their only child. Stefan attended elementary school in Klagenfurt, where he showed talent, and was recommended for enrollment at the in 1845. At thirteen, he experienced the revolutionary year of 1848, which inspired him to show sympathy toward the Slovene literary and national movement. After having graduated top of his class in high school, he briefly considered joining the Benedictine Order, but his great interest in physics prevailed. He left for Vienna in 1853 to study mathematics and physics. His professor of physics in the gymnasium was Karel Robida, who wrote the first Slovene physics textbook. Stefan then earned his habilitation in mathematical physics at the University of Vienna in 1858. During his student years, he also wrote and published a number of poems in Slovene. Stefan taught physics at the University of Vienna, was Director of the Physical Institute from 1866, Vice-President of the Vienna Academy of Sciences, and member of several scientific institutions in Europe. He died in Vienna, Austria-Hungary. His life and work were extensively documented by the physicist Janez Strnad. Work Stefan published nearly 80 scientific articles, mostly in the Bulletins of the Vienna Academy of Sciences. He is best known for originating Stefan's law in 1879, a physical power law stating that the total radiation from a black body is proportional to the fourth power of its thermodynamic temperature T: He derived this law from the measurements of the French physicists Dulong and Petit. As both incident radiation and blackbody emission are always equal, this equation applies equally to the temperature of any ideal body subject to incident radiation across its surface. In 1884, the law was extended to apply to grey-body emissions by Stefan's student Ludwig Boltzmann and hence is known as Stefan–Boltzmann law. Boltzmann treated a heat engine with light as a working matter. This law is the only physical law of nature named after a Slovene physicist. Today, the law is derived from Planck's law of black-body radiation: With his law, Stefan determined the temperature of the Sun's surface, which he calculated to be . This was the first sensible value for the temperature of the Sun. Stefan provided the first measurements of the thermal conductivity of gases, treated evaporation, and among others studied diffusion, heat conduction in fluids. For his treatise on optics, the University of Vienna bestowed the Lieben Prize on him. Because of his early work in calculating evaporation and diffusion rates, flow from a droplet or particle that is induced by evaporation or sublimation at the surface is now called the Stefan flow. Very important are also his electromagnetic equations, defined in vector notation, and works in the kinetic theory of heat. Stefan was among the first physicists in Europe who fully understood Maxwell's electromagnetic theory and one of the few outside England who expanded on it. He calculated inductivity of a coil with a quadratic cross-section, and he corrected Maxwell's miscalculation. He also researched a phenomenon called the skin effect, where high-frequency electric current is greater on the surface of a conductor than in its interior. In mathematics, the Stefan problems or Stefan's tasks with movable boundary are well known. The problem was first studied by Lamé and Clapeyron in 1831. Stefan solved the problem when he was calculating how quickly a layer of ice on water grows (Stefan's equation). Eponymous terms Several concepts in physics and mathematics are named after Joseph Stefan: Stefan–Boltzmann law Stefan–Boltzmann constant σ Stefan adhesion Stefan problem Stefan's equation Stefan's formula Stefan flow Stefan number Stefan tube Maxwell–Stefan diffusion The Jožef Stefan Institute, Slovenia's premier scientific establishment, is also named after him, and also: Stefan (crater) on the Moon References External links "Josef Stefan: His life and legacy in the thermal sciences," Experimental Thermal and Fluid Science, Volume 31, Issue 7, July 2007, 795–803, by John C. Crepeau Extended biography of Josef Stefan, by John C. Crepeau 1835 births 1893 deaths Slovenian physicists Physicists from Austria-Hungary Poets from Austria-Hungary Slovenian poets Slovenian male poets Carinthian Slovenes Fluid dynamicists Scientists from Klagenfurt Slovene Austro-Hungarians Mathematicians from Austria-Hungary 19th-century male writers Rectors of universities in Austria-Hungary	Josef Stefan	[ "Chemistry" ]	1,010	[ "Fluid dynamicists", "Fluid dynamics" ]
53,045	https://en.wikipedia.org/wiki/File%20Allocation%20Table	File Allocation Table (FAT) is a file system developed for personal computers and was the default filesystem for the MS-DOS and Windows 9x operating systems. Originally developed in 1977 for use on floppy disks, it was adapted for use on hard disks and other devices. The increase in disk drive capacity over time drove modifications to the design that resulted in versions: FAT12, FAT16, FAT32, and exFAT. FAT was replaced with NTFS as the default file system on Microsoft operating systems starting with Windows XP. Nevertheless, FAT continues to be commonly used on relatively small capacity solid-state storage technologies such as SD card, MultiMediaCard (MMC) and eMMC because of its compatibility and ease of implementation. Uses Historical FAT was used on hard disks throughout the DOS and Windows 9x eras. Microsoft introduced NTFS with the Windows NT platform in 1993, but FAT remained the standard for the home user until the introduction of Windows XP in 2001. Windows Me was the final version of Windows to use FAT as its default file system. For floppy disks, FAT has been standardized as ECMA-107 and ISO/IEC 9293:1994 (superseding ISO 9293:1987). These standards cover FAT12 and FAT16 with only short 8.3 filename support; long filenames with VFAT were partially patented. While FAT12 is used on floppy disks, FAT16 and FAT32 are typically found on the larger media. Modern FAT is used internally for the EFI system partition in the boot stage of EFI-compliant computers. FAT is still used in drives expected to be used by multiple operating systems, such as in shared Windows, Linux and DOS environments. Microsoft Windows additionally comes with a pre-installed tool to convert a FAT file system into NTFS directly without the need to rewrite all files, though this cannot be reversed easily. The FAT file system is used in removable media such as floppy disks, super-floppies, memory and flash memory cards or USB flash drives. FAT is supported by portable devices such as PDAs, digital cameras, camcorders, media players, and mobile phones. The DCF file system adopted by almost all digital cameras since 1998 defines a logical file system with 8.3 filenames and makes the use of either FAT12, FAT16, FAT32 or exFAT mandatory for its physical layer for compatibility. Technical details The file system uses an index table stored on the device to identify chains of data storage areas associated with a file, the File Allocation Table (FAT). The FAT is statically allocated at the time of formatting. The table is a linked list of entries for each cluster, a contiguous area of disk storage. Each entry contains either the number of the next cluster in the file, or else a marker indicating the end of the file, unused disk space, or special reserved areas of the disk. The root directory of the disk contains the number of the first cluster of each file in that directory. The operating system can then traverse the FAT, looking up the cluster number of each successive part of the disk file as a cluster chain until the end of the file is reached. Sub-directories are implemented as special files containing the directory entries of their respective files. Each entry in the FAT linked list is a fixed number of bits: 12, 16 or 32. The maximum size of a file or a disk drive that can be accessed is the product of the largest number that can be stored in the entries (less a few values reserved to indicate unallocated space or the end of a list) and the size of the disk cluster. Even if only one byte of storage is needed to extend a file, an entire cluster must be allocated to it. As a result, large numbers of small files can result in clusters being allocated that may contain mostly "empty" data to meet the minimum cluster size. Originally designed as an 8-bit file system, the maximum number of clusters must increase as disk drive capacity increases, and so the number of bits used to identify each cluster has grown. The successive major variants of the FAT format are named after the number of table element bits: 12 (FAT12), 16 (FAT16), and 32 (FAT32). Variants There are several variants of the FAT file system (e.g. FAT12, FAT16 and FAT32). FAT16 refers to both the original group of FAT file systems with 16-bit wide cluster entries and also to later variants. "VFAT" is an optional extension for long file names, which can work on top of any FAT file system. Volumes using VFAT long-filenames can be read also by operating systems not supporting the VFAT extension. Original 8-bit FAT The original FAT file system (or FAT structure, as it was called initially) was designed and implemented by Marc McDonald, based on a series of discussions between McDonald and Bill Gates. It was introduced with 8-bit table elements (and valid data cluster numbers up to 0xBF) in a precursor to Microsoft's Standalone Disk BASIC-80 for an 8080-based successor of the NCR 7200 model VI data-entry terminal, equipped with 8-inch (200 mm) floppy disks, in 1977 or 1978. In 1978, Standalone Disk BASIC-80 was ported to the 8086 using an emulator on a DEC PDP-10, since no real 8086 systems were available at this time. The FAT file system was also used in Microsoft's MDOS/MIDAS, an operating system for 8080/Z80 platforms written by McDonald since 1979. The Standalone Disk BASIC version supported three FATs, whereas this was a parameter for MIDAS. Reportedly, MIDAS was also prepared to support 10-bit, 12-bit and 16-bit FAT variants. While the size of directory entries was 16 bytes in Standalone Disk BASIC, MIDAS instead occupied 32 bytes per entry. Tim Paterson of Seattle Computer Products (SCP) was first introduced to Microsoft's FAT structure when he helped Bob O'Rear adapting the Standalone Disk BASIC-86 emulator port onto SCP's S-100 bus 8086 CPU board prototype during a guest week at Microsoft in May 1979. The final product was shown at Lifeboat Associates' booth stand at the National Computer Conference in New York on June 4–7, 1979, where Paterson learned about the more sophisticated FAT implementation in MDOS/MIDAS and McDonald talked to him about the design of the file system. FAT12 Between April and August 1980, while borrowing the FAT concept for SCP's own 8086 operating system QDOS 0.10, Tim Paterson extended the table elements to 12 bits, reduced the number of FATs to two, redefined the semantics of some of the reserved cluster values, and modified the disk layout, so that the root directory was now located between the FAT and the data area for his implementation of FAT12. Paterson also increased the nine-character (6.3) filename length limit to eleven characters to support CP/M-style 8.3 filenames and File Control Blocks. The format used in Microsoft Standalone Disk BASIC's 8-bit file system precursor was not supported by QDOS. By August 1980, QDOS had been renamed to 86-DOS. Starting with 86-DOS 0.42, the size and layout of directory entries was changed from 16 bytes to 32 bytes in order to add a file date stamp and increase the theoretical file size limit beyond the previous limit of 16 MB. 86-DOS 1.00 became available in early 1981. Later in 1981, 86-DOS evolved into Microsoft's MS-DOS and IBM PC DOS. The capability to read previously formatted volumes with 16-byte directory entries was dropped with MS-DOS 1.20. FAT12 used 12-bit entries for the cluster addresses; some values were reserved to mark the end of a chain of clusters, to mark unusable areas of the disk, or for other purposes, so the maximum number of clusters was limited to 4078. To conserve disk space, two 12-bit FAT entries used three consecutive 8-bit bytes on disk, requiring manipulation to unpack the 12-bit values. This was sufficient for the original floppy disk drives, and small hard disks up to 32 megabytes. The FAT16B version available with DOS 3.31 supported 32-bit sector numbers, and so increased the volume size limit. All the control structures fit inside the first track, to avoid head movement during read and write operations. Any bad sector in the control structures area would make the disk unusable. The DOS formatting tool rejected such disks completely. Bad sectors were allowed only in the file data area. Clusters containing bad sectors were marked unusable with the reserved value 0xFF7 in the FAT. While 86-DOS supported three disk formats (250.25 KB, 616 KB and 1232 KB, with FAT IDs 0xFF and 0xFE) on 8-inch (200 mm) floppy drives, IBM PC DOS 1.0, released with the original IBM Personal Computer in 1981, supported only an 8-sector floppy format with a formatted capacity of 160 KB (FAT ID 0xFE) for single-sided 5.25-inch floppy drives, and PC DOS 1.1 added support for a double-sided format with 320 KB (FAT ID 0xFF). PC DOS 2.0 introduced support for 9-sector floppy formats with 180 KB (FAT ID 0xFC) and 360 KB (FAT ID 0xFD). 86-DOS 1.00 and PC DOS 1.0 directory entries included only one date, the last modified date. PC DOS 1.1 added the last modified time. PC DOS 1.x file attributes included a hidden bit and system bit, with the remaining six bits undefined. At this time, DOS did not support sub-directories, but typically there were only a few dozen files on a diskette. The PC XT was the first PC with an IBM-supplied hard drive, and PC DOS 2.0 supported that hard drive with FAT12 (FAT ID 0xF8). The fixed assumption of 8 sectors per clusters on hard disks practically limited the maximum partition size to 16 MB for 512 byte sectors and 4 KB clusters. The BIOS Parameter Block (BPB) was introduced with PC DOS 2.0 as well, and this version also added read-only, archive, volume label, and directory attribute bits for hierarchical sub-directories. MS-DOS 3.0 introduced support for high-density 1.2 MB 5.25-inch diskettes (media descriptor 0xF9), which notably had 15 sectors per track, hence more space for the FATs. FAT12 remains in use on all common floppy disks, including 1.44 MB and later 2.88 MB disks (media descriptor byte 0xF0). Initial FAT16 In 1984, IBM released the PC AT, which required PC DOS 3.0 to access its 20 MB hard disk. Microsoft introduced MS-DOS 3.0 in parallel. Cluster addresses were increased to 16-bit, allowing for up to 65,526 clusters per volume. However, the maximum possible number of sectors and the maximum partition size of 32 MB did not change. Although cluster addresses were 16 bits, this format was not what today is commonly understood as FAT16. A partition type 0x04 indicates this form of FAT16 with less than 65,536 sectors (less than 32 MB for sector size 512). The benefit of FAT16 was the use of smaller clusters, making disk usage more efficient, particularly for large numbers of files only a few hundred bytes in size. As MS-DOS 3.0 formatted all 16 MB-32 MB partitions in the FAT16 format, a 20 MB hard disk formatted under MS-DOS 3.0 was not accessible by MS-DOS 2.0. MS-DOS 3.0 to MS-DOS 3.30 could still access FAT12 partitions under 15 MB, but required all 16 MB-32 MB partitions to be FAT16, and so could not access MS-DOS 2.0 partitions in this size range. MS-DOS 3.31 and higher could access 16 MB-32 MB FAT12 partitions again. Logical sectored FAT MS-DOS and PC DOS implementations of FAT12 and FAT16 could not access disk partitions larger than 32 megabytes. Several manufacturers developed their own FAT variants within their OEM versions of MS-DOS. Some vendors (AST and NEC) supported eight, instead of the standard four, primary partition entries in their custom extended Master Boot Record (MBR), and they adapted MS-DOS to use more than a single primary partition. Other vendors worked around the volume size limits imposed by the 16-bit sector entries by increasing the apparent size of the sectors the file system operated on. These logical sectors were larger (up to 8192 bytes) than the physical sector size (still 512 bytes) on the disk. The DOS-BIOS or System BIOS would then combine multiple physical sectors into logical sectors for the file system to work with. These changes were transparent to the file system implementation in the DOS kernel. The underlying DOS-BIOS translated these logical sectors into physical sectors according to partitioning information and the drive's physical geometry. The drawback of this approach was increased memory used for sector buffering and deblocking. Since older DOS versions could not use large logical sectors, the OEMs introduced new partition IDs for their FAT variants in order to hide them from off-the-shelf issues of MS-DOS and PC DOS. Known partition IDs for logical sectored FATs include: 0x08 (Commodore MS-DOS 3.x), 0x11 (Leading Edge MS-DOS 3.x), 0x14 (AST MS-DOS 3.x), 0x24 (NEC MS-DOS 3.30), 0x56 (AT&T MS-DOS 3.x), 0xE5 (Tandy MS-DOS), 0xF2 (Sperry IT MS-DOS 3.x, Unisys MS-DOS 3.3 – also used by Digital Research DOS Plus 2.1). OEM versions like Toshiba MS-DOS, Wyse MS-DOS 3.2 and 3.3, as well as Zenith MS-DOS are also known to have utilized logical sectoring. While non-standard and sub-optimal, these FAT variants are perfectly valid according to the specifications of the file system itself. Therefore, even if default issues of MS-DOS and PC DOS were not able to cope with them, most of these vendor-specific FAT12 and FAT16 variants can be mounted by more flexible file system implementations in operating systems such as DR-DOS, simply by changing the partition ID to one of the recognized types. Also, if they no longer need to be recognized by their original operating systems, existing partitions can be "converted" into FAT12 and FAT16 volumes more compliant with versions of MS-DOS/PC DOS 4.0–6.3, which do not support sector sizes different from 512 bytes, by switching to a BPB with 32-bit entry for the number of sectors, as introduced since DOS 3.31 (see FAT16B below), keeping the cluster size and reducing the logical sector size in the BPB down to 512 bytes, while at the same time increasing the counts of logical sectors per cluster, reserved logical sectors, total logical sectors, and logical sectors per FAT by the same factor. A parallel development in MS-DOS / PC DOS which allowed an increase in the maximum possible FAT size was the introduction of multiple FAT partitions on a hard disk. To allow the use of more FAT partitions in a compatible way, a new partition type was introduced in PC DOS 3.2 (1986), the extended partition (EBR), which is a container for an additional partition called logical drive. Since PC DOS 3.3 (April 1987), there is another, optional extended partition containing the next logical drive, and so on. The MBR of a hard disk can either define up to four primary partitions, or an extended partition in addition to up to three primary partitions. Final FAT16 In November 1987, Compaq Personal Computer DOS 3.31 (a modified OEM version of MS-DOS 3.3 released by Compaq with their machines) introduced what today is simply known as the FAT16 format, with the expansion of the 16-bit disk sector count to 32 bits in the BPB. Although the on-disk changes were minor, the entire DOS disk driver had to be converted to use 32-bit sector numbers, a task complicated by the fact that it was written in 16-bit assembly language. The result was initially called the DOS 3.31 Large File System. Microsoft's DSKPROBE tool refers to type 0x06 as BigFAT, whereas some older versions of FDISK described it as BIGDOS. Technically, it is known as FAT16B. Since older versions of DOS were not designed to cope with more than 65,535 sectors, it was necessary to introduce a new partition type for this format in order to hide it from pre-3.31 issues of DOS. The original form of FAT16 (with less than 65,536 sectors) had a partition type 0x04. To deal with disks larger than this, type 0x06 was introduced to indicate 65,536 or more sectors. In addition to this, the disk driver was expanded to cope with more than 65,535 sectors as well. The only other difference between the original FAT16 and the newer FAT16B format is the usage of a newer BPB format with 32-bit sector entry. Therefore, newer operating systems supporting the FAT16B format can cope also with the original FAT16 format without any necessary changes. If partitions to be used by pre-DOS 3.31 issues of DOS need to be created by modern tools, the only criteria theoretically necessary to meet are a sector count of less than 65536, and the usage of the old partition ID (0x04). In practice however, type 0x01 and 0x04 primary partitions should not be physically located outside the first 32 MB of the disk, due to other restrictions in MS-DOS 2.x, which could not cope with them otherwise. In 1988, the FAT16B improvement became more generally available through DR DOS 3.31, PC DOS 4.0, OS/2 1.1, and MS-DOS 4.0. The limit on partition size was dictated by the 8-bit signed count of sectors per cluster, which originally had a maximum power-of-two value of 64. With the standard hard disk sector size of 512 bytes, this gives a maximum of 32 KB cluster size, thereby fixing the "definitive" limit for the FAT16 partition size at 2 GB for sector size 512. On magneto-optical media, which can have 1 or 2 KB sectors instead of 0.5 KB, this size limit is proportionally larger. Much later, Windows NT increased the maximum cluster size to 64 KB, by considering the sectors-per-cluster count as unsigned. However, the resulting format was not compatible with any other FAT implementation of the time, and it generated greater internal fragmentation. Windows 98, SE and ME also supported reading and writing this variant, but its disk utilities did not work with it and some FCB services are not available for such volumes. This contributes to a confusing compatibility situation. Prior to 1995, versions of DOS accessed the disk via CHS addressing only. When Windows 95(MS-DOS 7.0) introduced LBA disk access, partitions could start being physically located outside the first c. 8 GB of this disk and thereby out of the reach of the traditional CHS addressing scheme. Partitions partially or fully located beyond the CHS barrier therefore had to be hidden from non-LBA-enabled operating systems by using the new partition type 0x0E in the partition table instead. FAT16 partitions using this partition type are also named FAT16X. The only difference, compared to previous FAT16 partitions, is the fact that some CHS-related geometry entries in the BPB record, namely the number of sectors per track and the number of heads, may contain no or misleading values and should not be used. The number of root directory entries available for FAT12 and FAT16 is determined when the volume is formatted, and is stored in a 16-bit field. For a given number RDE and sector size SS, the number RDS of root directory sectors is RDS = ceil((RDE × 32) / SS), and RDE is normally chosen to fill these sectors, i.e., RDE × 32 = RDS × SS. FAT12 and FAT16 media typically use 512 root directory entries on non-floppy media. Some third-party tools, like mkdosfs, allow the user to set this parameter. FAT32 In order to overcome the volume size limit of FAT16, while at the same time allowing DOS real-mode code to handle the format, Microsoft designed a new version of the file system, FAT32, which supported an increased number of possible clusters, but could reuse most of the existing code, so that the conventional memory footprint was increased by less than 5 KB under DOS. Cluster values are represented by 32-bit numbers, of which 28 bits are used to hold the cluster number. Maximal sizes The FAT32 boot sector uses a 32-bit field for the sector count, limiting the maximal FAT32 volume size to 2 terabytes with a sector size of 512 bytes. The maximum FAT32 volume size is 16 TB with a sector size of 4,096 bytes. The built-in Windows shell disk format tool on Windows NT arbitrarily only supports volume sizes up to 32 GB, but Windows supports reading and writing to preexisting larger FAT32 volumes, and these can be created with the command prompt, PowerShell or third-party tools, or by formatting the volume on a non-Windows system or on a Windows 9x system with FAT32 support and then transferring it to the Windows NT system. In August 2024, Microsoft released an update to Windows 11 preview builds that allows for the creation of FAT32 partitions up to 2TB in size. The maximal possible size for a file on a FAT32 volume is 4 GB minus 1 byte, or 4,294,967,295 (232 − 1) bytes. This limit is a consequence of the 4-byte file length entry in the directory table and would also affect relatively huge FAT16 partitions enabled by a sufficient sector size. Like FAT12 and FAT16, FAT32 does not include direct built-in support for long filenames, but FAT32 volumes can optionally hold VFAT long filenames in addition to short filenames in exactly the same way as VFAT long filenames have been optionally implemented for FAT12 and FAT16 volumes. Development FAT32 was introduced with Windows 95 OSR2(MS-DOS 7.1) in 1996, although reformatting was needed to use it, and DriveSpace 3 (the version that came with Windows 95 OSR2 and Windows 98) never supported it. Windows 98 introduced a utility to convert existing hard disks from FAT16 to FAT32 without loss of data. In the Windows NT line, native support for FAT32 arrived in Windows 2000. A free FAT32 driver for Windows NT 4.0 was available from Winternals, a company later acquired by Microsoft. The acquisition of the driver from official sources is no longer possible. Since 1998, Caldera's dynamically loadable DRFAT32 driver could be used to enable FAT32 support in DR-DOS. The first version of DR-DOS to natively support FAT32 and LBA access was OEM DR-DOS 7.04 in 1999. That same year IMS introduced native FAT32 support with REAL/32 7.90, and IBM 4690 OS added FAT32 support with version 2. Ahead Software provided another dynamically loadable FAT32.EXE driver for DR-DOS 7.03 with Nero Burning ROM in 2004. IBM introduced native FAT32 support with OEM PC DOS 7.1 in 1999. Two partition types have been reserved for FAT32 partitions, 0x0B and 0x0C. The latter type is also named FAT32X in order to indicate usage of LBA disk access instead of CHS. On such partitions, CHS-related geometry entries, namely the CHS sector addresses in the MBR as well as the number of sectors per track and the number of heads in the EBPB record, may contain no or misleading values and should not be used. Extensions Extended attributes OS/2 heavily depends on extended attributes (EAs) and stores them in a hidden file called "EA␠DATA.␠SF" in the root directory of the FAT12 or FAT16 volume. This file is indexed by two previously reserved bytes in the file's (or directory's) directory entry at offset 0x14. In the FAT32 format, these bytes hold the upper 16 bits of the starting cluster number of the file or directory, hence making it impossible to store OS/2 EAs on FAT32 using this method. However, the third-party FAT32 installable file system (IFS) driver FAT32.IFS version 0.70 and higher by Henk Kelder & Netlabs for OS/2, eComStation and ArcaOS stores extended attributes in extra files with filenames having the string "␠EA.␠SF" appended to the regular filename of the file to which they belong. The driver also utilizes the byte at offset 0x0C in directory entries to store a special mark byte indicating the presence of extended attributes to help speed up things. (This extension is critically incompatible with the FAT32+ method to store files larger than 4 GB minus 1 on FAT32 volumes.) Extended attributes are accessible via the Workplace Shell desktop, through REXX scripts, and many system GUI and command-line utilities (such as 4OS2). To accommodate its OS/2 subsystem, Windows NT supports the handling of extended attributes in HPFS, NTFS, FAT12 and FAT16. It stores EAs on FAT12, FAT16 and HPFS using exactly the same scheme as OS/2, but does not support any other kind of ADS as held on NTFS volumes. Trying to copy a file with any ADS other than EAs from an NTFS volume to a FAT or HPFS volume gives a warning message with the names of the ADSs that will be lost. It does not support the FAT32.IFS method to store EAs on FAT32 volumes. Windows 2000 onward acts exactly as Windows NT, except that it ignores EAs when copying to FAT32 without any warning (but shows the warning for other ADSs, like "Macintosh Finder Info" and "Macintosh Resource Fork"). Cygwin uses "EA␠DATA.␠SF" files as well. Long file names One of the user experience goals for the designers of Windows 95 was the ability to use long filenames (LFNs—up to 255 UTF-16 code units long), in addition to classic 8.3 filenames (SFNs). For backward and forward compatibility, LFNs were implemented as an optional extension on top of the existing FAT file system structures using a workaround in the way directory entries are laid out. This transparent method to store long file names in the existing FAT file systems without altering their data structures is usually known as VFAT (for "Virtual FAT") after the Windows 95 virtual device driver. Non VFAT-enabled operating systems can still access the files under their short file name alias without restrictions; however, the associated long file names may be lost when files with long filenames are copied under non VFAT-aware operating systems. In Windows NT, support for VFAT long filenames began with version 3.5. Linux provides a VFAT filesystem driver to work with FAT volumes with VFAT long filenames. For some time, a UVFAT driver was available to provide combined support for UMSDOS-style permissions with VFAT long filenames. OS/2 added long filename support to FAT using extended attributes (EA) before the introduction of VFAT. Thus, VFAT long filenames are invisible to OS/2, and EA long filenames are invisible to Windows; therefore, experienced users of both operating systems would have to manually rename the files. Human68K supported up to 18.3 filenames and (Shift JIS) Kanji characters in a proprietary FAT file system variant. In order to support Java applications, the FlexOS-based IBM 4690 OS version 2 introduced its own virtual file system (VFS) architecture to store long filenames in the FAT file system in a backwards-compatible fashion. If enabled, the virtual filenames (VFN) are available under separate logical drive letters, whereas the real filenames (RFN) remain available under the original drive letters. Forks and alternate data streams The FAT file system itself is not designed for supporting alternate data streams (ADS), but some operating systems that heavily depend on them have devised various methods for handling them on FAT volumes. Such methods either store the additional information in extra files and directories (classic Mac OS and macOS), or give new semantics to previously unused fields of the FAT on-disk data structures (OS/2 and Windows NT). Mac OS using PC Exchange stores its various dates, file attributes and long filenames in a hidden file called "FINDER.DAT", and resource forks (a common Mac OS ADS) in a subdirectory called "RESOURCE.FRK", in every directory where they are used. From PC Exchange 2.1 onwards, they store the Mac OS long filenames as standard FAT long filenames and convert FAT filenames longer than 31 characters to unique 31-character filenames, which can then be made visible to Macintosh applications. macOS stores resource forks and metadata (file attributes, other ADS) using AppleDouble format in a hidden file with a name constructed from the owner filename prefixed with "._", and Finder stores some folder and file metadata in a hidden file called ".DS_Store" (but note that Finder uses .DS_Store even on macOS' native filesystem, HFS+). UMSDOS permissions and filenames Early Linux distributions also supported a format known as UMSDOS, a FAT variant with Unix file attributes (such as long file name and access permissions) stored in a separate file called "--linux-.---". UMSDOS fell into disuse after VFAT was released and it is not enabled by default in Linux from version 2.5.7 onwards. For some time, Linux also provided combined support for UMSDOS-style permissions and VFAT long filenames through UVFAT. FAT+ In 2007 the open FAT+ draft proposed how to store larger files up to 256 GB minus 1 byte, or 274,877,906,943 (238 − 1) bytes, on slightly modified and otherwise backward-compatible FAT32 volumes, but imposes a risk that disk tools or FAT32 implementations not aware of this extension may truncate or delete files exceeding the normal FAT32 file size limit. Support for FAT32+ and FAT16+ is limited to some versions of DR-DOS and not available in mainstream operating systems. (This extension is critically incompatible with the /EAS option of the FAT32.IFS method to store OS/2 extended attributes on FAT32 volumes.) Derivatives Turbo FAT In its NetWare File System (NWFS) Novell implemented a heavily modified variant of a FAT file system for the NetWare operating system. For larger files it utilized a performance feature named Turbo FAT. FATX FATX is a family of file systems designed for Microsoft's Xbox video game console hard disk drives and memory cards, introduced in 2001. While resembling the same basic design ideas as FAT16 and FAT32, the FATX16 and FATX32 on-disk structures are simplified, but fundamentally incompatible with normal FAT16 and FAT32 file systems, making it impossible for normal FAT file system drivers to mount such volumes. The non-bootable superblock sector is 4 KB in size and holds an 18 byte large BPB-like structure completely different from normal BPBs. Clusters are typically 16 KB in size and there is only one copy of the FAT on the Xbox. Directory entries are 64 bytes in size instead of the normal 32 bytes. Files can have filenames up to 42 characters long using the OEM character set and be up to 4 GB minus 1 byte in size. The on-disk timestamps hold creation, modification and access dates and times but differ from FAT: in FAT, the epoch is 1980; in FATX, the epoch is 2000. On the Xbox 360, the epoch is 1980. exFAT exFAT is a file system introduced with Windows Embedded CE 6.0 in November 2006 and brought to the Windows NT family with Vista Service Pack 1 and Windows XP Service Pack 3 (or separate installation of Windows XP Update KB955704). It is loosely based on the File Allocation Table architecture, but incompatible, proprietary and protected by patents. exFAT is intended for use on flash drives and memory cards such as SDXC and Memory Stick XC, where FAT32 is otherwise used. Vendors usually pre-format SDXC cards with it. Its main benefit is its exceeding of the 4 GB file size limit, as file size references are stored with eight instead of four bytes, increasing the limit to 264 − 1 bytes. Microsoft's GUI and command-line format utilities offer it as an alternative to NTFS (and, for smaller partitions, to FAT16B and FAT32). The MBR partition type is 0x07 (the same as used for IFS, HPFS, and NTFS). Logical geometry information located in the VBR is stored in a format not resembling any kind of BPB. In early 2010, the file system was reverse-engineered by the SANS Institute. On August 28, 2019, Microsoft published the technical specification for exFAT so that it can be used in the Linux kernel and other operating systems. Patents Microsoft applied for, and was granted, a series of patents for key parts of the FAT file system in the mid-1990s. All four pertain to long-filename extensions to FAT first seen in Windows 95: U.S. patent 5,579,517, U.S. patent 5,745,902, U.S. patent 5,758,352, U.S. patent 6,286,013 (all expired since 2013). On December 3, 2003, Microsoft announced that it would be offering licenses for use of its FAT specification and "associated intellectual property", at the cost of a royalty per unit sold, with a maximum royalty per license agreement. To this end, Microsoft cited four patents on the FAT file system as the basis of its intellectual property claims. In the EFI FAT32 specification, Microsoft specifically grants a number of rights, which many readers have interpreted as permitting operating system vendors to implement FAT. Non-Microsoft patents affecting FAT include: U.S. patent 5,367,671, specific to the OS/2 extended object attributes (expired in 2011). Challenges and lawsuits The Public Patent Foundation (PUBPAT) submitted evidence to the US Patent and Trademark Office (USPTO) in 2004 disputing the validity of U.S. patent 5,579,517, including prior art references from Xerox and IBM. The USPTO opened an investigation and concluded by rejecting all claims in the patent. The next year, the USPTO further announced that following the re-examination process, it affirmed the rejection of '517 and additionally found U.S. patent 5,758,352 invalid on the grounds that the patent had incorrect assignees. However, in 2006, the USPTO ruled that features of Microsoft's implementation of the FAT system were "novel and non-obvious", reversing both earlier decisions and leaving the patents valid. In February 2009, Microsoft filed a patent infringement lawsuit against TomTom alleging that the device maker's products infringe on patents related to VFAT long filenames. As some TomTom products are based on Linux, this marked the first time that Microsoft tried to enforce its patents against the Linux platform. The lawsuit was settled out of court the following month with an agreement that Microsoft be given access to four of TomTom's patents, that TomTom will drop support for the VFAT long filenames from its products, and that in return Microsoft not seek legal action against TomTom for the five-year duration of the settlement agreement. In October 2010, Microsoft filed a patent infringement lawsuit against Motorola alleging several patents (including two of the VFAT patents) were not licensed for use in the Android operating system. They also submitted a complaint to the ITC. Developers of open source software have designed methods intended to circumvent Microsoft's patents. In 2013, patent EP0618540 "common name space for long and short filenames" (expired since 2014) was invalidated in Germany. After the appeal was withdrawn, this judgment became final on the 28th October 2015. See also Comparison of file systems Design of the FAT file system Drive letter assignment List of file systems Transaction-Safe FAT File System Notes References External links Description of the FAT32 File System: Microsoft Knowledge Base Article 154997 MS-DOS: Directory and Subdirectory Limitations: Microsoft Knowledge Base Article 39927 Overview of FAT, HPFS, and NTFS File Systems: Microsoft Knowledge Base Article 100108 Microsoft Technet; Volume and file size limits of FAT file systems, copy made by Internet Archive Wayback Machine of an article with summary of limits in FAT32 which is no longer available on Microsoft website. Chen, Raymond; Microsoft TechNet: A Brief and Incomplete History of FAT32 Fdisk does not recognize full size of hard disks larger than : Microsoft Knowledge Base Article 263044, copy made by Internet Archive Wayback Machine. Explains inability to work with extremely large volumes under Windows 95/98. Microsoft Windows XP: FAT32 File System, copy made by the Internet Archive's Wayback Machine of an article with summary of limits in FAT32 which is no longer available on Microsoft website. 1977 software Computer file systems Disk file systems DOS technology Ecma standards File systems supported by the Linux kernel Windows components Windows disk file systems	File Allocation Table	[ "Technology" ]	8,044	[ "Computer standards", "Ecma standards" ]
53,057	https://en.wikipedia.org/wiki/Pareto%20distribution	The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto, but the concepts are distinct, and only Pareto distributions with shape value () of log45 ≈ 1.16 precisely reflect it. Empirical observation has shown that this 80-20 distribution fits a wide range of cases, including natural phenomena and human activities. Definitions If X is a random variable with a Pareto (Type I) distribution, then the probability that X is greater than some number x, i.e., the survival function (also called tail function), is given by where xm is the (necessarily positive) minimum possible value of X, and α is a positive parameter. The type I Pareto distribution is characterized by a scale parameter xm and a shape parameter α, which is known as the tail index. If this distribution is used to model the distribution of wealth, then the parameter α is called the Pareto index. Cumulative distribution function From the definition, the cumulative distribution function of a Pareto random variable with parameters α and xm is Probability density function It follows (by differentiation) that the probability density function is When plotted on linear axes, the distribution assumes the familiar J-shaped curve which approaches each of the orthogonal axes asymptotically. All segments of the curve are self-similar (subject to appropriate scaling factors). When plotted in a log–log plot, the distribution is represented by a straight line. Properties Moments and characteristic function The expected value of a random variable following a Pareto distribution is The variance of a random variable following a Pareto distribution is (If α ≤ 2, the variance does not exist.) The raw moments are The moment generating function is only defined for non-positive values t ≤ 0 as Thus, since the expectation does not converge on an open interval containing we say that the moment generating function does not exist. The characteristic function is given by where Γ(a, x) is the incomplete gamma function. The parameters may be solved for using the method of moments. Conditional distributions The conditional probability distribution of a Pareto-distributed random variable, given the event that it is greater than or equal to a particular number exceeding , is a Pareto distribution with the same Pareto index but with minimum instead of : This implies that the conditional expected value (if it is finite, i.e. ) is proportional to : In case of random variables that describe the lifetime of an object, this means that life expectancy is proportional to age, and is called the Lindy effect or Lindy's Law. A characterization theorem Suppose are independent identically distributed random variables whose probability distribution is supported on the interval for some . Suppose that for all , the two random variables and are independent. Then the common distribution is a Pareto distribution. Geometric mean The geometric mean (G) is Harmonic mean The harmonic mean (H) is Graphical representation The characteristic curved 'long tail' distribution, when plotted on a linear scale, masks the underlying simplicity of the function when plotted on a log-log graph, which then takes the form of a straight line with negative gradient: It follows from the formula for the probability density function that for x ≥ xm, Since α is positive, the gradient −(α + 1) is negative. Related distributions Generalized Pareto distributions There is a hierarchy of Pareto distributions known as Pareto Type I, II, III, IV, and Feller–Pareto distributions. Pareto Type IV contains Pareto Type I–III as special cases. The Feller–Pareto distribution generalizes Pareto Type IV. Pareto types I–IV The Pareto distribution hierarchy is summarized in the next table comparing the survival functions (complementary CDF). When μ = 0, the Pareto distribution Type II is also known as the Lomax distribution. In this section, the symbol xm, used before to indicate the minimum value of x, is replaced by σ. The shape parameter α is the tail index, μ is location, σ is scale, γ is an inequality parameter. Some special cases of Pareto Type (IV) are The finiteness of the mean, and the existence and the finiteness of the variance depend on the tail index α (inequality index γ). In particular, fractional δ-moments are finite for some δ > 0, as shown in the table below, where δ is not necessarily an integer. Feller–Pareto distribution Feller defines a Pareto variable by transformation U = Y−1 − 1 of a beta random variable ,Y, whose probability density function is where B( ) is the beta function. If then W has a Feller–Pareto distribution FP(μ, σ, γ, γ1, γ2). If and are independent Gamma variables, another construction of a Feller–Pareto (FP) variable is and we write W ~ FP(μ, σ, γ, δ1, δ2). Special cases of the Feller–Pareto distribution are Inverse-Pareto Distribution / Power Distribution When a random variable follows a pareto distribution, then its inverse follows an Inverse Pareto distribution. Inverse Pareto distribution is equivalent to a Power distribution Relation to the exponential distribution The Pareto distribution is related to the exponential distribution as follows. If X is Pareto-distributed with minimum xm and index α, then is exponentially distributed with rate parameter α. Equivalently, if Y is exponentially distributed with rate α, then is Pareto-distributed with minimum xm and index α. This can be shown using the standard change-of-variable techniques: The last expression is the cumulative distribution function of an exponential distribution with rate α. Pareto distribution can be constructed by hierarchical exponential distributions. Let and . Then we have and, as a result, . More in general, if (shape-rate parametrization) and , then . Equivalently, if and , then . Relation to the log-normal distribution The Pareto distribution and log-normal distribution are alternative distributions for describing the same types of quantities. One of the connections between the two is that they are both the distributions of the exponential of random variables distributed according to other common distributions, respectively the exponential distribution and normal distribution. (See the previous section.) Relation to the generalized Pareto distribution The Pareto distribution is a special case of the generalized Pareto distribution, which is a family of distributions of similar form, but containing an extra parameter in such a way that the support of the distribution is either bounded below (at a variable point), or bounded both above and below (where both are variable), with the Lomax distribution as a special case. This family also contains both the unshifted and shifted exponential distributions. The Pareto distribution with scale and shape is equivalent to the generalized Pareto distribution with location , scale and shape and, conversely, one can get the Pareto distribution from the GPD by taking and if . Bounded Pareto distribution The bounded (or truncated) Pareto distribution has three parameters: α, L and H. As in the standard Pareto distribution α determines the shape. L denotes the minimal value, and H denotes the maximal value. The probability density function is , where L ≤ x ≤ H, and α > 0. Generating bounded Pareto random variables If U is uniformly distributed on (0, 1), then applying inverse-transform method is a bounded Pareto-distributed. Symmetric Pareto distribution The purpose of the Symmetric and Zero Symmetric Pareto distributions is to capture some special statistical distribution with a sharp probability peak and symmetric long probability tails. These two distributions are derived from the Pareto distribution. Long probability tails normally means that probability decays slowly, and can be used to fit a variety of datasets. But if the distribution has symmetric structure with two slow decaying tails, Pareto could not do it. Then Symmetric Pareto or Zero Symmetric Pareto distribution is applied instead. The Cumulative distribution function (CDF) of Symmetric Pareto distribution is defined as following: The corresponding probability density function (PDF) is: This distribution has two parameters: a and b. It is symmetric about b. Then the mathematic expectation is b. When, it has variance as following: The CDF of Zero Symmetric Pareto (ZSP) distribution is defined as following: The corresponding PDF is: This distribution is symmetric about zero. Parameter a is related to the decay rate of probability and (a/2b) represents peak magnitude of probability. Multivariate Pareto distribution The univariate Pareto distribution has been extended to a multivariate Pareto distribution. Statistical inference Estimation of parameters The likelihood function for the Pareto distribution parameters α and xm, given an independent sample x = (x1, x2, ..., xn), is Therefore, the logarithmic likelihood function is It can be seen that is monotonically increasing with xm, that is, the greater the value of xm, the greater the value of the likelihood function. Hence, since x ≥ xm, we conclude that To find the estimator for α, we compute the corresponding partial derivative and determine where it is zero: Thus the maximum likelihood estimator for α is: The expected statistical error is: Malik (1970) gives the exact joint distribution of . In particular, and are independent and is Pareto with scale parameter xm and shape parameter nα, whereas has an inverse-gamma distribution with shape and scale parameters n − 1 and nα, respectively. Occurrence and applications General Vilfredo Pareto originally used this distribution to describe the allocation of wealth among individuals since it seemed to show rather well the way that a larger portion of the wealth of any society is owned by a smaller percentage of the people in that society. He also used it to describe distribution of income. This idea is sometimes expressed more simply as the Pareto principle or the "80-20 rule" which says that 20% of the population controls 80% of the wealth. As Michael Hudson points out (The Collapse of Antiquity [2023] p. 85 & n.7) "a mathematical corollary [is] that 10% would have 65% of the wealth, and 5% would have half the national wealth.” However, the 80-20 rule corresponds to a particular value of α, and in fact, Pareto's data on British income taxes in his Cours d'économie politique indicates that about 30% of the population had about 70% of the income. The probability density function (PDF) graph at the beginning of this article shows that the "probability" or fraction of the population that owns a small amount of wealth per person is rather high, and then decreases steadily as wealth increases. (The Pareto distribution is not realistic for wealth for the lower end, however. In fact, net worth may even be negative.) This distribution is not limited to describing wealth or income, but to many situations in which an equilibrium is found in the distribution of the "small" to the "large". The following examples are sometimes seen as approximately Pareto-distributed: All four variables of the household's budget constraint: consumption, labor income, capital income, and wealth. The sizes of human settlements (few cities, many hamlets/villages) File size distribution of Internet traffic which uses the TCP protocol (many smaller files, few larger ones) Hard disk drive error rates Clusters of Bose–Einstein condensate near absolute zero The values of oil reserves in oil fields (a few large fields, many small fields) The length distribution in jobs assigned to supercomputers (a few large ones, many small ones) The standardized price returns on individual stocks Sizes of sand particles The size of meteorites Severity of large casualty losses for certain lines of business such as general liability, commercial auto, and workers compensation. Amount of time a user on Steam will spend playing different games. (Some games get played a lot, but most get played almost never.) In hydrology the Pareto distribution is applied to extreme events such as annually maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Pareto distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis. In Electric Utility Distribution Reliability (80% of the Customer Minutes Interrupted occur on approximately 20% of the days in a given year). Relation to Zipf's law The Pareto distribution is a continuous probability distribution. Zipf's law, also sometimes called the zeta distribution, is a discrete distribution, separating the values into a simple ranking. Both are a simple power law with a negative exponent, scaled so that their cumulative distributions equal 1. Zipf's can be derived from the Pareto distribution if the values (incomes) are binned into ranks so that the number of people in each bin follows a 1/rank pattern. The distribution is normalized by defining so that where is the generalized harmonic number. This makes Zipf's probability density function derivable from Pareto's. where and is an integer representing rank from 1 to N where N is the highest income bracket. So a randomly selected person (or word, website link, or city) from a population (or language, internet, or country) has probability of ranking . Relation to the "Pareto principle" The "80–20 law", according to which 20% of all people receive 80% of all income, and 20% of the most affluent 20% receive 80% of that 80%, and so on, holds precisely when the Pareto index is . This result can be derived from the Lorenz curve formula given below. Moreover, the following have been shown to be mathematically equivalent: Income is distributed according to a Pareto distribution with index α > 1. There is some number 0 ≤ p ≤ 1/2 such that 100p % of all people receive 100(1 − p)% of all income, and similarly for every real (not necessarily integer) n > 0, 100pn % of all people receive 100(1 − p)n percentage of all income. α and p are related by This does not apply only to income, but also to wealth, or to anything else that can be modeled by this distribution. This excludes Pareto distributions in which 0 < α ≤ 1, which, as noted above, have an infinite expected value, and so cannot reasonably model income distribution. Relation to Price's law Price's square root law is sometimes offered as a property of or as similar to the Pareto distribution. However, the law only holds in the case that . Note that in this case, the total and expected amount of wealth are not defined, and the rule only applies asymptotically to random samples. The extended Pareto Principle mentioned above is a far more general rule. Lorenz curve and Gini coefficient The Lorenz curve is often used to characterize income and wealth distributions. For any distribution, the Lorenz curve L(F) is written in terms of the PDF f or the CDF F as where x(F) is the inverse of the CDF. For the Pareto distribution, and the Lorenz curve is calculated to be For the denominator is infinite, yielding L=0. Examples of the Lorenz curve for a number of Pareto distributions are shown in the graph on the right. According to Oxfam (2016) the richest 62 people have as much wealth as the poorest half of the world's population. We can estimate the Pareto index that would apply to this situation. Letting ε equal we have: or The solution is that α equals about 1.15, and about 9% of the wealth is owned by each of the two groups. But actually the poorest 69% of the world adult population owns only about 3% of the wealth. The Gini coefficient is a measure of the deviation of the Lorenz curve from the equidistribution line which is a line connecting [0, 0] and [1, 1], which is shown in black (α = ∞) in the Lorenz plot on the right. Specifically, the Gini coefficient is twice the area between the Lorenz curve and the equidistribution line. The Gini coefficient for the Pareto distribution is then calculated (for ) to be (see Aaberge 2005). Random variate generation Random samples can be generated using inverse transform sampling. Given a random variate U drawn from the uniform distribution on the unit interval [0, 1], the variate T given by is Pareto-distributed. See also References Notes External links syntraf1.c is a C program to generate synthetic packet traffic with bounded Pareto burst size and exponential interburst time. Actuarial science Continuous distributions Eponyms in economics Power laws Probability distributions with non-finite variance Management science Exponential family distributions Vilfredo Pareto	Pareto distribution	[ "Mathematics", "Biology" ]	3,587	[ "Behavior", "Applied mathematics", "Behavioural sciences", "Actuarial science", "Management science" ]
53,058	https://en.wikipedia.org/wiki/Regular%20space	In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms. Definitions A topological space X is a regular space if, given any closed set F and any point x that does not belong to F, there exists a neighbourhood U of x and a neighbourhood V of F that are disjoint. Concisely put, it must be possible to separate x and F with disjoint neighborhoods. A or is a topological space that is both regular and a Hausdorff space. (A Hausdorff space or T2 space is a topological space in which any two distinct points are separated by neighbourhoods.) It turns out that a space is T3 if and only if it is both regular and T0. (A T0 or Kolmogorov space is a topological space in which any two distinct points are topologically distinguishable, i.e., for every pair of distinct points, at least one of them has an open neighborhood not containing the other.) Indeed, if a space is Hausdorff then it is T0, and each T0 regular space is Hausdorff: given two distinct points, at least one of them misses the closure of the other one, so (by regularity) there exist disjoint neighborhoods separating one point from (the closure of) the other. Although the definitions presented here for "regular" and "T3" are not uncommon, there is significant variation in the literature: some authors switch the definitions of "regular" and "T3" as they are used here, or use both terms interchangeably. This article uses the term "regular" freely, but will usually say "regular Hausdorff", which is unambiguous, instead of the less precise "T3". For more on this issue, see History of the separation axioms. A is a topological space where every point has an open neighbourhood that is regular. Every regular space is locally regular, but the converse is not true. A classical example of a locally regular space that is not regular is the bug-eyed line. Relationships to other separation axioms A regular space is necessarily also preregular, i.e., any two topologically distinguishable points can be separated by neighbourhoods. Since a Hausdorff space is the same as a preregular T0 space, a regular space which is also T0 must be Hausdorff (and thus T3). In fact, a regular Hausdorff space satisfies the slightly stronger condition T2½. (However, such a space need not be completely Hausdorff.) Thus, the definition of T3 may cite T0, T1, or T2½ instead of T2 (Hausdorffness); all are equivalent in the context of regular spaces. Speaking more theoretically, the conditions of regularity and T3-ness are related by Kolmogorov quotients. A space is regular if and only if its Kolmogorov quotient is T3; and, as mentioned, a space is T3 if and only if it's both regular and T0. Thus a regular space encountered in practice can usually be assumed to be T3, by replacing the space with its Kolmogorov quotient. There are many results for topological spaces that hold for both regular and Hausdorff spaces. Most of the time, these results hold for all preregular spaces; they were listed for regular and Hausdorff spaces separately because the idea of preregular spaces came later. On the other hand, those results that are truly about regularity generally don't also apply to nonregular Hausdorff spaces. There are many situations where another condition of topological spaces (such as normality, pseudonormality, paracompactness, or local compactness) will imply regularity if some weaker separation axiom, such as preregularity, is satisfied. Such conditions often come in two versions: a regular version and a Hausdorff version. Although Hausdorff spaces aren't generally regular, a Hausdorff space that is also (say) locally compact will be regular, because any Hausdorff space is preregular. Thus from a certain point of view, regularity is not really the issue here, and we could impose a weaker condition instead to get the same result. However, definitions are usually still phrased in terms of regularity, since this condition is more well known than any weaker one. Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition. Regular spaces should also be contrasted with normal spaces. Examples and nonexamples A zero-dimensional space with respect to the small inductive dimension has a base consisting of clopen sets. Every such space is regular. As described above, any completely regular space is regular, and any T0 space that is not Hausdorff (and hence not preregular) cannot be regular. Most examples of regular and nonregular spaces studied in mathematics may be found in those two articles. On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems. Of course, one can easily find regular spaces that are not T0, and thus not Hausdorff, such as an indiscrete space, but these examples provide more insight on the T0 axiom than on regularity. An example of a regular space that is not completely regular is the Tychonoff corkscrew. Most interesting spaces in mathematics that are regular also satisfy some stronger condition. Thus, regular spaces are usually studied to find properties and theorems, such as the ones below, that are actually applied to completely regular spaces, typically in analysis. There exist Hausdorff spaces that are not regular. An example is the K-topology on the set of real numbers. More generally, if is a fixed nonclosed subset of with empty interior with respect to the usual Euclidean topology, one can construct a finer topology on by taking as a base the collection of all sets and for open in the usual topology. That topology will be Hausdorff, but not regular. Elementary properties Suppose that X is a regular space. Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G. In fancier terms, the closed neighbourhoods of x form a local base at x. In fact, this property characterises regular spaces; if the closed neighbourhoods of each point in a topological space form a local base at that point, then the space must be regular. Taking the interiors of these closed neighbourhoods, we see that the regular open sets form a base for the open sets of the regular space X. This property is actually weaker than regularity; a topological space whose regular open sets form a base is semiregular. References Separation axioms Properties of topological spaces Topology	Regular space	[ "Physics", "Mathematics" ]	1,520	[ "Properties of topological spaces", "Space (mathematics)", "Topological spaces", "Topology", "Space", "Geometry", "Spacetime" ]
53,064	https://en.wikipedia.org/wiki/Kerckhoffs%27s%20principle	Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be secure, even if everything about the system, except the key, is public knowledge. This concept is widely embraced by cryptographers, in contrast to security through obscurity, which is not. Kerckhoffs's principle was phrased by American mathematician Claude Shannon as "the enemy knows the system", i.e., "one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them". In that form, it is called Shannon's maxim. Another formulation by American researcher and professor Steven M. Bellovin is: In other words — design your system assuming that your opponents know it in detail. (A former official at NSA's National Computer Security Center told me that the standard assumption there was that serial number 1 of any new device was delivered to the Kremlin.) Origins The invention of telegraphy radically changed military communications and increased the number of messages that needed to be protected from the enemy dramatically, leading to the development of field ciphers which had to be easy to use without large confidential codebooks prone to capture on the battlefield. It was this environment which led to the development of Kerckhoffs' requirements. Auguste Kerckhoffs was a professor of German language at Ecole des Hautes Etudes Commerciales (HEC) in Paris. In early 1883, Kerckhoffs' article, La Cryptographie Militaire, was published in two parts in the Journal of Military Science, in which he stated six design rules for military ciphers. Translated from French, they are: The system must be practically, if not mathematically, indecipherable; It should not require secrecy, and it should not be a problem if it falls into enemy hands; It must be possible to communicate and remember the key without using written notes, and correspondents must be able to change or modify it at will; It must be applicable to telegraph communications; It must be portable, and should not require several persons to handle or operate; Lastly, given the circumstances in which it is to be used, the system must be easy to use and should not be stressful to use or require its users to know and comply with a long list of rules. Some are no longer relevant given the ability of computers to perform complex encryption. The second rule, now known as Kerckhoffs's principle, is still critically important. Explanation of the principle Kerckhoffs viewed cryptography as a rival to, and a better alternative than, steganographic encoding, which was common in the nineteenth century for hiding the meaning of military messages. One problem with encoding schemes is that they rely on humanly-held secrets such as "dictionaries" which disclose for example, the secret meaning of words. Steganographic-like dictionaries, once revealed, permanently compromise a corresponding encoding system. Another problem is that the risk of exposure increases as the number of users holding the secrets increases. Nineteenth century cryptography, in contrast, used simple tables which provided for the transposition of alphanumeric characters, generally given row-column intersections which could be modified by keys which were generally short, numeric, and could be committed to human memory. The system was considered "indecipherable" because tables and keys do not convey meaning by themselves. Secret messages can be compromised only if a matching set of table, key, and message falls into enemy hands in a relevant time frame. Kerckhoffs viewed tactical messages as only having a few hours of relevance. Systems are not necessarily compromised, because their components (i.e. alphanumeric character tables and keys) can be easily changed. Advantage of secret keys Using secure cryptography is supposed to replace the difficult problem of keeping messages secure with a much more manageable one, keeping relatively small keys secure. A system that requires long-term secrecy for something as large and complex as the whole design of a cryptographic system obviously cannot achieve that goal. It only replaces one hard problem with another. However, if a system is secure even when the enemy knows everything except the key, then all that is needed is to manage keeping the keys secret. There are a large number of ways the internal details of a widely used system could be discovered. The most obvious is that someone could bribe, blackmail, or otherwise threaten staff or customers into explaining the system. In war, for example, one side will probably capture some equipment and people from the other side. Each side will also use spies to gather information. If a method involves software, someone could do memory dumps or run the software under the control of a debugger in order to understand the method. If hardware is being used, someone could buy or steal some of the hardware and build whatever programs or gadgets needed to test it. Hardware can also be dismantled so that the chip details can be examined under the microscope. Maintaining security A generalization some make from Kerckhoffs's principle is: "The fewer and simpler the secrets that one must keep to ensure system security, the easier it is to maintain system security." Bruce Schneier ties it in with a belief that all security systems must be designed to fail as gracefully as possible: Any security system depends crucially on keeping some things secret. However, Kerckhoffs's principle points out that the things kept secret ought to be those least costly to change if inadvertently disclosed. For example, a cryptographic algorithm may be implemented by hardware and software that is widely distributed among users. If security depends on keeping that secret, then disclosure leads to major logistic difficulties in developing, testing, and distributing implementations of a new algorithm – it is "brittle". On the other hand, if keeping the algorithm secret is not important, but only the keys used with the algorithm must be secret, then disclosure of the keys simply requires the simpler, less costly process of generating and distributing new keys. Applications In accordance with Kerckhoffs's principle, the majority of civilian cryptography makes use of publicly known algorithms. By contrast, ciphers used to protect classified government or military information are often kept secret (see Type 1 encryption). However, it should not be assumed that government/military ciphers must be kept secret to maintain security. It is possible that they are intended to be as cryptographically sound as public algorithms, and the decision to keep them secret is in keeping with a layered security posture. Security through obscurity It is moderately common for companies, and sometimes even standards bodies as in the case of the CSS encryption on DVDs, to keep the inner workings of a system secret. Some argue this "security by obscurity" makes the product safer and less vulnerable to attack. A counter-argument is that keeping the innards secret may improve security in the short term, but in the long run, only systems that have been published and analyzed should be trusted. Steven Bellovin and Randy Bush commented: References Notes External links Reference to Kerckhoffs's original paper, with scanned original text Computer architecture statements Cryptography	Kerckhoffs's principle	[ "Mathematics", "Engineering" ]	1,494	[ "Applied mathematics", "Cryptography", "Cybersecurity engineering" ]
53,135	https://en.wikipedia.org/wiki/Magnetic%20anomaly%20detector	A magnetic anomaly detector (MAD) is an instrument used to detect minute variations in the Earth's magnetic field. The term typically refers to magnetometers used by military forces to detect submarines (a mass of ferromagnetic material creates a detectable disturbance in the magnetic field). Military MAD equipment is a descendant of geomagnetic survey or aeromagnetic survey instruments used to search for minerals by detecting their disturbance of the normal earth-field. History Geoexploration by measuring and studying variations in the Earth's magnetic field has been conducted by scientists since 1843. The first uses of magnetometers were for the location of ore deposits. Thalen's "The Examination of Iron Ore Deposits by Magnetic Measurements", published in 1879, was the first scientific treatise describing this practical use. Magnetic anomaly detectors employed to detect submarines during World War II harnessed the fluxgate magnetometer, an inexpensive and easy to use technology developed in the 1930s by Victor Vacquier of Gulf Oil for finding ore deposits. MAD gear was used by both Japanese and U.S. anti-submarine forces, either towed by ship or mounted in aircraft to detect shallow submerged enemy submarines. The Japanese called the technology jikitanchiki (磁気探知機, "Magnetic Detector"). After the war, the U.S. Navy continued to develop MAD gear as a parallel development with sonar detection technologies. Satellite, near-surface and oceanic data from detectors was used to create the World Digital Magnetic Anomaly Map published by the Commission for the Geological Map of the World (CGMW) in July 2007. Operation The magnetic anomaly from a submarine is usually very small. One source estimates that it is only about 0.2 nT at a distance of 600 m. Another source estimates that a 100m long and 10 m wide submarine would produce a magnetic flux of 13.33 nT at 500m, 1.65 nT at 1km and 0.01 nT at 5km. To reduce interference from electrical equipment or metal in the fuselage of the aircraft, the MAD sensor is placed at the end of a boom or on a towed aerodynamic device. Even so, the submarine must be very near the aircraft's position and close to the sea surface for detection of the anomaly, because magnetic fields decrease as the inverse cube of distance, one source gives a detection slant range of 500m. The size of the submarine, its hull composition and orientation, as well as the water depth and complexity of the natural magnetic field, determine the detection range. MAD devices are usually mounted on aircraft. For example, one study showed that a horizontal detection range of 450–800m, when aircraft was 200m above a submarine, decreased to less than 150m when the aircraft was 400m above the submarine. If the sea floor has sunken ships, then submarines may operate near them to confuse magnetic anomaly detectors. MAD has certain advantages over other detection methods. It is a passive detection method. Unlike sonar it is not impacted by meteorological conditions; indeed above sea state 5, MAD may be the only reliable method for submarine detection. Other uses For aeromagnetic survey applications the magnetic sensor can be mounted on an aircraft (typically on a long probe in front of or behind the aircraft to reduce the magnetic effects of the aircraft itself) or in a towed device. A chart is produced that geologists and geophysicists can study to determine the distribution and concentration of magnetic minerals which are related to geology and mineral deposits. See also Submarine detection system Autolycus, exhaust plume detector References Anti-submarine warfare Military electronics Geophysics Naval weapons of the United States Military sensor technology	Magnetic anomaly detector	[ "Physics" ]	737	[ "Applied and interdisciplinary physics", "Geophysics" ]
53,136	https://en.wikipedia.org/wiki/Weapon%20of%20mass%20destruction	A weapon of mass destruction (WMD) is a biological, chemical, radiological, nuclear, or any other weapon that can kill or significantly harm many people or cause great damage to artificial structures (e.g., buildings), natural structures (e.g., mountains), or the biosphere. The scope and usage of the term has evolved and been disputed, often signifying more politically than technically. Originally coined in reference to aerial bombing with chemical explosives during World War II, it has later come to refer to large-scale weaponry of warfare-related technologies, such as biological, chemical, radiological, or nuclear warfare. Early uses of this term The first use of the term "weapon of mass destruction" on record is by Cosmo Gordon Lang, Archbishop of Canterbury, in 1937 in reference to the bombing of Guernica, Spain: At the time, nuclear weapons had not been developed fully. Japan conducted research on biological weapons , and chemical weapons had seen wide battlefield use in World War I. Their use was outlawed by the Geneva Protocol of 1925. Italy used mustard agent against civilians and soldiers in Ethiopia in 1935–36. Following the atomic bombings of Hiroshima and Nagasaki that ended World War II and during the Cold War, the term came to refer more to non-conventional weapons. The application of the term to specifically nuclear and radiological weapons is traced by William Safire to the Russian phrase "Оружие массового поражения" – oruzhiye massovogo porazheniya (weapon of mass destruction). William Safire credits James Goodby (of the Brookings Institution) with tracing what he considers the earliest known English-language use soon after the nuclear bombing of Hiroshima and Nagasaki (although it is not quite verbatim): a communique from a 15 November 1945, meeting of Harry Truman, Clement Attlee and Mackenzie King (probably drafted by Vannevar Bush, as Bush claimed in 1970) referred to "weapons adaptable to mass destruction." Safire says Bernard Baruch used that exact phrase in 1946 (in a speech at the United Nations probably written by Herbert Bayard Swope). The phrase found its way into the very first resolution the United Nations General assembly adopted in January 1946 in London, which used the wording "the elimination from national armaments of atomic weapons and of all other weapons adaptable to mass destruction." The resolution also created the Atomic Energy Commission (predecessor of the International Atomic Energy Agency (IAEA)). An exact use of this term was given in a lecture titled "Atomic Energy as a Contemporary Problem" by J. Robert Oppenheimer. He delivered the lecture to the Foreign Service and the State Department, on 17 September 1947. It is a very far reaching control which would eliminate the rivalry between nations in this field, which would prevent the surreptitious arming of one nation against another, which would provide some cushion of time before atomic attack, and presumably therefore before any attack with weapons of mass destruction, and which would go a long way toward removing atomic energy at least as a source of conflict between the powers. The term was also used in the introduction to the hugely influential U.S. government document known as NSC 68 written in 1950. During a speech at Rice University on 12 September 1962, President John F. Kennedy spoke of not filling space "with weapons of mass destruction, but with instruments of knowledge and understanding." The following month, during a televised presentation about the Cuban Missile Crisis on 22 October 1962, Kennedy made reference to "offensive weapons of sudden mass destruction." An early use of the exact phrase in an international treaty is in the Outer Space Treaty of 1967, but the treaty provides no definition of the phrase, and the treaty also categorically prohibits the stationing of "weapons" and the testing of "any type of weapon" in outer space, in addition to its specific prohibition against placing in orbit, or installing on celestial bodies, "any objects carrying nuclear weapons or any other kinds of weapons of mass destruction." Evolution of its use During the Cold War, the term "weapons of mass destruction" was primarily a reference to nuclear weapons. At the time, in the West the euphemism "strategic weapons" was used to refer to the American nuclear arsenal. However, there is no precise definition of the "strategic" category, neither considering range nor yield of the nuclear weapon. Subsequent to Operation Opera, the destruction of a pre-operational nuclear reactor inside Iraq by the Israeli Air Force in 1981, the Israeli prime minister, Menachem Begin, countered criticism by saying that "on no account shall we permit an enemy to develop weapons of mass destruction against the people of Israel." This policy of pre-emptive action against real or perceived weapons of mass destruction became known as the Begin Doctrine. The term "weapons of mass destruction" continued to see periodic use, usually in the context of nuclear arms control; Ronald Reagan used it during the 1986 Reykjavík Summit, when referring to the 1967 Outer Space Treaty. Reagan's successor, George H. W. Bush, used the term in a 1989 speech to the United Nations, primarily in reference to chemical arms. The end of the Cold War reduced U.S. reliance on nuclear weapons as a deterrent, causing it to shift its focus to disarmament. With the 1990 invasion of Kuwait and 1991 Gulf War, Iraq's nuclear, biological, and chemical weapons programs became a particular concern of the first Bush Administration. Following the war, Bill Clinton and other western politicians and media continued to use the term, usually in reference to ongoing attempts to dismantle Iraq's weapons programs. After the 11 September 2001 attacks and the 2001 anthrax attacks in the United States, an increased fear of nonconventional weapons and asymmetric warfare took hold in many countries. The fear reached a crescendo with the 2002 Iraq disarmament crisis and the alleged existence of weapons of mass destruction in Iraq that became the primary justification for the 2003 invasion of Iraq; however, American forces found none in Iraq. They found old stockpiles of chemical munitions including sarin and mustard agents, but all were considered to be unusable because of corrosion or degradation. Iraq, however, declared a chemical weapons stockpile in 2009 which U.N. personnel had secured after the 1991 Gulf War. The stockpile contained mainly chemical precursors, but some munitions remained usable. Because of its prolific use and (worldwide) public profile during this period, the American Dialect Society voted "weapons of mass destruction" (and its abbreviation, "WMD") the word of the year in 2002, and in 2003 Lake Superior State University added WMD to its list of terms banished for "Mis-use, Over-use and General Uselessness" (and "as a card that trumps all forms of aggression"). In its criminal complaint against the main suspect of the Boston Marathon bombing of 15 April 2013, the FBI refers to a pressure-cooker improvised bomb as a "weapon of mass destruction." There have been calls to classify at least some classes of cyber weapons as WMD, in particular those aimed to bring about large-scale (physical) destruction, such as by targeting critical infrastructure. However, some scholars have objected to classifying cyber weapons as WMD on the grounds that they "cannot [currently] directly injure or kill human beings as efficiently as guns or bombs" or clearly "meet the legal and historical definitions" of WMD. Definitions of the term United States Strategic definition The most widely used definition of "weapons of mass destruction" is that of nuclear, biological, or chemical weapons (NBC) although there is no treaty or customary international law that contains an authoritative definition. Instead, international law has been used with respect to the specific categories of weapons within WMD, and not to WMD as a whole. While nuclear, chemical and biological weapons are regarded as the three major types of WMDs, some analysts have argued that radiological materials as well as missile technology and delivery systems such as aircraft and ballistic missiles could be labeled as WMDs as well. However, there is an argument that nuclear and biological weapons do not belong in the same category as chemical and "dirty bomb" radiological weapons, which have limited destructive potential (and close to none, as far as property is concerned), whereas nuclear and biological weapons have the unique ability to kill large numbers of people with very small amounts of material, and thus could be said to belong in a class by themselves. The NBC definition has also been used in official U.S. documents, by the U.S. President, the U.S. Central Intelligence Agency, the U.S. Department of Defense, and the U.S. Government Accountability Office. Other documents expand the definition of WMD to also include radiological or conventional weapons. The U.S. military refers to WMD as: This may also refer to nuclear ICBMs (intercontinental ballistic missiles). The significance of the words separable and divisible part of the weapon is that missiles such as the Pershing II and the SCUD are considered weapons of mass destruction, while aircraft capable of carrying bombloads are not. In 2004, the United Kingdom's Butler Review recognized the "considerable and long-standing academic debate about the proper interpretation of the phrase 'weapons of mass destruction. The committee set out to avoid the general term but when using it, employed the definition of United Nations Security Council Resolution 687, which defined the systems which Iraq was required to abandon: "Nuclear weapons or nuclear-weapons-usable material or any sub-systems or components or any research, development, support or manufacturing facilities relating to [nuclear weapons]. Chemical and biological weapons and all stocks of agents and all related subsystems and components and all research, development, support and manufacturing facilities. Ballistic missiles with a range greater than 150 kilometres and related major parts, and repair and production facilities." Chemical weapons expert Gert G. Harigel considers only nuclear weapons true weapons of mass destruction, because "only nuclear weapons are completely indiscriminate by their explosive power, heat radiation and radioactivity, and only they should therefore be called a weapon of mass destruction". He prefers to call chemical and biological weapons "weapons of terror" when aimed against civilians and "weapons of intimidation" for soldiers. Testimony of one such soldier expresses the same viewpoint. For a period of several months in the winter of 2002–2003, U.S. Deputy Secretary of Defense Paul Wolfowitz frequently used the term "weapons of mass terror", apparently also recognizing the distinction between the psychological and the physical effects of many things currently falling into the WMD category. Gustavo Bell Lemus, the Vice President of Colombia, at 9 July 2001 United Nations Conference on the Illicit Trade in Small Arms and Light Weapons in All Its Aspects, quoted the Millennium Report of the UN Secretary-General to the General Assembly, in which Kofi Annan said that small arms could be described as WMD because the fatalities they cause "dwarf that of all other weapons systems – and in most years greatly exceed the toll of the atomic bombs that devastated Hiroshima and Nagasaki". An additional condition often implicitly applied to WMD is that the use of the weapons must be strategic. In other words, they would be designed to "have consequences far outweighing the size and effectiveness of the weapons themselves". The strategic nature of WMD also defines their function in the military doctrine of total war as targeting the means a country would use to support and supply its war effort, specifically its population, industry, and natural resources. Within U.S. civil defense organizations, the category is now Chemical, Biological, Radiological, Nuclear, and Explosive (CBRNE), which defines WMD as: (1) Any explosive, incendiary, poison gas, bomb, grenade, or rocket having a propellant charge of more than four ounces [113 g], missile having an explosive or incendiary charge of more than one-quarter ounce [7 g], or mine or device similar to the above. (2) Poison gas. (3) Any weapon involving a disease organism. (4) Any weapon that is designed to release radiation at a level dangerous to human life. Military definition For the general purposes of national defense, the U.S. Code defines a weapon of mass destruction as: any weapon or device that is intended, or has the capability, to cause death or serious bodily injury to a significant number of people through the release, dissemination, or impact of: toxic or poisonous chemicals or their precursors a disease organism radiation or radioactivity For the purposes of the prevention of weapons proliferation, the U.S. Code defines weapons of mass destruction as "chemical, biological, and nuclear weapons, and chemical, biological, and nuclear materials used in the manufacture of such weapons". Criminal (civilian) definition For the purposes of U.S. criminal law concerning terrorism, weapons of mass destruction are defined as: any "destructive device" defined as any explosive, incendiary, or poison gas – bomb, grenade, rocket having a propellant charge of more than four ounces, missile having an explosive or incendiary charge of more than one-quarter ounce, mine, or device similar to any of the devices described in the preceding clauses any weapon that is designed or intended to cause death or serious bodily injury through the release, dissemination, or impact of toxic or poisonous chemicals, or their precursors any weapon involving a biological agent, toxin, or vector any weapon that is designed to release radiation or radioactivity at a level dangerous to human life The Federal Bureau of Investigation's definition is similar to that presented above from the terrorism statute: any "destructive device" as defined in Title 18 USC Section 921: any explosive, incendiary, or poison gas – bomb, grenade, rocket having a propellant charge of more than four ounces, missile having an explosive or incendiary charge of more than one-quarter ounce, mine, or device similar to any of the devices described in the preceding clauses any weapon designed or intended to cause death or serious bodily injury through the release, dissemination, or impact of toxic or poisonous chemicals or their precursors any weapon involving a disease organism any weapon designed to release radiation or radioactivity at a level dangerous to human life any device or weapon designed or intended to cause death or serious bodily injury by causing a malfunction of or destruction of an aircraft or other vehicle that carries humans or of an aircraft or other vehicle whose malfunction or destruction may cause said aircraft or other vehicle to cause death or serious bodily injury to humans who may be within range of the vector in its course of travel or the travel of its debris. Indictments and convictions for possession and use of WMD such as truck bombs, pipe bombs, shoe bombs, and cactus needles coated with a biological toxin have been obtained under 18 USC 2332a. As defined by 18 USC §2332 (a), a Weapon of Mass Destruction is: (A) any destructive device as defined in section 921 of the title; (B) any weapon that is designed or intended to cause death or serious bodily injury through the release, dissemination, or impact of toxic or poisonous chemicals, or their precursors; (C) any weapon involving a biological agent, toxin, or vector (as those terms are defined in section 178 of this title); or (D) any weapon that is designed to release radiation or radioactivity at a level dangerous to human life; Under the same statute, conspiring, attempting, threatening, or using a Weapon of Mass Destruction may be imprisoned for any term of years or for life, and if resulting in death, be punishable by death or by imprisonment for any terms of years or for life. They can also be asked to pay a maximum fine of $250,000. The Washington Post reported on 30 March 2006: "Jurors asked the judge in the death penalty trial of Zacarias Moussaoui today to define the term 'weapons of mass destruction' and were told it includes airplanes used as missiles". Moussaoui was indicted and tried for conspiracy to both destroy aircraft and use weapons of mass destruction, among others. The surviving Boston Marathon bombing perpetrator, Dzhokhar Tsarnaev, was charged in June 2013 with the federal offense of "use of a weapon of mass destruction" after he and his brother Tamerlan Tsarnaev allegedly placed crude shrapnel bombs, made from pressure cookers packed with ball bearings and nails, near the finish line of the Boston Marathon. He was convicted in April 2015. The bombing resulted in three deaths and at least 264 injuries. International law The development and use of WMD is governed by several international conventions and treaties. Use, possession, and access Nuclear weapons Nuclear weapons use the energy inside of an atom's nucleus to create massive explosions. This goal is achieved through nuclear fission and fusion. Nuclear fission is when the nucleus of an atom is split into smaller nuclei. This process can be induced by shooting a neutron at the nucleus of an atom. When the neutron is absorbed by the atom, it becomes unstable, causing it to split and release energy. Modern nuclear weapons start this process by detonating chemical explosives around a pit of either uranium-235 or plutonium-239 metal. The force from this detonation is directed inwards, causing the pit of uranium or plutonium to compress to a dense point. Once the uranium/plutonium is dense enough, neutrons are then injected. This starts a fission chain reaction also known as an atomic explosion. Nuclear fusion is essentially the opposite of fission. It is the fusing together of nuclei, not the splitting of it. When exposed to extreme pressure and temperature, some lightweight nuclei can fuse together and form heavier nuclei, releasing energy in the process. Fusion weapons (also known as “thermonuclear” or “hydrogen” weapons) use the fission process to initiate fusion. Fusion weapons use the energy released from a fission explosion to fuse hydrogen isotopes together. The energy released from these weapons creates a fireball, which reaches tens of million degrees. A temperature of this magnitude is similar to the temperature found at center of the sun, so it shouldn't be any surprise to learn that the sun runs on fusion as well. The only country to have used a nuclear weapon in war is the United States, which dropped two atomic bombs on the Japanese cities of Hiroshima and Nagasaki during World War II. At the start of 2023, nine states—the United States, Russia, the United Kingdom, France, China, India, Pakistan, the Democratic People's Republic of Korea (DPRK, or North Korea) and Israel—together possessed approximately 12 512 nuclear weapons, of which 9576 were considered to be potentially operationally available. An estimated 3844 of these warheads were deployed with operational forces, including about 2000 that were kept in a state of high operational alert—the same number as the previous year. South Africa developed a small nuclear arsenal in the 1980s but disassembled them in the early 1990s, making it the only country to have fully given up an independently developed nuclear weapons arsenal. Belarus, Kazakhstan, and Ukraine inherited stockpiles of nuclear arms following the break-up of the Soviet Union, but relinquished them to the Russian Federation. Countries where nuclear weapons are deployed through nuclear sharing agreements include Belgium, Germany, Italy, the Netherlands, and Turkey. Biological weapons The history of biological warfare goes back at least to the Mongol siege of Caffa in 1346 and possibly much farther back to antiquity. It is believed that the Ancient Greeks contaminated their adversaries' wells by placing animal corpses in them. However, only by the turn of the 20th century did advances in microbiology allow for the large-scale weaponization of pathogens. During First World War, German military attempted to introduce anthrax into Allied livestock. In Second World War, Japan conducted aerial attacks on China using fleas carrying the bubonic plague. During the 20th century, at least nine states have operated offensive biological weapons programs, including Canada (1946–1956), France (1921–1972), Iraq (1985–1990s), Japan (1930s–1945), Rhodesia, South Africa (1981–1993), the Soviet Union (1920s–1992), the United Kingdom (1934–1956), and the United States (1943–1969). The Japanese biological weapons program, which was run by the secret Imperial Japanese Army Unit 731 during the Sino-Japanese War (1937–1945), became infamous for conducting often fatal human experiments on prisoners and producing biological weapons for combat use. The Soviet Union covertly operated the world's largest, longest, and most sophisticated biological weapons program, in violation of its obligations under international law. International restrictions on biological warfare began with the 1925 Geneva Protocol, which prohibits the use but not the possession or development of biological and chemical weapons. Upon ratification of the Geneva Protocol, several countries made reservations regarding its applicability and use in retaliation. Due to these reservations, it was in practice a "no-first-use" agreement only. The 1972 Biological Weapons Convention (BWC) supplements the Geneva Protocol by prohibiting the development, production, acquisition, transfer, stockpiling, and use of biological weapons. Having entered into force on 26 March 1975, the BWC was the first multilateral disarmament treaty to ban the production of an entire category of weapons of mass destruction. As of March 2021, 183 states have become party to the treaty. Chemical weapons Chemical weapons have been used around the world by various civilizations since ancient times. The oldest reported case of a chemical substance being used as a weapon was in 256 AD during the siege of Dura-Europos. A mixture of tar and sulfur was used to produce sulfur oxides, which helped take control of the city. In the industrial era, chemical weapons were used extensively by both sides during World War I, and by the Axis powers during World War II (both in battle and in extermination camp gas chambers) though Allied powers also stockpiled them. International restrictions on chemical warfare began with the Hague Conventions of 1899 and 1907, and was expanded significantly by the 1925 Geneva Protocol. These treaties prohibited the use of poisons or chemical agents in international warfare, but did not place restrictions on development or weapon stockpiles. Since 1997, the Chemical Weapons Convention (CWC) has expanded restrictions to prohibit any use and development of chemical weapons except for very limited purposes (research, medical, pharmaceutical or protective). As of 2018, a handful of countries have known inventories, and many are in the process of being safely destroyed. Nonetheless, proliferation and use in war zones remains an active concern, most recently the use of chemical weapons in the Syrian Civil War. Ethics and international legal status Some commentators classify some or all the uses of nuclear, chemical, or biological weapons during wartime as a war crime (or crime against humanity if widespread) because they kill civilians (who are protected by the laws of war) indiscriminately or are specifically prohibited by international treaties (which have become more comprehensive over time). Proponents of use say that specific uses of such weapons have been necessary for defense or to avoid more deaths in a protracted war. The tactic of terror bombing from aircraft, and generally targeting cities with area bombardment or saturation carpet bombing has also been criticized, defended, and prohibited by treaty in the same way; the destructive effect of conventional saturation bombing is similar to that of a nuclear weapon. United States politics Due to the potentially indiscriminate effects of WMD, the fear of a WMD attack has shaped political policies and campaigns, fostered social movements, and has been the central theme of many films. Support for different levels of WMD development and control varies nationally and internationally. Yet understanding of the nature of the threats is not high, in part because of imprecise usage of the term by politicians and the media. Fear of WMD, or of threats diminished by the possession of WMD, has long been used to catalyze public support for various WMD policies. They include mobilization of pro- and anti-WMD campaigners alike, and generation of popular political support. The term WMD may be used as a powerful buzzword or to generate a culture of fear. It is also used ambiguously, particularly by not distinguishing among the different types of WMD. A television commercial called Daisy, promoting Democrat Lyndon Johnson's 1964 presidential candidacy, invoked the fear of a nuclear war and was an element in Johnson's subsequent election. Later, United States' President George W. Bush used the threat of potential WMD in Iraq as justification for the 2003 invasion of Iraq. Broad reference to Iraqi WMD in general was seen as an element of President Bush's arguments. The claim that Iraq possessed Weapons of Mass Destruction (WMD) was a major factor that led to the invasion of Iraq in 2003 by Coalition forces. Over 500 munitions containing mustard agent and sarin were discovered throughout Iraq since 2003; they were made in the 1980s and are no longer usable as originally intended due to corrosion. The American Heritage Dictionary defines a weapon of mass destruction as: "a weapon that can cause widespread destruction or kill large numbers of people, especially a nuclear, chemical, or biological weapon." In other words, it does not have to be nuclear, biological or chemical (NBC). For example, Dzhokhar Tsarnaev, one of the perpetrators of the Boston Marathon bombing, was charged under United States law 18 U.S.C. 2332A for using a weapon of mass destruction and that was a pressure cooker bomb. In other words, it was a weapon that caused large-scale death and destruction, without being an NBC weapon. Media coverage In March 2004, the Center for International and Security Studies at Maryland (CISSM) released a report examining the media's coverage of WMD issues during three separate periods: nuclear weapons tests by India and Pakistan in May 1998; the U.S. announcement of evidence of a North Korean nuclear weapons program in October 2002; and revelations about Iran's nuclear program in May 2003. The CISSM report argues that poor coverage resulted less from political bias among the media than from tired journalistic conventions. The report's major findings were that: In a separate study published in 2005, a group of researchers assessed the effects reports and retractions in the media had on people's memory regarding the search for WMD in Iraq during the 2003 Iraq War. The study focused on populations in two coalition countries (Australia and the United States) and one opposed to the war (Germany). Results showed that U.S. citizens generally did not correct initial misconceptions regarding WMD, even following disconfirmation; Australian and German citizens were more responsive to retractions. Dependence on the initial source of information led to a substantial minority of Americans exhibiting false memory that WMD were indeed discovered, while they were not. This led to three conclusions: The repetition of tentative news stories, even if they are subsequently disconfirmed, can assist in the creation of false memories in a substantial proportion of people. Once information is published, its subsequent correction does not alter people's beliefs unless they are suspicious about the motives underlying the events the news stories are about. When people ignore corrections, they do so irrespective of how certain they are that the corrections occurred. A poll conducted between June and September 2003 asked people whether they thought evidence of WMD had been discovered in Iraq since the war ended. They were also asked which media sources they relied upon. Those who obtained their news primarily from Fox News were three times as likely to believe that evidence of WMD had been discovered in Iraq than those who relied on PBS and NPR for their news, and one third more likely than those who primarily watched CBS. Based on a series of polls taken from June–September 2003. In 2006, Fox News reported the claims of two Republican lawmakers that WMDs had been found in Iraq, based upon unclassified portions of a report by the National Ground Intelligence Center. Quoting from the report, Senator Rick Santorum said "Since 2003, coalition forces have recovered approximately 500 weapons munitions which contain degraded mustard or sarin nerve agent". According to David Kay, who appeared before the U.S. House Armed Services Committee to discuss these badly corroded munitions, they were leftovers, many years old, improperly stored or destroyed by the Iraqis. Charles Duelfer agreed, stating on NPR's Talk of the Nation: "When I was running the ISG – the Iraq Survey Group – we had a couple of them that had been turned in to these IEDs, the improvised explosive devices. But they are local hazards. They are not a major, you know, weapon of mass destruction." Later, wikileaks would show that WMDs of these kinds continued to be found as the Iraqi occupation continued. Many news agencies, including Fox News, reported the conclusions of the CIA that, based upon the investigation of the Iraq Survey Group, WMDs are yet to be found in Iraq. Public perceptions Awareness and opinions of WMD have varied during the course of their history. Their threat is a source of unease, security, and pride to different people. The anti-WMD movement is embodied most in nuclear disarmament, and led to the formation of the British Campaign for Nuclear Disarmament in 1957. In order to increase awareness of all kinds of WMD, in 2004 the nuclear physicist and Nobel Peace Prize winner Joseph Rotblat inspired the creation of The WMD Awareness Programme to provide trustworthy and up to date information on WMD worldwide. In 1998, the University of New Mexico's Institute for Public Policy released their third report on U.S. perceptions – including the general public, politicians and scientists – of nuclear weapons since the breakup of the Soviet Union. Risks of nuclear conflict, proliferation, and terrorism were seen as substantial. While maintenance of the U.S. nuclear arsenal was considered above average in importance, there was widespread support for a reduction in the stockpile, and very little support for developing and testing new nuclear weapons. Also in 1998, nuclear weapons became an issue in India's election of March, in relation to political tensions with neighboring Pakistan. Prior to the election the Bharatiya Janata Party (BJP) announced it would "declare India a nuclear weapon state" after coming to power. BJP won the elections, and on 14 May, three days after India tested nuclear weapons for the second time, a public opinion poll reported that a majority of Indians favored the country's nuclear build-up. On 15 April 2004, the Program on International Policy Attitudes (PIPA) reported that U.S. citizens showed high levels of concern regarding WMD, and that preventing the spread of nuclear weapons should be "a very important U.S. foreign policy goal", accomplished through multilateral arms control rather than the use of military threats. A majority also believed the United States should be more forthcoming with its biological research and its Nuclear Non-Proliferation Treaty commitment of nuclear arms reduction. A Russian opinion poll conducted on 5 August 2005 indicated half the population believed new nuclear powers have the right to possess nuclear weapons. 39% believed the Russian stockpile should be reduced, though not eliminated. In popular culture Weapons of mass destruction and their related impacts have been a mainstay of popular culture since the beginning of the Cold War, as both political commentary and humorous outlet. The actual phrase "weapons of mass destruction" has been used similarly and as a way to characterise any powerful force or product since the Iraqi weapons crisis in the lead up to the Coalition invasion of Iraq in 2003. Science-fiction may introduce novel weapons of mass destruction with much greater yields or impact than anything in reality. Common hazard symbols Radioactive weaponry or hazard symbol The international radioactivity symbol (also known as trefoil) first appeared in 1946, at the University of California, Berkeley Radiation Laboratory. At the time, it was rendered as magenta, and was set on a blue background. It is drawn with a central circle of radius R, the blades having an internal radius of 1.5R and an external radius of 5R, and separated from each other by 60°. It is meant to represent a radiating atom. The International Atomic Energy Agency found that the trefoil radiation symbol is unintuitive and can be variously interpreted by those uneducated in its meaning; therefore, its role as a hazard warning was compromised as it did not clearly indicate "danger" to many non-Westerners and children who encountered it. As a result of research, a new radiation hazard symbol (ISO 21482) was developed in 2007 to be placed near the most dangerous parts of radiation sources featuring a skull, someone running away, and using a red rather than yellow background. The red background is intended to convey urgent danger, and the sign is intended to be used on equipment where very strong ionizing radiation can be encountered if the device is dismantled or otherwise tampered with. The intended use of the sign is not in a place where the normal user will see it, but in a place where it will be seen by someone who has started to dismantle a radiation-emitting device or equipment. The aim of the sign is to warn people such as scrap metal workers to stop work and leave the area. Biological weaponry or hazard symbol Developed by Dow Chemical company in the 1960s for their containment products. According to Charles Dullin, an environmental-health engineer who contributed to its development: See also CBRN defense Commission on the Prevention of WMD proliferation and terrorism List of CBRN warfare forces Core (game theory) Ethnic bioweapon Fallout shelter Game theory Global Partnership Against the Spread of Weapons and Materials of Mass Destruction Commission on the Intelligence Capabilities of the United States Regarding Weapons of Mass Destruction Kinetic bombardment List of global issues Mutual assured destruction NBC suit New physical principles weapons Nuclear terrorism Operations Plus WMD Orbital bombardment Russia and weapons of mass destruction Strategic bombing United States and weapons of mass destruction Weapons of Mass Destruction Commission References Bibliography Curley, Robert, ed. Weapons of Mass Destruction (Britannica Educational Publishing, 2011) Graham Jr, Thomas, and Thomas Graham. Common sense on weapons of mass destruction (University of Washington Press, 2011) Hutchinson, Robert. Weapons of Mass Destruction: The no-nonsense guide to nuclear, chemical and biological weapons today (Hachette UK, 2011) Definition and origin "WMD: Words of mass dissemination" (12 February 2003), BBC News. Bentley, Michelle, "War and/of Worlds: Constructing WMD in U.S. Foreign Policy", Security Studies 22 (Jan. 2013), 68–97. Michael Evans, "What makes a weapon one of mass destruction?" (6 February 2004), The Times. Bruce Schneier, "Definition of 'Weapon of Mass Destruction'" (6 April 2009), Schneier on Security. Stefano Felician, Le armi di distruzione di massa, CEMISS, Roma, 2010, International law United Nations Security Council Resolution 1540 David P. Fidler, "Weapons of Mass Destruction and International Law" (February 2003), American Society of International Law. Joanne Mariner, "FindLaw Forum: Weapons of mass destruction and international law's principle that civilians cannot be targeted" (20 November 2001), CNN. Compliance with international WMD regimes Media , by Susan D. Moeller, Center for International and Security Studies at Maryland, 2004. Ethics Public perceptions Steven Kull et al., Americans on WMD Proliferation (15 April 2004), Program on International Policy Attitudes/Knowledge Networks survey. External links Mass murder Man-made disasters	Weapon of mass destruction	[ "Biology" ]	7,340	[]
53,144	https://en.wikipedia.org/wiki/Nuclear%20explosive	A nuclear explosive is an explosive device that derives its energy from nuclear reactions. Almost all nuclear explosive devices that have been designed and produced are nuclear weapons intended for warfare. Other, non-warfare, applications for nuclear explosives have occasionally been proposed. For example, nuclear pulse propulsion is a form of spacecraft propulsion that would use nuclear explosives to provide impulse to a spacecraft. A similar application is the proposal to use nuclear explosives for asteroid deflection. From 1958 to 1965 the United States government ran a project to design a nuclear explosive powered nuclear pulse rocket called Project Orion. Never built, this vessel would use repeated nuclear explosions to propel itself and was considered surprisingly practical. It is thought to be a feasible design for interstellar travel. Nuclear explosives were once considered for use in large-scale excavation. A nuclear explosion could be used to create a harbor, or a mountain pass, or possibly large underground cavities for use as storage space. It was thought that detonating a nuclear explosive in oil-rich rock could make it possible to extract more from the deposit, e.g. note the Canadian Project Oilsand. From 1958 to 1973 the U.S. government exploded 28 nuclear test-shots in a project called Operation Plowshare. The purpose of the operation was to use peaceful nuclear explosions for moving and lifting enormous amounts of earth and rock during construction projects such as building reservoirs. The Soviet Union conducted a much more vigorous program of 122 nuclear tests, some with multiple devices, between 1965 and 1989 under the auspices of Program No. 7 – Nuclear Explosions for the National Economy. As controlled nuclear fusion has proven difficult to use as an energy source, an alternate proposal for producing fusion power has been to detonate nuclear fusion explosives inside very large underground chambers and then using the heat produced, which would be absorbed by a molten salt coolant which would also absorb neutrons. The 1970s PACER (fusion) project investigated fusion detonation as a power source. Failure to meet objectives, along with the realization of the dangers of nuclear fallout and other residual radioactivity, and with the enactment of various agreements such as the Partial Test Ban Treaty and the Outer Space Treaty, has led to the termination of most of these programs. References External links Nuclear Weapons Frequently Asked Questions https://www.nti.org/education-center/treaties-and-regimes/treaty-banning-nuclear-test-atmosphere-outer-space-and-under-water-partial-test-ban-treaty-ptbt/ Nuclear physics	Nuclear explosive	[ "Physics" ]	511	[ "Nuclear physics" ]
53,217	https://en.wikipedia.org/wiki/Exotic%20atom	An exotic atom is an otherwise normal atom in which one or more sub-atomic particles have been replaced by other particles. For example, electrons may be replaced by other negatively charged particles such as muons (muonic atoms) or pions (pionic atoms). Because these substitute particles are usually unstable, exotic atoms typically have very short lifetimes and no exotic atom observed so far can persist under normal conditions. Muonic atoms In a muonic atom (previously called a mu-mesic atom, now known to be a misnomer as muons are not mesons), an electron is replaced by a muon, which, like the electron, is a lepton. Since leptons are only sensitive to weak, electromagnetic and gravitational forces, muonic atoms are governed to very high precision by the electromagnetic interaction. Since a muon is more massive than an electron, the Bohr orbits are closer to the nucleus in a muonic atom than in an ordinary atom, and corrections due to quantum electrodynamics are more important. Study of muonic atoms' energy levels as well as transition rates from excited states to the ground state therefore provide experimental tests of quantum electrodynamics. Muon-catalyzed fusion is a technical application of muonic atoms. Other muonic atoms can be formed when negative muons interact with ordinary matter. The muon in muonic atoms can either decay or get captured by a proton. Muon capture is very important in heavier muonic atoms, but shortens the muon's lifetime from 2.2 μs to only 0.08 μs. Muonic hydrogen Muonic hydrogen is like normal hydrogen with the electron replaced by a negative muon—that is a proton orbited by a muon. It is important in addressing the proton radius puzzle. Muonic helium (Hydrogen-4.1) The symbol 4.1H (Hydrogen-4.1) has been used to describe the exotic atom muonic helium (4He-μ), which is like helium-4 in having two protons and two neutrons. However one of its electrons is replaced by a muon, which also has charge –1. Because the muon's orbital radius is less than the electron's orbital radius (due to the mass ratio), the muon can be considered as a part of the nucleus. The atom then has a nucleus with two protons, two neutrons and one muon, with total nuclear charge +1 (from two protons and one muon) and only one electron outside, so that it is effectively an isotope of hydrogen instead of an isotope of helium. A muon's weight is approximately 0.1 Da so the isotopic mass is 4.1. Since there is only one electron outside the nucleus, the hydrogen-4.1 atom can react with other atoms. Its chemical behavior behaves more like a hydrogen atom than an inert helium atom. Hadronic atoms A hadronic atom is an atom in which one or more of the orbital electrons are replaced by a negatively charged hadron. Possible hadrons include mesons such as the pion or kaon, yielding a pionic atom or a kaonic atom (see Kaonic hydrogen), collectively called mesonic atoms; antiprotons, yielding an antiprotonic atom; and the particle, yielding a or sigmaonic atom. Unlike leptons, hadrons can interact via the strong force, so the orbitals of hadronic atoms are influenced by nuclear forces between the nucleus and the hadron. Since the strong force is a short-range interaction, these effects are strongest if the atomic orbital involved is close to the nucleus, when the energy levels involved may broaden or disappear because of the absorption of the hadron by the nucleus. Hadronic atoms, such as pionic hydrogen and kaonic hydrogen, thus provide experimental probes of the theory of strong interactions, quantum chromodynamics. Onium An onium (plural: onia) is the bound state of a particle and its antiparticle. The classic onium is positronium, which consists of an electron and a positron bound together as a metastable state, with a relatively long lifetime of 142 ns in the triplet state. Positronium has been studied since the 1950s to understand bound states in quantum field theory. A recent development called non-relativistic quantum electrodynamics (NRQED) used this system as a proving ground. Pionium, a bound state of two oppositely charged pions, is useful for exploring the strong interaction. This should also be true of protonium, which is a proton–antiproton bound state. Understanding bound states of pionium and protonium is important in order to clarify notions related to exotic hadrons such as mesonic molecules and pentaquark states. Kaonium, which is a bound state of two oppositely charged kaons, has not been observed experimentally yet. The true analogs of positronium in the theory of strong interactions, however, are not exotic atoms but certain mesons, the quarkonium states, which are made of a heavy quark such as the charm or bottom quark and its antiquark. (Top quarks are so heavy that they decay through the weak force before they can form bound states.) Exploration of these states through non-relativistic quantum chromodynamics (NRQCD) and lattice QCD are increasingly important tests of quantum chromodynamics. Muonium, despite its name, is not an onium state containing a muon and an antimuon, because IUPAC assigned that name to the system of an antimuon bound with an electron. However, the production of a muon–antimuon bound state, which is an onium (called true muonium), has been theorized. The same applies to the ditauonium (or "true tauonium") exotic QED atom. Hypernuclear atoms Atoms may be composed of electrons orbiting a hypernucleus that includes strange particles called hyperons. Such hypernuclear atoms are generally studied for their nuclear behaviour, falling into the realm of nuclear physics rather than atomic physics. Quasiparticle atoms In condensed matter systems, specifically in some semiconductors, there are states called excitons, which are bound states of an electron and an electron hole. Exotic molecules An exotic molecule contains one or more exotic atoms. Di-positronium, two bound positronium atoms Positronium hydride, a positronium atom bound to a hydrogen atom "Exotic molecule" can also refer to a molecule having some other uncommon property such as pyramidal hexamethylbenzene and a Rydberg atom. See also References Quantum chromodynamics	Exotic atom	[ "Physics" ]	1,419	[ "Exotic atoms", "Subatomic particles", "Nuclear physics", "Atoms", "Matter" ]
53,256	https://en.wikipedia.org/wiki/Advogato	Advogato was an online community and social networking site dedicated to free software development and created by Raph Levien. In 2007, Steve Rainwater took over maintenance and new development from Raph. In 2016, Rainwater's running instance was shut down and backed up to archive.org. History Advogato described itself as "the free software developer's advocate." Advogato was an early pioneer of blogs, formerly known as "online diaries", and one of the earliest social networking websites. Advogato combined the most recent entries from each user's diary together into a single continuous feed called the recentlog, directly inspiring the creation of the Planet aggregator somewhat later. Several high-profile members of the free software and open source software movements were users of the site, including Richard M. Stallman, Eric Raymond, Alan Cox, Bruce Perens, and Jamie Zawinski. Because Advogato was the first website to use a robust, attack-resistant trust metric and to release the underlying code for that trust mechanism under a free software license, it has been the basis of numerous research papers on trust metrics and social networking (see the list below for specific examples). Advogato's early adoption of an XML-RPC interface led to its use as an example of how such interfaces could be used by web programmers. Advogato saw use as a testbed for social networking and semantic web technologies. Tim Berners-Lee, who was an Advogato user himself, included Advogato in a short list of sites notable for their early adoption of the FOAF as a method of exporting user RDF URIs. Trust metric The motivating idea for Advogato was to try out in practice Levien's ideas about attack-resistant trust metrics, having users certify each other in a kind of peer review process and use this information to avoid the abuses that plague open community sites. Levien observed that his notion of attack-resistant trust metric was fundamentally very similar to the PageRank algorithm used by Google to rate article interest. In the case of Advogato, the trust metric was designed to include all individuals who could reasonably be considered members of the Free Software and Open Source communities while excluding others. The implementation of this trust metric was through an Apache module called mod_virgule. mod_virgule is free software, licensed under the GPL and written in C. Despite the trust metric, posting privileges to the front page of Advogato were gained by controversial individuals, leading some to claim Advogato's trust metric solution was faulty. Misunderstanding of the purpose of Advogato's trust metric was common, which often led to the assumption that it should exclude specific individuals on the basis that they were known cranks. See also Everything2 Kuro5hin Slashdot References Advogato and mod_virgule references Raph Levien (2004). Attack Resistant Trust Metrics. Early draft of abandoned PhD manuscript. Raph Levien (2007). Lessons From Advogato (video) (abstract). Google Tech Talks, June 25, 2007. Jesse Ruderman (2004). A comparison of two trust metrics. Mary Tyler (2004). Behind four Linux community sites. Linux.com feature. Even better than Slashdot, Salon.com Social Forces and Constraint in the Attainment of Community Status Steve Rainwater (maintainer of mod_virgule 2007 - 2016). External links Rusty Foster, 2004. 'User Sponsorship and Managed Growth'. Kuro5hin article. modified codebase with backend PostgreSQL, currently seeking maintainer/new owner by Steven Rainwater '' Free software websites Reputation management Defunct social networking services Blog hosting services Internet properties established in 1999 Internet properties disestablished in 2017	Advogato	[ "Technology" ]	799	[ "Computing websites", "Free software websites" ]
53,259	https://en.wikipedia.org/wiki/Cable%20modem	A cable modem is a type of network bridge that provides bi-directional data communication via radio frequency channels on a hybrid fiber-coaxial (HFC), radio frequency over glass (RFoG) and coaxial cable infrastructure. Cable modems are primarily used to deliver broadband Internet access in the form of cable Internet, taking advantage of the high bandwidth of a HFC and RFoG network. They are commonly deployed in the Americas, Asia, Australia, and Europe. History MITRE Cablenet Internet Experiment Note (IEN) 96 (1979) describes an early RF cable modem system. From pages 2 and 3 of IEN 96: The Cable-Bus System The MITRE/Washington Cablenet system is based on a technology developed at MITRE/Bedford. Similar cable-bus systems are in operation at a number of government sites, e.g. Walter Reed Army Hospital, and the NASA Johnson Space Center, but these are all standalone, local-only networks. The system uses standard community antenna television (CATV) coaxial cable and microprocessor based Bus Interface Units (BIUs) to connect subscriber computers and terminals to the cable. ... The cable bus consists of two parallel coaxial cables, one inbound and the other outbound. The inbound cable and outbound cable are connected at one end, the headend, and electrically terminated at their other ends. This architecture takes advantage of the well developed unidirectional CATV components. The topology is dendritic (i.e. branched like a tree). ... The BIUs contain Radio Frequency (RF) modems which modulate a carrier signal to transmit digital information using 1 MHz of the available bandwidth in the 24 MHz frequency range. The remainder of the 294 MHz bandwidth can be used to carry other communication channels, such as off-the-air TV, FM, closed circuit TV, or a voice telephone system, or, other digital channels. The data rate of our test-bed system is 307.2 kbps. IEEE 802.3b (10BROAD36) The IEEE 802 Committee defined 10BROAD36 in 802.3b-1985 as a IEEE 802.3/Ethernet broadband system to run up to over CATV coax network cabling. The word broadband as used in the original IEEE 802.3 specifications implied operation in frequency-division multiplexed (FDM) channel bands as opposed to digital baseband square-waveform modulations (also known as line coding), which begin near zero Hz and theoretically consume infinite frequency bandwidth. (In real-world systems, higher-order signal components become indistinguishable from background noise.) In the market 10BROAD36 equipment was not developed by many vendors nor deployed in many user networks as compared to equipment for IEEE 802.3/Ethernet baseband standards such as 10BASE5 (1983), 10BASE2 (1985), 10BASE-T (1990), etc. IEEE 802.7 The IEEE 802 Committee also specified a broadband CATV digital networking standard in 1989 with 802.7-1989. However, like 10BROAD36, 802.7-1989 saw little commercial success. Hybrid networks Hybrid Networks developed, demonstrated and patented the first high-speed, asymmetrical cable modem system in 1990. A key Hybrid Networks insight was that in the nascent days of the Internet, data downloading constitutes the majority of the data traffic, and this can be served adequately with a highly asymmetrical data network (i.e. a large downstream data pipe and many small upstream data pipes). This allowed CATV operators to offer high-speed data services immediately without first requiring an expensive system upgrade. Also key was that it saw that the upstream and downstream communications could be on the same or different communications media using different protocols working in each direction to establish a closed-loop communications system. The speeds and protocols used in each direction would be very different. The earliest systems used the public switched telephone network (PSTN) for the return path since very few cable systems were bi-directional. Later systems used CATV for the upstream as well as the downstream path. Hybrid's system architecture is used for most cable modem systems today. LANcity LANcity was an early pioneer in cable modems, developing a proprietary system that was widely deployed in the U.S. LANcity, which was led by the Iranian-American engineer Rouzbeh Yassini, was then acquired by Bay Networks. Bay Networks was subsequently acquired by Nortel. Nortel at the time had formed a joint-venture with Antec called ARRIS Interactive. Because of contractual agreements with Antec involving this joint venture, Nortel spun the LANCity group out into the ARRIS Interactive joint-venture. ARRIS continues to make cable modems and cable modem termination system (CMTS) equipment compliant with the DOCSIS standard. Zenith homeworks Zenith offered a cable modem technology using its own protocol which it introduced in 1993, being one of the first cable modem providers. The Zenith Cable Modem technology was used by several cable television systems in the United States and other countries, including Cox Communications San Diego, Knology in the Southeast United States, Ameritech's Americast service (later to be sold off to Wide Open West after the SBC / Ameritech merger), Cogeco in Hamilton Ontario and Cablevision du Nord de Québec in Val-d'Or. Zenith Homeworks used BPSK (Bi-Phase Shift Keyed) modulation to achieve 500 Kbit/sec in 600 kHz, or ec in 6 MHz. Com21 Com21 was another early pioneer in cable modems, and quite successful until proprietary systems were made obsolete by the DOCSIS standardization. The Com21 system used a ComController as the central bridge in CATV network head-ends, the ComPort cable modem in various models and the NMAPS management system using HP OpenView as the platform. Later they also introduced a return path multiplexer to overcome noise problems when combining return path signals from multiple areas. The proprietary protocol was based on Asynchronous Transfer Mode (ATM). The central ComController switch was a modular system offering one downstream channel (transmitter) and one management module. The remaining slots could be used for upstream receivers (2 per card), dual Ethernet 10BaseT and later also Fast-Ethernet and ATM interfaces. The ATM interface became the most popular, as it supported the increasing bandwidth demands and also supported VLANs. Com21 developed a DOCSIS modem, but the company filed for bankruptcy in 2003 and closed. The DOCSIS CMTS assets of COM21 were acquired by ARRIS. CDLP CDLP was a proprietary system manufactured by Motorola. CDLP customer premises equipment (CPE) was capable of both PSTN (telephone network) and radio frequency (cable) return paths. The PSTN-based service was considered 'one-way cable' and had many of the same drawbacks as satellite Internet service; as a result, it quickly gave way to "two-way cable." Cable modems that used the RF cable network for the return path were considered 'two-way cable', and were better able to compete with the bi-directional digital subscriber line (DSL) service. The standard is in little use now as new providers use, and existing providers having changed to, the DOCSIS standard. The Motorola CDLP proprietary CyberSURFR is an example of a device that was built to the CDLP standard, capable of a peak downstream and upstream. CDLP supported a maximum downstream bandwidth of which could be reached by using several cable modems. The Australian ISP BigPond employed this system when it started cable modem tests in 1996. For a number of years cable Internet access was only available in Sydney, Melbourne and Brisbane via CDLP. This network ran parallel to the newer DOCSIS system for several years. In 2004, the CDLP network was terminated and replaced by DOCSIS. CDLP has been also rolled out at the French cable operator Numericable before upgrading its IP broadband network using DOCSIS. DVB/DAVIC Digital Video Broadcasting (DVB) and Digital Audio Visual Council (DAVIC) are European-formed organizations that developed some cable modem standards. However, these standards have not been as widely adopted as DOCSIS. IEEE 802.14 In the mid-1990s the IEEE 802 committee formed a subcommittee (802.14) to develop a standard for cable modem systems. IEEE 802.14 developed a draft standard, which was ATM-based. However, the 802.14 working group was disbanded when North American multi system operators (MSOs) instead backed the then-fledgling DOCSIS 1.0 specification, which generally used best-effort service and was IP-based (with extension codepoints to support ATM for QoS in the future). MSOs were interested in quickly deploying service to compete for broadband Internet access customers instead of waiting on the slower, iterative, and deliberative processes of standards development committees. Albert A. Azzam was Secretary of the IEEE 802.14 Working Group, and his book, High-Speed Cable Modems, describes many of the proposals submitted to 802.14. IETF Although the Internet Engineering Task Force (IETF) generally does not generate complete cable modem standards, the IETF chartered Working Groups (WGs) that produced various standards related to cable modem technologies (including 802.14, DOCSIS, PacketCable, and others). In particular, the IETF WGs on IP over Cable Data Network (IPCDN) and IP over Digital Video Broadcasting (DVB) produced some standards applicable to cable modem systems, primarily in the areas of Simple Network Management Protocol (SNMP) Management Information Bases (MIBs) for cable modems and other networking equipment that operates over CATV networks. DOCSIS In the late 1990s, a consortium of US cable operators, known as "MCNS" formed to quickly develop an open and interoperable cable modem specification. The group essentially combined technologies from the two dominant proprietary systems at the time, taking the physical layer from the Motorola CDLP system and the MAC layer from the LANcity system. When the initial specification had been drafted, the MCNS consortium handed over control of it to CableLabs which maintained the specification, promoted it in various standards organizations (notably SCTE and ITU), developed a certification testing program for cable modem equipment, and has since drafted multiple extensions to the original specification. While deployed DOCSIS RFI 1.0 equipment generally only supported best-effort service, the DOCSIS RFI 1.0 Interim-01 document discussed quality of servce (QoS) extensions and mechanisms using IntServ, RSVP, RTP, and Synchronous Transfer Mode (STM) telephony (as opposed to ATM). DOCSIS RFI 1.1 later added more robust and standardized QoS mechanisms to DOCSIS. DOCSIS 2.0 added support for S-CDMA PHY, while DOCSIS 3.0 added IPv6 support and channel bonding to allow a single cable modem to use concurrently more than one upstream channel and more than one downstream channel in parallel. Virtually all cable modems operating in the field today are compliant with one of the DOCSIS versions. Because of the differences in the European PAL and US's NTSC systems two main versions of DOCSIS exist, DOCSIS and EuroDOCSIS. The main differences are found in the width of RF-channels: 6 MHz for the US and 8 MHz for Europe. A third variant of DOCSIS was developed in Japan and has seen limited deployment in that country. Although interoperability "was the whole point of the DOCSIS project," most cable operators only approve a very restricted list of cable modems on their network, identifying the 'allowed' modems by their brand, models, sometimes firmware version and occasionally going as far as imposing a hardware version of the modem, instead of simply allowing a supported DOCSIS version. Multimedia over Coax Alliance In 2004, the Multimedia over Coax Alliance (MoCA) was established to develop industry standard for the connected home, using the existing coaxial cabling. Initially developed for in-home networking with MoCA 1.0/1.1, the MoCA standards has continued to develop with MoCA 2.0/2.1 in 2010 and MoCa 2.5 in 2016. In 2017, Multimedia over Coax Alliance introduced MoCA Access specification, based on the MoCA 2.5 standard, suitable for addressing broadband network access in-building using coaxial cabling. MoCA Access extends MoCA 2.5 in-home networking to fit operators and ISPs that are installing fiber-to-the-basement/drop point (FTTB/FTTdp) and want to use the existing coax for connection to each apartment or house." Multimedia terminal adapter With the development of voice over Internet Protocol (VoIP) telephony, analog telephone adapters (ATA) have been incorporated into many cable modems for providing telephone service. An embedded ATA is known as an embedded multimedia terminal adapter (E-MTA). Many cable TV service providers also offer VoIP-based telephone service via the cable infrastructure (PacketCable). Some high-speed Internet customers may use VoIP telephony by subscribing to a third-party service, such as Vonage, MagicJack+ and NetTALK. Network architectural functions In network topology, a cable modem is a network bridge that conforms to IEEE 802.1D for Ethernet networking (with some modifications). The cable modem bridges Ethernet frames between a customer LAN and the coax network. Technically, it is a modem because it must modulate data to transmit it over the cable network, and it must demodulate data from the cable network to receive it. It implements an Ethernet PHY on its LAN interface, and a DOCSIS-defined cable-specific PHY on its HFC cable interface. The term cable modem refers to this cable-specific PHY. The Network Layer is implemented as an IP host in that it has its own IP address used by the network operator to maintain the device. In the transport layer the cable modem supports UDP in association with its own IP address, and it supports filtering based on TCP and UDP port numbers to, for example, block forwarding of NetBIOS traffic out of the customer's LAN. In the Application Layer, the cable modem supports certain protocols that are used for management and maintenance, notably Dynamic Host Configuration Protocol (DHCP), SNMP, and TFTP. Some cable modems may incorporate a router and a DHCP server to provide the LAN with IP network addressing. From a data forwarding and network topology perspective, this router functionality is typically kept distinct from the cable modem functionality (at least logically) even though the two may share a single enclosure and appear as one unit, sometimes called a residential gateway. So, the cable modem function will have its own IP address and MAC address as will the router. Cable modem flap Cable modems can have a problem known in industry jargon as "flap" or "flapping". A modem flap is when the connection by the modem to the head-end has been dropped (gone offline) and then comes back online. The time offline or rate of flap is not typically recorded, only the incidence. While this is a common occurrence and usually unnoticed, if a modem's flap is extremely high, these disconnects can cause service to be disrupted. If there are usability problems due to flap the typical cause is a defective modem or very high amounts of traffic on the service provider's network (upstream utilization too high). Types of flap include reinsertions, hits and misses, and power adjustments. Known vulnerabilities In January 2020, a vulnerability affecting cable modems using Broadcom chipsets was disclosed and named Cable Haunt. Security researchers say that the vulnerability affects hundreds of millions of devices. Exploits are possible because of the use of default credentials in the spectrum analyzer component of the modem (mostly used for debugging purposes) accessible through a network port which is open by default in the vulnerable models. See also Cable modem termination system (CMTS) Cable telephone Internet access with a cable modem List of device bandwidths NABU Network Triple play (telecommunications) HomePNA References Further reading External links Digital cable Cable television technology Modems Internet access	Cable modem	[ "Technology" ]	3,430	[ "Internet access", "IT infrastructure" ]
53,268	https://en.wikipedia.org/wiki/Convolution%20theorem	In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. Functions of a continuous variable Consider two functions and with Fourier transforms and : where denotes the Fourier transform operator. The transform may be normalized in other ways, in which case constant scaling factors (typically or ) will appear in the convolution theorem below. The convolution of and is defined by: In this context the asterisk denotes convolution, instead of standard multiplication. The tensor product symbol is sometimes used instead. The convolution theorem states that: Applying the inverse Fourier transform produces the corollary: The theorem also generally applies to multi-dimensional functions. Consider functions in Lp-space with Fourier transforms : where indicates the inner product of : and The convolution of and is defined by: Also: Hence by Fubini's theorem we have that so its Fourier transform is defined by the integral formula: Note that Hence by the argument above we may apply Fubini's theorem again (i.e. interchange the order of integration): This theorem also holds for the Laplace transform, the two-sided Laplace transform and, when suitably modified, for the Mellin transform and Hartley transform (see Mellin inversion theorem). It can be extended to the Fourier transform of abstract harmonic analysis defined over locally compact abelian groups. Periodic convolution (Fourier series coefficients) Consider -periodic functions and which can be expressed as periodic summations: and In practice the non-zero portion of components and are often limited to duration but nothing in the theorem requires that. The Fourier series coefficients are: where denotes the Fourier series integral. The product: is also -periodic, and its Fourier series coefficients are given by the discrete convolution of the and sequences: The convolution: is also -periodic, and is called a periodic convolution. The corresponding convolution theorem is: Functions of a discrete variable (sequences) By a derivation similar to Eq.1, there is an analogous theorem for sequences, such as samples of two continuous functions, where now denotes the discrete-time Fourier transform (DTFT) operator. Consider two sequences and with transforms and : The of and is defined by: The convolution theorem for discrete sequences is: Periodic convolution and as defined above, are periodic, with a period of 1. Consider -periodic sequences and : and These functions occur as the result of sampling and at intervals of and performing an inverse discrete Fourier transform (DFT) on samples (see ). The discrete convolution: is also -periodic, and is called a periodic convolution. Redefining the operator as the -length DFT, the corresponding theorem is: And therefore: Under the right conditions, it is possible for this -length sequence to contain a distortion-free segment of a convolution. But when the non-zero portion of the or sequence is equal or longer than some distortion is inevitable. Such is the case when the sequence is obtained by directly sampling the DTFT of the infinitely long impulse response. For and sequences whose non-zero duration is less than or equal to a final simplification is: This form is often used to efficiently implement numerical convolution by computer. (see and ) As a partial reciprocal, it has been shown that any linear transform that turns convolution into a product is the DFT (up to a permutation of coefficients). A time-domain derivation proceeds as follows: A frequency-domain derivation follows from , which indicates that the DTFTs can be written as: The product with is thereby reduced to a discrete-frequency function: where the equivalence of and follows from . Therefore, the equivalence of (5a) and (5b) requires: We can also verify the inverse DTFT of (5b): Convolution theorem for inverse Fourier transform There is also a convolution theorem for the inverse Fourier transform: Here, "" represents the Hadamard product, and "" represents a convolution between the two matrices. so that Convolution theorem for tempered distributions The convolution theorem extends to tempered distributions. Here, is an arbitrary tempered distribution: But must be "rapidly decreasing" towards and in order to guarantee the existence of both, convolution and multiplication product. Equivalently, if is a smooth "slowly growing" ordinary function, it guarantees the existence of both, multiplication and convolution product. In particular, every compactly supported tempered distribution, such as the Dirac delta, is "rapidly decreasing". Equivalently, bandlimited functions, such as the function that is constantly are smooth "slowly growing" ordinary functions. If, for example, is the Dirac comb both equations yield the Poisson summation formula and if, furthermore, is the Dirac delta then is constantly one and these equations yield the Dirac comb identity. See also Moment-generating function of a random variable Notes References Further reading Additional resources For a visual representation of the use of the convolution theorem in signal processing, see: Johns Hopkins University's Java-aided simulation: http://www.jhu.edu/signals/convolve/index.html Theorems in Fourier analysis Articles containing proofs de:Faltung (Mathematik)#Faltungstheorem 2 fr:Produit de convolution	Convolution theorem	[ "Mathematics" ]	1,208	[ "Articles containing proofs" ]
53,277	https://en.wikipedia.org/wiki/Fat%20acceptance%20movement	The fat acceptance movement (also known by various other names, such as fat pride, fat empowerment, fat liberation, and fat activism) is a social movement which seeks to eliminate the social stigma of obesity. Areas of contention include the aesthetic, legal, and medical approaches to fat people. The modern fat acceptance movement began in the late 1960s. Besides its political role, the fat acceptance movement also constitutes a subculture which acts as a social group for its members. The fat acceptance movement has been criticized for not adding value to the debate over human health, with some critics accusing the movement of "promoting a lifestyle that can have dire health consequences". History The history of the fat acceptance movement can be dated back to 1967 when 500 people met in New York's Central Park to protest against anti-fat bias. Sociologist Charlotte Cooper has argued that the history of the fat activist movement is best understood in waves, similar to the feminist movement, with which she believes it is closely tied. Cooper believes that fat activists have suffered similar waves of activism followed by burnout, with activists in the following wave often unaware of the history of the movement, resulting in a lack of continuity. Other scholars, such as Amy Erdman Farrell, have argued that the history of fat activism that traditionally gets told is a dominantly white history. The intersectional work of fat activists of color frequently gets overlooked within this traditional history. First wave First wave activities consisted of isolated activists drawing attention to the dominant model of obesity and challenging it as only one of several possible models. During the early part of the 20th century, obesity was seen as detrimental to the community, via decreasing human efficiency, and that obese people interfere with labor productivity in the coastal areas of the United States. This kind of political climate was the background of the fat acceptance movement, which originated in the late 1960s. Like other social movements from this period, the fat acceptance movement, initially known as "Fat Pride", "Fat Power", or "Fat Liberation", often consisted of people acting in an impromptu fashion. A "fat-in" was staged in New York's Central Park in 1967. Called by radio personality Steve Post, the "Fat-in" consisted of a group of 500 people eating, carrying signs and photographs of Twiggy (a model famous for her thin figure), and burning diet books. In 1967, Lew Louderback wrote an article in the Saturday Evening Post called "More People Should be FAT" in response to discrimination against his wife. The article led to a meeting between Louderback and William Fabrey, who went on to found the first organization for fat people and their supporters, originally named the 'National Association to Aid Fat Americans' and currently called the National Association to Advance Fat Acceptance (NAAFA). NAAFA was founded in America, in 1969, by Bill Fabrey in response to discrimination against his wife. He primarily intended it to campaign for fat rights, however, a reporter attending the 2001 NAAFA conference notes that few attendees were active in fat rights politics and that most women came to shop for fashion, wear it on the conference catwalk or to meet a potential partner. Since 1991, Fabrey has worked as a director with the Council on Size and Weight Discrimination, specializing in the history of the size acceptance movement. In 1972, the feminist group The Fat Underground was formed. It began as a radical chapter of NAAFA and spun off to become independent when NAAFA expressed concerns about its promotion of a stronger activist philosophy. The FU were inspired by and, in some cases, members of the Radical Therapy Collective, a feminist group that believed that many psychological problems were caused by oppressive social institutions and practices. Founded by Sara Fishman (then Sara Aldebaran) and Judy Freespirit, the Fat Underground took issue with what they saw as a growing bias against obesity in the scientific community. They coined the saying, "a diet is a cure that doesn't work, for a disease that doesn't exist". Shortly afterward, Fishman moved to Connecticut, where, along with Karen Scott-Jones, she founded the New Haven Fat Liberation Front, an organization similar to the Fat Underground in its scope and focus. In 1983, the two groups collaborated to publish a seminal book in the field of fat activism, Shadow on a Tightrope, which collected several fat activist position papers initially distributed by the Fat Underground, as well as poems and essays from other writers. In 1979, Carole Shaw coined the term Big Beautiful Woman (BBW) and launched a fashion and lifestyle magazine of the same name aimed at plus-sized women. The original print magazine ceased publication in May 2003, but continued in various online formats. The term "BBW" has become widely used to refer to any fat woman (sometimes in a derogatory way). Several other periodicals focusing on fashion and lifestyle for "fuller-figured" women were published in print from the early 1980s to the mid 2010s. From 1984 to 2000, Radiance: The Magazine for Large Women was published in print to "support women 'all sizes of large in living proud, full, active lives, at whatever weight, with self-love and self-respect." In the UK, the London Fat Women's Group was formed, the first British fat activist group, and was active between approximately 1985 and 1989. Other first wave activities included the productions of zines such as Figure 8 and Fat!So? by Marilyn Wann. The latter went on to become a book of the same name. Second wave In the second wave, the fat acceptance movement became more widespread in the US and started to spread to other countries. Ideas from the movement began to appear in the mainstream. Publishers became more willing to publish fat acceptance themed literature. The 1980s witnessed an increase in activist organizations, publications, and conferences. In 1989, a group of people including actress Anne Zamberlan formed the first French organization for fat acceptance, Allegro fortissimo. Organizations began holding conferences and conventions, including NAAFA. By the 1990s, input from the fat acceptance movement began to be incorporated into research papers by some members of the medical professions such as new anti-dieting programs and models of obesity management. Third wave The fat acceptance movement has seen a diversification of projects during the third wave. Activities have addressed issues of both fat and race, class, sexuality, and other issues. Size discrimination has been increasingly addressed in the arts, as well. Campaigning themes The fat acceptance movement argues that fat people are targets of hatred and discrimination. In particular, advocates suggest obese women are subjected to more social pressure than obese men. The movement argues that these attitudes comprise a fat phobic entrenched societal norm, evident in many social institutions, including the mass media, where fat people are often ridiculed, or held up as objects of pity. Discrimination includes a lack of equal access to transportation and employment. Members of the fat acceptance movement perceive negative societal attitudes as persistent, and as being based on the presumption that fatness reflects negatively on a person's character. Fat activists push for change in societal, personal, and medical attitudes toward fat people. Fat acceptance organizations engage in public education about what they describe as myths concerning fat people. Discrimination Fat people experience many different kinds of discrimination because of their weight. This discrimination appears in healthcare, employment, education, personal relationships, and the media. Fat individuals also argue clothing stores discriminate against them. For example, some women have complained that "one size fits all" stores, which offer a single size for each item, do not cater to those above a certain weight. Public transport has also been subject to criticism due to lack of inclusivity to fat people as seats and walkways are often too small to accommodate them. On the subject of horseback riding, there has been disagreement between fat acceptance activists and animal rights activists. Health Fat activists argue that anti-fat stigma and aggressive diet promotion have led to an increase in psychological and physiological problems among fat people. For instance, individuals who experience weight discrimination have reported facing more psychological distress, more loneliness, and lower well-being. Along with this, weight discrimination can heighten risk for obesity, chronic inflammation, and disease burden. People can indulge in health-risk behaviors, such as avoiding physical activity. Experiencing and internalizing weight stigma are identified as critical risk factors leading to eating pathology. Concerns are also raised that modern culture's focus on weight loss does not have a foundation in scientific research, but instead is an example of using science as a means to control deviance, as a part of society's attempt to deal with something that it finds disturbing. Diet critics cite the high failure rate of permanent weight-loss attempts, and the dangers of "yo-yo" weight fluctuations and weight-loss surgeries. Fat activists argue that the health issues of obesity and being overweight have been exaggerated or misrepresented, and that health issues are used as a cover for cultural and aesthetic prejudices against fat. Proponents of fat acceptance maintain that people of all shapes and sizes can strive for fitness and physical health. They believe that healthy behaviors can be independent of body weight. Informed by this approach, psychologists who were unhappy with the treatment of fat people in the medical world initiated the Health at Every Size movement. It has five basic tenets: (1) enhancing health, (2) size and self-acceptance (3) the pleasure of eating well, (4) the joy of movement, and (5) an end to weight bias. Some proponents also claim that people with obesity can be metabolically healthy. Some medical studies have challenged that "healthy obesity" concept, although the definitions of metabolically healthy obesity are not standardized across studies. Gender Fat women The issues faced by fat women in society have been a central theme of the fat acceptance movement since its inception. Although the first organization, National Association to Advance Fat Acceptance, and the first book, Fat Power (1970), were both created by men, in each case they were responses to weight discrimination experienced by their wives. Women soon started campaigning on their behalf with the first feminist group, 'The Fat Underground', being formed in 1973. Issues addressed regarding women have included body image, and in particular the thin ideal and its effect on women. Critics say NAAFA, which opposes dieting and weight-loss surgery, is an apologist for an unhealthy lifestyle. But NAAFA says it does no such thing, that some people are just bigger and no less deserving of the same rights as everyone else. Fat men The fat acceptance movement has primarily focused on a feminist model of patriarchal oppression of fat women, most clearly represented by the encouragement of women to diet. However, Sander L. Gilman argues that, until the 20th century, dieting has historically been a man's activity. He continues, "Obesity eats away at the idealized image of the masculine just as surely as it does the idealized image of the feminine." William Banting was the author of an 1863 booklet called Letter On Corpulence, which modern diets have used as a model. Men respond to being overweight differently, (i.e., having a Body Mass Index of 25 or more), being half as likely as women to diet, a quarter as likely to undergo weightloss surgery and only a fifth as likely to report feeling shame about their weight. Irmgard Tischner identifies this behavior as rooted in notions of masculinity that require disregard for healthcare: "Men do not have to care about their size or health, as they have women to care about those things for them". Some gay men have moved beyond disregard for size to fat acceptance and fat activism with movements like chub culture, which started as Girth & Mirth clubs in San Francisco in 1976 and the bear culture which fetishizes big, hairy men. Ganapati Durgadas argues that fat bisexual and gay men "are reminders of the feminine stigma with which heterosexism still tars queer men". In a comparison of queer fat positive zines, the lesbian-produced Fat Girl was found to have political debate content absent from gay male orientated zines such as Bulk Male and Big Ad. Joel Barraquiel Tan comments: "If fat is a feminist issue, then fat or heft is a fetishized one for gay men. Gay men tend to sexualize difference, where lesbians have historically politicized it." A fat heterosexual man is known as a "Big Handsome Man" (BHM), in counterpart to a Big Beautiful Woman. Like some fat and gay men, BHMs have sexualized their difference and receive validation of this identity from BBWs or straight women known as "Female Fat Admirers". Legislation In the 1970s, fat people in the United States began seeking legal redress for discrimination based on weight, primarily in the workplace but also for being denied access to, or treated differently in regards to, services or entertainment. The results of these cases have varied considerably, although in some instances the Americans with Disabilities Act (ADA) has been successfully used to argue cases of discrimination against fat people. Roth and Solovay argue that, as with transgender people, a major cause for the variation in success is the extent to which litigants are apologetic for their size (with more apologetic plaintiffs finding more success): What is the difference between a million-dollar weight case award and a losing case? Like the difference between many winning and losing transgender cases, it's all about the attitude. Does the claimant's attitude and experience about weight/gender reinforce or challenge dominant stereotypes? Winning cases generally adopt a legal posture that reinforces social prejudices. Cases that challenge societal prejudices generally lose. The Americans with Disabilities Act continues to be used as there is no USA federal law against weight discrimination; however, the state of Michigan passed a law against weight discrimination in 1976. The cities of Washington, D.C., San Francisco (2000), Santa Cruz, Binghamton, Urbana (1990s), New York (2023), and Madison (1970s) have also passed laws prohibiting weight discrimination. In the cities that have a weight discrimination law, it is rare for more than one case a year to be brought, except for San Francisco which may have as many as six. Opinions amongst city enforcement workers vary as to why the prosecution numbers are so low, although they all suggested that both overweight people and employers were unaware of the protective legislation and it was also noted that the cities with anti-weight discrimination laws tended to be liberal college towns. Not all legal changes have protected the rights of fat people. Despite recommendations from the Equal Employment Opportunity Commission to the contrary, in 2009 the United States Court of Appeals for the Sixth Circuit decided that fat people will only qualify as disabled if it can be proved that their weight is caused by an underlying condition, supporting the concept that being obese is not inherently a disability. The Supreme Court of Texas came to a similar conclusion in 2023. But in 2018, the Washington Supreme Court provided weight-related disability bias protection without evidence of a related medical condition. Other countries besides the United States have considered legislation to protect the rights of fat people. In the UK an All-Party Parliamentary Group published a report in 2012 called Reflections on Body Image that found that one in five British people had been victimized because of their weight. The report recommended that Members of Parliament investigated putting "appearance-based discrimination" under the same legal basis as sexual or racial discrimination via the Equality Act 2010 which makes it illegal to harass, victimize or discriminate against anyone in the workplace based on several named categories, including size or weight. The Equality Act came into force on 1 October 2010, it brings together over 116 separate pieces of legislation into one single Act. The Act provides a legal framework to protect the rights of individuals and advance equality of opportunity for all. Fat studies There has also been an emerging body of academic studies called Fat Studies. Marilyn Wann argues that fat studies moved beyond being an individual endeavor to being a field of study with the 2004 conference Fat Attitudes: An Examination of an American Subculture and the Representation of the Female Body. The American Popular Culture Association regularly includes panels on the subject. In many colleges, student groups with a fat activist agenda have emerged, including Hampshire, Smith, and Antioch. Fat studies are now available as an interdisciplinary course of study at some colleges, taking a similar approach to other identity studies such as women's studies, queer studies, and African American studies. As of 2011, there were two Australian courses and ten American courses that were primarily focused on fat studies or Health at Every Size, and numerous other courses that had some fat acceptance content. Taylor & Francis publish an online Fat Studies journal. The first national Fat Studies seminar was held at York in May 2008, leading to the 2009 publication Fat Studies in the UK, edited by Corinna Tomrley and Ann Kalosky Naylor. Division within the movement The fat acceptance movement has been divided in its response to proposed legislation defining morbidly obese people as disabled. NAAFA board member Peggy Howell says: "There's a lot of conflict in the size acceptance community over this. I don't consider myself disabled, and some people don't like 'fat' being considered a disability." An example of the positive perspective of obesity being classified as a disability in wider society is noted by a person interviewed by Amy Erdman in her book Fat Shame: "[Deborah Harper] makes a point to tell me how impressed she is with the way many do make quiet and polite accommodations for her." Women are particularly active within the fat acceptance movement and membership of fat acceptance organizations is dominated by middle-class women in the heaviest 1–2% of the population. Members have criticized the lack of representation in the movement from men, people of color, and people of lower socioeconomic status. Criticism The fat acceptance movement has been criticized from several perspectives. The primary criticism is that fat acceptance ignores studies that have shown health issues to be linked to obesity and hence encourages an unhealthy lifestyle. In 2008, Lily-Rygh Glen, a writer, musician, and former fat acceptance activist, interviewed multiple women who claimed to be rejected by their peers within the movement and labeled "traitors" when they changed their diets. Medical criticism Human health is a multi-faceted issue; more and more rigorous scientific research reveals the relationship between weight and health is complex. The fat acceptance movement has been criticized for not adding value to the debate over human health, with some critics accusing the movement of "promoting a lifestyle that can have dire health consequences". There is a considerable amount of evidence that being obese is connected to increased all-cause mortality and diseases, and significant weight loss (>10%), using a variety of diets, improves or reverses metabolic syndromes and other health outcomes associated with obesity. Barry Franklin, director of a cardio rehab facility, stated: "I don't want to take on any specific organization but... A social movement that would suggest health at any size in many respects can be misleading." Franklin also agrees that fit people who are obese have cardiovascular mortality rates that are lower than thin, unfit people, and proponents of the fat acceptance movement argue that people of all shapes and sizes can choose behaviors that support their fitness and physical health. See also Body positivity Disability rights movement Epidemiology of obesity Health At Every Size Fat tax Hanne Blank Obesity paradox Plus-size model References Citations Sources (A) Medical Practitioners' Guide to Benefits of Adapting Environments for the Obese, Michigan State University study by Angela Berg MD and Joyce Burke MD, MSU.edu The Routledge International Handbook of Fat Studies edited by Cat Pausé & Sonya Renee Taylor External links What's Fat Activism? History of fat activism from a UK perspective. Obesity Identity politics Intersectional feminism Discrimination	Fat acceptance movement	[ "Biology" ]	4,076	[ "Behavior", "Aggression", "Discrimination" ]
53,289	https://en.wikipedia.org/wiki/File%20Transfer%20Protocol	The File Transfer Protocol (FTP) is a standard communication protocol used for the transfer of computer files from a server to a client on a computer network. FTP is built on a client–server model architecture using separate control and data connections between the client and the server. FTP users may authenticate themselves with a plain-text sign-in protocol, normally in the form of a username and password, but can connect anonymously if the server is configured to allow it. For secure transmission that protects the username and password, and encrypts the content, FTP is often secured with SSL/TLS (FTPS) or replaced with SSH File Transfer Protocol (SFTP). The first FTP client applications were command-line programs developed before operating systems had graphical user interfaces, and are still shipped with most Windows, Unix, and Linux operating systems. Many dedicated FTP clients and automation utilities have since been developed for desktops, servers, mobile devices, and hardware, and FTP has been incorporated into productivity applications such as HTML editors and file managers. An FTP client used to be commonly integrated in web browsers, where file servers are browsed with the URI prefix "ftp://". In 2021, FTP support was dropped by Google Chrome and Firefox, two major web browser vendors, due to it being superseded by the more secure SFTP and FTPS; although neither of them have implemented the newer protocols. History of FTP servers The original specification for the File Transfer Protocol was written by Abhay Bhushan and published as on 16 April 1971. Until 1980, FTP ran on NCP, the predecessor of TCP/IP. The protocol was later replaced by a TCP/IP version, (June 1980) and (October 1985), the current specification. Several proposed standards amend , for example (February 1994) enables Firewall-Friendly FTP (passive mode), (June 1997) proposes security extensions, (September 1998) adds support for IPv6 and defines a new type of passive mode. Protocol overview Communication and data transfer FTP may run in active or passive mode, which determines how the data connection is established. (This sense of "mode" is different from that of the MODE command in the FTP protocol.) In active mode, the client starts listening for incoming data connections from the server on port M. It sends the FTP command PORT M to inform the server on which port it is listening. The server then initiates a data channel to the client from its port 20, the FTP server data port. In situations where the client is behind a firewall and unable to accept incoming TCP connections, passive mode may be used. In this mode, the client uses the control connection to send a PASV command to the server and then receives a server IP address and server port number from the server, which the client then uses to open a data connection from an arbitrary client port to the server IP address and server port number received. Both modes were updated in September 1998 to support IPv6. Further changes were introduced to the passive mode at that time, updating it to extended passive mode. The server responds over the control connection with three-digit status codes in ASCII with an optional text message. For example, "200" (or "200 OK") means that the last command was successful. The numbers represent the code for the response and the optional text represents a human-readable explanation or request (e.g. <Need account for storing file>). An ongoing transfer of file data over the data connection can be aborted using an interrupt message sent over the control connection. FTP needs two ports (one for sending and one for receiving) because it was originally designed to operate on top of Network Control Protocol (NCP), which was a simplex protocol that utilized two port addresses, establishing two connections, for two-way communications. An odd and an even port were reserved for each application layer application or protocol. The standardization of TCP and UDP reduced the need for the use of two simplex ports for each application down to one duplex port, but the FTP protocol was never altered to only use one port, and continued using two for backwards compatibility. NAT and firewall traversal FTP normally transfers data by having the server connect back to the client, after the PORT command is sent by the client. This is problematic for both NATs and firewalls, which do not allow connections from the Internet towards internal hosts. For NATs, an additional complication is that the representation of the IP addresses and port number in the PORT command refer to the internal host's IP address and port, rather than the public IP address and port of the NAT. There are two approaches to solve this problem. One is that the FTP client and FTP server use the PASV command, which causes the data connection to be established from the FTP client to the server. This is widely used by modern FTP clients. Another approach is for the NAT to alter the values of the PORT command, using an application-level gateway for this purpose. Data types While transferring data over the network, five data types are defined: ASCII (TYPE A): Used for text. Data is converted, if needed, from the sending host's character representation to "8-bit ASCII" before transmission, and (again, if necessary) to the receiving host's character representation, including newlines. As a consequence, this mode is inappropriate for files that contain data other than ASCII. Image (TYPE I, commonly called Binary mode): The sending machine sends each file byte by byte, and the recipient stores the bytestream as it receives it. (Image mode support has been recommended for all implementations of FTP). EBCDIC (TYPE E): Used for plain text between hosts using the EBCDIC character set. Local (TYPE L n): Designed to support file transfer between machines which do not use 8-bit bytes, e.g. 36-bit systems such as DEC PDP-10s. For example, "TYPE L 9" would be used to transfer data in 9-bit bytes, or "TYPE L 36" to transfer 36-bit words. Most contemporary FTP clients/servers only support L 8, which is equivalent to I. Unicode text files using UTF-8 (TYPE U): defined in an expired Internet Draft which never became an RFC, though it has been implemented by several FTP clients/servers. Note these data types are commonly called "modes", although ambiguously that word is also used to refer to active-vs-passive communication mode (see above), and the modes set by the FTP protocol MODE command (see below). For text files (TYPE A and TYPE E), three different format control options are provided, to control how the file would be printed: Non-print (TYPE A N and TYPE E N) – the file does not contain any carriage control characters intended for a printer Telnet (TYPE A T and TYPE E T) – the file contains Telnet (or in other words, ASCII C0) carriage control characters (CR, LF, etc) ASA (TYPE A A and TYPE E A) – the file contains ASA carriage control characters These formats were mainly relevant to line printers; most contemporary FTP clients/servers only support the default format control of N. File structures File organization is specified using the STRU command. The following file structures are defined in section 3.1.1 of RFC959: F or FILE structure (stream-oriented). Files are viewed as an arbitrary sequence of bytes, characters or words. This is the usual file structure on Unix systems and other systems such as CP/M, MS-DOS and Microsoft Windows. (Section 3.1.1.1) R or RECORD structure (record-oriented). Files are viewed as divided into records, which may be fixed or variable length. This file organization is common on mainframe and midrange systems, such as MVS, VM/CMS, OS/400 and VMS, which support record-oriented filesystems. P or PAGE structure (page-oriented). Files are divided into pages, which may either contain data or metadata; each page may also have a header giving various attributes. This file structure was specifically designed for TENEX systems, and is generally not supported on other platforms. RFC1123 section 4.1.2.3 recommends that this structure not be implemented. Most contemporary FTP clients and servers only support STRU F. STRU R is still in use in mainframe and minicomputer file transfer applications. Data transfer modes Data transfer can be done in any of three modes: Stream mode (MODE S): Data is sent as a continuous stream, relieving FTP from doing any processing. Rather, all processing is left up to TCP. No End-of-file indicator is needed, unless the data is divided into records. Block mode (MODE B): Designed primarily for transferring record-oriented files (STRU R), although can also be used to transfer stream-oriented (STRU F) text files. FTP puts each record (or line) of data into several blocks (block header, byte count, and data field) and then passes it on to TCP. Compressed mode (MODE C): Extends MODE B with data compression using run-length encoding. Most contemporary FTP clients and servers do not implement MODE B or MODE C; FTP clients and servers for mainframe and minicomputer operating systems are the exception to that. Some FTP software also implements a DEFLATE-based compressed mode, sometimes called "Mode Z" after the command that enables it. This mode was described in an Internet Draft, but not standardized. GridFTP defines additional modes, MODE E and MODE X, as extensions of MODE B. Additional commands More recent implementations of FTP support the Modify Fact: Modification Time (MFMT) command, which allows a client to adjust that file attribute remotely, enabling the preservation of that attribute when uploading files. To retrieve a remote file timestamp, there's MDTM command. Some servers (and clients) support nonstandard syntax of the MDTM command with two arguments, that works the same way as MFMT Login FTP login uses normal username and password scheme for granting access. The username is sent to the server using the USER command, and the password is sent using the PASS command. This sequence is unencrypted "on the wire", so may be vulnerable to a network sniffing attack. If the information provided by the client is accepted by the server, the server will send a greeting to the client and the session will commence. If the server supports it, users may log in without providing login credentials, but the same server may authorize only limited access for such sessions. Anonymous FTP A host that provides an FTP service may provide anonymous FTP access. Users typically log into the service with an 'anonymous' (lower-case and case-sensitive in some FTP servers) account when prompted for user name. Although users are commonly asked to send their email address instead of a password, no verification is actually performed on the supplied data. Many FTP hosts whose purpose is to provide software updates will allow anonymous logins. Software support File managers Many file managers tend to have FTP access implemented, such as File Explorer (formerly Windows Explorer) on Microsoft Windows. This client is only recommended for small file transfers from a server, due to limitations compared to dedicated client software. It does not support SFTP. Both the native file managers for KDE on Linux (Dolphin and Konqueror) support FTP as well as SFTP. On Android, the My Files file manager on Samsung Galaxy has a built-in FTP and SFTP client. Web browser For a long time, most common web browsers were able to retrieve files hosted on FTP servers, although not all of them had support for protocol extensions such as FTPS. When an FTP—rather than an HTTP—URL is supplied, the accessible contents on the remote server are presented in a manner that is similar to that used for other web content. Google Chrome removed FTP support entirely in Chrome 88, also affecting other Chromium-based browsers such as Microsoft Edge. Firefox 88 disabled FTP support by default, with Firefox 90 dropping support entirely. FireFTP is a discontinued browser extension that was designed as a full-featured FTP client to be run within Firefox, but when Firefox dropped support for FTP the extension developer recommended using Waterfox. Some browsers, such as the text-based Lynx, still support FTP. Syntax FTP URL syntax is described in , taking the form: ftp://[user[:password]@]host[:port]/[url-path] (the bracketed parts are optional). For example, the URL ftp://public.ftp-servers.example.com/mydirectory/myfile.txt represents the file myfile.txt from the directory mydirectory on the server public.ftp-servers.example.com as an FTP resource. The URL ftp://user001:secretpassword@private.ftp-servers.example.com/mydirectory/myfile.txt adds a specification of the username and password that must be used to access this resource. More details on specifying a username and password may be found in the browsers' documentation (e.g., Firefox and Internet Explorer). By default, most web browsers use passive (PASV) mode, which more easily traverses end-user firewalls. Some variation has existed in how different browsers treat path resolution in cases where there is a non-root home directory for a user. Download manager Most common download managers can receive files hosted on FTP servers, while some of them also give the interface to retrieve the files hosted on FTP servers. DownloadStudio allows not only download a file from FTP server but also view the list of files on a FTP server. Other LibreOffice declared its FTP support deprecated from 7.4 release, this was later removed in 24.2 release. Security FTP was not designed to be a secure protocol, and has many security weaknesses. In May 1999, the authors of listed a vulnerability to the following problems: Brute-force attack FTP bounce attack Packet capture Port stealing (guessing the next open port and usurping a legitimate connection) Spoofing attack Username enumeration DoS or DDoS FTP does not encrypt its traffic; all transmissions are in clear text, and usernames, passwords, commands and data can be read by anyone able to perform packet capture (sniffing) on the network. This problem is common to many of the Internet Protocol specifications (such as SMTP, Telnet, POP and IMAP) that were designed prior to the creation of encryption mechanisms such as TLS or SSL. Common solutions to this problem include: Using the secure versions of the insecure protocols, e.g., FTPS instead of FTP and TelnetS instead of Telnet. Using a different, more secure protocol that can handle the job, e.g. SSH File Transfer Protocol or Secure Copy Protocol. Using a secure tunnel such as Secure Shell (SSH) or virtual private network (VPN). FTP over SSH FTP over SSH is the practice of tunneling a normal FTP session over a Secure Shell connection. Because FTP uses multiple TCP connections (unusual for a TCP/IP protocol that is still in use), it is particularly difficult to tunnel over SSH. With many SSH clients, attempting to set up a tunnel for the control channel (the initial client-to-server connection on port 21) will protect only that channel; when data is transferred, the FTP software at either end sets up new TCP connections (data channels) and thus have no confidentiality or integrity protection. Otherwise, it is necessary for the SSH client software to have specific knowledge of the FTP protocol, to monitor and rewrite FTP control channel messages and autonomously open new packet forwardings for FTP data channels. Software packages that support this mode include: Tectia ConnectSecure (Win/Linux/Unix) of SSH Communications Security's software suite FTP over SSH should not be confused with SSH File Transfer Protocol (SFTP). Derivatives FTPS Explicit FTPS is an extension to the FTP standard that allows clients to request FTP sessions to be encrypted. This is done by sending the "AUTH TLS" command. The server has the option of allowing or denying connections that do not request TLS. This protocol extension is defined in . Implicit FTPS is an outdated standard for FTP that required the use of a SSL or TLS connection. It was specified to use different ports than plain FTP. SSH File Transfer Protocol The SSH file transfer protocol (chronologically the second of the two protocols abbreviated SFTP) transfers files and has a similar command set for users, but uses the Secure Shell protocol (SSH) to transfer files. Unlike FTP, it encrypts both commands and data, preventing passwords and sensitive information from being transmitted openly over the network. It cannot interoperate with FTP software, though some FTP client software offers support for the SSH file transfer protocol as well. Trivial File Transfer Protocol Trivial File Transfer Protocol (TFTP) is a simple, lock-step FTP that allows a client to get a file from or put a file onto a remote host. One of its primary uses is in the early stages of booting from a local area network, because TFTP is very simple to implement. TFTP lacks security and most of the advanced features offered by more robust file transfer protocols such as File Transfer Protocol. TFTP was first standardized in 1981 and the current specification for the protocol can be found in . Simple File Transfer Protocol Simple File Transfer Protocol (the first protocol abbreviated SFTP), as defined by , was proposed as an (unsecured) file transfer protocol with a level of complexity intermediate between TFTP and FTP. It was never widely accepted on the Internet, and is now assigned Historic status by the IETF. It runs through port 115, and often receives the initialism of SFTP. It has a command set of 11 commands and support three types of data transmission: ASCII, binary and continuous. For systems with a word size that is a multiple of 8 bits, the implementation of binary and continuous is the same. The protocol also supports login with user ID and password, hierarchical folders and file management (including rename, delete, upload, download, download with overwrite, and download with append). FTP commands FTP reply codes Below is a summary of FTP reply codes that may be returned by an FTP server. These codes have been standardized in by the IETF. The reply code is a three-digit value. The first digit is used to indicate one of three possible outcomes — success, failure, or to indicate an error or incomplete reply: 2yz – Success reply 4yz or 5yz – Failure reply 1yz or 3yz – Error or Incomplete reply The second digit defines the kind of error: x0z – Syntax. These replies refer to syntax errors. x1z – Information. Replies to requests for information. x2z – Connections. Replies referring to the control and data connections. x3z – Authentication and accounting. Replies for the login process and accounting procedures. x4z – Not defined. x5z – File system. These replies relay status codes from the server file system. The third digit of the reply code is used to provide additional detail for each of the categories defined by the second digit. See also References Further reading – CWD Command of FTP. July 1975. – (Standard) File Transfer Protocol (FTP). J. Postel, J. Reynolds. October 1985. – (Informational) Firewall-Friendly FTP. February 1994. – (Informational) How to Use Anonymous FTP. May 1994. – FTP Operation Over Big Address Records (FOOBAR). June 1994. – Uniform Resource Locators (URL). December 1994. – (Proposed Standard) FTP Security Extensions. October 1997. – (Proposed Standard) Feature negotiation mechanism for the File Transfer Protocol. August 1998. – (Proposed Standard) Extensions for IPv6, NAT, and Extended passive mode. September 1998. – (Informational) FTP Security Considerations. May 1999. – (Proposed Standard) Internationalization of the File Transfer Protocol. July 1999. – (Proposed Standard) Extensions to FTP. P. Hethmon. March 2007. – (Proposed Standard) FTP Command and Extension Registry. March 2010. – (Proposed Standard) File Transfer Protocol HOST Command for Virtual Hosts. March 2014. IANA FTP Commands and Extensions registry – The official registry of FTP Commands and Extensions External links FTP Server Online Tester Authentication, encryption, mode and connectivity. Anonymous FTP Servers by Country Code TLD (2012): Application layer protocols Clear text protocols Computer-related introductions in 1971 History of the Internet Internet Standards Network file transfer protocols OS/2 commands Unix network-related software File sharing	File Transfer Protocol	[ "Technology" ]	4,487	[ "OS/2 commands", "Computing commands" ]
53,293	https://en.wikipedia.org/wiki/Tangloids	Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors. A description of the game appeared in the book "Martin Gardner's New Mathematical Diversions from Scientific American" by Martin Gardner from 1996 in a section on the mathematics of braiding. Two flat blocks of wood each pierced with three small holes are joined with three parallel strings. Each player holds one of the blocks of wood. The first player holds one block of wood still, while the other player rotates the other block of wood for two full revolutions. The plane of rotation is perpendicular to the strings when not tangled. The strings now overlap each other. Then the first player tries to untangle the strings without rotating either piece of wood. Only translations (moving the pieces without rotating) are allowed. Afterwards, the players reverse roles; whoever can untangle the strings fastest is the winner. Try it with only one revolution. The strings are of course overlapping again but they can not be untangled without rotating one of the two wooden blocks. The Balinese cup trick, appearing in the Balinese candle dance, is a different illustration of the same mathematical idea. The anti-twister mechanism is a device intended to avoid such orientation entanglements. A mathematical interpretation of these ideas can be found in the article on quaternions and spatial rotation. Mathematical articulation This game serves to clarify the notion that rotations in space have properties that cannot be intuitively explained by considering only the rotation of a single rigid object in space. The rotation of vectors does not encompass all of the properties of the abstract model of rotations given by the rotation group. The property being illustrated in this game is formally referred to in mathematics as the "double covering of SO(3) by SU(2)". This abstract concept can be roughly sketched as follows. Rotations in three dimensions can be expressed as 3x3 matrices, a block of numbers, one each for x,y,z. If one considers arbitrarily tiny rotations, one is led to the conclusion that rotations form a space, in that if each rotation is thought of as a point, then there are always other nearby points, other nearby rotations that differ by only a small amount. In small neighborhoods, this collection of nearby points resembles Euclidean space. In fact, it resembles three-dimensional Euclidean space, as there are three different possible directions for infinitesimal rotations: x, y and z. This properly describes the structure of the rotation group in small neighborhoods. For sequences of large rotations, however, this model breaks down; for example, turning right and then lying down is not the same as lying down first and then turning right. Although the rotation group has the structure of 3D space on the small scale, that is not its structure on the large scale. Systems that behave like Euclidean space on the small scale, but possibly have a more complicated global structure are called manifolds. Famous examples of manifolds include the spheres: globally, they are round, but locally, they feel and look flat, ergo "flat Earth". Careful examination of the rotation group reveals that it has the structure of a 3-sphere with opposite points identified. That means that for every rotation, there are in fact two different, distinct, polar opposite points on the 3-sphere that describe that rotation. This is what the tangloids illustrate. The illustration is actually quite clever. Imagine performing the 360 degree rotation one degree at a time, as a set of tiny steps. These steps take you on a path, on a journey on this abstract manifold, this abstract space of rotations. At the completion of this 360 degree journey, one has not arrived back home, but rather instead at the polar opposite point. And one is stuck there -- one can't actually get back to where one started until one makes another, a second journey of 360 degrees. The structure of this abstract space, of a 3-sphere with polar opposites identified, is quite weird. Technically, it is a projective space. One can try to imagine taking a balloon, letting all the air out, then gluing together polar opposite points. If attempted in real life, one soon discovers it can't be done globally. Locally, for any small patch, one can accomplish the flip-and-glue steps; one just can't do this globally. (Keep in mind that the balloon is , the 2-sphere; it's not the 3-sphere of rotations.) To further simplify, one can start with , the circle, and attempt to glue together polar opposites; one still gets a failed mess. The best one can do is to draw straight lines through the origin, and then declare, by fiat, that the polar opposites are the same point. This is the basic construction of any projective space. The so-called "double covering" refers to the idea that this gluing-together of polar opposites can be undone. This can be explained relatively simply, although it does require the introduction of some mathematical notation. The first step is to blurt out "Lie algebra". This is a vector space endowed with the property that two vectors can be multiplied. This arises because a tiny rotation about the x-axis followed by a tiny rotation about the y-axis is not the same as reversing the order of these two; they are different, and the difference is a tiny rotation in along the z-axis. Formally, this inequivalence can be written as , keeping in mind that x, y and z are not numbers but infinitesimal rotations. They don't commute. One may then ask, "what else behaves like this?" Well, obviously the 3D rotation matrices do; after all, the whole point is that they do correctly, perfectly mathematically describe rotations in 3D space. As it happens, though, there are also 2x2, 4x4, 5x5, ... matrices that also have this property. One may reasonably ask "OK, so what is the shape of their manifolds?". For the 2x2 case, the Lie algebra is called su(2) and the manifold is called SU(2), and quite curiously, the manifold of SU(2) is the 3-sphere (but without the projective identification of polar opposites). This now allows one to play a bit of a trick. Take a vector in ordinary 3D space (our physical space) and apply a rotation matrix to it. One obtains a rotated vector . This is the result of applying an ordinary, "common sense" rotation to . But one also has the Pauli matrices ; these are 2x2 complex matrices that have the Lie algebra property that and so these model the behavior of infinitesimal rotations. Consider then the product . The "double covering" is the property that there exists not one, but two 2x2 matrices such that Here, denotes the inverse of ; that is, The matrix is an element of SU(2), and so for every matrix in SO(3), there are two corresponding : both and will do the trick. These two are the polar-opposites, and the projection is just boils down to the trivial observation that The tangeloid game is meant to illustrate that a 360 degree rotation takes one on a path from to . This is quite precise: one can consider a sequence of small rotations and the corresponding movement of ; the result does change sign. In terms of rotation angles the matrix will have a in it, but the matching will have a in it. Further elucidation requires actually writing out these formulas. The sketch can be completed with some general remarks. First, Lie algebras are generic, and for each one, there are one or more corresponding Lie groups. In physics, 3D rotations of normal 3D objects are obviously described by the rotation group, which is a Lie group of 3x3 matrices . However, the spinors, the spin-1/2 particles, rotate according to the matrices in SU(2). The 4x4 matrices describe the rotation of spin-3/2 particles, and the 5x5 matrices describe the rotations of spin-2 particles, and so on. The representation of Lie groups and Lie algebras are described by representation theory. The spin-1/2 representation belongs to the fundamental representation, and the spin-1 is the adjoint representation. The notion of double-covering used here is a generic phenomenon, described by covering maps. Covering maps are in turn a special case of fiber bundles. The classification of covering maps is done via homotopy theory; in this case, the formal expression of double-covering is to say that the fundamental group is where the covering group is just encoding the two equivalent rotations and above. In this sense, the rotation group provides the doorway, the key to the kingdom of vast tracts of higher mathematics. See also Orientation entanglement Plate trick References Mathematical games Spinors	Tangloids	[ "Mathematics" ]	1,851	[ "Recreational mathematics", "Mathematical games" ]
53,296	https://en.wikipedia.org/wiki/Niels%20Bohr%20Institute	The Niels Bohr Institute () is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics, and biophysics. Overview The institute was founded in 1921, as the Institute for Theoretical Physics of the University of Copenhagen, by the Danish theoretical physicist Niels Bohr, who had been on the staff of the University of Copenhagen since 1914, and who had been lobbying for its creation since his appointment as professor in 1916. On the 80th anniversary of Niels Bohr's birth – October 7, 1965 – the Institute officially became the Niels Bohr Institute. Much of its original funding came from the charitable foundation of the Carlsberg brewery, and later from the Rockefeller Foundation. During the 1920s, and 1930s, the institute was the center of the developing disciplines of atomic physics and quantum physics. Physicists from across Europe (and sometimes further abroad) often visited the institute to confer with Bohr on new theories and discoveries. The Copenhagen interpretation of quantum mechanics is named after work done at the institute during this time. Following his father's death in 1962, Aage Bohr succeeded him as director of the Niels Bohr Institute, a position he held until 1970. He remained active there until he retired in 1992. On January 1, 1993, the institute was merged with the Astronomic Observatory, the Ørsted Laboratory and the Geophysical Institute. The new resulting institute retained the name Niels Bohr Institute. Research sections The research at the Niels Bohr Institute spans Astronomy, Geophysics, Nanophysics, Particles Physics, Quantum Physics and Biophysics. Research at the institute is based on observations, fieldwork, laboratory experiments and theoretical models for the purpose of understanding basic laws and complex truths on this world. The Institute has a broad network of scientific cooperation, and a lively exchange of collaborators and guests with leading international research groups. Astrophysics A broad spectrum of astronomy and astrophysics is researched at the Niels Bohr Institute – everything from the visible Universe such as planets, stars and galaxies – to the invisible universe and the presence of dark energy and dark matter. The NBI astrophysicists participate in many international projects and have access to modern telescopes and satellites via, e.g. Denmark’s membership of the European Southern Observatory (ESO) and the European Space Agency (ESA), and to state-of-the-art supercomputers. Biocomplexity and Biophysics Biocomplexity is a cutting-edge area of research between physics and biology. By using the principles and methods of physics one can explore the living nature and biological phenomena. Researchers at BioComplexity continuously explore the diversity of complex phenomena in biological, physical and social systems, including pattern formation, complex and chaotic dynamics, fluid dynamics, game theory, networks and econophysics. Physics approaches are used to suggest and perform experiments and models of living systems. The systems range from proteins and gene regulation to larger-scale collective spatiotemporal structure formation. The research at the institute is often performed as a collaboration between physicists, biologists, medical doctors, and nanoscientists. Condensed Matter Physics Condensed matter physics is concerned with the understanding of the physical properties of solids and liquids, both naturally occurring and artificially produced. Condensed matter physics is the foundation for many every-day technologies, ranging from hardening of steel to integrated microchips. Modern research in condensed matter physics takes place in both large scale x-ray and neutron scattering facilities, as well as in locally based laboratories, where quantum phenomena are being explored at temperatures near absolute zero. There is a vivid exchange between condensed matter and neighboring research areas, including biophysics, nanoscience, chemistry, optics, and quantum information. Experimental Particle Physics How was the universe created, which inflation scenario played out in the first split second, what happened during the quark-gluon plasma era? What is the source of the mass spectrum of fundamental particles of matter and forces? These are some of the questions particle physicists are looking for answers to. The Particle Physicists work with the build up of matter in the early universe. They are searching for an explanation as to what the universe's smallest components were composed of in the first milliseconds after the Big Bang 14 billion years ago and what forces held them together. Physics of Ice, Climate and Earth The section for the Physics of Ice, Climate and Earth at the Niels Bohr Institute studies the elements of the Earth and climate system – the atmosphere, oceans, ice sheets and glaciers, sea ice, and the solid Earth itself – and the interactions between them. Quantum Optics and Photonics The Quantum Optics section conducts experimental and theoretical research in Quantum Optics, in particular, in Quantum Information Processing, Quantum Sensors , and Quantum Technologies. We use photons, from optics to microwaves interacting with a wide variety of quantum matter, such as quantum dots, single atoms, atomic ensembles and mechanical oscillators. The overarching theme is generation and manipulation of non-classical entangled states for quantum simulation, sensing and communication. The research directions span from fundamental research to device engineering. Theoretical high energy, astroparticle and gravitational physics The Theoretical high energy, astroparticle and gravitational physics at the Niels Bohr Institute is involved in a wide scope of research activities centered around quantum theories of gauge fields, gravity and astrophysics. Research areas include scattering amplitudes, effective field theory, black holes, holography, lattice simulations, quantum gravity, integrability, astroparticle physics, and cosmology. Research Centres Cosmic Dawn The Cosmic Dawn Center is an Astronomy/Cosmology research center, founded as a collaboration between the University of Copenhagen and DTU Space of the Danish Technical University (DTU). The center is led by center director and NBI Professor Sune Toft and center co-director Thomas Greve, Professor at DTU and UCL. The main objective of the center is to investigate the period known as the Cosmic Dawn (the transition period following the Cosmic Dark Ages), i.e. the reionization of the Universe and the formation of the first galaxies, through observations as well as through theory and simulations. Goals Research conducted at the center is focused on the specific period in the history of the Universe known as the Cosmic Dawn. This largely unexplored period, 300-600 million years after the Big Bang is when the first stars, black holes, and galaxies are believed to have formed. Many of the observations used by the center originate from the Atacama Large Millimeter Array (ALMA), one of the more powerful telescopes in the world. In the future, the center aims to mainly use the James Webb Space Telescope and the Euclid Telescope of the European Space Agency (ESA). DAWN scientists were instrumental in the construction of three instruments (NIRSpec, MIRI and NIRISS) for the project, and will be involved in the analysis of the first data from the telescope. Published research As of April 18, 2020, DAWN authors have published at least 187 refereed papers garnering 1602 citations, which, among others, can be found at the NASA/ADS library. Observation of inverse Compton emission from a long γ-ray burst: Identification of strontium in the merger of two neutron stars: Signatures of a jet cocoon in early spectra of a supernova associated with a γ-ray burst: Stellar Velocity Dispersion of a Massive Quenching Galaxy at z = 4.01: Medal of Honour in 2010, the year of the 125th anniversary of the birth of Niels Bohr, the institute established the Niels Bohr Institute Medal of Honour. It is an annual award for "a particularly outstanding researcher who is working in the spirit of Niels Bohr: International cooperation and the exchange of knowledge". The medal is made by Danish sculptor Rikke Raben for the Niels Bohr Institute. On the front is a portrait of Niels Bohr, the atom sign and stars. The illustration on the back is inspired by a quote from Bohr: What is it that we human beings ultimately depend on? We depend on our words. We are suspended in language. Our task is to communicate experience and ideas to others. On the back of the medal: Unity of Knowledge – the title of a lecture given by Bohr at Columbia University in 1954. Nosce te ipsum is Latin and means "know thyself". This quote originates from the Oracle of Delphi, in the Temple of Apollo in Greece. Recipients: 2010: Leo Kadanoff 2011: Andre Geim 2012: Juan Ignacio Cirac Sasturain 2013: Fabiola Gianotti 2014: Glaciologist Jérôme Chappellaz 2015: Astrophysicist Brian Schmidt 2016: Gerard 't Hooft 2017: 2019: David R. Nelson 2020: Paul J. Steinhardt 2021: Jun Ye See also Niels Bohr Nano-Science Center (Copenhagen University) Institute for Theoretical Physics (disambiguation) Center for Theoretical Physics (disambiguation) List of physics awards References External links Niels Bohr Institute (en), Niels Bohr Institutet (dk) Dark Cosmology Centre (en) Discovery Center (en) (DAWN) DTU Space University of Copenhagen Research institutes in Denmark Physics research institutes Niels Bohr Physics awards Research institutes established in 1921 1921 establishments in Denmark Theoretical physics institutes	Niels Bohr Institute	[ "Physics", "Technology" ]	1,940	[ "Science and technology awards", "Theoretical physics", "Physics awards", "Theoretical physics institutes" ]
53,297	https://en.wikipedia.org/wiki/DESY	DESY, short for Deutsches Elektronen-Synchrotron (English: German Electron Synchrotron), is a national research centre for fundamental science located in Hamburg and Zeuthen near Berlin in Germany. It operates particle accelerators used to investigate the structure, dynamics and function of matter, and conducts a broad spectrum of interdisciplinary scientific research in four main areas: particle and high energy physics; photon science; astroparticle physics; and the development, construction and operation of particle accelerators. Its name refers to its first project, an electron synchrotron. DESY is publicly financed by the Federal Republic of Germany and the Federal States of Hamburg and Brandenburg and is a member of the Helmholtz Association. Functions and mission DESY's function is to conduct fundamental research for solely civil and peaceful purposes. It specialises in particle accelerator development, construction and operation, particle physics, astroparticle physics and photon science research to explore the fundamental relationships between the structure, dynamics and function of matter. In cooperation with its partner organisations, its photon science research spans surface physics, material science, chemistry, molecular biology, geophysics and medicine through the use of synchrotron radiation and free-electron lasers. In addition to operating its own large accelerator facilities, DESY participates in many major international research projects, for example the European X-Ray Free-Electron Laser in Germany, the Large Hadron Collider in Switzerland, the Belle II experiment in Japan, the IceCube Neutrino Observatory at the South Pole and the worldwide Cherenkov Telescope Array. Sites DESY operates in two locations. The primary location is in the Bahrenfeld quarter of Hamburg. In 1992, DESY expanded to a second site in Zeuthen near Berlin. Hamburg The DESY Hamburg site is located in the quarter Bahrenfeld, in the west of the city in the district of Altona. Its main accelerators are located here. Zeuthen Following German reunification, DESY expanded to a second site in Zeuthen near Berlin. In 1939, the German Postal Ministry founded a nuclear physics laboratory there. After World War II, the laboratory was first named "Institute X", to become the Institute for High Energy Physics (), the high-energy physics laboratory of the German Democratic Republic belonging to the Academy of Sciences of the GDR. The institute was merged with DESY on 1 January 1992. It focuses on parallel computing for theoretical particle physics, the development and construction of electron sources for X-ray lasers as well as astroparticle physics with a focus on gamma-ray and neutrino astronomy. Employees and training DESY employs about 3,000 staff members from more than 60 nations. Most staff work at the Hamburg site, with about 270 at the Zeuthen site. These numbers include more than 130 trainees in various industrial-technical professions and about 500 PhD students and postdocs supervised by DESY. In addition, there are numerous master students from various universities. Budget and financing The research centre is a foundation under civil law financed by public funds. In 2020, DESY had an annual budget of about 232 million euros (according to the German federal budget plan, excluding expenditure for investments and special financing expenses). In addition, it had a third-party funding income of about 18 million euros. 90% of the annual budget is provided by the German Federal Ministry of Education and Research () and 10% respectively by the Free and Hanseatic City of Hamburg and the German federal state of Brandenburg. Particle accelerators and other facilities DESY's accelerators were not all built at once, but were rather added one by one to meet the growing demand of the scientists for higher and higher energies to gain more insight into particle structures. In the course of the construction of new accelerators, the older ones were converted to pre-accelerators or to sources for synchrotron radiation for laboratories with new research tasks. DESY The DESY synchrotron (short for "Deutsches Elektronen-Synchrotron") has been in operation since 1964. Its circumference is 300 m. It was used until 1978 for particle physics experiments and first measurements with synchrotron radiation. Since then, rebuilt and upgraded several times, it has served as a pre-accelerator and as a test beam facility delivering high-energy particle beams for testing detector systems. DORIS The DORIS storage ring (short for Double Ring Storage Facility) operated from 1974 to 2013. It had a circumference of 289 m. Until 1992, it collided electrons with positrons for particle physics experiments (including the ARGUS experiment). From 1980 on, the synchrotron radiation generated by DORIS was used for photon science experiments; from 1993 to 2012, the storage ring served exclusively as a synchrotron radiation source. The particle physics experiment OLYMPUS then ran in 2012 before DORIS was shut down at the beginning of 2013. PETRA The PETRA storage ring (short for Positron–Electron Tandem Ring Accelerator) has been in operation since 1978. It has a circumference of 2,304 m. Until 1986, electrons and positrons collided in PETRA for research in particle physics (experiments JADE, MARK-J, TASSO and PLUTO). From 1990 on, PETRA served as a pre-accelerator for the HERA storage ring, and from 1995 on also as a synchrotron radiation source with two test experimental stations. Since 2009, the facility has been delivering hard X-ray beams of very high brilliance to over 40 experimental stations under the name PETRA III. HERA The HERA storage ring (short for Hadron–Electron Ring Accelerator) operated from 1992 to 2007. It has a circumference of 6,336 m. It was DESY's largest ring accelerator and Germany's largest research instrument to date. Until 2007, HERA was the only storage ring facility in the world to enable collisions of electrons or positrons with protons for particle physics (experiments H1, ZEUS, HERMES and HERA-B) for studies of the inner structure of the proton. FLASH The free-electron laser (FEL) FLASH (short for Free-Electron Laser in Hamburg) has been in operation since 2000. It has a length of 315 m. It is based on a test facility for superconducting accelerator technology built in 1997 for the TESLA project and has served as a user facility for experiments with the generated FEL radiation since 2005. FLASH provides ultrashort light pulses in the extreme ultraviolet and soft X-ray range for seven experimental stations and is also used as a test facility for the development of accelerator and FEL technologies. European XFEL accelerator DESY operates the 1.7 km superconducting linear accelerator of the European XFEL X-ray free-electron laser, an international research facility that delivers ultrashort light pulses in the high-energy X-ray range. PITZ Since 2001, the DESY site in Zeuthen has been home to the photoinjector test facility PITZ, a linear accelerator used to study, optimise and prepare the electron sources for FLASH and (since 2015) for the European XFEL. Other facilities The building of the former DORIS storage ring now houses the SINBAD ("Short Innovative Bunches and Accelerators at DESY") accelerator complex with various infrastructures for accelerator R&D: the linear accelerator ARES for accelerator research with ultrashort electron pulses for medical purposes, the AXSIS facility for terahertz-driven acceleration to generate ultrashort X-ray pulses for materials science or medical imaging, and the high-power laser KALDERA for research into laser-driven plasma acceleration. The LUX facility is also used for research into laser-driven plasma acceleration, the FLASHForward experiment at FLASH for electron-beam-driven plasma acceleration. The relativistic electron beam source REGAE generates ultrashort electron pulses for time-resolved diffraction experiments. The tunnel of the former HERA storage ring now houses the ALPS II experiment, which uses converted superconducting dipole magnets of the HERA proton ring to study extremely light particles. Computing DESY provides extensive storage and computing capacity for research in all its divisions. As part of the Worldwide LHC Computing Grid (WLCG), DESY also operates a Tier-2 computer centre that offers computing and storage systems for the ATLAS, CMS and LHCb experiments at the Large Hadron Collider (LHC). In addition, the DESY grid infrastructure is used by other experiments such as Belle II or IceCube. DESY (Hamburg) also provides the Maxwell Cluster, a high-performance computing platform. Research areas Research at DESY is organised into four divisions: Accelerators, Photon Science, Particle Physics and Astroparticle Physics. The Accelerator division develops fundamental technologies for the accelerator facilities that DESY and its partners use in their scientific mission. In addition to the operation and further development of existing facilities (PETRA IV and FLASH2020+ projects, expansion of the European XFEL), essential activities include research into new accelerator concepts, in particular plasma wakefield acceleration, and the improvement of superconducting radio frequency accelerator technology. In the Photon Science division, photons are being used to study the structure, dynamics and function of matter. To this end, the division develops, builds and operates beamlines and experiments at the DESY light sources PETRA III and FLASH. Every year, more than 3,000 researchers – most of them from universities, but also from non-university research institutions and industry – from over 40 countries conduct experiments at the light sources and in the laboratories at DESY. The research spectrum ranges from basic research to applied research and industrial collaborations in physics, chemistry, biology, medicine, life sciences, earth sciences, materials research as well as the study of cultural heritage. The Particle Physics division is involved in the large-scale experiments at the Large Hadron Collider (LHC) at CERN near Geneva. As part of the international collaborations that run the ATLAS and CMS experiments, DESY contributes to many developments at the LHC, from hardware design and data analysis to preparations for the planned upgrades. DESY also participates in the Belle II experiment at the electron–positron collider SuperKEKB at the research centre KEK in Tsukuba, Japan, as well as in developments for possible future electron–positron linear colliders. It is also active in theoretical particle physics. The Astroparticle Physics division investigates high-energy processes in the universe. Detectors and telescopes are used to analyse neutrinos and gamma rays from space, which can provide information about cosmic phenomena: black holes, exploding stars and radiation bursts of extreme intensity. To this end, DESY is involved in the gamma telescopes MAGIC, H.E.S.S. and VERITAS as well as the Fermi Gamma-ray Space Telescope, and it contributes to the planned Cherenkov Telescope Array (CTA). It is the second largest partner in the IceCube observatory at the South Pole. History DESY was founded on 18 December 1959 in Hamburg. According to its statutes, DESY's mission is "the promotion of basic scientific research [...] in particular through the development, construction and operation of accelerators and their scientific use, in photon science and in the fields of particle and astroparticle physics, as well as through research and development work related thereto". From 1959 to 2007, the DESY accelerators were primarily used for particle physics, initially with the eponymous DESY electron synchrotron (1964–present), followed by DORIS (Double Ring Storage Facility, 1974–1992), PETRA (Positron–Electron Tandem Ring Facility, 1978–present) and HERA (Hadron–Electron Ring Accelerator, 1992–2007). In 1987, the ARGUS experiment at DORIS was the first to observe a large mixing of B mesons and thus a process in which matter and antimatter behave differently. The most important discovery of the experiments TASSO, JADE, MARK-J and PLUTO at PETRA was the detection of the gluon, the messenger particle of the strong force, in 1979. From 1990, PETRA served as a pre-accelerator for the even larger storage ring HERA with its four experiments H1, ZEUS, HERMES and HERA-B. HERA was the only storage ring facility in the world in which protons collided with electrons or positrons. In these collisions, the point-like electron acted like a probe, scanning the inner structure of the proton and making it visible with high resolution. HERA's precise insights into the interior of the proton formed the basis for numerous other particle physics experiments, especially at the Large Hadron Collider (LHC) at the research centre CERN and for numerous developments in theoretical particle physics. In parallel, as early as the 1960s, research groups from DESY, various universities and the Max Planck Society developed the technology for using the synchrotron radiation produced by the accelerators. To meet the rapidly growing national and European demand, DESY founded its own large laboratory: the Hamburg Synchrotron Radiation Laboratory HASYLAB, which opened in 1980. It provided measuring stations at DORIS, and it was here that the Israeli biochemist Ada Yonath (Nobel Prize in Chemistry 2009) conducted experiments from 1986 to 2004 that led to her deciphering the ribosome. From 1995, both synchrotron radiation and particle physics experiments were conducted at PETRA. In 2009, the PETRA facility was upgraded for exclusive use as a synchrotron radiation source for hard X-rays (PETRA III). Today, PETRA III serves over 40 experimental stations, and there are plans to expand it into the PETRA IV 3D X-ray microscope. With the shutdown of DORIS in early 2013, the name HASYLAB was abandoned, and the use of DESY's light sources has since been carried out in its Photon Science division. In the early 1990s, DESY began to develop a new technology: radio frequency accelerator technology based on superconducting cavities made of niobium, which are cooled to approximately 2 K (−271 °C) with liquid helium. The first accelerator on this basis was a test facility for superconducting linear accelerators at DESY to test the principle of self-amplified spontaneous emission (SASE) of X-ray laser light. The SASE theory was developed and refined at DESY and at institutes in Russia, Italy and the USA from 1980 onwards. In 2000 to 2001, the test facility at DESY was the first free-electron laser in the world to produce light flashes in the vacuum ultraviolet and soft X-ray range. Today, the FLASH facility produces ultrashort light pulses in the soft X-ray range for seven experimental stations. Since 2020, it has been expanded to further optimise the properties of the radiation (FLASH2020+ project). From 2009 to 2016, an international consortium led by DESY developed the European X-ray free-electron laser European XFEL. The international research facility, which involves 12 European shareholder countries, is operated by the non-profit company European XFEL GmbH. The core of the facility is a 1.7 km superconducting linear accelerator. With an electron energy of 17.5 GeV, it is the most powerful superconducting linear accelerator in the world to date. DESY operates the accelerator on behalf of European XFEL GmbH. Since 2010, DESY has been developing plasma-based accelerator technology (both laser- and electron-beam-driven) as a possible alternative to conventional accelerator technologies, with the aim of enabling compact accelerators for photon science, particle physics as well as medical and industrial applications. Chairpersons of the DESY Directorate DESY is headed by a Directorate consisting of the directors of the four divisions (Accelerators, Photon Science, Particle Physics and Astroparticle Physics) and the administration as well as the delegate of the Directorate for innovation. Chairpersons of the Directorate so far have been: 1959 to 1970: Willibald Jentschke, Founding Director 1971 to 1972: Wolfgang Paul 1973 to 1980: Herwig Schopper 1981 to 1993: Volker Soergel 1993 to 1999: Bjørn H. Wiik 1999 to early 2009: Albrecht Wagner since 2 March 2009: Helmut Dosch Joint research centres The DESY campus in Hamburg is the location of several national and international centres in which DESY participates. These are: Center for Free-Electron Laser Science (CFEL): Investigation of ultrafast phenomena with free-electron lasers and optical lasers, studies of light–matter interaction under extreme conditions Centre for Structural Systems Biology (CSSB): Structural systems biology to study infection processes at the molecular level of viruses, bacteria and parasites Centre for X-ray and Nano Science (CXNS): Investigation of condensed matter with X-ray and complementary methods, high-resolution X-ray imaging, analysis of material processes Knowledge and technology transfer DESY aims to promote start-ups and bring know-how from fundamental research into application. It offers commercial companies support for industrial issues, e.g. through special industry access to photon sources and laboratories, develops ideas, applications and products based on fundamental research, and supports its employees in founding start-ups based on DESY technologies in the Hamburg and Brandenburg regions. DESY offers start-ups access to offices, laboratories and workshops in the DESY Innovation Village and the Start-up Labs Bahrenfeld, established together with the University of Hamburg and the Free and Hanseatic City of Hamburg. References External links Buildings and structures in Altona, Hamburg Education in Hamburg Free-electron lasers Organisations based in Hamburg Particle physics facilities Physics in Germany Physics research institutes Research institutes in Germany Synchrotron radiation facilities	DESY	[ "Materials_science" ]	3,671	[ "Materials testing", "Synchrotron radiation facilities" ]
53,299	https://en.wikipedia.org/wiki/Brookhaven%20National%20Laboratory	Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratory located in Upton, New York, a hamlet of the Town of Brookhaven. It was formally established in 1947 at the site of Camp Upton, a former U.S. Army base on Long Island. Located approximately 60 miles east of New York City, it is managed by Stony Brook University and Battelle Memorial Institute. Research at BNL includes nuclear and high energy physics, energy science and technology, environmental and bioscience, nanoscience, and national security. The 5,300 acre campus contains several large research facilities, including the Relativistic Heavy Ion Collider and National Synchrotron Light Source II. Seven Nobel Prizes have been awarded for work conducted at Brookhaven Lab. Overview BNL operations are overseen by a Department of Energy Site office, is staffed by approximately 2,750 scientists, engineers, technicians, and support personnel, and hosts 4,000 guest investigators every year. The laboratory is guarded by a Department of Energy Protective Force, has a full service fire department, and has its own ZIP code (11973). In total, the lab spans a area that is mostly coterminous with the hamlet of Upton, New York. BNL is served by a rail spur operated as-needed by the New York and Atlantic Railway. Co-located with the laboratory is the New York, NY, weather forecast office of the National Weather Service. Major programs Although originally conceived as a nuclear research facility, Brookhaven Lab's mission has greatly expanded. Its foci are now: Nuclear and high-energy physics Physics and chemistry of materials Environmental and climate research Nanomaterials Energy research Nonproliferation Structural biology Accelerator physics Operation Brookhaven National Lab was originally owned by the Atomic Energy Commission and is now owned by that agency's successor, the United States Department of Energy (DOE). DOE subcontracts the research and operation to universities and research organizations. It is currently operated by Brookhaven Science Associates LLC, which is an equal partnership of Stony Brook University and Battelle Memorial Institute. From 1947 to 1998, it was operated by Associated Universities, Inc. (AUI), but AUI lost its contract in the wake of two incidents: a 1994 fire at the facility's high-flux beam reactor that exposed several workers to radiation and reports in 1997 of a tritium leak into the groundwater of the Long Island Central Pine Barrens on which the facility sits. History Foundations Following World War II, the US Atomic Energy Commission was created to support government-sponsored peacetime research on atomic energy. The effort to build a nuclear reactor in the American northeast was fostered largely by physicists Isidor Isaac Rabi and Norman Foster Ramsey Jr., who during the war witnessed many of their colleagues at Columbia University leave for new remote research sites following the departure of the Manhattan Project from its campus. Their effort to house this reactor near New York City was rivalled by a similar effort at the Massachusetts Institute of Technology to have a facility near Boston. Involvement was quickly solicited from representatives of northeastern universities to the south and west of New York City such that this city would be at their geographic center. In March 1946 a nonprofit corporation was established that consisted of representatives from nine major research universities — Columbia, Cornell, Harvard, Johns Hopkins, MIT, Princeton, University of Pennsylvania, University of Rochester, and Yale University. Out of 17 considered sites in the Boston-Washington corridor, Camp Upton on Long Island was eventually chosen as the most suitable in consideration of space, transportation, and availability. The camp had been a training center for the US Army during both World War I and World War II, and a Japanese internment camp during the latter. Following the war, Camp Upton was no longer needed, and a plan was conceived to convert the military camp into a research facility. On March 21, 1947, the Camp Upton site was officially transferred from the U.S. War Department to the new U.S. Atomic Energy Commission (AEC), predecessor to the U.S. Department of Energy (DOE). Research and facilities Reactor history In 1947 construction began on the first nuclear reactor at Brookhaven, the Brookhaven Graphite Research Reactor. This reactor, which opened in 1950, was the first reactor to be constructed in the United States after World War II. The High Flux Beam Reactor operated from 1965 to 1999. In 1959 Brookhaven built the first US reactor specifically tailored to medical research, the Brookhaven Medical Research Reactor, which operated until 2000. Accelerator history In 1952 Brookhaven began using its first particle accelerator, the Cosmotron. At the time the Cosmotron was the world's highest energy accelerator, being the first to impart more than 1 GeV of energy to a particle. The Cosmotron was retired in 1966, after it was superseded in 1960 by the new Alternating Gradient Synchrotron (AGS). The AGS was used in research that resulted in three Nobel Prizes, including the discovery of the muon neutrino, the charm quark, and CP violation. In 1970 in BNL started the ISABELLE project to develop and build two proton intersecting storage rings. The groundbreaking for the project was in October 1978. In 1981, with the tunnel for the accelerator already excavated, problems with the superconducting magnets needed for the ISABELLE accelerator brought the project to a halt, and the project was eventually cancelled in 1983. The National Synchrotron Light Source operated from 1982 to 2014 and was involved with two Nobel Prize-winning discoveries. It has since been replaced by the National Synchrotron Light Source II. After ISABELLE'S cancellation, physicist at BNL proposed that the excavated tunnel and parts of the magnet assembly be used in another accelerator. In 1984 the first proposal for the accelerator now known as the Relativistic Heavy Ion Collider (RHIC) was put forward. The construction got funded in 1991 and RHIC has been operational since 2000. One of the world's only two operating heavy-ion colliders, RHIC is as of 2010 the second-highest-energy collider after the Large Hadron Collider. RHIC is housed in a tunnel 2.4 miles (3.9 km) long and is visible from space. On January 9, 2020, It was announced by Paul Dabbar, undersecretary of the US Department of Energy Office of Science, that the BNL eRHIC design has been selected over the conceptual design put forward by Thomas Jefferson National Accelerator Facility as the future Electron–ion collider (EIC) in the United States. In addition to the site selection, it was announced that the BNL EIC had acquired CD-0 (mission need) from the Department of Energy. BNL's eRHIC design proposes upgrading the existing Relativistic Heavy Ion Collider, which collides beams light to heavy ions including polarized protons, with a polarized electron facility, to be housed in the same tunnel. Other discoveries In 1958, Brookhaven scientists created one of the world's first video games, Tennis for Two. In 1967, Brookhaven scientists patented Maglev, a transportation technology that utilizes magnetic levitation. In 2024, Brookhaven National Laboratories scientists discovered a new kind of antimatter nucleus. Major facilities Relativistic Heavy Ion Collider (RHIC), which was designed to research quark–gluon plasma and the sources of proton spin. Until 2009 it was the world's most powerful heavy ion collider. It is the only collider of spin-polarized protons. Center for Functional Nanomaterials (CFN), used for the study of nanoscale materials. National Synchrotron Light Source II (NSLS-II), Brookhaven's newest user facility, opened in 2015 to replace the National Synchrotron Light Source (NSLS), which had operated for 30 years. NSLS was involved in the work that won the 2003 and 2009 Nobel Prize in Chemistry. Alternating Gradient Synchrotron, a particle accelerator that was used in three of the lab's Nobel prizes. Accelerator Test Facility, generates, accelerates and monitors particle beams. Tandem Van de Graaff, once the world's largest electrostatic accelerator. Computational Science resources, including access to a massively parallel Blue Gene series supercomputer that is among the fastest in the world for scientific research, run jointly by Brookhaven National Laboratory and Stony Brook University. Interdisciplinary Science Building, with unique laboratories for studying high-temperature superconductors and other materials important for addressing energy challenges. NASA Space Radiation Laboratory, where scientists use beams of ions to simulate cosmic rays and assess the risks of space radiation to human space travelers and equipment. Off-site contributions It is a contributing partner to ATLAS experiment, one of the four detectors located at the Large Hadron Collider (LHC). It is currently operating at CERN near Geneva, Switzerland. Brookhaven was also responsible for the design of the SNS accumulator ring in partnership with Spallation Neutron Source in Oak Ridge, Tennessee. Brookhaven plays a role in a range of neutrino research projects around the world, including the Daya Bay Reactor Neutrino Experiment in China and the Deep Underground Neutrino Experiment at Fermi National Accelerator Laboratory. Public access For other than approved Public Events, the Laboratory is closed to the general public. The lab is open to the public on several Sundays during the summer for tours and special programs. The public access program is referred to as 'Summer Sundays' and takes place in July, and features a science show and a tour of the lab's major facilities. The laboratory also hosts science fairs, science bowls, and robotics competitions for local schools, and lectures, concerts, and scientific talks for the local community. The Lab estimates that each year it enhances the science education of roughly 35,000 K-12 students on Long Island, more than 200 undergraduates, and 550 teachers from across the United States. Environmental cleanup In January 1997, ground water samples taken by BNL staff revealed concentrations of tritium that were twice the allowable federal drinking water standards—some samples taken later were 32 times the standard. The tritium was found to be leaking from the laboratory's High Flux Beam Reactor's spent-fuel pool into the aquifer that provides drinking water for nearby Suffolk County residents. DOE's and BNL's investigation of this incident concluded that the tritium had been leaking for as long as 12 years without DOE's or BNL's knowledge. Installing wells that could have detected the leak was first discussed by BNL engineers in 1993, but the wells were not completed until 1996. The resulting controversy about both BNL's handling of the tritium leak and perceived lapses in DOE's oversight led to the termination of AUI as the BNL contractor in May 1997. The responsibility for failing to discover Brookhaven's tritium leak has been acknowledged by laboratory managers, and DOE admits it failed to properly oversee the laboratory's operations. Brookhaven officials repeatedly treated the need for installing monitoring wells that would have detected the tritium leak as a low priority despite public concern and the laboratory's agreement to follow local environmental regulations. DOE's on-site oversight office, the Brookhaven Group, was directly responsible for Brookhaven's performance, but it failed to hold the laboratory accountable for meeting all of its regulatory commitments, especially its agreement to install monitoring wells. Senior DOE leadership also shared responsibility because they failed to put in place an effective system that encourages all parts of DOE to work together to ensure that contractors meet their responsibilities on environmental, safety and health issues. Unclear responsibilities for environment, safety and health matters has been a recurring problem for DOE management. Since 1993, DOE has spent more than US$580 million on remediating soil and groundwater contamination at the lab site and completed several high-profile projects. These include the decommissioning and decontamination of the Brookhaven Graphite Research Reactor, removal of mercury-contaminated sediment from the Peconic River, and installation and operation of 16 on- and off-site groundwater treatment systems that have cleaned more than 25 billion gallons of groundwater since 1996. Shortly after winning the contract to operate the lab in 1997, BSA formed a Community Advisory Council (CAC) to advise the laboratory director on cleanup projects and other items of interest to the community. The CAC represents a diverse range of interests and values of individuals and groups who are interested in or affected by the actions of the Laboratory. It consists of representatives from 26 local business, civic, education, environment, employee, government, and health organizations. The CAC sets its own agenda, brings forth issues important to the community, and works to provide consensus recommendations to Laboratory management. Nobel Prizes Nobel Prize in Physics 1957 – Chen Ning Yang and Tsung-Dao Lee – parity laws 1976 – Samuel C. C. Ting – J/Psi particle 1980 – James Cronin and Val Logsdon Fitch – CP-violation 1988 – Leon M. Lederman, Melvin Schwartz, Jack Steinberger – Muon neutrino 2002 – Raymond Davis, Jr. – Solar neutrino Nobel Prize in Chemistry 2003 – Roderick MacKinnon – Ion channel 2009 – Venkatraman Ramakrishnan and Thomas A. Steitz – Ribosome See also Center for the Advancement of Science in Space—operates the US National Laboratory on the ISS. Goldhaber fellows References "Dr. Strangelet or: How I Learned to Stop Worrying and Love the Big Bang" External links Brookhaven National Lab official website Physics Today: DOE Shuts Brookhaven Lab's HFBR in a Triumph of Politics Over Science 404 Summer Sundays at Brookhaven National Laboratory Annotated bibliography for Brookhaven Laboratory from the Alsos Digital Library for Nuclear Issues Headlines Digitized Brookhaven National Laboratory reports from the TRAIL project, hosted at University of North Texas Libraries and TRAIL Stony Brook University United States Department of Energy national laboratories Federally Funded Research and Development Centers Nuclear research institutes Particle physics facilities Brookhaven, New York Tourist attractions in Suffolk County, New York Battelle Memorial Institute Superfund sites in New York (state) 1947 establishments in New York (state) Physics research institutes Theoretical physics institutes Institutes associated with CERN Energy infrastructure on Long Island, New York Research institutes in New York (state)	Brookhaven National Laboratory	[ "Physics", "Engineering" ]	2,952	[ "Nuclear research institutes", "Theoretical physics", "Nuclear organizations", "Theoretical physics institutes" ]
53,300	https://en.wikipedia.org/wiki/SLAC%20National%20Accelerator%20Laboratory	SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a federally funded research and development center in Menlo Park, California, United States. Founded in 1962, the laboratory is now sponsored by the United States Department of Energy and administrated by Stanford University. It is the site of the Stanford Linear Accelerator, a 3.2 kilometer (2-mile) linear accelerator constructed in 1966 that could accelerate electrons to energies of 50 GeV. Today SLAC research centers on a broad program in atomic and solid-state physics, chemistry, biology, and medicine using X-rays from synchrotron radiation and a free-electron laser as well as experimental and theoretical research in elementary particle physics, accelerator physics, astroparticle physics, and cosmology. The laboratory is under the programmatic direction of the United States Department of Energy Office of Science. History Founded in 1962 as the Stanford Linear Accelerator Center, the facility is located on of Stanford University-owned land on Sand Hill Road in Menlo Park, California, just west of the university's main campus. The main accelerator is long, making it the longest linear accelerator in the world, and has been operational since 1966. Research at SLAC has produced three Nobel Prizes in Physics: 1976: The charm quark; see J/ψ meson 1990: Quark structure inside protons and neutrons 1995: The tau lepton SLAC's meeting facilities also provided a venue for the Homebrew Computer Club and other pioneers of the home computer revolution of the late 1970s and early 1980s. In 1984, the laboratory was named an ASME National Historic Engineering Landmark and an IEEE Milestone. SLAC developed and, in December 1991, began hosting the first World Wide Web server outside of Europe. In the early-to-mid 1990s, the Stanford Linear Collider (SLC) investigated the properties of the Z boson using the Stanford Large Detector. As of 2005, SLAC employed over 1,000 people, some 150 of whom were physicists with doctorate degrees, and served over 3,000 visiting researchers yearly, operating particle accelerators for high-energy physics and the Stanford Synchrotron Radiation Laboratory (SSRL) for synchrotron light radiation research, which was "indispensable" in the research leading to the 2006 Nobel Prize in Chemistry awarded to Stanford Professor Roger D. Kornberg. In October 2008, the Department of Energy announced that the center's name would be changed to SLAC National Accelerator Laboratory. The reasons given include a better representation of the new direction of the lab and the ability to trademark the laboratory's name. Stanford University had legally opposed the Department of Energy's attempt to trademark "Stanford Linear Accelerator Center". In March 2009, it was announced that the SLAC National Accelerator Laboratory was to receive $68.3 million in Recovery Act Funding to be disbursed by Department of Energy's Office of Science. In October 2016, Bits and Watts launched as a collaboration between SLAC and Stanford University to design "better, greener electric grids". SLAC later pulled out over concerns about an industry partner, the state-owned Chinese electric utility. In April of 2024, SLAC completed two decades of work constructing the world's largest digital camera for the Legacy Survey of Space and Time (LSST) project at the Vera C. Rubin Observatory in Chile. The camera is expected to become operational in 2025. Components Accelerator The main accelerator was an RF linear accelerator that accelerated electrons and positrons up to 50 GeV. At long, the accelerator was the longest linear accelerator in the world, and was claimed to be "the world's most straight object." until 2017 when the European x-ray free electron laser opened. The main accelerator is buried below ground and passes underneath Interstate Highway 280. The above-ground klystron gallery atop the beamline, was the longest building in the United States until the LIGO project's twin interferometers were completed in 1999. It is easily distinguishable from the air and is marked as a visual waypoint on aeronautical charts. A portion of the original linear accelerator is now part of the Linac Coherent Light Source. Stanford Linear Collider The Stanford Linear Collider was a linear accelerator that collided electrons and positrons at SLAC. The center of mass energy was about 90 GeV, equal to the mass of the Z boson, which the accelerator was designed to study. Grad student Barrett D. Milliken discovered the first Z event on 12 April 1989 while poring over the previous day's computer data from the Mark II detector. The bulk of the data was collected by the SLAC Large Detector, which came online in 1991. Although largely overshadowed by the Large Electron–Positron Collider at CERN, which began running in 1989, the highly polarized electron beam at SLC (close to 80%) made certain unique measurements possible, such as parity violation in Z Boson-b quark coupling. Presently no beam enters the south and north arcs in the machine, which leads to the Final Focus, therefore this section is mothballed to run beam into the PEP2 section from the beam switchyard. SLAC Large Detector The SLAC Large Detector (SLD) was the main detector for the Stanford Linear Collider. It was designed primarily to detect Z bosons produced by the accelerator's electron-positron collisions. Built in 1991, the SLD operated from 1992 to 1998. PEP PEP (Positron-Electron Project) began operation in 1980, with center-of-mass energies up to 29 GeV. At its apex, PEP had five large particle detectors in operation, as well as a sixth smaller detector. About 300 researchers made used of PEP. PEP stopped operating in 1990, and PEP-II began construction in 1994. PEP-II From 1999 to 2008, the main purpose of the linear accelerator was to inject electrons and positrons into the PEP-II accelerator, an electron-positron collider with a pair of storage rings in circumference. PEP-II was host to the BaBar experiment, one of the so-called B-Factory experiments studying charge-parity symmetry. Stanford Synchrotron Radiation Lightsource The Stanford Synchrotron Radiation Lightsource (SSRL) is a synchrotron light user facility located on the SLAC campus. Originally built for particle physics, it was used in experiments where the J/ψ meson was discovered. It is now used exclusively for materials science and biology experiments which take advantage of the high-intensity synchrotron radiation emitted by the stored electron beam to study the structure of molecules. In the early 1990s, an independent electron injector was built for this storage ring, allowing it to operate independently of the main linear accelerator. Fermi Gamma-ray Space Telescope SLAC plays a primary role in the mission and operation of the Fermi Gamma-ray Space Telescope, launched in August 2008. The principal scientific objectives of this mission are: To understand the mechanisms of particle acceleration in AGNs, pulsars, and SNRs. To resolve the gamma-ray sky: unidentified sources and diffuse emission. To determine the high-energy behavior of gamma-ray bursts and transients. To probe dark matter and fundamental physics. KIPAC The Kavli Institute for Particle Astrophysics and Cosmology (KIPAC) is partially housed on the grounds of SLAC, in addition to its presence on the main Stanford campus. PULSE The Stanford PULSE Institute (PULSE) is a Stanford Independent Laboratory located in the Central Laboratory at SLAC. PULSE was created by Stanford in 2005 to help Stanford faculty and SLAC scientists develop ultrafast x-ray research at LCLS. PULSE research publications can be viewed here. LCLS The Linac Coherent Light Source (LCLS) is a free electron laser facility located at SLAC. The LCLS is partially a reconstruction of the last 1/3 of the original linear accelerator at SLAC, and can deliver extremely intense x-ray radiation for research in a number of areas. It achieved first lasing in April 2009. The laser produces hard X-rays, 109 times the relative brightness of traditional synchrotron sources and is the most powerful x-ray source in the world. LCLS enables a variety of new experiments and provides enhancements for existing experimental methods. Often, x-rays are used to take "snapshots" of objects at the atomic level before obliterating samples. The laser's wavelength, ranging from 6.2 to 0.13 nm (200 to 9500 electron volts (eV)) is similar to the width of an atom, providing extremely detailed information that was previously unattainable. Additionally, the laser is capable of capturing images with a "shutter speed" measured in femtoseconds, or million-billionths of a second, necessary because the intensity of the beam is often high enough so that the sample explodes on the femtosecond timescale. LCLS-II The LCLS-II project is to provide a major upgrade to LCLS by adding two new X-ray laser beams. The new system will utilize the of existing tunnel to add a new superconducting accelerator at 4 GeV and two new sets of undulators that will increase the available energy range of LCLS. The advancement from the discoveries using this new capabilities may include new drugs, next-generation computers, and new materials. FACET In 2012, the first two-thirds (~2 km) of the original SLAC LINAC were recommissioned for a new user facility, the Facility for Advanced Accelerator Experimental Tests (FACET). This facility was capable of delivering 20 GeV, 3 nC electron (and positron) beams with short bunch lengths and small spot sizes, ideal for beam-driven plasma acceleration studies. The facility ended operations in 2016 for the constructions of LCLS-II which will occupy the first third of the SLAC LINAC. The FACET-II project will re-establish electron and positron beams in the middle third of the LINAC for the continuation of beam-driven plasma acceleration studies in 2019. NLCTA The Next Linear Collider Test Accelerator (NLCTA) is a 60-120 MeV high-brightness electron beam linear accelerator used for experiments on advanced beam manipulation and acceleration techniques. It is located at SLAC's end station B. A list of relevant research publications can be viewed here . Theoretical Physics SLAC also performs theoretical research in elementary particle physics, including in areas of quantum field theory, collider physics, astroparticle physics, and particle phenomenology. Other discoveries SLAC has also been instrumental in the development of the klystron, a high-power microwave amplification tube. There is active research on plasma acceleration with recent successes such as the doubling of the energy of 42 GeV electrons in a meter-scale accelerator. There was a Paleoparadoxia found at the SLAC site, and its skeleton can be seen at a small museum there in the Breezeway. The SSRL facility was used to reveal hidden text in the Archimedes Palimpsest. X-rays from the synchrotron radiation lightsource caused the iron in the original ink to glow, allowing the researchers to photograph the original document that a Christian monk had scrubbed off. See also Accelerator physics Cyclotron Dipole magnet Electromagnetism List of particles List of United States college laboratories conducting basic defense research Particle beam Quadrupole magnet Spallation Neutron Source Wolfgang Panofsky (1961–84, SLAC Director; Professor, Stanford University) References External links SLAC Today , SLAC's online newspaper, published weekdays symmetry magazine, SLAC's monthly particle physics magazine, with Fermilab Particle physics facilities Stanford University Laboratories in California United States Department of Energy national laboratories Federally Funded Research and Development Centers Buildings and structures in San Mateo County, California Experimental particle physics Menlo Park, California University and college laboratories in the United States Research institutes established in 1962 1962 establishments in California Theoretical physics institutes Research institutes in the San Francisco Bay Area	SLAC National Accelerator Laboratory	[ "Physics" ]	2,503	[ "Theoretical physics", "Theoretical physics institutes", "Experimental physics", "Particle physics", "Experimental particle physics" ]
53,301	https://en.wikipedia.org/wiki/Fermilab	Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Fermilab's Main Injector, two miles (3.3 km) in circumference, is the laboratory's most powerful particle accelerator. The accelerator complex that feeds the Main Injector is under upgrade, and construction of the first building for the new PIP-II linear accelerator began in 2020. Until 2011, Fermilab was the home of the 6.28 km (3.90 mi) circumference Tevatron accelerator. The ring-shaped tunnels of the Tevatron and the Main Injector are visible from the air and by satellite. Fermilab aims to become a world center in neutrino physics. It is the host of the multi-billion dollar Deep Underground Neutrino Experiment (DUNE) now under construction. The project has suffered delays and, in 2022, the journals Science and Scientific American each published articles describing the project as "troubled". Ongoing neutrino experiments are ICARUS (Imaging Cosmic and Rare Underground Signals) and NOνA (NuMI Off-Axis νe Appearance). Completed neutrino experiments include MINOS (Main Injector Neutrino Oscillation Search), MINOS+, MiniBooNE and SciBooNE (SciBar Booster Neutrino Experiment) and MicroBooNE (Micro Booster Neutrino Experiment). On-site experiments outside of the neutrino program include the SeaQuest fixed-target experiment and Muon g-2. Fermilab continues to participate in the work at the Large Hadron Collider (LHC); it serves as a Tier 1 site in the Worldwide LHC Computing Grid. Fermilab also pursues research in quantum information science. It founded the Fermilab Quantum Institute in 2019. Since 2020, it also is home to the SQMS (Superconducting Quantum Materials and Systems) Center. Due to serious performance issues over the period of a decade, the Department of Energy established new management for Fermilab on January 1, 2025. Fermilab is currently managed by the Fermi Forward Discovery Group, LLC (FFDG). This consortium is led by the 2007-2024 management group, the Fermi Research Alliance (FRA), with Amentum Environment & Energy, Inc., and Longenecker & Associates as new additions. Due to the management crisis, the Director of the Laboratory, Lea Merminga, resigned on January 13, 2025 and is temporarily replaced by Acting Director Young-Kee Kim, from the University of Chicago. Fermilab is a part of the Illinois Technology and Research Corridor. Argonne National Laboratory, which is another US DOE national laboratory located approximately 20 miles away. Asteroid 11998 Fermilab is named in honor of the laboratory. History Weston, Illinois, was a community next to Batavia voted out of existence by its village board in 1966 to provide a site for Fermilab. The laboratory was founded in 1969 as the National Accelerator Laboratory; it was renamed in honor of Enrico Fermi in 1974. The laboratory's first director was Robert Rathbun Wilson, under whom the laboratory opened ahead of time and under budget. Many of the sculptures on the site are of his creation. He is the namesake of the site's high-rise laboratory building, whose unique shape has become the symbol for Fermilab and which is the center of activity on the campus. After Wilson stepped down in 1978 to protest the lack of funding for the lab, Leon M. Lederman took on the job. It was under his guidance that the original accelerator was replaced with the Tevatron, an accelerator capable of colliding protons and antiprotons at a combined energy of 1.96 TeV. Lederman stepped down in 1989 and remained director emeritus until his death. The science education center at the site was named in his honor. The later directors are: John Peoples, 1989 to 1999 Michael S. Witherell, July 1999 to June 2005 Piermaria Oddone, July 2005 to July 2013 Nigel Lockyer, September 2013 to April 2022 Lia Merminga, April 2022 to January 2025 Young-Kee Kim (interim), January 2025 to present Accelerators Tevatron Prior to the startup in 2008 of the Large Hadron Collider (LHC) near Geneva, Switzerland, the Tevatron was the most powerful particle accelerator in the world, accelerating protons and antiprotons to energies of 980 GeV, and producing proton-antiproton collisions with energies of up to 1.96 TeV, the first accelerator to reach one "tera-electron-volt" energy. At , it was the world's fourth-largest particle accelerator in circumference. One of its most important achievements was the 1995 discovery of the top quark, announced by research teams using the Tevatron's CDF and DØ detectors. It was shut down in 2011. Fermilab Accelerator Complex Since 2013, the first stage in the acceleration process (pre-accelerator injector) in the Fermilab chain of accelerators takes place in two ion sources which ionize hydrogen gas. The gas is introduced into a container lined with molybdenum electrodes, each a matchbox-sized, oval-shaped cathode and a surrounding anode, separated by 1 mm and held in place by glass ceramic insulators. A cavity magnetron generates a plasma to form the ions near the metal surface. The ions are accelerated by the source to 35 keV and matched by low energy beam transport (LEBT) into the radio-frequency quadrupole (RFQ) which applies a 750 keV electrostatic field giving the ions their second acceleration. At the exit of RFQ, the beam is matched by medium energy beam transport (MEBT) into the entrance of the linear accelerator (linac). The next stage of acceleration is a linear particle accelerator (linac). This stage consists of two segments. The first segment has five drift tube cavities, operating at 201 MHz. The second stage has seven side-coupled cavities, operating at 805 MHz. At the end of linac, the particles are accelerated to 400 MeV, or about 70% of the speed of light. Immediately before entering the next accelerator, the H− ions pass through a carbon foil, becoming H+ ions (protons). The resulting protons then enter the booster ring, a circumference circular accelerator whose magnets bend beams of protons around a circular path. The protons travel around the Booster about 20,000 times in 33 milliseconds, adding energy with each revolution until they leave the Booster accelerated to 8 GeV. In 2021, the lab announced that its latest superconducting YBCO magnet could increase field strength at a rate of 290 tesla per second, reaching a peak magnetic field strength of around 0.5 tesla. The final acceleration is applied by the Main Injector [circumference ], which is the smaller of the two rings in the last picture below (foreground). Completed in 1999, it has become Fermilab's "particle switchyard" in that it can route protons to any of the experiments installed along the beam lines after accelerating them to 120 GeV. Until 2011, the Main Injector provided protons to the antiproton ring [circumference ] and the Tevatron for further acceleration but now provides the last push before the particles reach the beam line experiments. Proton improvement plan Recognizing higher demands of proton beams to support new experiments, Fermilab began to improve their accelerators in 2011. Expected to continue for many years, the project has two phases: Proton Improvement Plan (PIP) and Proton Improvement Plan-II (PIP-II). PIP (2011–2018) The overall goals of PIP are to increase the repetition rate of the Booster beam from 7 Hz to 15 Hz and replace old hardware to increase reliability of the operation. Before the start of the PIP project, a replacement of the pre-accelerator injector was underway. The replacement of almost 40 year-old Cockcroft–Walton generators to RFQ started in 2009 and completed in 2012. At the Linac stage, the analog beam position monitor (BPM) modules were replaced with digital boards in 2013. A replacement of Linac vacuum pumps and related hardware is expected to be completed in 2015. A study on the replacement of 201 MHz drift tubes is still ongoing. At the boosting stage, a major component of the PIP is to upgrade the Booster ring to 15 Hz operation. The Booster has 19 radio frequency stations. Originally, the Booster stations were operating without solid-state drive system which was acceptable for 7 Hz but not 15 Hz operation. A demonstration project in 2004 converted one of the stations to solid state drive before the PIP project. As part of the project, the remaining stations were converted to solid state in 2013. Another major part of the PIP project is to refurbish and replace 40 year-old Booster cavities. Many cavities have been refurbished and tested to operate at 15 Hz. The completion of cavity refurbishment is expected in 2015, after which the repetition rate can be gradually increased to 15 Hz operation. A longer term upgrade is to replace the Booster cavities with a new design. The research and development of the new cavities is underway, with replacement expected in 2018. PIP-II The goals of PIP-II include a plan to delivery 1.2 MW of proton beam power from the Main Injector to the Deep Underground Neutrino Experiment target at 120 GeV and the power near 1 MW at 60 GeV with a possibility to extend the power to 2 MW in the future. The plan should also support the current 8 GeV experiments including Mu2e, Muon g−2, and other short-baseline neutrino experiments. These require an upgrade to the Linac to inject to the Booster with 800 MeV. The first option considered was to add 400 MeV "afterburner" superconducting Linac at the tail end of the existing 400 MeV. This would have required moving the existing Linac up . However, there were many technical issues with this approach. Instead, Fermilab is building a new 800 MeV superconducting Linac to inject to the Booster ring. Construction of the first building for the PIP-II accelerator began in 2020. The new Linac site will be located on top of a small portion of Tevatron near the Booster ring in order to take advantage of existing electrical and water, and cryogenic infrastructure. The PIP-II Linac will have low energy beam transport line (LEBT), radio frequency quadrupole (RFQ), and medium energy beam transport line (MEBT) operated at the room temperature at with a 162.5 MHz and energy increasing from 0.03 MeV. The first segment of Linac will be operated at 162.5 MHz and energy increased up to 11 MeV. The second segment of Linac will be operated at 325 MHz and energy increased up to 177 MeV. The last segment of linac will be operated at 650 MHz and will have the final energy level of 800 MeV. As of 2022, the estimated PIP-II accelerator start date for the accelerator is 2028. The project was approved for construction in April 2022 with an expected cost to the Department of Energy of $978M and with an additional $330M in contributions from international partners. Experiments Discoveries by Fermilab experiments The following particles were first directly observed at Fermilab: The top quark announced in 1995 by the DØ experiment and CDF experiment. The bottom quark, which was observed as a quark-antiquark pair called the Upsilon meson announced in 1977 by Experiment 228. The tau neutrino, announced in July 2000 by the DONUT collaboration. The bottom Omega baryon (), announced by the DØ experiment of Fermilab in 2008. In 1999, physicists at on the KTeV experiment were also the first to observe direct CP violation in kaon decays. The DØ experiment and CDF experiment each made important contributions to the observation of the Higgs Boson, announced in 2012. Evolution of the post-Tevatron experimental program Fermilab dismantled the CDF (Collider Detector at Fermilab) experiment to make the space available for IARC (Illinois Accelerator Research Center). Fermilab physicists continue to play a key role in the world-wide collider program. The LHC Physics Center (LPC) at Fermilab is a regional center of the Compact Muon Solenoid Collaboration (the experiment is housed at CERN). The LPC offers a vibrant community of CMS scientists from the US and plays a major role in the CMS detector commissioning, and in the design and development of the detector upgrade. Fermilab is the host laboratory for USCMS, which includes researchers from 50 U.S. universities including 715 students. Fermilab hosts the largest CMS Tier 1 computing center, handling approximately 40% of global CMS Tier 1 computing requests. On February 9, 2022, Fermilab's Patricia McBride (physicist) was elected spokesperson of the CMS collaboration. During this time-frame, the laboratory also established a new program in research in cutting-edge information science, including the development of quantum teleportation technology for the quantum internet and increasing the lifetime of superconducting resonators for use in quantum computers. On-site program in the 2020s The on-site program in the 2020s is largely focused on the Intensity Frontier of particle physics, especially neutrino physics and rare physics searches using muons. A program exploring nucleon structure is also continuing. List of recent past, ongoing, and planned experiments running on-site ANNIE: The Accelerator Neutrino Neutron Interaction Experiment (Status, June 2023: completed run, planned future run) Deep Underground Neutrino Experiment (DUNE), formerly known as Long Baseline Neutrino Experiment (LBNE) (Status, June 2023: planned future run) ICARUS experiment: Originally located at the Laboratori Nazionali del Gran Sasso (LNGS) and moved to Fermilab. (Status, June 2023: running) MiniBooNE: Mini Booster Neutrino Experiment (Status, June 2023: completed run) MicroBooNE: Micro Booster Neutrino Experiment (Status, June 2023: completed run) MINERνA: Main INjector ExpeRiment with νs on As (Status, June 2023: completed run) Mu2e: Muon-to-Electron Conversion Experiment (Status, June 2023: planned future run) Muon g−2: Measurement of the anomalous magnetic dipole moment of the muon (Status, June 2023: completed run) NOνA: NuMI Off-axis νe Appearance (Status, June 2023: running) SeaQuest (Status, June 2023: completed run) SBND: Short-Baseline Neutrino Detector (Status, June 2023: planned future run) SpinQuest (Status, June 2023: planned future run) LBNF/DUNE Fermilab strives to become the world leader in neutrino physics through the Deep Underground Neutrino Experiment at the Long Baseline Neutrino Facility. Other leaders are CERN, which leads in Accelerator physics with the Large Hadron Collider (LHC), and Japan, which has been approved to build and lead the International Linear Collider (ILC). Fermilab will be the site of LBNF's future beamline, and the Sanford Underground Research Facility (SURF), in Lead, SD, is the site selected to house the massive far detector. The term "baseline" refers to the distance between the neutrino source and the detector. The far detector current design is for four modules of instrumented liquid argon with a fiducial volume of 10 kilotons each. According to the 2016 Conceptual Design Report, the first two modules were expected to be complete in 2024, with the beam operational in 2026. The final modules were planned to be operational in 2027. In 2022, the cost for two far detector modules and the beam, alone, had risen to $3B. This led to a decision by the Department of Energy Office of Science to phase the experiment. Phase I would consist of two modules, to be completed in 2028–29, and the beamline, to be completed in 2032. The installation of phase II, the remaining two far detector modules, is not yet planned and will be at a cost above the $3B estimate for phase I. A large prototype detector constructed at CERN took data with a test beam from 2018 to 2020. The results show that ProtoDUNE performed with greater than 99% efficiency. LBNF/DUNE program in neutrino physics plans to measure fundamental physical parameters with high precision and to explore physics beyond the Standard Model. The measurements DUNE will make are expected to greatly increase the physics community's understanding of neutrinos and their role in the universe, thereby better elucidating the nature of matter and anti-matter. It will send the world's highest-intensity neutrino beam to a near detector on the Fermilab site and the far detector 800 miles (1300 km) away at SURF. About other neutrino experiments The MiniBooNE detector was a diameter sphere containing 800 tons of mineral oil lined with 1,520 phototube detectors. An estimated 1 million neutrino events were recorded each year. SciBooNE sat in the same neutrino beam as MiniBooNE but had fine-grained tracking capabilities. The NOνA experiment uses, and the MINOS experiment used, Fermilab's NuMI (Neutrinos at the Main Injector) beam, which is an intense beam of neutrinos that travels through the Earth to the Soudan Mine in Minnesota and the Ash River, Minnesota, site of the NOνA far detector. In 2017, the ICARUS neutrino experiment was moved from CERN to Fermilab. Muon g−2 Muon g−2: (pronounced "gee minus two") is a particle physics experiment to measure the anomaly of the magnetic moment of a muon to a precision of 0.14 ppm, which will be a sensitive test of the Standard Model. Fermilab is continuing an experiment conducted at Brookhaven National Laboratory to measure the anomalous magnetic dipole moment of the muon. The magnetic dipole moment (g) of a charged lepton (electron, muon, or tau) is very nearly 2. The difference from 2 (the "anomalous" part) depends on the lepton, and can be computed quite exactly based on the current Standard Model of particle physics. Measurements of the electron are in excellent agreement with this computation. The Brookhaven experiment did this measurement for muons, a much more technically difficult measurement due to their short lifetime, and detected a tantalizing, but not definitive, 3 σ discrepancy between the measured value and the computed one. The Brookhaven experiment ended in 2001, but 10 years later Fermilab acquired the equipment, and is working to make a more accurate measurement (smaller σ) which will either eliminate the discrepancy or, hopefully, confirm it as an experimentally observable example of physics beyond the Standard Model. Central to the experiment is a 50 foot-diameter superconducting magnet with an exceptionally uniform magnetic field. This was transported, in one piece, from Brookhaven in Long Island, New York, to Fermilab in the summer of 2013. The move traversed 3,200 miles over 35 days, mostly on a barge down the East Coast and up the Mississippi. The magnet was refurbished and powered on in September 2015, and has been confirmed to have the same (0.13%) p-p basic magnetic field uniformity that it had before the move. The project worked on shimming the magnet to improve its magnetic field uniformity. This had been done at Brookhaven, but was disturbed by the move and had to be re-done at Fermilab. In 2018, the experiment started taking data at Fermilab. In 2021, the laboratory reported that results from initial study involving the particle challenged the Standard Model, with the potential for discovery of new forces and particles. In August 2023, the Fermilab group said they may be getting closer to proving the existence of a new force of nature. They have found more evidence that sub-atomic particles, called muons, are not behaving in the way predicted by the current theory of sub-atomic physics. Delays, cost overruns, safety failures, and management turmoil in the 2010s and 2020s Starting in the 2010s, delays and cost over-runs led to substantial concerns about mismanagement of the laboratory. Oversight issues that developed between 2014 and 2024 In 2014, the Particle Physics Project Prioritization Panel ("P5") recommended three major initiatives for construction on the Fermilab site. Two were particle physics experiments: the Deep Underground Neutrino Experiment and Mu2e. The third was the PIPII accelerator upgrade described above. Also, P5 recommended Fermilab participation in LHC at CERN. As of 2022, two P5-recommended Fermilab projects had suffered substantial delays: The Deep Underground Neutrino Experiment with the enabling Long Baseline Neutrino Facility was proposed to P5 as a $1B project; the cost estimate in 2021 dollars was more than $3B, with far detector operations beginning 2029 and full operation by 2032. The Mu2e experiment was to produce preliminary results in 2020, but this is now delayed until 2026. Even smaller experiments, below the cost-level of individual P5 approval, that were proposed at the time of the 2014 P5 suffered considerable delay. The Short-Baseline Near Detector (SBND) that was proposed in 2014 with a $10M cost scale was originally scheduled for data taking in spring 2018, but is now scheduled to begin in autumn 2023. The Department of Energy raised flags as early as Fiscal Year (FY) 2019. Each year, the US Department of Energy Office of Science reviews and grades the national laboratories in its portfolio on eight performance metrics. Fermilab has received the lowest grades among the national laboratories in FY2019, 2020, 2021 and 2022. A rare C grade was assigned for project management in 2021, reflective of the delays and cost overruns. In an article in the journal Science, James Decker, who was principal deputy director of DOE's Office of Science from 1973 to 2007, stated that the performance evaluation for 2021 was "one of the most scathing I have seen". Also, in 2020, the high-energy physics community expressed concern that the cost of major projects at Fermilab have led to diversion of funds from the high-energy physics core research program, harming the health of the field. Congress increased the annual HEP budget from less than $800 million by about $250M to more than $1 billion—a 30% increase that went mainly to support large projects at Fermilab. The Fermilab project delays led to substantial change in leadership in 2022. In September 2021, Nigel Lockyer, Director of Fermilab, resigned. Lockyer was replaced by Lia Merminga, head of the PIP II project. On March 31, 2022, James Siegrist, associate director for High Energy Physics in the Department of Energy Office of Science, who had overseen the response to the P5 report, stepped down. In September 2022, it was announced that deputy director for Research Joseph Lykken would step down, to be replaced by Yale Professor Bonnie Fleming, who previously served as Deputy Chief Research Officer for the neutrino program at Fermilab. Regina (Gina) Rameika joined the DOE's Office of Science as the associate director for the Office of High Energy Physics in his place on November 7, 2022, moving from her role as spokesperson of the DUNE Experiment. Although these replacements represent a substantial turn-over of the top ranks, the new management was drawn from the 2014-2022 management team and Fermilab has continued to suffer turmoil since this change-over. In particular, new issues arose with regard to safety and access of employees, visitors and contractors. On May 25, 2023, a contractor fell 23 ft while attempting to secure reinforcing bars on a wall for the new PIP II project site. The contractor was air-lifted to hospital in an accident considered the worst on site in decades. A DOE-appointed Accident Investigation Board concluded that the incident was preventable and "recommended a long list of managerial and safety controls needed to prevent a recurrence of such an accident." As a result of the accident, the $1B PIP II project that is crucial for the success of the DUNE Experiment has been delayed. On September 1, 2023, Chief Research Officer Bonnie Fleming announced that the Fermilab accelerator system was temporarily shut down for safety reasons. On September 9, 2022, DOE issued order DOE O 420.2D entitled "Safety of Accelerators". This document establishes the accelerator-specific safety requirements for DOE-funded accelerators and their operations. Fermilab management had one year to comply with the order, but did not meet the requirements in that timeframe. The Fermilab Main Accelerator resumed running after the DOE O 420.2D implementation was complete, in late spring, 2024. In mid-2024, Fermilab faced a budget shortfall. This resulted in an initial furlough of employees and closure of its operations and public access for one week in August---an action that added to the considerable strife at the laboratory. The need for a furlough was surprising since the budget grew "a hefty 7.6% to $739 million" in fiscal year (FY) 2024. Beyond this, the six month accelerator shut down for DOE O 420.2D noncompliance should have represented substantial savings in the operations budget. According to the journal Science, the crisis stemmed from poorly managed growth: "from 2022 to 2023 alone, [laboratory staff] grew by 176 members, or 9%, to 2160." The steps taken did not fully address the issue, and in November, 2.5% of the workforce was laid off. Despite this, Tracy Marc, head of Fermilab's media services, told WTTW News that "the overall financial health of the laboratory remains intact and is being managed". 2024 Whistleblower Report On July 15, 2024, a report containing very serious allegations of cover-ups at the laboratory was uploaded to the arXiv physics preprint server. The allegations, which were also reported in the press, included: "The alleged sexual assault of the NOvA and DUNE collaborator who filed and won her 2022 lawsuit in the UK [after it] was dismissed by FNAL staff." "A cover-up of a case of guns on site in 2023, with promotion of the perpetrator and pretextuous firing of the witness." "A cover-up of an attempt at badly hurting with an industrial vehicle a female electrician by a ... male employee." "A cover-up of Beryllium windows blasting, with subsequent promotion of the person in charge." "A hostile work environment, where constructive criticism is most often ignored and retaliated against." The report also recounted a litany of complaints concerning day-to-day running of the laboratory that have been reported in this article, above, as well as a new claim of "PIP-II contingency overruns within one year from CD3 approval" that could potentially impact the LBNF/DUNE program. For credibility, the report provided detailed eye-witness accounts to support the allegations. Beyond that, some information was previously publicly reported. For example, the first allegation concerning an egregious case of sexual harassment was reported in The Guardian and the fact that the claimant had submitted a complaint to Fermilab which took no action appeared in court documents. Scientists expressed fear of retribution by Fermilab leadership. In order for the whistleblowers to remain anonymous, the report was uploaded to the arXiv preprint server by Giorgio Bellettini, a respected leader in the field of particle physics who served as spokesman of the collaboration for the Collider Detector at Fermilab twice. A second signed letter of support from William Barletta of the Massachusetts Institute of Technology was also included. The report was delivered to the deputy director for Operations of the DOE Office of Science Dr. Juston Fontaine and the DOE Under Secretary for Science and Innovation Geraldine Richmond in June 2024. It was released to the public one month later, after DOE officials did not respond. On July 29, 2024, Fermilab Director Lia Merminga issued a terse response to concerned scientists, saying: "The [whistleblower] document asserts various challenges at Fermilab, some of which are inaccurate, and others of which [the Fermi Research Alliance] has been working hard to address for some time." At an All Hands Meeting, Merminga also told scientific staff to "stop whining.” New Management in 2025 by the Fermi Forward Discovery Group, LLC In view of the many issues facing the laboratory, in January 2023, the DOE announced a two-year process to rebid the contract for the management of the laboratory due to the performance issues. The DOE announcement of the competition explained: "the purpose of this contract competition is to solicit and award a new M&O contract that will result in improved contractor performance and efficiencies at FNAL. DOE expects that this competition will elicit new and innovative approaches for planning the Laboratory's future." At an informational meeting for potential bidders on March 1, 2023, the presentation slides expanded upon issues under "Major Challenges/Risks" including highlighting the concern: "The Laboratory continues to have challenges in Financial Management and Acquisition Management. Audits repeatedly highlight the same deficiencies and control failures year after year. Any corrective actions implemented have resulted in little to no progress. Significant procurement issues have hindered the laboratory's ability to successfully deliver efficient and effective business systems/resources to enable the Science Mission. Substantial concerns remain regarding the ability to expend Government funds in an effective, efficient, and compliant manner." The myriad issues facing a new contractor were listed in January 2024 in the news section of the journal Nature. On October 1, 2024, the Department of Energy awarded the contract to operate Fermi National Accelerator to the newly-formed Fermi Forward Discovery Group, LLC (FFDG). FFDG will assume management of Fermilab operations on January 1, 2025, with a five-year contract. The FFDG represents an incremental change in management from the previous decade because the group includes the past management team for the laboratory, the FRA, that consisted of the University of Chicago and the Universities Research Association (URA). There are two additions: Amentum Environment & Energy, Inc., which specializes in advanced engineering, and Longenecker & Associates, which specializes in project management. Thus, the selection leaves the scientific and human resources management unchanged, but does strengthen expertise to deliver large projects. In response to the ongoing crisis, Director Lia Merminga resigned on January 13, 2025. Young-Kee Kim, Albert A. Michelson Distinguished Service Professor of Physics at the University of Chicago, is serving as Acting Director during the search for a replacement . Kim served as Deputy Director of Fermilab from 2006-2013, and so is an experienced interim replacement. Site Access Fermi National Accelerator Laboratory (aka Fermilab) was founded in 1967 as an open science research laboratory, and, to this day, does not conduct classified research. The initial plans called for Fermilab to employ a guard force "...to control movement of personnel onto the site when tests are being conducted" as noted in the December 1971 Environmental Statement and "..to enforce the site boundary". Early leadership moved toward greater public openness allowing for ease of scientific collaboration and public enjoyment to include the relocated bison heard. In the late 2010s and early 2020s, the management of Fermilab began to introduce severe restrictions on access to the Fermilab site by the public and by scientists. By spring 2023, the restrictions had become so onerous that more than 2500 physicists and visitors to the laboratory signed an "open petition to elected representatives to reopen Fermilab." The petition stated that: "The access policy changes undermine critical aspects of the scientific process as well as the basic functioning of Fermilab. Hosting research meetings, interviewing prospective employees, collaborating with scientists outside the lab, and enacting our famously impactful education programs have all been hindered." With respect to the general public, the petition stated: "Today, the general public is only permitted to access the main road, and with ID requirements that are becoming increasingly stringent, soon its doors will be closed to tourists and even to some immigrants. We can no longer drive or bike around the premises freely. The dog park, Wilson Hall with its exhibits on the top floor, and other areas are no longer generally accessible. Fishing and other activities open to the public have been canceled." The petition emphatically requested that access policies be reverted to the open laboratory model that governed the laboratory prior to 2020. In May 2023, Director Lia Merminga posted a response to the petition on the Fermilab website, noting that some areas on site remain open to the public during specific hours with ID access requirements. Merminga's response justifies the new restrictions because the lab "manage[s] a large amount of non-public information"---reasoning that conflicts with the petition that points out that the lab is fully tax-payer funded, does no classified research, and has a government mandate to publish all of its scientific results. Further coverage of the petition and the management response appeared in the magazines Physics Today and Physics World. In keeping with Real ID requirements for DOE facilities, all unescorted adult visitors entering the site must present a government-issued photo ID compliant with the Real ID Act. Up-to-date specifics about access can be found on the Fermilab website. Architecture Fermilab's first director, Robert Wilson, insisted that the site's aesthetic complexion not be marred by a collection of concrete block buildings. The design of the administrative building (Wilson Hall) was inspired by St. Pierre's Cathedral in Beauvais, France, though it was realized in a Brutalist style. Several of the buildings and sculptures within the Fermilab reservation represent various mathematical constructs as part of their structure. The Archimedean Spiral is the defining shape of several pumping stations as well as the building housing the MINOS experiment. The reflecting pond at Wilson Hall also showcases a hyperbolic obelisk, designed by Wilson. Some of the high-voltage transmission lines carrying power through the laboratory's land are built to echo the Greek letter π. One can also find structural examples of the DNA double-helix spiral and a nod to the geodesic sphere. Wilson's sculptures on the site include Tractricious, a free-standing arrangement of steel tubes near the Industrial Complex constructed from parts and materials recycled from the Tevatron collider, and the soaring Broken Symmetry, which greets those entering the campus via the Pine Street entrance. Crowning the Ramsey Auditorium is a representation of the Möbius strip with a diameter of more than . Also scattered about the access roads and village are a massive hydraulic press and old magnetic containment channels, all painted blue. Wildlife In 1967, Wilson brought five American bison to the site, a bull and four cows, and an additional 21 were provided by the Illinois Department of Conservation. Some fearful locals believed at first that the bison were introduced in order to serve as an alarm if and when radiation at the laboratory reached dangerous levels, but they were assured by Fermilab that this claim had no merit. Today, the Fermilab bison herd is a popular attraction that draws many visitors and the grounds are also a sanctuary for other local wildlife populations. A Christmas Bird Count has occurred at the lab every year since 1976. Working with the Forest Preserve District of DuPage County, Fermilab has introduced barn owls to selected structures around the grounds. Tritium on site During running, particle beams produce tritium, an isotope of hydrogen consisting of a proton and two neutrons that is weakly radioactive with a half-life of 12.3 years. This can bind with oxygen to form tritiated water. Tritium levels measured on site are low compared to federal health and environmental standards. Fermilab monitors tritium leaving the site in surface and sewer water, and provides an FAQ sheet for those who want to learn more. At an informational meeting for potential bidders for the management contract, held on March 1, 2023, the presentation slides indicated that although the rate of tritium leaving site is below the required standards, there is sufficient tritium contamination on site to represent a "challenge". In particular, tritium produced in the NuMI beamline that sends neutrinos to experiments in Minnesota has been pumped into the industrial water cooling system that is used for equipment across the Fermilab campus. As a result, it is concluded that now "tritium contamination is largely throughout the research complex." See also Big Science Center for the Advancement of Science in Space — operates the US National Laboratory on the ISS CERN Fermi Linux LTS Scientific Linux Stanford Linear Accelerator Center References External links Fermi National Accelerator Laboratory Fermilab Today Daily newsletter Other Fermilab online publications Fermilab Virtual Tour Architecture at the Fermilab campus United States Department of Energy national laboratories Federally Funded Research and Development Centers Particle physics facilities Batavia, Illinois Buildings and structures in DuPage County, Illinois Buildings and structures in Kane County, Illinois Education in DuPage County, Illinois Education in Kane County, Illinois 1967 establishments in Illinois Theoretical physics institutes Nuclear research institutes Institutes associated with CERN Research institutes in Illinois	Fermilab	[ "Physics", "Engineering" ]	7,957	[ "Nuclear research institutes", "Theoretical physics", "Nuclear organizations", "Theoretical physics institutes" ]
53,306	https://en.wikipedia.org/wiki/Natural%20satellite	A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are colloquially referred to as moons, a derivation from the Moon of Earth. In the Solar System, there are six planetary satellite systems containing 288 known natural satellites altogether. Seven objects commonly considered dwarf planets by astronomers are also known to have natural satellites: , Pluto, Haumea, , Makemake, , and Eris. As of January 2022, there are 447 other minor planets known to have natural satellites. A planet usually has at least around 10,000 times the mass of any natural satellites that orbit it, with a correspondingly much larger diameter. The Earth–Moon system is a unique exception in the Solar System; at 3,474 kilometres (2,158 miles) across, the Moon is 0.273 times the diameter of Earth and about of its mass. The next largest ratios are the Neptune–Triton system at 0.055 (with a mass ratio of about 1 to 4790), the Saturn–Titan system at 0.044 (with the second mass ratio next to the Earth–Moon system, 1 to 4220), the Jupiter–Ganymede system at 0.038, and the Uranus–Titania system at 0.031. For the category of dwarf planets, Charon has the largest ratio, being 0.52 the diameter and 12.2% the mass of Pluto. Terminology The first known natural satellite was the Moon, but it was considered a "planet" until Copernicus' introduction of De revolutionibus orbium coelestium in 1543. Until the discovery of the Galilean satellites in 1610 there was no opportunity for referring to such objects as a class. Galileo chose to refer to his discoveries as Planetæ ("planets"), but later discoverers chose other terms to distinguish them from the objects they orbited. The first to use the term satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iouis satellitibus erronibus ("Narration About Four Satellites of Jupiter Observed") in 1610. He derived the term from the Latin word satelles, meaning "guard", "attendant", or "companion", because the satellites accompanied their primary planet in their journey through the heavens. The term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of "moon". In 1957, however, the launching of the artificial object Sputnik created a need for new terminology. The terms man-made satellite and artificial moon were very quickly abandoned in favor of the simpler satellite. As a consequence, the term has become linked primarily with artificial objects flown in space. Because of this shift in meaning, the term moon, which had continued to be used in a generic sense in works of popular science and fiction, has regained respectability and is now used interchangeably with natural satellite, even in scientific articles. When it is necessary to avoid both the ambiguity of confusion with Earth's natural satellite the Moon and the natural satellites of the other planets on the one hand, and artificial satellites on the other, the term natural satellite (using "natural" in a sense opposed to "artificial") is used. To further avoid ambiguity, the convention is to capitalize the word Moon when referring to Earth's natural satellite (a proper noun), but not when referring to other natural satellites (common nouns). Many authors define "satellite" or "natural satellite" as orbiting some planet or minor planet, synonymous with "moon" – by such a definition all natural satellites are moons, but Earth and other planets are not satellites. A few recent authors define "moon" as "a satellite of a planet or minor planet", and "planet" as "a satellite of a star" – such authors consider Earth as a "natural satellite of the Sun". Definition of a moon There is no established lower limit on what is considered a "moon". Every natural celestial body with an identified orbit around a planet of the Solar System, some as small as a kilometer across, has been considered a moon, though objects a tenth that size within Saturn's rings, which have not been directly observed, have been called moonlets. Small asteroid moons (natural satellites of asteroids), such as Dactyl, have also been called moonlets. The upper limit is also vague. Two orbiting bodies are sometimes described as a double planet rather than a primary and satellite. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition of what constitutes a moon. Some authors consider the Pluto–Charon system to be a double (dwarf) planet. The most common dividing line on what is considered a moon rests upon whether the barycentre is below the surface of the larger body, though this is somewhat arbitrary because it depends on distance as well as relative mass. Origin and orbital characteristics The natural satellites orbiting relatively close to the planet on prograde, uninclined circular orbits (regular satellites) are generally thought to have been formed out of the same collapsing region of the protoplanetary disk that created its primary. In contrast, irregular satellites (generally orbiting on distant, inclined, eccentric and/or retrograde orbits) are thought to be captured asteroids possibly further fragmented by collisions. Most of the major natural satellites of the Solar System have regular orbits, while most of the small natural satellites have irregular orbits. The Moon and the Moons of Pluto are exceptions among large bodies in that they are thought to have originated from the collision of two large protoplanetary objects early in the Solar System's history (see the giant impact hypothesis). The material that would have been placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting natural satellites. As opposed to planetary-sized bodies, asteroid moons are thought to commonly form by this process. Triton is another exception; although large and in a close, circular orbit, its motion is retrograde and it is thought to be a captured dwarf planet. Temporary satellites The capture of an asteroid from a heliocentric orbit is not always permanent. According to simulations, temporary satellites should be a common phenomenon. The only observed examples are , , . was a temporary satellite of Earth for nine months in 2006 and 2007. Tidal locking Most regular moons (natural satellites following relatively close and prograde orbits with small orbital inclination and eccentricity) in the Solar System are tidally locked to their respective primaries, meaning that the same side of the natural satellite always faces its planet. This phenomenon comes about through a loss of energy due to tidal forces raised by the planet, slowing the rotation of the satellite until it is negligible. Exceptions are known; one such exception is Saturn's natural satellite Hyperion, which rotates chaotically because of the gravitational influence of Titan. Pluto's four, circumbinary small moons also rotate chaotically due to Charon's influence. In contrast, the outer natural satellites of the giant planets (irregular satellites) are too far away to have become locked. For example, Jupiter's Himalia, Saturn's Phoebe, and Neptune's Nereid have rotation periods in the range of ten hours, whereas their orbital periods are hundreds of days. Satellites of satellites No "moons of moons" or subsatellites (natural satellites that orbit a natural satellite of a planet) are currently known. In most cases, the tidal effects of the planet would make such a system unstable. However, calculations performed after the 2008 detection of a possible ring system around Saturn's moon Rhea indicate that satellites orbiting Rhea could have stable orbits. Furthermore, the suspected rings are thought to be narrow, a phenomenon normally associated with shepherd moons. However, targeted images taken by the Cassini spacecraft failed to detect rings around Rhea. It has also been proposed that Saturn's moon Iapetus had a satellite in the past; this is one of several hypotheses that have been put forward to account for its equatorial ridge. Light-curve analysis suggests that Saturn's irregular satellite Kiviuq is extremely prolate, and is likely a contact binary or even a binary moon. Trojan satellites Two natural satellites are known to have small companions at both their and Lagrangian points, sixty degrees ahead and behind the body in its orbit. These companions are called trojan moons, as their orbits are analogous to the trojan asteroids of Jupiter. The trojan moons are Telesto and Calypso, which are the leading and following companions, respectively, of the Saturnian moon Tethys; and Helene and Polydeuces, the leading and following companions of the Saturnian moon Dione. Asteroid satellites The discovery of 243 Ida's natural satellite Dactyl in the early 1990s confirmed that some asteroids have natural satellites; indeed, 87 Sylvia has two. Some, such as 90 Antiope, are double asteroids with two comparably sized components. Shape Neptune's moon Proteus is the largest irregularly shaped natural satellite; the shapes of Eris' moon Dysnomia and ' moon Vanth are unknown. All other known natural satellites that are at least the size of Uranus's Miranda have lapsed into rounded ellipsoids under hydrostatic equilibrium, i.e. are "round/rounded satellites" and are sometimes categorized as planetary-mass moons. (Dysnomia's density is known to be high enough that it is probably a solid ellipsoid as well.) The larger natural satellites, being tidally locked, tend toward ovoid (egg-like) shapes: squat at their poles and with longer equatorial axes in the direction of their primaries (their planets) than in the direction of their motion. Saturn's moon Mimas, for example, has a major axis 9% greater than its polar axis and 5% greater than its other equatorial axis. Methone, another of Saturn's moons, is only around 3 km in diameter and visibly egg-shaped. The effect is smaller on the largest natural satellites, where their gravity is greater relative to the effects of tidal distortion, especially those that orbit less massive planets or, as in the case of the Moon, at greater distances. Geological activity Of the twenty known natural satellites in the Solar System that are large enough to be gravitationally rounded, several remain geologically active today. Io is the most volcanically active body in the Solar System, while Europa, Enceladus, Titan and Triton display evidence of ongoing tectonic activity and cryovolcanism. In the first three cases, the geological activity is powered by the tidal heating resulting from having eccentric orbits close to their giant-planet primaries. (This mechanism would have also operated on Triton in the past before its orbit was circularized.) Many other natural satellites, such as Earth's Moon, Ganymede, Tethys, and Miranda, show evidence of past geological activity, resulting from energy sources such as the decay of their primordial radioisotopes, greater past orbital eccentricities (due in some cases to past orbital resonances), or the differentiation or freezing of their interiors. Enceladus and Triton both have active features resembling geysers, although in the case of Triton solar heating appears to provide the energy. Titan and Triton have significant atmospheres; Titan also has hydrocarbon lakes. All four of the Galilean moons have atmospheres, though they are extremely thin. Four of the largest natural satellites, Europa, Ganymede, Callisto, and Titan, are thought to have subsurface oceans of liquid water, while smaller Enceladus also supports a global subsurface ocean of liquid water. Occurrence in the Solar System Besides planets and dwarf planets objects within our Solar System known to have natural satellites are 76 in the asteroid belt (five with two each), four Jupiter trojans, 39 near-Earth objects (two with two satellites each), and 14 Mars-crossers. There are also 84 known natural satellites of trans-Neptunian objects. Some 150 additional small bodies have been observed within the rings of Saturn, but only a few were tracked long enough to establish orbits. Planets around other stars are likely to have satellites as well, and although numerous candidates have been detected to date, none have yet been confirmed. Of the inner planets, Mercury and Venus have no natural satellites; Earth has one large natural satellite, known as the Moon; and Mars has two tiny natural satellites, Phobos and Deimos. The giant planets have extensive systems of natural satellites, including half a dozen comparable in size to Earth's Moon: the four Galilean moons, Saturn's Titan, and Neptune's Triton. Saturn has an additional six mid-sized natural satellites massive enough to have achieved hydrostatic equilibrium, and Uranus has five. It has been suggested that some satellites may potentially harbour life. Among the objects generally agreed by astronomers to be dwarf planets, Ceres and have no known natural satellites. Pluto has the relatively large natural satellite Charon and four smaller natural satellites; Styx, Nix, Kerberos, and Hydra. Haumea has two natural satellites; , , Makemake, , and have one each. The Pluto–Charon system is unusual in that the center of mass lies in open space between the two, a characteristic sometimes associated with a double-planet system. The seven largest natural satellites in the Solar System (those bigger than 2,500 km across) are Jupiter's Galilean moons (Ganymede, Callisto, Io, and Europa), Saturn's moon Titan, Earth's moon, and Neptune's captured natural satellite Triton. Triton, the smallest of these, has more mass than all smaller natural satellites together. Similarly in the next size group of nine mid-sized natural satellites, between 1,000 km and 1,600 km across, Titania, Oberon, Rhea, Iapetus, Charon, Ariel, Umbriel, Dione, and Tethys, the smallest, Tethys, has more mass than all smaller natural satellites together. As well as the natural satellites of the various planets, there are also over 80 known natural satellites of the dwarf planets, minor planets and other small Solar System bodies. Some studies estimate that up to 15% of all trans-Neptunian objects could have satellites. The following is a comparative table classifying the natural satellites in the Solar System by diameter. The column on the right includes some notable planets, dwarf planets, asteroids, and trans-Neptunian objects for comparison. The natural satellites of the planets are named after mythological figures. These are predominantly Greek, except for the Uranian natural satellites, which are named after Shakespearean characters. The twenty satellites massive enough to be round are in bold in the table below. Minor planets and satellites where there is disagreement in the literature on roundness are italicized in the table below. See also Moons of planets Moons of dwarf planets and small Solar System bodies References External links All moons Natural Satellite Physical Parameters (JPL-NASA, with refs – last updated July 2006) Moons of the Solar System (The Planetary Society, as of March 2009) The JPL's Solar System Dynamics page Planetary Names: Planet and Satellite Names and Discoverers "Upper size limit for moons explained" Kelly Young. Nature (vol 441, p. 834) 14 June 2006 Images of planets and major moons (not to scale) The Planetary Society – Moon Montage(s) Album of moon images by Kevin M. Gill The Atlas of Moons by the National Geographic Society Jupiter's moons * Scott S. Sheppard Scott S. Sheppard Saturn's moons Satellite-hunters find four new moons of the planet Saturn David Brand \| 26 October 2000 Saturn's New Satellite S/2003 S1 Scott S. Sheppard Solar System	Natural satellite	[ "Astronomy" ]	3,289	[ "Outer space", "Solar System" ]
53,311	https://en.wikipedia.org/wiki/Hermann%20von%20Helmholtz	Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, the largest German association of research institutions, was named in his honour. In the fields of physiology and psychology, Helmholtz is known for his mathematics concerning the eye, theories of vision, ideas on the visual perception of space, colour vision research, the sensation of tone, perceptions of sound, and empiricism in the physiology of perception. In physics, he is known for his theories on the conservation of energy and on the electrical double layer, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics. Although credit is shared with Julius von Mayer, James Joule, and Daniel Bernoulli—among others—for the energy conservation principles that eventually led to the first law of thermodynamics, he is credited with the first formulation of the energy conservation principle in its maximally general form. As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science. By the late nineteenth century, Helmholtz's development of a broadly Kantian methodology, including the a priori determination of the manifold of possible orientations in perceptual space, had inspired new readings of Kant and contributed to the late modern neo-Kantianism movement in philosophy. Biography Early years Helmholtz was born in Potsdam, the son of the local gymnasium headmaster, Ferdinand Helmholtz, who had studied classical philology and philosophy, and who was a close friend of the publisher and philosopher Immanuel Hermann Fichte. Helmholtz's work was influenced by the philosophy of Johann Gottlieb Fichte and Immanuel Kant. He tried to trace their theories in empirical matters like physiology. As a young man, Helmholtz was interested in natural science, but his father wanted him to study medicine. Helmholtz earned a medical doctorate at Medizinisch-chirurgisches Friedrich-Wilhelm-Institute in 1842 and served a one-year internship at the Charité hospital (because there was financial support for medical students). Trained primarily in physiology, Helmholtz wrote on many other topics, ranging from theoretical physics to the age of the Earth, and to the origin of the Solar System. University posts Helmholtz's first academic position was as a teacher of anatomy at the Academy of Arts in Berlin in 1848. He then moved to take a post of associate professor of physiology at the Prussian University of Königsberg, where he was appointed in 1849. In 1855 he accepted a full professorship of anatomy and physiology at the University of Bonn. He was not particularly happy in Bonn, however, and three years later he transferred to the University of Heidelberg, in Baden, where he served as professor of physiology. In 1871 he accepted his final university position, as professor of physics at the Friedrich Wilhelm University in Berlin. Research Mechanics His first important scientific achievement, an 1847 treatise on the conservation of energy, was written in the context of his medical studies and philosophical background. His work on energy conservation came about while studying muscle metabolism. He tried to demonstrate that no energy is lost in muscle movement, motivated by the implication that there were no vital forces necessary to move a muscle. This was a rejection of the speculative tradition of Naturphilosophie and vitalism which was at that time a dominant philosophical paradigm in German physiology. He was working against the argument, promoted by some vitalists, that "living force" can power a machine indefinitely. Drawing on the earlier work of Sadi Carnot, Benoît Paul Émile Clapeyron and James Prescott Joule, he postulated a relationship between mechanics, heat, light, electricity and magnetism by treating them all as manifestations of a single force, or energy in today's terminology. He published his theories in his book Über die Erhaltung der Kraft (On the Conservation of Force, 1847). In the 1850s and 60s, building on the publications of William Thomson, Helmholtz and William Rankine helped popularize the idea of the heat death of the universe. In fluid dynamics, Helmholtz made several contributions, including Helmholtz's theorems for vortex dynamics in inviscid fluids. Sensory physiology Helmholtz was a pioneer in the scientific study of human vision and audition. Inspired by psychophysics, he was interested in the relationships between measurable physical stimuli and their correspondent human perceptions. For example, the amplitude of a sound wave can be varied, causing the sound to appear louder or softer, but a linear step in sound pressure amplitude does not result in a linear step in perceived loudness. The physical sound needs to be increased exponentially in order for equal steps to seem linear, a fact that is used in current electronic devices to control volume. Helmholtz paved the way in experimental studies on the relationship between the physical energy (physics) and its appreciation (psychology), with the goal in mind to develop "psychophysical laws". The sensory physiology of Helmholtz was the basis of the work of Wilhelm Wundt, a student of Helmholtz, who is considered one of the founders of experimental psychology. More explicitly than Helmholtz, Wundt described his research as a form of empirical philosophy and as a study of the mind as something separate. Helmholtz had, in his early repudiation of Naturphilosophie, stressed the importance of materialism, and was focusing more on the unity of "mind" and body. Ophthalmic optics In 1851, Helmholtz revolutionized the field of ophthalmology with the invention of the ophthalmoscope; an instrument used to examine the inside of the human eye. This made him world-famous overnight. Helmholtz's interests at that time were increasingly focused on the physiology of the senses. His main publication, titled Handbuch der Physiologischen Optik (Handbook of Physiological Optics or Treatise on Physiological Optics; English translation of the 3rd volume here), provided empirical theories on depth perception, colour vision, and motion perception, and became the fundamental reference work in his field during the second half of the nineteenth century. In the third and final volume, published in 1867, Helmholtz described the importance of unconscious inferences for perception. The Handbuch was first translated into English under the editorship of James P. C. Southall on behalf of the Optical Society of America in 1924–5. His theory of accommodation went unchallenged until the final decade of the 20th century. Helmholtz continued to work for several decades on several editions of the handbook, frequently updating his work because of his dispute with Ewald Hering who held opposite views on spatial and colour vision. This dispute divided the discipline of physiology during the second half of the 1800s. Nerve physiology In 1849, while at Königsberg, Helmholtz measured the speed at which the signal is carried along a nerve fibre. At that time most people believed that nerve signals passed along nerves immeasurably fast. He used a recently dissected sciatic nerve of a frog and the calf muscle to which it attached. He used a galvanometer as a sensitive timing device, attaching a mirror to the needle to reflect a light beam across the room to a scale which gave much greater sensitivity. Helmholtz reported transmission speeds in the range of 24.6 – 38.4 meters per second. Acoustics and aesthetics In 1863, Helmholtz published Sensations of Tone, once again demonstrating his interest in the physics of perception. This book influenced musicologists into the twentieth century. Helmholtz invented the Helmholtz resonator to identify the various frequencies or pitches of the pure sine wave components of complex sounds containing multiple tones. Helmholtz showed that different combinations of resonators could mimic vowel sounds: Alexander Graham Bell in particular was interested in this but, not being able to read German, misconstrued Helmholtz's diagrams as meaning that Helmholtz had transmitted multiple frequencies by wire—which would allow multiplexing of telegraph signals—whereas, in reality, electrical power was used only to keep the resonators in motion. Bell failed to reproduce what he thought Helmholtz had done but later said that, had he been able to read German, he would not have gone on to invent the telephone on the harmonic telegraph principle. The translation by Alexander J. Ellis was first published in 1875 (the first English edition was from the 1870 third German edition; Ellis's second English edition from the 1877 fourth German edition was published in 1885; the 1895 and 1912 third and fourth English editions were reprints of the second). Electromagnetism Helmholtz studied electrical oscillations from 1869 to 1871, and in a lecture delivered to the Naturhistorisch-medizinischen Verein zu Heidelberg (Natural History and Medical Association of Heidelberg) on 30 April 1869, titled On Electrical Oscillations, he indicated that the perceptible damped electrical oscillations in a coil connected to a Leyden jar were about second in duration. In 1871, Helmholtz moved from Heidelberg to Berlin to become a professor of physics. He became interested in electromagnetism, and the Helmholtz equation is named for him. Although he made no major contributions to this field, his student Heinrich Rudolf Hertz became famous as the first to demonstrate electromagnetic radiation. Oliver Heaviside criticised Helmholtz's electromagnetic theory because it allowed the existence of longitudinal waves. Based on work on Maxwell's equations, Heaviside pronounced that longitudinal waves could not exist in a vacuum or a homogeneous medium. Heaviside did not note, however, that longitudinal electromagnetic waves can exist at a boundary or in an enclosed space. Philosophy Helmholtz' scientific work in physiology and mechanics occasioned much that he is known for in philosophy of science, including ideas on the relation between the laws of perception and the laws of nature and his rejection of the exclusive use of Euclidean geometry. His philosophy of science wavered between some version of empiricism and transcendentalism. Despite the speculative associations of the latter, his philosophy of science is thoroughly indebted to his use of mathematical physics to supplant vitalism and articulate the general conservation of energy principle. His rejection of Euclidean geometry as the only possible science of space is central to understanding his appropriation of Kant's philosophy of space, which ostensibly requires Euclidean geometry to be that exclusive a priori science of physical space. Helmholtz introduced a new conception of the a priori in space: that of the determination of the manifold of possible orientations in perceptual space. These developments inspired new readings of Kant and contributed to the rise of late modern neo-Kantianism movement in philosophy. Students and associates Other students and research associates of Helmholtz at Berlin included Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, Arthur König, Henry Augustus Rowland, Albert A. Michelson, Wilhelm Wundt, Fernando Sanford and Michael I. Pupin. Leo Koenigsberger, who was his colleague from 1869 to 1871 in Heidelberg, wrote the definitive biography of him in 1902. Honours and legacy In 1873, Helmholtz was elected as a member of the American Philosophical Society. In 1881, Helmholtz was elected Honorary Fellow of the Royal College of Surgeons in Ireland. On 10 November 1881, he was awarded the Légion d'honneur: au grade de Commandeur, or Level 3 – a senior grade. (No. 2173). In 1883, Professor Helmholtz was honoured by the Emperor, being raised to the nobility, or Adel. The Adelung meant that he and his family were now styled: von Helmholtz. The distinction was not a peerage or title, but it was hereditary and conferred a certain social cachet. Helmholtz was conferred the Honorary Membership of the Institution of Engineers and Shipbuilders in Scotland in 1884. The largest German association of research institutions, the Helmholtz Association, is named after him. The asteroid 11573 Helmholtz and the lunar crater Helmholtz as well as the crater Helmholtz on Mars were named in his honour. In Charlottenburg, Berlin, the street Helmholtzstraße is named after von Helmholtz. Works Translated works On the Conservation of Force (1847) HathiTrust On the Conservation of Force (1895) Introduction to a Series of Lectures Delivered at Carlsruhe in the Winter of 1862–1863, English translation On the Sensations of Tone as a Physiological Basis for the Theory of Music (downloadable from California Digital Library) Third Edition of English Translation, based on Fourth German Edition of 1877, By Hermann von Helmholtz, Alexander John Ellis, Published by Longmans, Green, 1895, 576 pages On the Sensations of Tone as a Physiological Basis for the Theory of Music (downloadable from Google Books) Fourth Edition, By Hermann von Helmholtz, Alexander John Ellis, Published by Longmans, Green, 1912, 575 pages Treatise on Physiological Optics (1910) three volumes. English translation by Optical Society of America (1924–25). Popular lectures on scientific subjects (1885) Popular lectures on scientific subjects second series (1908) See also Helmholtz coil List of people from Berlin List of things named after Hermann von Helmholtz Neo-Kantianism Theory of Colours References Citations Sources Cahan, David Helmholtz: A Life in Science. University of Chicago Press, 2018. . Cohen, Robert, and Wartofsky, Marx, eds. and trans. Reidel. Helmholtz: Epistemological Writings, 1977. Ewald, William B., ed. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press, 1996. 1876. "The origin and meaning of geometrical axioms", 663–88. 1878. "The facts in perception", 698–726. 1887. "Numbering and measuring from an epistemological viewpoint", 727–52. Groundwater, Jennifer. Alexander Graham Bell: The Spirit of Invention. Calgary: Altitude Publishing, 2005. . Jackson, Myles W. Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (MIT Press, 2006). Kahl, Russell, ed. Wesleyan. Selected Writings of Hermann von Helmholtz, Uni. Press., 1971. Koenigsberger, Leo. Hermann von Helmholtz, translated by Frances A. Welby (Dover, 1965) MacKenzie, Catherine. Alexander Graham Bell. Whitefish, Montana: Kessinger Publishing, 2003. . Retrieved 29 July 2009. Shulman, Seth. The Telephone Gambit: Chasing Alexander Bell's Secret. New York: Norton & Company, 2008. . Further reading David Cahan: Helmholtz: A Life in Science (University of Chicago, 2018). Steven Shapin, "A Theorist of (Not Quite) Everything" (review of David Cahan, Helmholtz: A Life in Science, University of Chicago Press, 2018, , 937 pp.), The New York Review of Books, vol. 66, no. 15 (10 October 2019), pp. 29–31. David Cahan (Ed.): Hermann von Helmholtz and the Foundations of Nineteenth-Century Science. Univ. California, Berkeley 1994, . Gregor Schiemann: Hermann von Helmholtz's Mechanism: The Loss of Certainty. A Study on the Transition from Classical to Modern Philosophy of Nature. Dordrecht: Springer 2009, . Franz Werner: Hermann Helmholtz´ Heidelberger Jahre (1858–1871). (= Sonderveröffentlichungen des Stadtarchivs Heidelberg 8). Mit 52 Abbildungen. Berlin / Heidelberg (Springer) 1997. Kenneth L. Caneva: Helmholtz and the Conservation of Energy: Contexts of Creation and Reception. The MIT Press, Cambridge, MA, 2021, ISBN 978-0-262-04573-5 External links "Hermann von Helmholtz" (Obituary). Royal Society (Great Britain). (1894). Proceedings of the Royal Society of London. London: Printed by Taylor and Francis. p. xvii. "Hermann von Helmholtz" in Stanford Encyclopedia of Philosophy, written by Lydia Patton Biography, bibliography and access to digital sources in the Virtual Laboratory of the Max Planck Institute for the History of Science (Die Lehre von den Tonempfindungen) Helmholtz's (1867) Handbuch der physiologischen Optik – digital facsimile from the Linda Hall Library 1821 births 1894 deaths Acousticians Color scientists German fluid dynamicists Foreign members of the Royal Society Foreign associates of the National Academy of Sciences German biophysicists 19th-century German physicists German untitled nobility German ophthalmologists Academic staff of the Humboldt University of Berlin Recipients of the Pour le Mérite (civil class) Members of the Prussian Academy of Sciences Members of the Royal Swedish Academy of Sciences People from Potsdam Scientists from the Province of Brandenburg Recipients of the Copley Medal Recipients of the Matteucci Medal Thermodynamicists Academic staff of the University of Bonn Academic staff of Heidelberg University Academic staff of the University of Königsberg Vision scientists Auditory scientists Physicians of the Charité Members of the Royal Society of Sciences in Uppsala	Hermann von Helmholtz	[ "Physics", "Chemistry" ]	3,628	[ "Thermodynamics", "Thermodynamicists" ]
53,325	https://en.wikipedia.org/wiki/List%20of%20civil%20engineers	This list of civil engineers is a list of notable people who have been trained in or have practiced civil engineering. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z References Civil engineers de:Liste bekannter Ingenieure	List of civil engineers	[ "Technology", "Engineering" ]	65	[ "Lists of engineers", "Civil engineering", "Lists of people in STEM fields", "Civil engineers" ]
53,332	https://en.wikipedia.org/wiki/Saffron	Saffron () is a spice derived from the flower of Crocus sativus, commonly known as the "saffron crocus". The vivid crimson stigma and styles, called threads, are collected and dried for use mainly as a seasoning and colouring agent in food. The saffron crocus was slowly propagated throughout much of Eurasia and was later brought to parts of North Africa, North America, and Oceania. Saffron's taste and iodoform-like or hay-like fragrance result from the phytochemicals picrocrocin and safranal. It also contains a carotenoid pigment, crocin, which imparts a rich golden-yellow hue to dishes and textiles. Its recorded history is attested in a 7th-century BC Assyrian botanical treatise, and it has been traded and used for thousands of years. As of 2024, Iran produced some 90% of the world total for saffron. At US$5,000 per kg or higher, saffron has long been the world's costliest spice by weight. Etymology A degree of uncertainty surrounds the origin of the English word "saffron". It might stem from the 12th-century Old French term safran, which comes from the Latin word , from the Persian (, za'farān), from the Persian word zarparān () meaning "gold strung" (implying either the golden stamens of the flower or the golden colour it creates when used as flavour). Species Description The domesticated saffron crocus, Crocus sativus, is an autumn-flowering perennial plant unknown in the wild. It probably descends from the eastern Mediterranean autumn-flowering Crocus cartwrightianus which is also known as "wild saffron" and is native to mainland Greece, Euboea, Crete, Skyros and some islands of the Cyclades. The similar species C. thomasii and C. pallasii were considered as other possible ancestors. As a genetically monomorphic clone incapable of seed production, it was slowly propagated by humans throughout much of Eurasia. Various origins had been suggested for saffron, including Iran, Greece, Mesopotamia. and Kashmir. It is a sterile triploid form, which means that three homologous sets of chromosomes make up each specimen's genetic complement; C. sativus bears eight chromosomal bodies per set, making for 24 in total. Being sterile, the purple flowers of C. sativus fail to produce viable seeds; reproduction hinges on human assistance: clusters of corms, underground, bulb-like, starch-storing organs, must be dug up, divided, and replanted. A corm survives for one season, producing via vegetative division up to ten "cormlets" that can grow into new plants in the next season. The compact corms are small, brown globules that can measure as large as in diameter, have a flat base, and are shrouded in a dense mat of parallel fibres; this coat is referred to as the "corm tunic". Corms also bear vertical fibres, thin and net-like, that grow up to above the plant's neck. The plant sprouts 5–11 white and non-photosynthetic leaves known as cataphylls. These membrane-like structures cover and protect 5 to 11 true leaves as they bud and develop on the crocus flower. The latter are thin, straight, and blade-like green foliage leaves, which are , in diameter, which either expand after the flowers have opened ("hysteranthous") or do so simultaneously with their blooming ("synanthous"). C. sativus cataphylls are suspected by some to manifest prior to blooming when the plant is irrigated relatively early in the growing season. Its floral axes, or flower-bearing structures, bear bracteoles, or specialised leaves, that sprout from the flower stems; the latter are known as pedicels. After aestivating in spring, the plant sends up its true leaves, each up to in length. Only in October, after most other flowering plants have released their seeds, do its brilliantly hued flowers develop; they range from a light pastel shade of lilac to a darker and more striated mauve. The flowers possess a sweet, honey-like fragrance. Upon flowering, the plants are in height and bear up to four flowers. A three-pronged style in length, emerges from each flower. Each prong terminates with a vivid crimson stigma, which is the distal end of a carpel. Cultivation The saffron crocus, unknown in the wild, probably descends from Crocus cartwrightianus. It is a triploid that is "self-incompatible" and male sterile; it undergoes aberrant meiosis and is hence incapable of independent sexual reproduction—all propagation is by vegetative multiplication via manual "divide-and-set" of a starter clone or by interspecific hybridisation. Crocus sativus thrives in the Mediterranean maquis, an ecotype superficially resembling the North American chaparral, and similar climates where hot and dry summer breezes sweep semi-arid lands. It can nonetheless survive cold winters, tolerating frosts as low as and short periods of snow cover. Some reports suggest saffron can tolerate an air temperature range from −22 to 40 °C. Irrigation is required if grown outside of moist environments such as Kashmir, where annual rainfall averages ; saffron-growing regions in Greece ( annually) and Spain () are far drier than the main cultivating Iranian regions. What makes this possible is the timing of the local wet seasons; generous spring rains and drier summers are optimal. Rain immediately preceding flowering boosts saffron yields; rainy or cold weather during flowering promotes disease and reduces yields. Persistently damp and hot conditions harm the crops, and rabbits, rats, and birds cause damage by digging up corms. Nematodes, leaf rusts, and corm rot pose other threats. Yet Bacillus subtilis inoculation may provide some benefit to growers by speeding corm growth and increasing stigma biomass yield. The plants fare poorly in shady conditions; they grow best in full sunlight. Fields that slope towards the sunlight are optimal (i.e., south-sloping in the Northern Hemisphere). Planting is mostly done in June in the Northern Hemisphere, where corms are lodged deep; its roots, stems, and leaves can develop between October and February. Planting depth and corm spacing, in concert with climate, are critical factors in determining yields. Mother corms planted deeper yield higher-quality saffron, though they form fewer flower buds and daughter corms. Italian growers optimise thread yield by planting deep and in rows apart; depths of optimise flower and corm production. Greek, Moroccan, and Spanish growers employ distinct depths and spacings that suit their locales. C. sativus prefers friable, loose, low-density, well-watered, and well-drained clay-calcareous soils with high organic content. Traditional raised beds promote good drainage. Soil organic content was historically boosted via application of some of manure. Afterwards, and with no further manure application, corms were planted. After a period of dormancy through the summer, the corms send up their narrow leaves and begin to bud in early autumn. Only in mid-autumn do they flower. Harvests are by necessity a speedy affair: after blossoming at dawn, flowers quickly wilt as the day passes. All plants bloom within a window of one or two weeks. Stigmas are dried quickly upon extraction and (preferably) sealed in airtight containers. Harvesting The high retail value of saffron is maintained on world markets because of labour-intensive harvesting methods, which require some – equivalently, . Forty hours of labour are needed to pick 150,000 flowers. One freshly picked crocus flower yields on average 30 mg of fresh saffron or 7 mg dried; roughly 150 flowers yield of dry saffron threads; to produce of dried saffron, of flowers are needed; the yield of dried spice from fresh saffron is only . Spice Phytochemistry and sensory properties Saffron contains some 28 volatile and aroma-yielding compounds, dominated by ketones and aldehydes. Its main aroma-active compounds are safranal – the main compound responsible for saffron aroma – 4-ketoisophorone, and dihydrooxophorone. Saffron also contains nonvolatile phytochemicals, including the carotenoids zeaxanthin, lycopene, various α- and β-carotenes, as well as crocetin and its glycoside crocein, which are the most biologically active components. Because crocetin is smaller and more water-soluble than the other carotenoids, it is more rapidly absorbed. The yellow-orange colour of saffron is primarily the result of α-crocin. This crocin is trans-crocetin di-(β-D-gentiobiosyl) ester; it bears the systematic (IUPAC) name 8,8-diapo-8,8-carotenoic acid. This means that the crocin underlying saffron's aroma is a digentiobiose ester of the carotenoid crocetin. Crocins themselves are a series of hydrophilic carotenoids that are either monoglycosyl or diglycosyl polyene esters of crocetin. Crocetin is a conjugated polyene dicarboxylic acid that is hydrophobic, and thus oil-soluble. When crocetin is esterified with two water-soluble gentiobioses, which are sugars, a product results that is itself water-soluble. The resultant α-crocin is a carotenoid pigment that may make up more than 10% of dry saffron's mass. The two esterified gentiobioses make α-crocin ideal for colouring water-based and non-fatty foods such as rice dishes. The bitter glucoside picrocrocin is responsible for saffron's pungent flavour. Picrocrocin (chemical formula: ; systematic name: 4-(β-D-glucopyranosyloxy)-2,6,6-trimethylcyclohex-1-ene-1-carbaldehyde) is a union of an aldehyde sub-molecule known as safranal (systematic name: 2,6,6-trimethylcyclohexa-1,3-diene-1-carbaldehyde) and a carbohydrate. It has insecticidal and pesticidal properties, and may comprise up to 4% of dry saffron. Picrocrocin is a truncated version of the carotenoid zeaxanthin that is produced via oxidative cleavage, and is the glycoside of the terpene aldehyde safranal. When saffron is dried after its harvest, the heat, combined with enzymatic action, splits picrocrocin to yield D–glucose and a free safranal molecule. Safranal, a volatile oil, gives saffron much of its distinctive aroma. Safranal is less bitter than picrocrocin and may comprise up to 70% of dry saffron's volatile fraction in some samples. A second molecule underlying saffron's aroma is 2-hydroxy-4,4,6-trimethyl-2,5-cyclohexadien-1-one, which produces a scent described as saffron, dried hay-like. Chemists find this is the most powerful contributor to saffron's fragrance, despite its presence in a lesser quantity than safranal. Dry saffron is highly sensitive to fluctuating pH levels, and rapidly breaks down chemically in the presence of light and oxidising agents. It must, therefore, be stored in air-tight containers to minimise contact with atmospheric oxygen. Saffron is somewhat more resistant to heat. Grades and ISO 3632 categories Saffron is not all of the same quality and strength. Strength is related to several factors including the amount of style picked along with the red stigma. Age of the saffron is also a factor. More style included means the saffron is less strong gram for gram because the colour and flavour are concentrated in the red stigmas. Saffron from Iran, Spain, and Kashmir is classified into various grades according to the relative amounts of red stigma and yellow styles it contains. Grades of Iranian saffron are: sargol (, red stigma tips only, strongest grade), pushal or pushali (red stigmas plus some yellow style, lower strength), "bunch" saffron (red stigmas plus large amount of yellow style, presented in a tiny bundle like a miniature wheatsheaf) and konge (yellow style only, claimed to have aroma but with very little, if any, colouring potential). Grades of Spanish saffron are coupé (the strongest grade, like Iranian sargol), mancha (like Iranian pushal), and in order of further decreasing strength rio, standard and sierra saffron. The word mancha in the Spanish classification can have two meanings: a general grade of saffron or a very high quality Spanish-grown saffron from a specific geographical origin. Real Spanish-grown La Mancha saffron has PDO protected status and this is displayed on the product packaging. Spanish growers fought hard for Protected Status because they felt that imports of Iranian saffron re-packaged in Spain and sold as "Spanish Mancha saffron" were undermining the genuine La Mancha brand. Similar was the case in Kashmir where imported Iranian saffron is mixed with local saffron and sold as "Kashmir brand" at a higher price. In Kashmir, saffron is mostly classified into two main categories called mongra (stigma alone) and lachha (stigmas attached with parts of the style). Countries producing less saffron do not have specialised words for different grades and may only produce one grade. Artisan producers in Europe and New Zealand have offset their higher labour charges for saffron harvesting by targeting quality, only offering extremely high-grade saffron. In addition to descriptions based on how the saffron is picked, saffron may be categorised under the international standard ISO 3632 after laboratory measurement of crocin (responsible for saffron's colour), picrocrocin (taste), and safranal (fragrance or aroma) content. However, often there is no clear grading information on the product packaging and little of the saffron readily available in the UK is labelled with ISO category. This lack of information makes it hard for customers to make informed choices when comparing prices and buying saffron. Under ISO 3632, determination of non-stigma content ("floral waste content") and other extraneous matter such as inorganic material ("ash") are also key. Grading standards are set by the International Organization for Standardization, a federation of national standards bodies. ISO 3632 deals exclusively with saffron and establishes three categories: III (poorest quality), II, and I (finest quality). Formerly there was also category IV, which was below category III. Samples are assigned categories by gauging the spice's crocin and picrocrocin content, revealed by measurements of specific spectrophotometric absorbance. Safranal is treated slightly differently and rather than there being threshold levels for each category, samples must give a reading of 20–50 for all categories. These data are measured through spectrophotometry reports at certified testing laboratories worldwide. Higher absorbances imply greater levels of crocin, picrocrocin and safranal, and thus a greater colouring potential and therefore strength per gram. The absorbance reading of crocin is known as the "colouring strength" of that saffron. Saffron's colouring strength can range from lower than 80 (for all category IV saffron) up to 200 or greater (for category I). The world's finest samples (the selected, most red-maroon, tips of stigmas picked from the finest flowers) receive colouring strengths in excess of 250, making such saffron over three times more powerful than category IV saffron. Market prices for saffron types follow directly from these ISO categories. Sargol and coupé saffron would typically fall into ISO 3632 category I. Pushal and Mancha would probably be assigned to category II. On many saffron packaging labels, neither the ISO 3632 category nor the colouring strength (the measurement of crocin content) is displayed. However, many growers, traders, and consumers reject such lab test numbers. Some people prefer a more holistic method of sampling batches of threads for taste, aroma, pliability, and other traits in a fashion similar to that practised by experienced wine tasters. Adulteration Despite attempts at quality control and standardisation, an extensive history of saffron adulteration, particularly among the cheapest grades, continues into modern times. Adulteration was first documented in Europe's Middle Ages, when those found selling adulterated saffron were executed under the Safranschou code. Typical methods include mixing in extraneous substances like beetroot, pomegranate fibres, red-dyed silk fibres, or the saffron crocus's tasteless and odourless yellow stamens. Other methods included dousing saffron fibres with viscid substances like honey or vegetable oil to increase their weight. Powdered saffron is more prone to adulteration, with turmeric, paprika, and other powders used as diluting fillers. Adulteration can also consist of selling mislabelled mixes of different saffron grades. Thus, high-grade Kashmiri saffron is often sold and mixed with cheaper Iranian imports; these mixes are then marketed as pure Kashmiri saffron. Safflower is a common substitute sometimes sold as saffron. The spice is reportedly counterfeited with horse hair, corn silk, or shredded paper. Tartrazine or sunset yellow have been used to colour counterfeit powdered saffron. In recent years, saffron adulterated with the colouring extract of gardenia fruits has been detected in the European market. This form of fraud is difficult to detect due to the presence of flavonoids and crocines in the gardenia-extracts similar to those naturally occurring in saffron. Detection methods have been developed by using HPLC and mass spectrometry to determine the presence of geniposide, a compound present in the fruits of gardenia, but not in saffron. Types The various saffron crocus cultivars give rise to thread types that are often regionally distributed and characteristically distinct. Varieties (not varieties in the botanical sense) from Spain, including the tradenames "Spanish Superior" and "Creme", are generally mellower in colour, flavour, and aroma; they are graded by government-imposed standards. Italian varieties are slightly more potent than Spanish. Greek saffron produced in the town of Krokos is PDO protected due to its particularly high-quality colour and strong flavour. Various "boutique" crops are available from New Zealand, France, Switzerland, England, the United States, and other countries—some of them organically grown. In the US, Pennsylvania Dutch saffron—known for its "earthy" notes—is marketed in small quantities. Consumers may regard certain cultivars as "premium" quality. The "Aquila" saffron, or zafferano dell'Aquila, is defined by high safranal and crocin content, distinctive thread shape, unusually pungent aroma, and intense colour; it is grown exclusively on eight hectares in the Navelli Valley of Italy's Abruzzo region, near L'Aquila. It was first introduced to Italy by a Dominican friar from inquisition-era Spain. But the biggest saffron cultivation in Italy is in San Gavino Monreale, Sardinia, where it is grown on 40 hectares, representing 60% of Italian production; it too has unusually high crocin, picrocrocin, and safranal content. Another is the "Mongra" or "Lacha" saffron of Kashmir (Crocus sativus 'Cashmirianus'), which is among the most difficult for consumers to obtain. Repeated droughts, blights, and crop failures in Kashmir combined with an Indian export ban, contribute to its prohibitive overseas prices. Kashmiri saffron is recognizable by its dark maroon-purple hue, making it among the world's darkest. In 2020, Kashmir Valley saffron was certified with a geographical indication from the Government of India. World production Almost all saffron grows in a belt from Spain in the west to India in the east. Iran is responsible for around 88% of global production. In 2018, Iran cultivated an area of producing 174 tonnes from a productivity of 4 kg/ha. Afghanistan comes second, which produced over 67 tons in 2023. Spain is the third largest producer, while the United Arab Emirates, Greece, the Indian subcontinent and Morocco are among minor producers. According to the statistics for saffron trade in 2019, Iran was ranked as the world's largest producer of saffron, supplying 430 tons of the total 450 tons of saffron produced worldwide and is expected to reach 500 tons in 2020. India, producing only 22 tons of saffron annually, ranked second. Other countries reported based on their share in global saffron production included Greece (7.2 tons), Afghanistan (6 tons), Morocco (2.6 tons), Spain (2.3 tons), Italy (1 ton), China (1 ton), and Azerbaijan (0.23 ton). Trade Saffron prices at wholesale and retail rates range from . In Western countries, the average retail price in 1974 was . In February 2013, a retail bottle containing could be purchased for $16.26 or the equivalent of , or as little as about in larger quantities. There are between . Vivid crimson colouring, slight moistness, elasticity, and lack of broken-off thread debris are all traits of fresh saffron. Uses Saffron has a long history of use in traditional medicine. Saffron has also been used as a fabric dye, particularly in China and India, and in perfumery. It is used for religious purposes in India. In the European E number categorisation for food elements and additives, Saffron is coded as E164. Consumption Saffron's aroma is often described by connoisseurs as reminiscent of metallic honey with grassy or hay-like notes, while its taste has also been noted as hay-like and sweet. Saffron also contributes a luminous yellow-orange colouring to foods. Saffron is widely used in Persian, Indian, European, and Arab cuisines. Confectioneries and liquors also often include saffron. Saffron is used in dishes ranging from the jewelled rice and khoresh of Iran, the Milanese risotto of Italy, the paella of Spain, the bouillabaisse of France, to the biryani with various meat accompaniments in South Asia. Saffron is also used in the preparation of the Golden Ham, a precious dry-cured ham made with saffron from San Gimignano. Common saffron substitutes include safflower (Carthamus tinctorius, which is often sold as "Portuguese saffron" or "açafrão"), annatto, and turmeric (Curcuma longa). In Medieval Europe, turmeric was also known as "Indian saffron" because of its yellow-orange colour. Nutrition Dried saffron is 65% carbohydrates, 6% fat, 11% protein (table) and 12% water. In one tablespoon (2 grams; a quantity much larger than is likely to be ingested in normal use) manganese is present as 29% of the Daily Value, while other micronutrients have negligible content (table). Toxicity Ingesting less than of saffron is not toxic for humans, but doses greater than can become increasingly toxic. Mild toxicity includes dizziness, nausea, vomiting, and diarrhea, whereas at higher doses there can be reduced platelet count and spontaneous bleeding. Storage Saffron will not spoil, but will lose flavour within six months if not stored in an airtight, cool and dark place. Freezer storage can maintain flavour for up to two years. Research As of 2020, saffron constituents, such as crocin, crocetin, and safranal, were under preliminary research for their potential to affect mental depression. Saffron has also been studied for its possible effect on cardiovascular risk factors, and in erectile dysfunction. History Saffron likely originated in Iran, Greece, Mesopotamia, or Kashmir. Harold McGee states that it was domesticated in or near Greece during the Bronze Age. C. sativus is probably a triploid form of Crocus cartwrightianus, which is also known as "wild saffron". Saffron crocus was slowly propagated by humans throughout much of Eurasia and was later brought to parts of North Africa, North America, and Oceania. Several wild species of Crocus similar to the commercial plant are known to have been harvested in recent times for use as saffron. Crocus ancyrensis was used to make saffron in Sivas in Central Turkey, the corms were also eaten. Crocus cartwrightianus was harvested on Andros in the islands of the Cyclades, for medicinal purposes and the stigmas for making a pigment called Zafran. Crocus longiflorus stigmas were used for saffron in Sicily. Crocus thomasii stigmas were used to flavour dishes around Taranto, South Italy. In Syria the stigmas of an unknown wild species were collected by women and children, sun-dried and pressed into small tablets which were sold in the Bazaars. Not all ancient depictions or descriptions of saffron spice or flowers are certain to be the same species as the modern commercial species used for spice. West Asia Saffron was detailed in a 7th-century BC Assyrian botanical reference compiled under Ashurbanipal. Documentation of saffron's use over the span of 3,500 years has been uncovered. Saffron-based pigments have indeed been found in 50,000-year-old depictions of prehistoric places in northwest Iran. The Sumerians later used wild-growing saffron in their remedies and magical potions. Saffron was an article of long-distance trade before the Minoan palace culture's 2nd millennium BC peak. Ancient Persians cultivated Persian saffron (Crocus sativus var. haussknechtii now called Crocus haussknechtii by botanists) in Derbent, Isfahan, and Khorasan by the 10th century BC. At such sites, saffron threads were woven into textiles, ritually offered to divinities, and used in dyes, perfumes, medicines, and body washes. Saffron threads would thus be scattered across beds and mixed into hot teas as a curative for bouts of melancholy. Non-Persians also feared the Persians' usage of saffron as a drugging agent and aphrodisiac. During his Asian campaigns, Alexander the Great used Persian saffron in his infusions, rice, and baths as a curative for battle wounds. Alexander's troops imitated the practice from the Persians and brought saffron-bathing to Greece. South Asia Conflicting theories explain saffron's arrival in South Asia. Kashmiri and Chinese accounts date its arrival anywhere between 2500 and 900 years ago. Historians studying ancient Persian records date the arrival to sometime prior to 500 BC, attributing it to a Persian transplantation of saffron corms to stock new gardens and parks. Phoenicians then marketed Kashmiri saffron as a dye and a treatment for melancholy. Its use in foods and dyes subsequently spread throughout South Asia. Buddhist monks wear saffron-coloured robes; however, the robes are not dyed with costly saffron but turmeric, a less expensive dye, or jackfruit. Monks' robes are dyed the same colour to show equality with each other, and turmeric or ochre were the cheapest, most readily available dyes. Gamboge is also used to dye the robes. East Asia Some historians believe that saffron came to China with Mongol invaders from Persia. Yet it is mentioned in ancient Chinese medical texts, including the forty-volume Shennong Bencaojing, a pharmacopoeia written around 300–200 BC. Traditionally credited to the legendary Yan Emperor and the deity Shennong, it discusses 252 plant-based medical treatments for various disorders. Nevertheless, around the 3rd century AD, the Chinese were referring to it as having a Kashmiri provenance. According to the herbalist Wan Zhen, "the habitat of saffron is in Kashmir, where people grow it principally to offer it to the Buddha". Wan also reflected on how it was used in his time: "The flower withers after a few days, and then the saffron is obtained. It is valued for its uniform yellow colour. It can be used to aromatise wine." South East Mediterranean Minoan depictions of saffron are now considered to be Crocus cartwrightianus. The Minoans portrayed saffron in their palace frescoes by 1600–1500 BC; they hint at its possible use as a therapeutic drug. Ancient Greek legends told of sea voyages to Cilicia, where adventurers sought what they believed were the world's most valuable threads. Another legend tells of Crocus and Smilax, whereby Crocus is bewitched and transformed into the first saffron crocus. Ancient perfumers in Egypt, physicians in Gaza, townspeople in Rhodes, and the Greek hetaerae courtesans used saffron in their scented waters, perfumes and potpourris, mascaras and ointments, divine offerings, and medical treatments. In late Ptolemaic Egypt, Cleopatra used saffron in her baths so that lovemaking would be more pleasurable. Egyptian healers used saffron as a treatment for all varieties of gastrointestinal ailments. Saffron was also used as a fabric dye in such Levantine cities as Sidon and Tyre in Lebanon. Aulus Cornelius Celsus prescribes saffron in medicines for wounds, cough, colic, and scabies, and in the mithridatium. Western Europe Saffron was a notable ingredient in certain Roman recipes such as jusselle and conditum. Such was the Romans' love of saffron that Roman colonists took it with them when they settled in southern Gaul, where it was extensively cultivated until Rome's fall. With this fall, European saffron cultivation plummeted. Competing theories state that saffron only returned to France with 8th-century AD Moors or with the Avignon papacy in the 14th century AD. Similarly, the spread of Islamic civilisation may have helped reintroduce the crop to Spain and Italy. The 14th-century Black Death caused demand for saffron-based medicaments to peak, and Europe imported large quantities of threads via Venetian and Genoan ships from southern and Mediterranean lands such as Rhodes. The theft of one such shipment by noblemen sparked the fourteen-week-long Saffron War. The conflict and resulting fear of rampant saffron piracy spurred corm cultivation in Basel; it thereby grew prosperous. The crop then spread to Nuremberg, where endemic and insalubrious adulteration brought on the Safranschou code—whereby culprits were variously fined, imprisoned, and executed. Meanwhile, cultivation continued in southern France, Italy, and Spain. Direct archaeological evidence of mediaeval saffron consumption in Scandinavia comes from the wreck of the royal Danish-Norwegian flagship, Gribshunden. The ship sank in 1495 while on a diplomatic mission to Sweden. Excavations in 2021 revealed concentrations of saffron threads and small "pucks" of compressed saffron powder, along with fresh ginger, cloves, and pepper. Surprisingly, the saffron retained its distinctive odour even after more than 500 years of submersion in the Baltic Sea. The Essex town of Saffron Walden, named for its new specialty crop, emerged as a prime saffron growing and trading centre in the 16th and 17th centuries but cultivation there was abandoned; saffron was re-introduced around 2013 as well as other parts of the UK (Cheshire). The Americas Europeans introduced saffron to the Americas when immigrant members of the Schwenkfelder Church left Europe with a trunk containing its corms. Church members had grown it widely in Europe. By 1730, the Pennsylvania Dutch cultivated saffron throughout eastern Pennsylvania. Spanish colonies in the Caribbean bought large amounts of this new American saffron, and high demand ensured that saffron's list price on the Philadelphia commodities exchange was equal to gold. Trade with the Caribbean later collapsed in the aftermath of the War of 1812, when many saffron-bearing merchant vessels were destroyed. Yet the Pennsylvania Dutch continued to grow lesser amounts of saffron for local trade and use in their cakes, noodles, and chicken or trout dishes. American saffron cultivation survives into modern times, mainly in Lancaster County, Pennsylvania. Gallery References Bibliography External links Saffron Food colorings Incense material Arab spices Greek cuisine Indian spices Iranian cuisine Iraqi cuisine Spices Spanish cuisine	Saffron	[ "Physics" ]	7,219	[ "Incense material", "Materials", "Matter" ]
53,351	https://en.wikipedia.org/wiki/Satellite%20constellation	A satellite constellation is a group of artificial satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global or near-global coverage, such that at any time everywhere on Earth at least one satellite is visible. Satellites are typically placed in sets of complementary orbital planes and connect to globally distributed ground stations. They may also use inter-satellite communication. Other satellite groups Satellite constellations should not be confused with: satellite clusters, which are groups of satellites moving very close together in almost identical orbits (see satellite formation flying); satellite series or satellite programs (such as Landsat), which are generations of satellites launched in succession; satellite fleets, which are groups of satellites from the same manufacturer or operator that function independently from each other (not as a system). Overview Satellites in medium Earth orbit (MEO) and low Earth orbit (LEO) are often deployed in satellite constellations, because the coverage area provided by a single satellite only covers a small area that moves as the satellite travels at the high angular velocity needed to maintain its orbit. Many MEO or LEO satellites are needed to maintain continuous coverage over an area. This contrasts with geostationary satellites, where a single satellite, at a much higher altitude and moving at the same angular velocity as the rotation of the Earth's surface, provides permanent coverage over a large area. For some applications, in particular digital connectivity, the lower altitude of MEO and LEO satellite constellations provide advantages over a geostationary satellite, with lower path losses (reducing power requirements and costs) and latency. The propagation delay for a round-trip internet protocol transmission via a geostationary satellite can be over 600ms, but as low as 125ms for a MEO satellite or 30ms for a LEO system. Examples of satellite constellations include the Global Positioning System (GPS), Galileo and GLONASS constellations for navigation and geodesy in MEO, the Iridium and Globalstar satellite telephony services and Orbcomm messaging service in LEO, the Disaster Monitoring Constellation and RapidEye for remote sensing in Sun-synchronous LEO, Russian Molniya and Tundra communications constellations in highly elliptic orbit, and satellite broadband constellations, under construction from Starlink and OneWeb in LEO, and operational from O3b in MEO. Design Walker Constellation There are a large number of constellations that may satisfy a particular mission. Usually constellations are designed so that the satellites have similar orbits, eccentricity and inclination so that any perturbations affect each satellite in approximately the same way. In this way, the geometry can be preserved without excessive station-keeping thereby reducing the fuel usage and hence increasing the life of the satellites. Another consideration is that the phasing of each satellite in an orbital plane maintains sufficient separation to avoid collisions or interference at orbit plane intersections. Circular orbits are popular, because then the satellite is at a constant altitude requiring a constant strength signal to communicate. A class of circular orbit geometries that has become popular is the Walker Delta Pattern constellation. This has an associated notation to describe it which was proposed by John Walker. His notation is: i: t/p/f where: i is the inclination; t is the total number of satellites; p is the number of equally spaced planes; and f is the relative spacing between satellites in adjacent planes. The change in true anomaly (in degrees) for equivalent satellites in neighbouring planes is equal to f × 360 / t. For example, the Galileo navigation system is a Walker Delta 56°:24/3/1 constellation. This means there are 24 satellites in 3 planes inclined at 56 degrees, spanning the 360 degrees around the equator. The "1" defines the phasing between the planes, and how they are spaced. The Walker Delta is also known as the Ballard rosette, after A. H. Ballard's similar earlier work. Ballard's notation is (t,p,m) where m is a multiple of the fractional offset between planes. Another popular constellation type is the near-polar Walker Star, which is used by Iridium. Here, the satellites are in near-polar circular orbits across approximately 180 degrees, travelling north on one side of the Earth, and south on the other. The active satellites in the full Iridium constellation form a Walker Star of 86.4°:66/6/2, i.e. the phasing repeats every two planes. Walker uses similar notation for stars and deltas, which can be confusing. These sets of circular orbits at constant altitude are sometimes referred to as orbital shells. Orbital shell In spaceflight, an orbital shell is a set of artificial satellites in circular orbits at a certain fixed altitude. In the design of satellite constellations, an orbital shell usually refers to a collection of circular orbits with the same altitude and, oftentimes, orbital inclination, distributed evenly in celestial longitude (and mean anomaly). For a sufficiently high inclination and altitude the orbital shell covers the entire orbited body. In other cases the coverage extends up to a certain maximum latitude. Several existing satellite constellations typically use a single orbital shell. New large megaconstellations have been proposed that consist of multiple orbital shells. List of satellite constellations Navigational satellite constellations Communications satellite constellations Broadcasting Sirius Satellite Radio XM Satellite Radio SES Othernet Molniya (discontinued) Monitoring Spire (AIS, ADS-B) Iridium (AIS, ADS-B, IoT) Myriota (IoT) Swarm Technologies (IoT) Astrocast (IoT) TDRSS Internet access Other Internet access systems are proposed or currently being developed: Some systems were proposed but never realized: Progress Boeing Satellite is transferring the application to OneWeb LeoSat shut down completely in 2019 The OneWeb constellation had 6 pilot satellites in February 2019, 74 satellites launched as of 21 March 2020 but filed for bankruptcy on 27 March 2020 Starlink: first mission (Starlink 0) launched on 24 May 2019; 955 satellites launched, 51 deorbited, 904 in orbit ; public beta test in limited latitude range started in November 2020 O3b mPOWER: first 2 satellites launched December 2022; 9 more in 2023–2024, with the initial service start expected in Q3 2023. Telesat LEO: two prototypes: 2018 launch CASIC Hongyun: prototype launched in December 2018 CASC Hongyan prototype launched in December 2018, might be merged with Hongyun Project Kuiper: FCC filing in July 2019. Prototypes launched in October 2023. Earth observation satellite constellations RADARSAT Constellation Planet Labs Pléiades 1A and 1B Satellogic RapidEye Disaster Monitoring Constellation A-train SPOT 6 and SPOT 7 Spire Synspective See also Satellite internet constellation Light pollution Space debris Types of geocentric orbit Orbital mechanics Notes References External links Satellite constellation simulation tools: AVM Dynamics Satellite Constellation Modeler SaVi Satellite Constellation Visualization Transfinite Visualyse Professional More information: Internetworking with satellite constellations - a PhD thesis (2001) Lloyd's satellite constellations - last updated 20 July 2011 Examination and analysis of polar low Earth orbit constellation-IEEE Satellites Satellites by type	Satellite constellation	[ "Astronomy" ]	1,467	[ "Satellites", "Outer space" ]
53,391	https://en.wikipedia.org/wiki/Befunge	Befunge is a two-dimensional stack-based, reflective, esoteric programming language. It differs from conventional languages in that programs are arranged on a two-dimensional grid. "Arrow" instructions direct the control flow to the left, right, up or down, and loops are constructed by sending the control flow in a cycle. It has been described as "a cross between Forth and Lemmings". Befunge was created by Chris Pressey in 1993 for the Amiga. The language was designed to be as hard to compile as possible, featuring self-modifying code and a multi-dimensional playfield. Despite this, several compilers have been written for the language. The original Befunge-93 specification limited programs to an 80x25 grid, and while not Turing-complete, subsequent extensions like Funge-98 expanded the concept to achieve Turing completeness. The name "Befunge" originated from a typing error in an online discussion. While it was designed to be difficult to compile, compilers such as bef2c and Betty have managed to implement the language using various techniques. Befunge programs are characterized by their use of arrows to change control flow, and they can produce outputs like random number sequences or classic "Hello, World!" messages. History The language was originally created by Chris Pressey in 1993 for the Amiga, as an attempt to devise a language which is as hard to compile as possible. Note that the p command allows for self-modifying code. Nevertheless, a number of compilers have subsequently been written. A number of extensions to the original "Befunge-93" specification also exist, most notably Funge-98, which extends the concept to an arbitrary number of dimensions and can be multithreaded, with multiple instruction pointers operating simultaneously on the same space. Befunge-extensions and variants are called Fungeoids or just Funges. The Befunge-93 specification restricts each valid program to a grid of 80 instructions horizontally by 25 instructions vertically. Program execution which exceeds these limits "wraps around" to a corresponding point on the other side of the grid; a Befunge program is in this manner topologically equivalent to a torus. Since a Befunge-93 program can only have a single stack and its storage array is bounded, the Befunge-93 language is not Turing-complete (however, it has been shown that Befunge-93 is Turing Complete with unbounded stack word size). The later Funge-98 specification provides Turing completeness by removing the size restrictions on the program; rather than wrapping around at a fixed limit, the movement of a Funge-98 instruction pointer follows a model dubbed "Lahey-space" after its originator, Chris Lahey. In this model, the grid behaves like a torus of finite size with respect to wrapping, while still allowing itself to be extended indefinitely. Etymology The word Befunge is derived from a typing error in an online discussion, where the word 'before' was intended. Compilation As stated, the design goal for Befunge was to create a language which was difficult to compile. This was attempted with the implementation of self-modifying code (the 'p' instruction can write new instructions into the playfield) and a multi-dimensional playfield (the same instruction can be executed in four different directions). Nevertheless, these obstacles have been overcome, to some degree, and Befunge compilers have been written using appropriate techniques. The bef2c compiler included with the standard Befunge-93 distribution uses threaded code: each instruction is compiled to a snippet of C code, and control flows through the snippets just as it does in a Befunge interpreter (that is, conditionally on the value of some 'direction' register). This does not result in a significant advantage over a good interpreter. Note that the bef2c compiler is not correct since it does not handle either 'p' or string mode, but it would not be impossible to make it do so (although the C language might not be well-suited for this). The etty compiler, for example, treats every possible straight line of instructions as a subprogram, and if a 'p' instruction alters that subprogram, that subprogram is recompiled. This variation on just-in-time compilation results in a much better advantage over an interpreter, since many instructions can be executed in native code without making intervening decisions on the 'direction' register. Sample Befunge-93 code The technique of using arrows to change control flow is demonstrated in the random number generator program below. The Befunge instruction pointer begins in the upper left corner and will travel to the right if not redirected. Following the arrows around, the ? instructions send the instruction pointer in random cardinal directions until the pointer hits a digit, pushing it to the stack. Then the arrows navigate to the . to output the digit from the stack and return the pointer to the first directional randomiser. There is no @ to terminate this program, so it produces an endless stream of random numbers from 1 to 9. v>>>>>v 12345 ^?^ > ? ?^ v?v 6789 >>>> v ^ .< The following code is an example of the classic "Hello World!" program. First the letters "olleH" are pushed onto the stack as ASCII numbers. These are then popped from the stack in LIFO order and output as text characters to give "Hello". A space is character number 32 in ASCII, which here is constructed by multiplying 4 and 8, before being output as text. The remaining code then outputs "World!" in a similar way, followed by ASCII character 10 (a line feed character, moving the output cursor to a new line). > v v ,,,,,"Hello"< >48, v v,,,,,,"World!"< >25,@ The following code is a slightly more complicated version. It adds the ASCII character 10 (a line feed character) to the stack, and then pushes "!dlrow ,olleH" to the stack. Again, LIFO ordering means that "H" is now the top of the stack and will be the first printed, "e" is second, and so on. To print the characters, the program enters a loop that first duplicates the top value on the stack (so now the stack would look like "\n!dlrow ,olleHH"). Then the "_" operation will pop the duplicated value, and go right if it's a zero, left otherwise. (This assumes a compliant interpreter that "returns" 0 when popping an empty stack.) When it goes left, it pops and prints the top value as an ASCII character. It then duplicates the next character and loops back to the "_" test, continuing to print the rest of the stack until it is empty and so the next value popped is 0, at which point "@" ends the program. >25*"!dlrow ,olleH":v v:,_@ > ^ Befunge-93 instruction list Most one-dimensional programming languages require some syntactic distinction between comment text and source code — although that distinction may be as trivial as Brainfuck's rule that any character not in the set +-[]<>,. is a comment. Languages like Lisp and Python treat strings as comments in contexts where the values are not used. Similarly, in Befunge, there is no comment syntax: to embed documentation in the code, the programmer simply routes the control flow around the "comment" area, so that the text in that area is never executed. See also Brainfuck Carnage Heart – PlayStation programming game using a similar language INTERCAL Whitespace Malbolge Piet References External links Befunge-93 Specification Befunge-93 Reference Implementation Funge-98 Specification Esoteric programming languages Stack-oriented programming languages Non-English-based programming languages Programming languages created in 1993	Befunge	[ "Technology" ]	1,693	[ "Non-English-based programming languages", "Natural language and computing" ]
53,436	https://en.wikipedia.org/wiki/Bayonet	A bayonet (from Old French , now spelt ) is a knife, dagger, sword, or spike-shaped melee weapon designed to be mounted on the end of the barrel of a rifle, carbine, musket or similar long firearm, allowing the gun to be used as an improvised spear in close combat. The term is derived from the town of Bayonne in southwestern France, where bayonets were supposedly first used by Basques in the 17th century. From the early 17th to the early 20th century, it was an infantry melee weapon used for both offensive and defensive tactics, usually when charging in mass formations (human wave attacks). In contemporary times, bayonets are considered a weapon of last resort, and are rarely used in combat, although they are still used for ceremonial purposes (e.g, Military parades). History The term bayonette itself dates back to the 16th century, but it is not clear whether bayonets at the time were knives that could be fitted to the ends of firearms, or simply a type of knife. For example, Cotgrave's 1611 Dictionarie describes the bayonet as "a kind of small flat pocket dagger, furnished with knives; or a great knife to hang at the girdle". Likewise, Pierre Borel wrote in 1655 that a kind of long-knife called a bayonette was made in Bayonne but does not give any further description. There are some accounts that place the invention of the bayonet in either France or Germany as early as 1570. Plug bayonets The first recorded instance of a bayonet proper is found in the Chinese military treatise, published in 1606. It was in the form of the , a breech-loading musket that was issued with a roughly long plug bayonet, giving it an overall length of with the bayonet attached. It was labelled as a "gun-blade" () with it being described as a "short sword that can be inserted into the barrel and secured by twisting it slightly" that it is to be used "when the battle have depleted both gunpowder and bullets as well as fighting against bandits, when forces are closing into melee or encountering an ambush" and if one "cannot load the gun within the time it takes to cover two bu (3.2 meters) of ground they are to attach the bayonet and hold it like a spear". Early bayonets were of the "plug" type, where the bayonet was fitted directly into the barrel of the musket. This allowed light infantry to be converted to heavy infantry and hold off cavalry charges. The bayonet had a round handle that slid directly into the musket barrel. This naturally prevented the gun from being fired. The first known mention of the use of bayonets in European warfare was in the memoirs of Jacques de Chastenet, Vicomte de Puységur. He described the French using crude plug bayonets during the Thirty Years' War (1618–1648). However, it was not until 1671 that General Jean Martinet standardized and issued plug bayonets to the French regiment of fusiliers then raised. They were issued to part of an English dragoon regiment raised in 1672, and to the Royal Fusiliers when raised in 1685. Socket bayonets The major problem with plug bayonets was that when attached they made it impossible to fire the musket, requiring soldiers to wait until the last possible moment before a melee to fix the bayonet. The defeat of forces loyal to William of Orange by Jacobite Highlanders at the Battle of Killiecrankie in 1689 was due (among other things) to the use of the plug bayonet. The Highlanders closed to , fired a single volley, dropped their muskets, and using axes and swords quickly overwhelmed the loyalists before they had time to fix bayonets. Shortly thereafter, the defeated leader, Hugh Mackay, is believed to have introduced a socket bayonet of his own invention. Soon "socket" bayonets would incorporate both socket mounts and an offset blade that fit around the musket's barrel, which allowed the musket to be fired and reloaded while the bayonet was attached. An unsuccessful trial with socket or zigzag bayonets was made after the Battle of Fleurus in 1690, in the presence of King Louis XIV, who refused to adopt them, as they had a tendency to fall off the musket. Shortly after the Peace of Ryswick (1697), the English and Germans abolished the pike and introduced socket bayonets. The British socket bayonet had a spike with a triangular cross-section rather than a flat blade, with a flat side towards the muzzle and two fluted sides outermost to a length of . It had no lock to keep it fast to the muzzle, and was well-documented for falling off in the heat of battle. By the mid-18th century, socket bayonets had been adopted by most European armies. In 1703, the French infantry adopted a spring-loaded locking system that prevented the bayonet from accidentally separating from the musket. A triangular blade was introduced around 1715 and was stronger than the previous single or double-edged model. Sword bayonets The 18th century introduced the concept of the sword bayonet, a long-bladed weapon with a single- or double-edged blade that could also be used as a shortsword. Its initial purpose was to ensure that riflemen could form an infantry square properly to fend off cavalry attacks when in ranks with musketmen, whose weapons were longer. A prime early example of a sword bayonet-fitted rifle is the Pattern 1800 Infantry Rifle, later known as the "Baker Rifle". Sword bayonets were used by German Jagers in the 18th century. The hilt usually had quillons modified to accommodate the gun barrel and a hilt mechanism that enabled the bayonet to be attached to a bayonet lug. A sword bayonet could be used in combat as a sidearm, when detached from the musket or rifle. When the bayonet was attached to the musket or rifle, it effectively turned all long guns into a spear or glaive, which made it suitable for both thrusting and cutting attacks. While the British Army eventually discarded the sword bayonet, the socket bayonet survived the introduction of the rifled musket into British service in 1854. The new rifled musket copied the French locking ring system. The new bayonet proved its worth at the Battle of Alma and the Battle of Inkerman during the Crimean War, where the Imperial Russian Army learned to fear it. In the 1860s, European nations began to develop new bolt-action breechloading rifles (such as the Chassepot and Snider–Enfield) and sword bayonets suitable for mass production and used by police, pioneer, and engineer troops. The decision to redesign the bayonet into a short sword was viewed by some as an acknowledgement of the decline in importance of the fixed bayonet as a weapon in the face of new advances in firearms technology. As a British newspaper put it, "the committee, in recommending this new sword bayonet, appear to have had in view the fact that bayonets will henceforth be less frequently used than in former times as a weapon of offence and defence; they desired, therefore, to substitute an instrument of more general utility." Multipurpose bayonets One of these multipurpose designs was the 'sawback' bayonet, which incorporated saw teeth on the spine of the blade. The sawback bayonet was intended for use as a general-purpose utility tool as well as a weapon; the teeth were meant to facilitate the cutting of wood for various defensive works such as barbed-wire posts, as well as for butchering livestock. It was initially adopted by the German states in 1865; until the middle of WWI approximately 5% of every bayonet style was complemented with a sawback version, for example in Belgium in 1868, Great Britain in 1869 and Switzerland in 1878 (Switzerland introduced their last model in 1914). The original sawback bayonets were typically of the heavy sword-type, they were issued to engineers, with to some extent the bayonet aspect being secondary to the "tool" aspect. Later German sawbacks were more of a rank indicator than a functional saw. Generally, an average of 6% of all bayonets were sawbacks for non-commissioned officers. There were some exceptions, such as the kurzes Seitengewehr 1898 model, all of which were of the sawback design and meant for what was considered more prestigious units, such as machine gunners, telegraph troop and colonial troops. The sawback proved relatively ineffective as a cutting tool, and was soon outmoded by improvements in military logistics and transportation; most nations dropped the sawback feature by the early 20th century. The German army discontinued use of the sawback bayonet in 1917 after protests that the serrated blade caused unnecessarily severe wounds when used as a fixed bayonet. The trowel or spade bayonet was another multipurpose design, intended for use both as an offensive weapon as well as a digging tool for excavating entrenchments. In 1870, the US Army issued trowel bayonets to infantry regiments based on a design by Lieutenant-Colonel Edmund Rice, a US Army officer and Civil War veteran, which were manufactured by the Springfield Armory. Besides its utility as both a fixed bayonet and a digging implement, the Rice trowel bayonet could be used to plaster log huts and stone chimneys for winter quarters; sharpened on one edge, it could cut tent poles and pins. Ten thousand were eventually issued, and the design saw service during the 1877 Nez Perce campaign. Rice was given leave in 1877 to demonstrate his trowel bayonet to several nations in Europe. One infantry officer recommended it to the exclusion of all other designs, noting that "the entrenching tools of an army rarely get up to the front until the exigency for their use has passed." The Rice trowel bayonet was declared obsolete by the US Army in December 1881. "Reach" controversy Prior to World War I, bayonet doctrine was largely founded upon the concept of "reach"; that is, a soldier's theoretical ability, by use of an extremely long rifle and fixed bayonet, to stab an enemy soldier without having to approach within reach of his opponent's blade. A combined length of rifle and bayonet longer than that of the enemy infantryman's rifle and attached bayonet, like the infantryman's pike of bygone days, was thought to impart a tactical advantage on the battlefield. In 1886, the French army introduced a quadrangular épée spike for the bayonet of the Lebel Model 1886 rifle, the Épée-Baïonnette Modèle 1886, resulting in a rifle and bayonet with an overall length of . Germany responded by introducing a long sword bayonet for the Model 1898 Mauser rifle, which had a 29-inch barrel. The bayonet, the Seitengewehr 98, had a 50 cm (19.7-inch) blade. With an overall length of , the German army's rifle/bayonet combination was second only to the French Lebel for overall 'reach'. After 1900, Switzerland, Britain, and the United States adopted rifles with barrel lengths shorter than that of a rifled musket, but longer than that of a carbine. These were intended for general use by infantry and cavalry. The "reach" of the new short rifles with attached bayonets was reduced. Britain introduced the SMLE (Short, Magazine, Lee–Enfield), in 1904. The German M1898 Mauser rifle and attached sword bayonet was 20 cm (eight inches) longer than the SMLE and its P1903 bayonet, which used a twelve-inch (30 cm) blade. While the British P1903 and its similar predecessor, the P1888, was satisfactory in service, criticism soon arose regarding the shortened reach. One military writer of the day warned: "The German soldier has eight inches the better of the argument over the British soldier when it comes to crossing bayonets, and the extra eight inches easily turns the battle in favour of the longer, if both men are of equal skill." In 1905, the German Army adopted a shortened bayonet, the Seitengewehr 98/05 for engineer and pioneer troops, and in 1908, a short rifle as well, the Karabiner Model 1898AZ, which was produced in limited quantities for the cavalry, artillery, and other specialist troops. However, the long-barreled 98 Mauser rifle remained in service as the primary infantry small arm. Moreover, German military authorities continued to promote the idea of outreaching one's opponent on the battlefield by means of a longer rifle/bayonet combination, a concept prominently featured in its infantry bayonet training doctrines. These included the throw point or extended thrust-and-lunge attack. Using this tactic, the German soldier dropped into a half-crouch, with the rifle and fixed bayonet held close to the body. In this position the soldier next propelled his rifle forward, then dropped the supporting hand while taking a step forward with the right foot, simultaneously thrusting out the right arm to full length with the extended rifle held in the grip of the right hand alone. With a maximum 'kill zone' of some eleven feet, the throw point bayonet attack gave an impressive increase in 'reach', and was later adopted by other military forces, including the U.S. Army. In response to criticism over the reduced reach of the SMLE rifle and bayonet, British ordnance authorities introduced the P1907 bayonet in 1908, which had an elongated blade of some seventeen inches to compensate for the reduced overall length of the SMLE rifle. The 1907 bayonet was essentially a copy of the Japanese Type 30 bayonet, Britain having purchased a number of Japanese type 30 rifles for the Royal Navy during the preceding years. U.S. authorities in turn adopted a long (16-in. blade) bayonet for the M1903 Springfield short rifle, the M1905 bayonet; later, a long sword bayonet was also provided for the M1917 Enfield rifle. Reversal in opinion The experience of World War I reversed opinion on the value of long rifles and bayonets in typical infantry combat operations. Whether in the close confines of trench warfare, night time raiding and patrolling, or attacking across open ground, soldiers of both sides soon recognized the inherent limitations of a long and ungainly rifle and bayonet when used as a close-quarters battle weapon. Once Allied soldiers had been trained to expect the throw point or extended thrust-and-lunge attack, the method lost most of its tactical value on the World War I battlefield. It required a strong arm and wrist, was very slow to recover if the initial thrust missed its mark, and was easily parried by a soldier who was trained to expect it, thus exposing the German soldier to a return thrust which he could not easily block or parry. Instead of longer bayonets, infantry forces on both sides began experimenting with other weapons as auxiliary close-quarter arms, including the trench knife, trench club, handgun, hand grenade, and entrenching tool. Soldiers soon began employing the bayonet as a knife as well as an attachment for the rifle, and bayonets were often shortened officially or unofficially to make them more versatile and easier to use as tools, or to maneuver in close quarters. During World War II, bayonets were further shortened into knife-sized weapons in order to give them additional utility as fighting or utility knives. The vast majority of modern bayonets introduced since World War II are of the knife bayonet type. Bayonet charge The development of the bayonet from the 17th century onwards led to the bayonet charge becoming the main infantry tactic throughout the 18th, 19th, and early 20th century. The British Army under Wolesley, the later Duke of Wellington, evolved its tactics to adopt the "Volley and Bayonet Charge" from the earlier "Highland Charge" tactic of Highland regiments under his command. These proto "fire and maneuver" tactics were first introduced to the British Army by the 42nd Highlanders (Black Watch) at Fontenoy in 1745 although, they had been used by their antecedents, (The Independent Highland Watch Companies) prior to that. As early as the 19th century, military scholars were already noting that most bayonet charges did not result in close combat. Instead, one side usually fled before actual bayonet fighting ensued. The act of fixing bayonets has been held to be primarily connected to morale, the making of a clear signal to friend and foe of a willingness to kill at close quarters. The bayonet charge was above all a tool of shock. While charges were reasonably common in 18th and 19th century warfare, actual combat between formations with their bayonets was so rare as to be effectively nonexistent. Usually, a charge would only happen after a long exchange of gunfire, and one side would break and run before contact was actually made. Sir Charles Oman, nearing the end of his history of the Peninsular War (1807–1814) in which he had closely studied hundreds of battles and combats, only discovered a single example of, in his words, "one of the rarest things in the Peninsular War, a real hand-to-hand fight with the white weapon." Infantry melees were much more common in close country – towns, villages, earthworks and other terrain which reduced visibility to such ranges that hand-to-hand fighting was unavoidable. These melees, however, were not bayonet charges per se, as they were not executed or defended against by regular bodies of orderly infantry; rather, they were a chaotic series of individual combats where musket butts and fists were used alongside bayonets, swords, and polearms. Napoleonic wars The bayonet charge was a common tactic used during the Napoleonic wars. Despite its effectiveness, a bayonet charge did not necessarily cause substantial casualties through the use of the weapon itself. Detailed battle casualty lists from the 18th century showed that in many battles, less than 2% of all wounds treated were caused by bayonets. Antoine-Henri Jomini, a celebrated military author who served in numerous armies during the Napoleonic period, stated that the majority of bayonet charges in the open resulted with one side fleeing before any contact was made. Combat with bayonets did occur, but mostly on a small scale when units of opposing sides encountered each other in a confined environment, such as during the storming of fortifications or during ambush skirmishes in broken terrain. In an age of fire by massed volley, when compared to random unseen bullets, the threat of the bayonet was much more tangible and immediate – guaranteed to lead to a personal gruesome conclusion if both sides persisted. All this encouraged men to flee before the lines met. Thus, the bayonet was an immensely useful weapon for capturing ground from the enemy, despite seldom actually being used to inflict wounds. American Civil War During the American Civil War (1861–1865) the bayonet was found to be responsible for less than 1% of battlefield casualties, a hallmark of modern warfare. The use of bayonet charges to force the enemy to retreat was very successful in numerous small unit engagements at short range in the American Civil War, as most troops would retreat when charged while reloading. Although such charges inflicted few casualties, they often decided short engagements, and tactical possession of important defensive ground features. Additionally, bayonet drill could be used to rally men temporarily unnerved by enemy fire. While the overall Battle of Gettysburg was won by the Union armies due to a combination of terrain and massed artillery fire, a decisive point on the second day of the battle hinged on a bayonet charge at Little Round Top when Joshua Lawrence Chamberlain's 20th Maine Volunteer Infantry Regiment, running short of musket ammunition, charged downhill, surprising and capturing many of the surviving soldiers of the 15th Alabama Infantry Regiment and other Confederate regiments. Other bayonet charges occurred at Gettysburg, such as that of the 1st Minnesota Infantry Regiment. This was ordered in desperation by General Hancock earlier on July 2 in order to delay a Confederate brigade's advance long enough to bring up reinforcements for the holed Union line on Cemetery Ridge. Still another bayonet charge was conducted late in the evening on July 2 by the 137th New York Infantry Regiment defending the extreme right flank of the Union line on Culp's Hill. The charge of several companies managed to temporarily stall the advance of the 10th Virginia Infantry Regiment long enough for the 14th Brooklyn to move in on the 137th's right and repel the attack. Going over the top The popular image of World War I combat is of a wave of soldiers with bayonets fixed, "going over the top" and charging across no man's land into a hail of enemy fire. Although this was the standard method of fighting early in the war, it was rarely successful. British casualties on the first day of the Battle of the Somme were the worst in the history of the British army, with casualties, whom were killed. During World War I, no man's land was often hundreds of yards across. The area was usually devastated by the warfare and riddled with craters from artillery and mortar shells, and sometimes contaminated by chemical weapons. Heavily defended by machine guns, mortars, artillery, and riflemen on both sides, it was often covered with barbed wire and land mines, and littered with the rotting corpses of those who were not able to make it across the sea of projectiles, explosions, and flames. A bayonet charge through no man's land often resulted in the total annihilation of entire battalions. Banzai charges The advent of modern warfare in the 20th century made bayonet charges dubious affairs. During the Siege of Port Arthur (1904–1905), the Japanese used human wave attacks against Russian artillery and machine guns, suffering massive casualties. However, during the Second Sino-Japanese War, the Japanese were able to use bayonet charges effectively against poorly organized and lightly armed Chinese troops. "Banzai charges" became an accepted military tactic where Japanese forces were able to rout larger Chinese forces routinely. In the early stages of the Pacific War (1941–1945), a sudden bayonet charge could overwhelm unprepared enemy soldiers. Such charges became known to Allied forces as "Banzai charges" from the Japanese battle cry. By the end of the war, against well organized and heavily armed Allied forces, a banzai charge inflicted little damage but at high cost. They were sometimes conducted as a last resort by small groups of surviving soldiers when the main battle was already lost. Some Japanese commanders, such as General Tadamichi Kuribayashi, recognized the futility and waste of such attacks and expressly forbade their men from carrying them out. Indeed, the Americans were surprised that the Japanese did not employ banzai charges at the Battle of Iwo Jima. Human wave attack The term "human wave attack" was often misused to describe the Chinese short attack—a combination of infiltration and the shock tactics employed by the People's Liberation Army during the Korean War (1950–1953). A typical Chinese short attack was carried out at night by sending a series of small five-man fireteams to attack the weakest point of an enemy's defenses. The Chinese assault team would crawl undetected within grenade range, then launch surprise attacks with fixed bayonets against the defenders in order to breach the defenses by relying on maximum shock and confusion. If the initial shock failed to breach the defenses, additional fireteams would press on behind them and attack the same point until a breach was created. Once penetration was achieved, the bulk of the Chinese forces would move into the enemy rear and attack from behind. Due to primitive communication systems and tight political controls within the Chinese army, short attacks were often repeated until either the defenses were penetrated or the attackers were completely annihilated. This persistent attack pattern left a strong impression on UN forces that fought in Korea, giving birth to the description of "human wave". The term "human wave" was later used by journalists and military officials to convey the image of the American soldiers being assaulted by overwhelming numbers of Chinese on a broad front, which is inaccurate when compared with the normal Chinese practice of sending successive series of small teams against a weak point in the line. It was in fact rare for the Chinese to actually use densely concentrated infantry formations to absorb enemy firepower. Modern usage One use the Germans in World War II made of bayonets was to search for people in hiding. One person hiding in a house in the Netherlands wrote: "The Germans made lots of noise as they came upstairs, and they stabbed their bayonets into the wall. Then what we'd always feared actually happened: A bayonet went through the thin wallpaper above the closet, exposing the three people who were hiding there. 'Raus!' cried the Germans. 'Out!'". During the Korean War, the French Battalion and Turkish Brigade used bayonet charges against enemy combatants. In 1951, United States Army officer Lewis L. Millett led soldiers of the US Army's 27th Infantry Regiment in capturing a machine gun position with bayonets. Historian S. L. A. Marshall described the attack as "the most complete bayonet charge by American troops since Cold Harbor". The location subsequently became known as Bayonet Hill. This was the last bayonet charge by the US Army. Millett was awarded the Medal of Honor. On 23 October 1962, during the Sino-Indian War, 20 Indian soldiers led by Joginder Singh fixed bayonets and charged a force of 200 Chinese soldiers. While the charge would prove futile for Singh and his men, it initially threw the Chinese off guard and forced a retreat despite outnumbering them 10 to 1. On 8 May 1970, National Guardsmen attacked student demonstrators with bayonets at the University of New Mexico in Albuquerque. The demonstrators were protesting the war in Vietnam and Cambodia, and the killing of four students at Kent State University. Eleven were injured, some seriously. In 1982, the British Army mounted bayonet charges during the Falklands War, notably the 3rd Battalion, Parachute Regiment during the Battle of Mount Longdon and the 2nd Battalion, Scots Guards during the final assault of Mount Tumbledown. In 1995, during the Siege of Sarajevo, UN peacekeepers of the French 3rd Marine Infantry Regiment charged Serbian forces at the Battle of Vrbanja bridge. Actions led by the regiment allowed the UN peacekeepers to retreat from a threatened position. Two fatalities and seventeen wounded resulted. During the Second Gulf War and the war in Afghanistan, British Army units mounted several bayonet charges. In 2004, at the Battle of Danny Boy in Iraq, the Argyll and Sutherland Highlanders charged mortar positions of the Mahdi Army. The ensuing hand-to-hand fighting resulted in an estimate of over 40 insurgents killed and 35 bodies collected and nine prisoners. Sergeant Brian Wood, of the Princess of Wales's Royal Regiment, was awarded the Military Cross for his part in the battle. In 2009, Lieutenant James Adamson of the Royal Regiment of Scotland was awarded the Military Cross for a bayonet charge while in Afghanistan. Adamson had run out of ammunition so he immediately charged a Taliban fighter with his bayonet. Lance Corporal Sean Jones of The Princess of Wales's Regiment was awarded the Military Cross for his role in a 2011 bayonet charge. Contemporary bayonets Today, the bayonet is rarely used in one-to-one combat. Despite its limitations, many modern assault rifles (including bullpup designs) retain a bayonet lug and the bayonet is issued by many armies. The bayonet is used for controlling prisoners, or as a weapon of last resort. In addition, some authorities have concluded that the bayonet serves as a useful training aid in building morale and increasing desired aggressiveness in troops. Today's bayonets often double as multi-purpose utility knives, bottle openers or other tools. Issuing one modern multi-purpose bayonet/knife is also more cost effective than issuing separate specialty bayonets, and field/combat knives. Soviet Union The original AK-47 has an adequate but unremarkable bayonet. However, the AKM Type I bayonet (introduced in 1959) was an improvement of the original design. It has a Bowie style (clip-point) blade with saw-teeth along the spine, and can be used as a multi-purpose survival knife and wire-cutter when combined with its steel scabbard. The AK-74 bayonet 6Kh5 (introduced in 1983) represents a further refinement of the AKM bayonet. "It introduced a radical blade cross-section, that has a flat milled on one side near the edge and a corresponding flat milled on the opposite side near the false edge." The blade has a new spear point and an improved one-piece moulded plastic grip, making it a more effective fighting knife. It also has saw-teeth on the false edge and the usual hole for use as a wire-cutter. The wire cutting versions of the AK bayonets each have an electrically insulated handle and an electrically insulated part of the scabbard, so it can be used to cut an electrified wire. United States The American M16 rifle used the M7 bayonet which is based on earlier designs such as the M4, M5 and M6 models, all of which are direct descendants of the M3 Fighting Knife and have a spear-point blade with a half sharpened secondary edge. The newer M9 has a clip-point blade with saw-teeth along the spine, and can be used as a multi-purpose knife and wire-cutter when combined with its scabbard. It can even be used by troops to cut their way free through the relatively thin metal skin of a crashed helicopter or airplane. The current USMC OKC-3S bayonet bears a resemblance to the Marines' iconic Ka-Bar fighting knife with serrations near the handle. People's Republic of China The AK-47 was adopted by Communist China as the Type 56 assault rifle and includes an integral folding spike bayonet, similar to the SKS rifle. Some Type 56s may also use the AKM Type II bayonet. The latest Chinese rifle, the QBZ-95, has a multi-purpose knife bayonet similar to the US M9. Belgium The FN FAL has two types of bayonet. The first is a traditional spear point bayonet. The second is the Type C socket bayonet introduced in the 1960s. It has a hollow handle that fits over the muzzle and slots that lined up with those on the FALs 22 mm NATO-spec flash hider. Its spear-type blade is offset to the side of the handle to allow the bullet to pass beside the blade. United Kingdom The current British L3A1 socket bayonet is based on the FN FAL Type C socket bayonet with a clip-point blade. It has a hollow handle that fits over the SA80/L85 rifle's muzzle and slots that lined up with those on the flash eliminator. The blade is offset to the side of the handle to allow the bullet to pass beside the blade. It can also be used as a multi-purpose knife and wire-cutter when combined with its scabbard. The scabbard also has a sharpening stone and folding saw blade. The use of contemporary bayonets by the British army was noted during the Afghanistan war in 2004. Traditionally, bayonets are instead called swords in The Rifles. Germany The H&K G3 rifle uses two types of bayonets, both of which is mounted above the G3's rifle barrel. The first is the standard G3 bayonet which has a blade similar to the American M7 bayonet. The second is an Eickhorn KCB-70 type multi-purpose knife bayonet, featuring a clip-point with saw-back, a wire-cutter scabbard and a distinctive squared handgrip. For the H&K G36 there was little use of modified AKM type II knife bayonets from stocks of the former Nationale Volksarmee (National People's Army) of East Germany. The original muzzle-ring was cut away and a new, large diameter muzzle ring welded in place. The original leather belt hanger was replaced by a complex web and plastic belt hanger designed to fit the West German load bearing equipment. Austria The Steyr AUG uses two types of bayonet. The first and most common is an Eickhorn KCB-70 type multi-purpose bayonet with an M16 bayonet type interface. The second are the Glock Feldmesser 78 (Field Knife 78) and the Feldmesser 81 (Survival Knife 81), which can also be used as a bayonet, by engaging a socket in the pommel (covered by a plastic cap) into a bayonet adapter that can be fitted to the AUG rifle. These bayonets are noteworthy, as they were meant to be used primarily as field or survival knives and use as a bayonet was a secondary consideration. They can also be used as throwing knives and have a built-in bottle opener in the crossguard. France The French use a more traditional spear point bayonet with the current FAMAS bayonet which is nearly identical to that of the M1949/56 bayonet. The new French H&K 416F rifle uses the Eickhorn "SG 2000 WC-F", a multi-purpose combat knife/bayonet (similar to the KM2000) with a wire cutter. It weighs , is long with a half serrated blade for cutting through ropes. The synthetic handle and sheath have electrical insulation that protects up to 10,000 volts. The sheath also has a diamond blade sharpener. Photo gallery Linguistic impact The push-twist motion of fastening the older type of spike bayonet has given a name to: The "bayonet mount" used for various types of quick fastenings, such as camera lenses, also called a "bayonet connector" when used in electrical plugs. Several connectors and contacts including the bayonet-fitting light bulb that is common in the UK (as opposed to the continental European screw-fitting type). One type of connector for foil and sabre weapons used in modern fencing competitions is referred to as a "bayonet" connector. In chess, an aggressive variation of the King's Indian Defence is known as the "Bayonet Attack". The bayonet has become a symbol of military power. The term "at the point of a bayonet" refers to using military force or action to accomplish, maintain, or defend something (cf. Bayonet Constitution). Undertaking a task "with fixed bayonets" has this connotation of no room for compromise and is a phrase used particularly in politics. Badges and insignias The Australian Army 'Rising Sun' badge features a semicircle of bayonets. The Australian Army Infantry Combat Badge (ICB) takes the form of a vertically mounted Australian Army SLR (7.62mm self-loading rifle FN FAL) bayonet surrounded by an oval-shaped laurel wreath. The US Army Combat Action Badge, awarded to personnel who have come under fire since 2001 and who are not eligible for the Combat Infantryman Badge (due to the fact that only Infantry personnel may be awarded the Combat Infantryman Badge), has a bayonet as its central motif. The shoulder sleeve insignia for the 10th Mountain Division in the US Army features crossed bayonets. The US Army's 173rd Airborne Brigade Combat Team's shoulder patch features a bayonet wrapped in a wing, symbolizing their airborne status. The brigade regularly deploys in task forces under the name "Bayonet". The insignia of the British Army's School of Infantry is an SA80 bayonet against a red shield. It is worn as a Tactical recognition flash (TRF) by instructors at the Infantry Training Centre Catterick, the Infantry Battle School at Brecon and the Support Weapons School in Warminster. Fixed bayonets also feature on the cap badge and tactical recognition flash of the Small Arms School Corps. The vocation tab collar insignia for the Singapore Armed Forces Infantry Formation utilizes two crossed bayonets. The bayonet is often used as a symbol of the Infantry in Singapore. See also 1887 Constitution of the Hawaiian Kingdom, known as the Bayonet Constitution Aiki-jō wooden staff used in the Japanese martial art of Aikido, which in use resembles a bayonet more than a spear. Bayonet lug Combatives Jūkendō Spike bayonet Use of bayonets for crowd control Wilfred Owen mentions bayonets in the poem Soldier's Dream References Bibliography Further reading Hunting Weapons, Howard L Blackmore, 2000, Dover Publications External links World Bayonets Infantry Tactics During the Napoleonic Wars – Bayonet Fights, Bayonet Charges Edged and bladed weapons Firearm components French inventions	Bayonet	[ "Technology" ]	7,793	[ "Firearm components", "Components" ]
53,452	https://en.wikipedia.org/wiki/Euler%27s%20totient%20function	In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as or , and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor is equal to 1. The integers of this form are sometimes referred to as totatives of . For example, the totatives of are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since and . Therefore, . As another example, since for the only integer in the range from 1 to is 1 itself, and . Euler's totient function is a multiplicative function, meaning that if two numbers and are relatively prime, then . This function gives the order of the multiplicative group of integers modulo (the group of units of the ring ). It is also used for defining the RSA encryption system. History, terminology, and notation Leonhard Euler introduced the function in 1763. However, he did not at that time choose any specific symbol to denote it. In a 1784 publication, Euler studied the function further, choosing the Greek letter to denote it: he wrote for "the multitude of numbers less than , and which have no common divisor with it". This definition varies from the current definition for the totient function at but is otherwise the same. The now-standard notation comes from Gauss's 1801 treatise Disquisitiones Arithmeticae, although Gauss did not use parentheses around the argument and wrote . Thus, it is often called Euler's phi function or simply the phi function. In 1879, J. J. Sylvester coined the term totient for this function, so it is also referred to as Euler's totient function, the Euler totient, or Euler's totient. Jordan's totient is a generalization of Euler's. The cototient of is defined as . It counts the number of positive integers less than or equal to that have at least one prime factor in common with . Computing Euler's totient function There are several formulae for computing . Euler's product formula It states where the product is over the distinct prime numbers dividing . (For notation, see Arithmetical function.) An equivalent formulation is where is the prime factorization of (that is, are distinct prime numbers). The proof of these formulae depends on two important facts. Phi is a multiplicative function This means that if , then . Proof outline: Let , , be the sets of positive integers which are coprime to and less than , , , respectively, so that , etc. Then there is a bijection between and by the Chinese remainder theorem. Value of phi for a prime power argument If is prime and , then Proof: Since is a prime number, the only possible values of are , and the only way to have is if is a multiple of , that is, , and there are such multiples not greater than . Therefore, the other numbers are all relatively prime to . Proof of Euler's product formula The fundamental theorem of arithmetic states that if there is a unique expression where are prime numbers and each . (The case corresponds to the empty product.) Repeatedly using the multiplicative property of and the formula for gives This gives both versions of Euler's product formula. An alternative proof that does not require the multiplicative property instead uses the inclusion-exclusion principle applied to the set , excluding the sets of integers divisible by the prime divisors. Example In words: the distinct prime factors of 20 are 2 and 5; half of the twenty integers from 1 to 20 are divisible by 2, leaving ten; a fifth of those are divisible by 5, leaving eight numbers coprime to 20; these are: 1, 3, 7, 9, 11, 13, 17, 19. The alternative formula uses only integers: Fourier transform The totient is the discrete Fourier transform of the gcd, evaluated at 1. Let where for . Then The real part of this formula is For example, using and :Unlike the Euler product and the divisor sum formula, this one does not require knowing the factors of . However, it does involve the calculation of the greatest common divisor of and every positive integer less than , which suffices to provide the factorization anyway. Divisor sum The property established by Gauss, that where the sum is over all positive divisors of , can be proven in several ways. (See Arithmetical function for notational conventions.) One proof is to note that is also equal to the number of possible generators of the cyclic group ; specifically, if with , then is a generator for every coprime to . Since every element of generates a cyclic subgroup, and each subgroup is generated by precisely elements of , the formula follows. Equivalently, the formula can be derived by the same argument applied to the multiplicative group of the th roots of unity and the primitive th roots of unity. The formula can also be derived from elementary arithmetic. For example, let and consider the positive fractions up to 1 with denominator 20: Put them into lowest terms: These twenty fractions are all the positive ≤ 1 whose denominators are the divisors . The fractions with 20 as denominator are those with numerators relatively prime to 20, namely , , , , , , , ; by definition this is fractions. Similarly, there are fractions with denominator 10, and fractions with denominator 5, etc. Thus the set of twenty fractions is split into subsets of size for each dividing 20. A similar argument applies for any n. Möbius inversion applied to the divisor sum formula gives where is the Möbius function, the multiplicative function defined by and for each prime and . This formula may also be derived from the product formula by multiplying out to get An example: Some values The first 100 values are shown in the table and graph below: {\| class="wikitable" style="text-align: right" \|+ for ! + ! 1 \|\| 2 \|\| 3 \|\| 4 \|\| 5 \|\| 6 \|\| 7 \|\| 8 \|\| 9 \|\| 10 \|- ! 0 \| 1 \|\| 1 \|\| 2 \|\| 2 \|\| 4 \|\| 2 \|\| 6 \|\| 4 \|\| 6 \|\| 4 \|- ! 10 \| 10 \|\| 4 \|\| 12 \|\| 6 \|\| 8 \|\| 8 \|\| 16 \|\| 6 \|\| 18 \|\| 8 \|- ! 20 \| 12 \|\| 10 \|\| 22 \|\| 8 \|\| 20 \|\| 12 \|\| 18 \|\| 12 \|\| 28 \|\| 8 \|- ! 30 \| 30 \|\| 16 \|\| 20 \|\| 16 \|\| 24 \|\| 12 \|\| 36 \|\| 18 \|\| 24 \|\| 16 \|- ! 40 \| 40 \|\| 12 \|\| 42 \|\| 20 \|\| 24 \|\| 22 \|\| 46 \|\| 16 \|\| 42 \|\| 20 \|- ! 50 \| 32 \|\| 24 \|\| 52 \|\| 18 \|\| 40 \|\| 24 \|\| 36 \|\| 28 \|\| 58 \|\| 16 \|- ! 60 \| 60 \|\| 30 \|\| 36 \|\| 32 \|\| 48 \|\| 20 \|\| 66 \|\| 32 \|\| 44 \|\| 24 \|- ! 70 \| 70 \|\| 24 \|\| 72 \|\| 36 \|\| 40 \|\| 36 \|\| 60 \|\| 24 \|\| 78 \|\| 32 \|- ! 80 \| 54 \|\| 40 \|\| 82 \|\| 24 \|\| 64 \|\| 42 \|\| 56 \|\| 40 \|\| 88 \|\| 24 \|- ! 90 \| 72 \|\| 44 \|\| 60 \|\| 46 \|\| 72 \|\| 32 \|\| 96 \|\| 42 \|\| 60 \|\| 40 \|} In the graph at right the top line is an upper bound valid for all other than one, and attained if and only if is a prime number. A simple lower bound is , which is rather loose: in fact, the lower limit of the graph is proportional to . Euler's theorem This states that if and are relatively prime then The special case where is prime is known as Fermat's little theorem. This follows from Lagrange's theorem and the fact that is the order of the multiplicative group of integers modulo . The RSA cryptosystem is based on this theorem: it implies that the inverse of the function , where is the (public) encryption exponent, is the function , where , the (private) decryption exponent, is the multiplicative inverse of modulo . The difficulty of computing without knowing the factorization of is thus the difficulty of computing : this is known as the RSA problem which can be solved by factoring . The owner of the private key knows the factorization, since an RSA private key is constructed by choosing as the product of two (randomly chosen) large primes and . Only is publicly disclosed, and given the difficulty to factor large numbers we have the guarantee that no one else knows the factorization. Other formulae In particular: Compare this to the formula (see least common multiple). is even for . Moreover, if has distinct odd prime factors, For any and such that there exists an such that . where is the radical of (the product of all distinct primes dividing ). ( cited in) [Liu (2016)] (where is the Euler–Mascheroni constant). Menon's identity In 1965 P. Kesava Menon proved where is the number of divisors of . Divisibility by any fixed positive integer The following property, which is part of the « folklore » (i.e., apparently unpublished as a specific result: see the introduction of this article in which it is stated as having « long been known ») has important consequences. For instance it rules out uniform distribution of the values of in the arithmetic progressions modulo for any integer . For every fixed positive integer , the relation holds for almost all , meaning for all but values of as . This is an elementary consequence of the fact that the sum of the reciprocals of the primes congruent to 1 modulo diverges, which itself is a corollary of the proof of Dirichlet's theorem on arithmetic progressions. Generating functions The Dirichlet series for may be written in terms of the Riemann zeta function as: where the left-hand side converges for . The Lambert series generating function is which converges for . Both of these are proved by elementary series manipulations and the formulae for . Growth rate In the words of Hardy & Wright, the order of is "always 'nearly '." First but as n goes to infinity, for all These two formulae can be proved by using little more than the formulae for and the divisor sum function . In fact, during the proof of the second formula, the inequality true for , is proved. We also have Here is Euler's constant, , so and . Proving this does not quite require the prime number theorem. Since goes to infinity, this formula shows that In fact, more is true. and The second inequality was shown by Jean-Louis Nicolas. Ribenboim says "The method of proof is interesting, in that the inequality is shown first under the assumption that the Riemann hypothesis is true, secondly under the contrary assumption." For the average order, we have due to Arnold Walfisz, its proof exploiting estimates on exponential sums due to I. M. Vinogradov and N. M. Korobov. By a combination of van der Corput's and Vinogradov's methods, H.-Q. Liu (On Euler's function.Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 4, 769–775) improved the error term to (this is currently the best known estimate of this type). The "Big " stands for a quantity that is bounded by a constant times the function of inside the parentheses (which is small compared to ). This result can be used to prove that the probability of two randomly chosen numbers being relatively prime is . Ratio of consecutive values In 1950 Somayajulu proved In 1954 Schinzel and Sierpiński strengthened this, proving that the set is dense in the positive real numbers. They also proved that the set is dense in the interval (0,1). Totient numbers A totient number is a value of Euler's totient function: that is, an for which there is at least one for which . The valency or multiplicity of a totient number is the number of solutions to this equation. A nontotient is a natural number which is not a totient number. Every odd integer exceeding 1 is trivially a nontotient. There are also infinitely many even nontotients, and indeed every positive integer has a multiple which is an even nontotient. The number of totient numbers up to a given limit is for a constant . If counted accordingly to multiplicity, the number of totient numbers up to a given limit is where the error term is of order at most for any positive . It is known that the multiplicity of exceeds infinitely often for any . Ford's theorem proved that for every integer there is a totient number of multiplicity : that is, for which the equation has exactly solutions; this result had previously been conjectured by Wacław Sierpiński, and it had been obtained as a consequence of Schinzel's hypothesis H. Indeed, each multiplicity that occurs, does so infinitely often. However, no number is known with multiplicity . Carmichael's totient function conjecture is the statement that there is no such . Perfect totient numbers A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number. Applications Cyclotomy In the last section of the Disquisitiones Gauss proves that a regular -gon can be constructed with straightedge and compass if is a power of 2. If is a power of an odd prime number the formula for the totient says its totient can be a power of two only if is a first power and is a power of 2. The primes that are one more than a power of 2 are called Fermat primes, and only five are known: 3, 5, 17, 257, and 65537. Fermat and Gauss knew of these. Nobody has been able to prove whether there are any more. Thus, a regular -gon has a straightedge-and-compass construction if n is a product of distinct Fermat primes and any power of 2. The first few such are 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40,... . Prime number theorem for arithmetic progressions The RSA cryptosystem Setting up an RSA system involves choosing large prime numbers and , computing and , and finding two numbers and such that . The numbers and (the "encryption key") are released to the public, and (the "decryption key") is kept private. A message, represented by an integer , where , is encrypted by computing . It is decrypted by computing . Euler's Theorem can be used to show that if , then . The security of an RSA system would be compromised if the number could be efficiently factored or if could be efficiently computed without factoring . Unsolved problems Lehmer's conjecture If is prime, then . In 1932 D. H. Lehmer asked if there are any composite numbers such that divides . None are known. In 1933 he proved that if any such exists, it must be odd, square-free, and divisible by at least seven primes (i.e. ). In 1980 Cohen and Hagis proved that and that . Further, Hagis showed that if 3 divides then and . Carmichael's conjecture This states that there is no number with the property that for all other numbers , , . See Ford's theorem above. As stated in the main article, if there is a single counterexample to this conjecture, there must be infinitely many counterexamples, and the smallest one has at least ten billion digits in base 10. Riemann hypothesis The Riemann hypothesis is true if and only if the inequality is true for all where is Euler's constant and is the product of the first primes. See also Carmichael function (λ) Dedekind psi function (𝜓) Divisor function (σ) Duffin–Schaeffer conjecture Generalizations of Fermat's little theorem Highly composite number Multiplicative group of integers modulo Ramanujan sum Totient summatory function (𝛷) Notes References The Disquisitiones Arithmeticae has been translated from Latin into English and German. The German edition includes all of Gauss's papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes. References to the Disquisitiones are of the form Gauss, DA, art. nnn. . See paragraph 24.3.2. Dickson, Leonard Eugene, "History Of The Theory Of Numbers", vol 1, chapter 5 "Euler's Function, Generalizations; Farey Series", Chelsea Publishing 1952 . . . External links Euler's Phi Function and the Chinese Remainder Theorem — proof that is multiplicative Euler's totient function calculator in JavaScript — up to 20 digits Dineva, Rosica, The Euler Totient, the Möbius, and the Divisor Functions Plytage, Loomis, Polhill Summing Up The Euler Phi Function Modular arithmetic Multiplicative functions Articles containing proofs Algebra Number theory Leonhard Euler	Euler's totient function	[ "Mathematics" ]	3,898	[ "Discrete mathematics", "Algebra", "Multiplicative functions", "Arithmetic", "Articles containing proofs", "Modular arithmetic", "Number theory" ]
53,453	https://en.wikipedia.org/wiki/Fermat%27s%20little%20theorem	In number theory, Fermat's little theorem states that if is a prime number, then for any integer , the number is an integer multiple of . In the notation of modular arithmetic, this is expressed as For example, if and , then , and is an integer multiple of . If is not divisible by , that is, if is coprime to , then Fermat's little theorem is equivalent to the statement that is an integer multiple of , or in symbols: For example, if and , then , and is a multiple of . Fermat's little theorem is the basis for the Fermat primality test and is one of the fundamental results of elementary number theory. The theorem is named after Pierre de Fermat, who stated it in 1640. It is called the "little theorem" to distinguish it from Fermat's Last Theorem. History Pierre de Fermat first stated the theorem in a letter dated October 18, 1640, to his friend and confidant Frénicle de Bessy. His formulation is equivalent to the following: If is a prime and is any integer not divisible by , then is divisible by . Fermat's original statement was This may be translated, with explanations and formulas added in brackets for easier understanding, as: Every prime number [] divides necessarily one of the powers minus one of any [geometric] progression [] [that is, there exists such that divides ], and the exponent of this power [] divides the given prime minus one [divides ]. After one has found the first power [] that satisfies the question, all those whose exponents are multiples of the exponent of the first one satisfy similarly the question [that is, all multiples of the first have the same property]. Fermat did not consider the case where is a multiple of nor prove his assertion, only stating: (And this proposition is generally true for all series [sic] and for all prime numbers; I would send you a demonstration of it, if I did not fear going on for too long.) Euler provided the first published proof in 1736, in a paper titled "Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio" (in English: "Demonstration of Certain Theorems Concerning Prime Numbers") in the Proceedings of the St. Petersburg Academy, but Leibniz had given virtually the same proof in an unpublished manuscript from sometime before 1683. The term "Fermat's little theorem" was probably first used in print in 1913 in Zahlentheorie by Kurt Hensel: (There is a fundamental theorem holding in every finite group, usually called Fermat's little theorem because Fermat was the first to have proved a very special part of it.) An early use in English occurs in A.A. Albert's Modern Higher Algebra (1937), which refers to "the so-called 'little' Fermat theorem" on page 206. Further history Some mathematicians independently made the related hypothesis (sometimes incorrectly called the Chinese hypothesis) that if and only if is prime. Indeed, the "if" part is true, and it is a special case of Fermat's little theorem. However, the "only if" part is false: For example, , but 341 = 11 × 31 is a pseudoprime to base 2. See below. Proofs Several proofs of Fermat's little theorem are known. It is frequently proved as a corollary of Euler's theorem. Generalizations Euler's theorem is a generalization of Fermat's little theorem: For any modulus and any integer coprime to , one has where denotes Euler's totient function (which counts the integers from 1 to that are coprime to ). Fermat's little theorem is indeed a special case, because if is a prime number, then . A corollary of Euler's theorem is: For every positive integer , if the integer is coprime with , then for any integers and . This follows from Euler's theorem, since, if , then for some integer , and one has If is prime, this is also a corollary of Fermat's little theorem. This is widely used in modular arithmetic, because this allows reducing modular exponentiation with large exponents to exponents smaller than . Euler's theorem is used with not prime in public-key cryptography, specifically in the RSA cryptosystem, typically in the following way: if retrieving from the values of , and is easy if one knows . In fact, the extended Euclidean algorithm allows computing the modular inverse of modulo , that is, the integer such that It follows that On the other hand, if is the product of two distinct prime numbers, then . In this case, finding from and is as difficult as computing (this has not been proven, but no algorithm is known for computing without knowing ). Knowing only , the computation of has essentially the same difficulty as the factorization of , since , and conversely, the factors and are the (integer) solutions of the equation . The basic idea of RSA cryptosystem is thus: If a message is encrypted as , using public values of and , then, with the current knowledge, it cannot be decrypted without finding the (secret) factors and of . Fermat's little theorem is also related to the Carmichael function and Carmichael's theorem, as well as to Lagrange's theorem in group theory. Converse The converse of Fermat's little theorem fails for Carmichael numbers. However, a slightly weaker variant of the converse is Lehmer's theorem: If there exists an integer such that and for all primes dividing one has then is prime. This theorem forms the basis for the Lucas primality test, an important primality test, and Pratt's primality certificate. Pseudoprimes If and are coprime numbers such that is divisible by , then need not be prime. If it is not, then is called a (Fermat) pseudoprime to base . The first pseudoprime to base 2 was found in 1820 by Pierre Frédéric Sarrus: 341 = 11 × 31. A number that is a Fermat pseudoprime to base for every number coprime to is called a Carmichael number. Alternately, any number satisfying the equality is either a prime or a Carmichael number. Miller–Rabin primality test The Miller–Rabin primality test uses the following extension of Fermat's little theorem: If is an odd prime and with and odd > 0, then for every coprime to , either or there exists such that and . This result may be deduced from Fermat's little theorem by the fact that, if is an odd prime, then the integers modulo form a finite field, in which 1 modulo has exactly two square roots, 1 and −1 modulo . Note that holds trivially for , because the congruence relation is compatible with exponentiation. And holds trivially for since is odd, for the same reason. That is why one usually chooses a random in the interval . The Miller–Rabin test uses this property in the following way: given an odd integer for which primality has to be tested, write with and odd > 0, and choose a random such that ; then compute ; if is not 1 nor −1, then square it repeatedly modulo until you get −1 or have squared times. If and −1 has not been obtained by squaring, then is a composite and is a witness for the compositeness of . Otherwise, is a strong probable prime to base a; that is, it may be prime or not. If is composite, the probability that the test declares it a strong probable prime anyway is at most , in which case is a strong pseudoprime, and is a strong liar. Therefore after non-conclusive random tests, the probability that is composite is at most 4−k, and may thus be made as low as desired by increasing . In summary, the test either proves that a number is composite or asserts that it is prime with a probability of error that may be chosen as low as desired. The test is very simple to implement and computationally more efficient than all known deterministic tests. Therefore, it is generally used before starting a proof of primality. See also Fermat quotient Frobenius endomorphism -derivation Fractions with prime denominators: numbers with behavior relating to Fermat's little theorem RSA Table of congruences Modular multiplicative inverse Notes References Further reading Paulo Ribenboim (1995). The New Book of Prime Number Records (3rd ed.). New York: Springer-Verlag. . pp. 22–25, 49. External links János Bolyai and the pseudoprimes (in Hungarian) Fermat's Little Theorem at cut-the-knot Euler Function and Theorem at cut-the-knot Fermat's Little Theorem and Sophie's Proof Modular arithmetic Theorems about prime numbers	Fermat's little theorem	[ "Mathematics" ]	1,917	[ "Theorems about prime numbers", "Theorems in number theory", "Arithmetic", "Modular arithmetic", "Number theory" ]
53,455	https://en.wikipedia.org/wiki/Minkowski%27s%20theorem	In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. It can be extended from the integers to any lattice and to any symmetric convex set with volume greater than , where denotes the covolume of the lattice (the absolute value of the determinant of any of its bases). Formulation Suppose that is a lattice of determinant in the -dimensional real vector space and is a convex subset of that is symmetric with respect to the origin, meaning that if is in then is also in . Minkowski's theorem states that if the volume of is strictly greater than , then must contain at least one lattice point other than the origin. (Since the set is symmetric, it would then contain at least three lattice points: the origin 0 and a pair of points , where .) Example The simplest example of a lattice is the integer lattice of all points with integer coefficients; its determinant is 1. For , the theorem claims that a convex figure in the Euclidean plane symmetric about the origin and with area greater than 4 encloses at least one lattice point in addition to the origin. The area bound is sharp: if is the interior of the square with vertices then is symmetric and convex, and has area 4, but the only lattice point it contains is the origin. This example, showing that the bound of the theorem is sharp, generalizes to hypercubes in every dimension . Proof The following argument proves Minkowski's theorem for the specific case of Proof of the case: Consider the map Intuitively, this map cuts the plane into 2 by 2 squares, then stacks the squares on top of each other. Clearly has area less than or equal to 4, because this set lies within a 2 by 2 square. Assume for a contradiction that could be injective, which means the pieces of cut out by the squares stack up in a non-overlapping way. Because is locally area-preserving, this non-overlapping property would make it area-preserving for all of , so the area of would be the same as that of , which is greater than 4. That is not the case, so the assumption must be false: is not injective, meaning that there exist at least two distinct points in that are mapped by to the same point: . Because of the way was defined, the only way that can equal is for to equal for some integers and , not both zero. That is, the coordinates of the two points differ by two even integers. Since is symmetric about the origin, is also a point in . Since is convex, the line segment between and lies entirely in , and in particular the midpoint of that segment lies in . In other words, is a point in . But this point is an integer point, and is not the origin since and are not both zero. Therefore, contains a nonzero integer point. Remarks: The argument above proves the theorem that any set of volume contains two distinct points that differ by a lattice vector. This is a special case of Blichfeldt's theorem. The argument above highlights that the term is the covolume of the lattice . To obtain a proof for general lattices, it suffices to prove Minkowski's theorem only for ; this is because every full-rank lattice can be written as for some linear transformation , and the properties of being convex and symmetric about the origin are preserved by linear transformations, while the covolume of is and volume of a body scales by exactly under an application of . Applications Bounding the shortest vector Minkowski's theorem gives an upper bound for the length of the shortest nonzero vector. This result has applications in lattice cryptography and number theory. Theorem (Minkowski's bound on the shortest vector): Let be a lattice. Then there is a with . In particular, by the standard comparison between and norms, . Remarks: The constant in the bound can be improved, for instance by taking the open ball of radius as in the above argument. The optimal constant is known as the Hermite constant. The bound given by the theorem can be very loose, as can be seen by considering the lattice generated by . But it cannot be further improved in the sense that there exists a global constant such that there exists an -dimensional lattice satisfying for all . Furthermore, such lattice can be self-dual. Even though Minkowski's theorem guarantees a short lattice vector within a certain magnitude bound, finding this vector is in general a hard computational problem. Finding the vector within a factor guaranteed by Minkowski's bound is referred to as Minkowski's Vector Problem (MVP), and it is known that approximation SVP reduces to it using transference properties of the dual lattice. The computational problem is also sometimes referred to as HermiteSVP. The LLL-basis reduction algorithm can be seen as a weak but efficiently algorithmic version of Minkowski's bound on the shortest vector. This is because a -LLL reduced basis for has the property that ; see these lecture notes of Micciancio for more on this. As explained in, proofs of bounds on the Hermite constant contain some of the key ideas in the LLL-reduction algorithm. Applications to number theory Primes that are sums of two squares The difficult implication in Fermat's theorem on sums of two squares can be proven using Minkowski's bound on the shortest vector. Theorem: Every prime with can be written as a sum of two squares. Additionally, the lattice perspective gives a computationally efficient approach to Fermat's theorem on sums of squares: First, recall that finding any nonzero vector with norm less than in , the lattice of the proof, gives a decomposition of as a sum of two squares. Such vectors can be found efficiently, for instance using LLL-algorithm. In particular, if is a -LLL reduced basis, then, by the property that , . Thus, by running the LLL-lattice basis reduction algorithm with , we obtain a decomposition of as a sum of squares. Note that because every vector in has norm squared a multiple of , the vector returned by the LLL-algorithm in this case is in fact a shortest vector. Lagrange's four-square theorem Minkowski's theorem is also useful to prove Lagrange's four-square theorem, which states that every natural number can be written as the sum of the squares of four natural numbers. Dirichlet's theorem on simultaneous rational approximation Minkowski's theorem can be used to prove Dirichlet's theorem on simultaneous rational approximation. Algebraic number theory Another application of Minkowski's theorem is the result that every class in the ideal class group of a number field contains an integral ideal of norm not exceeding a certain bound, depending on , called Minkowski's bound: the finiteness of the class number of an algebraic number field follows immediately. Complexity theory The complexity of finding the point guaranteed by Minkowski's theorem, or the closely related Blichfeldt's theorem, have been studied from the perspective of TFNP search problems. In particular, it is known that a computational analogue of Blichfeldt's theorem, a corollary of the proof of Minkowski's theorem, is PPP-complete. It is also known that the computational analogue of Minkowski's theorem is in the class PPP, and it was conjectured to be PPP complete. See also Danzer set Pick's theorem Dirichlet's unit theorem Minkowski's second theorem Ehrhart's volume conjecture References Further reading ([1996 with minor corrections]) Wolfgang M. Schmidt.Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000. External links Stevenhagen, Peter. Number Rings. Geometry of numbers Convex analysis Theorems in number theory Articles containing proofs Hermann Minkowski	Minkowski's theorem	[ "Mathematics" ]	1,672	[ "Geometry of numbers", "Theorems in number theory", "Mathematical problems", "Articles containing proofs", "Mathematical theorems", "Number theory" ]
53,460	https://en.wikipedia.org/wiki/Statcoulomb	The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. In terms of the Gaussian base units, it is That is, it is defined so that the proportionality constant in Coulomb's law using CGS-ESU quantities is a dimensionless quantity equal to 1. Definition and relation to CGS base units Coulomb's law in the CGS-Gaussian system takes the form where F is the force, q and q are the two electric charges, and r is the distance between the charges. This serves to define charge as a quantity in the Gaussian system. The statcoulomb is defined such that if two electric charges of 1 statC each and have a separation of , the force of mutual electrical repulsion is 1 dyne. Substituting F = 1 dyn, q = q = 1 statC, and r = 1 cm, we get: From this it is also evident that the quantity dimension of electric charge as defined in the CGS-ESU and Gaussian systems is . Conversion between systems Conversion of a quantity to the corresponding quantity of the International System of Quantities (ISQ) that underlies the International System of Units (SI) by using the defining equations of each system. The SI uses the coulomb (C) as its unit of electric charge. The conversion factor between corresponding quantities with the units coulomb and statcoulomb depends on which quantity is to be converted. The most common cases are: For electric charge: For electric flux (): For electric flux density (): The symbol "≘" ('corresponds to') is used instead of "=" because the two sides cannot be equated. References Units of electrical charge Centimetre–gram–second system of units	Statcoulomb	[ "Physics", "Mathematics" ]	416	[ "Physical quantities", "Electric charge", "Quantity", "Units of electrical charge", "Units of measurement" ]
53,464	https://en.wikipedia.org/wiki/Cinnabar	Cinnabar (; ), or cinnabarite (), also known as mercurblende is the bright scarlet to brick-red form of mercury(II) sulfide (HgS). It is the most common source ore for refining elemental mercury and is the historic source for the brilliant red or scarlet pigment termed vermilion and associated red mercury pigments. Cinnabar generally occurs as a vein-filling mineral associated with volcanic activity and alkaline hot springs. The mineral resembles quartz in symmetry and it exhibits birefringence. Cinnabar has a mean refractive index near 3.2, a hardness between 2.0 and 2.5, and a specific gravity of approximately 8.1. The color and properties derive from a structure that is a hexagonal crystalline lattice belonging to the trigonal crystal system, crystals that sometimes exhibit twinning. Cinnabar has been used for its color since antiquity in the Near East, including as a rouge-type cosmetic, in the New World since the Olmec culture, and in China since as early as the Yangshao culture, where it was used in coloring stoneware. In Roman times, cinnabar was highly valued as paint for walls, especially interiors (since it darkened when used outdoors due to exposure to sunlight). Associated modern precautions for the use and handling of cinnabar arise from the toxicity of the mercury component, which was recognized as early as ancient Rome. Etymology The name comes from Greek (), a Greek word most likely applied by Theophrastus to several distinct substances. In Latin, it was sometimes known as minium, meaning also "red cinnamon", though both of these terms now refer specifically to lead tetroxide. Properties and structure Properties Cinnabar is generally found in a massive, granular, or earthy form and is bright scarlet to brick-red in color, though it occasionally occurs in crystals with a nonmetallic adamantine luster. It resembles quartz in its symmetry. It exhibits birefringence, and it has the second-highest refractive index of any mineral. Its mean refractive index is 3.08 (sodium light wavelengths), versus the indices for diamond and the non-mineral gallium(III) arsenide (GaAs), which are 2.42 and 3.93, respectively. The hardness of cinnabar is 2.0–2.5 on the Mohs scale, and its specific gravity 8.1. Structure Structurally, cinnabar belongs to the trigonal crystal system. It occurs as thick tabular or slender prismatic crystals or as granular to massive incrustations. Crystal twinning occurs as simple contact twins. Mercury(II) sulfide, HgS, adopts the cinnabar structure described, and one additional structure, i.e. it is dimorphous. Cinnabar is the more stable form, and is a structure akin to that of HgO: each Hg center has two short Hg−S bonds (each 2.36 Å), and four longer contacts (with 3.10, 3.10, 3.30 and 3.30 Å separations). In addition, HgS is found in a black, non-cinnabar polymorph (metacinnabar) that has the zincblende structure. Occurrence Cinnabar generally occurs as a vein-filling mineral associated with volcanic activity and alkaline hot springs. Cinnabar is deposited by epithermal ascending aqueous solutions (those near the surface and not too hot) far removed from their igneous source. It is associated with native mercury, stibnite, realgar, pyrite, marcasite, opal, quartz, chalcedony, dolomite, calcite, and barite. Cinnabar is found in essentially all mineral extraction localities that yield mercury, notably Almadén (Spain). This mine was exploited from Roman times until 1991, being for centuries the most important cinnabar deposit in the world. Good cinnabar crystals have also been found there. Cinnabar deposits appear in Giza (Egypt); Puerto Princesa (Philippines); Red Devil, Alaska; Murfreesboro, Arkansas; New Almaden Mine in San Jose, California; New Idria, California, the Hastings Mine and St. John's Mine both in Vallejo, California; Terlingua, Texas (United States); Idrija (Slovenia); near Obermoschel in the Palatinate; the La Ripa and Levigliani mines at the foot of the Apuan Alps and in Mount Amiata (Tuscany, Italy); Avala (Serbia); Huancavelica (Peru); the province of Guizhou in China and Western ghats in India where fine crystals have been obtained. It has been found in Dominica near its sulfur springs at the southern end of the island along the west coast. Cinnabar is still being deposited, such as from the hot waters of Sulphur Bank Mine in California and Steamboat Springs, Nevada (United States). Mining and extraction of mercury As the most common source of mercury in nature, cinnabar has been mined for thousands of years, even as far back as the Neolithic Age. During the Roman Empire it was mined both as a pigment, and for its mercury content. To produce liquid mercury (quicksilver), crushed cinnabar ore is roasted in rotary furnaces. Pure mercury separates from sulfur in this process and easily evaporates. A condensing column is used to collect the liquid metal, which is most often shipped in iron flasks. Toxicity Associated modern precautions for use and handling of cinnabar arise from the toxicity of the mercury component, which was recognized as early as in ancient Rome. Because of its mercury content, cinnabar can be toxic to human beings. Overexposure to mercury, mercury poisoning (mercurialism), was seen as an occupational disease to the ancient Romans. Though people in ancient South America often used cinnabar for art, or processed it into refined mercury (as a means to gild silver and gold to objects), the toxic properties of mercury were well known. It was dangerous to those who mined and processed cinnabar; it caused shaking, loss of sense, and death. Data suggests that mercury was retorted from cinnabar and the workers were exposed to the toxic mercury fumes. "Mining in the Spanish cinnabar mines of Almadén, southwest of Madrid, was regarded as being akin to a death sentence due to the shortened life expectancy of the miners, who were slaves or convicts." Decorative use Cinnabar has been used for its color since antiquity in the Near East, including as a rouge-type cosmetic, in the New World since the Olmec culture, and in China for writing on oracle bones as early as the Zhou dynasty. Late in the Song dynasty it was used in coloring lacquerware. Cinnabar's use as a color in the New World, since the Olmec culture, is exemplified by its use in royal burial chambers during the peak of Maya civilization, most dramatically in the 7th-century tomb of the Red Queen in Palenque, where the remains of a noble woman and objects belonging to her in her sarcophagus were completely covered with bright red powder made from cinnabar. The most popularly known use of cinnabar is in Chinese carved lacquerware, a technique that apparently originated in the Song dynasty. The danger of mercury poisoning may be reduced in ancient lacquerware by entraining the powdered pigment in lacquer, but could still pose an environmental hazard if the pieces were accidentally destroyed. In the modern jewellery industry, the toxic pigment is replaced by a resin-based polymer that approximates the appearance of pigmented lacquer. Two female mummies dated AD 1399 to 1475 found in Cerro Esmeralda in Chile in 1976 had clothes colored with cinnabar. Other forms Hepatic cinnabar, or paragite, is an impure brownish variety from the mines of Idrija in the Carniola region of Slovenia, in which the cinnabar is mixed with bituminous and earthy matter. Hypercinnabar crystallizes at high temperature in the hexagonal crystal system. Metacinnabar is a black-colored form of mercury(II) sulfide, which crystallizes in the cubic crystal system. Synthetic cinnabar is produced by treatment of mercury(II) salts with hydrogen sulfide to precipitate black, synthetic metacinnabar, which is then heated in water. This conversion is promoted by the presence of sodium sulfide. See also Classification of minerals List of minerals Mercury cycle Red pigments References Further reading External links MSDS for cinnabar Dartmouth Toxic Metals Research Program – Mercury Cinnabar visual reference Related articles Pompeian Red Sulfide minerals Mercury(II) minerals Trigonal minerals Blendes Minerals in space group 152 or 154 Traditional Chinese medicine Alchemical substances	Cinnabar	[ "Chemistry" ]	1,876	[ "Alchemical substances" ]
53,469	https://en.wikipedia.org/wiki/Cinnamon	Cinnamon is a spice obtained from the inner bark of several tree species from the genus Cinnamomum. Cinnamon is used mainly as an aromatic condiment and flavouring additive in a wide variety of cuisines, sweet and savoury dishes, breakfast cereals, snack foods, bagels, teas, hot chocolate and traditional foods. The aroma and flavour of cinnamon derive from its essential oil and principal component, cinnamaldehyde, as well as numerous other constituents including eugenol. Cinnamon is the name for several species of trees and the commercial spice products that some of them produce. All are members of the genus Cinnamomum in the family Lauraceae. Only a few Cinnamomum species are grown commercially for spice. Cinnamomum verum (alternatively C. zeylanicum), known as "Ceylon cinnamon" after its origins in Sri Lanka (formerly Ceylon), is considered to be "true cinnamon", but most cinnamon in international commerce is derived from four other species, usually and more correctly referred to as "cassia": C. burmanni (Indonesian cinnamon or Padang cassia), C. cassia (Chinese cinnamon or Chinese cassia), C. loureiroi (Saigon cinnamon or Vietnamese cassia), and the less common C. citriodorum (Malabar cinnamon). In 2021, world production of cinnamon was 226,753 tonnes, led by China with 43% of the total. Etymology The English word "cinnamon", attested in English since the 15th century, deriving from the Ancient Greek (, later κίνναμον : ), via Latin and medieval French intermediate forms. The Greek was borrowed from a Phoenician word, which was similar to the related Hebrew word (). The name "cassia", first recorded in late Old English from Latin, ultimately derives from the Hebrew word , a form of the verb , "to strip off bark". Early Modern English also used the names canel and canella, similar to the current names of cinnamon in several other European languages, which are derived from the Latin word , a diminutive of , "tube", from the way the bark curls up as it dries. History Cinnamon has been known from remote antiquity. It was imported to Egypt as early as 2000 BC, but those who reported that it had come from China had confused it with Cinnamomum cassia, a related species. Cinnamon was so highly prized among ancient nations that it was regarded as a gift fit for monarchs and even for a deity; an inscription records the gift of cinnamon and cassia to the temple of Apollo at Miletus. Its source was kept a trade secret in the Mediterranean world for centuries by those in the spice trade, in order to protect their monopoly as suppliers. Cinnamomum verum, which translates from Latin as "true cinnamon", is native to India, Sri Lanka, Bangladesh and Myanmar. Cinnamomum cassia (cassia) is native to China. Related species, all harvested and sold in the modern era as cinnamon, are native to Vietnam ("Saigon cinnamon"), Indonesia and other southeast Asian countries with warm climates. In Ancient Egypt, cinnamon was used to embalm mummies. From the Ptolemaic Kingdom onward, Ancient Egyptian recipes for kyphi, an aromatic used for burning, included cinnamon and cassia. The gifts of Hellenistic rulers to temples sometimes included cassia and cinnamon. The first Greek reference to is found in a poem by Sappho in the 7th century BC. According to Herodotus, both cinnamon and cassia grew in Arabia, together with incense, myrrh and , and were guarded by winged serpents. Herodotus, Aristotle and other authors named Arabia as the source of cinnamon; they recounted that giant "cinnamon birds" collected the cinnamon sticks from an unknown land where the cinnamon trees grew and used them to construct their nests. Pliny the Elder wrote that cinnamon was brought around the Arabian Peninsula on "rafts without rudders or sails or oars", taking advantage of the winter trade winds. He also mentioned cassia as a flavouring agent for wine, and that the tales of cinnamon being collected from the nests of cinnamon birds was a traders' fiction made up to charge more. However, the story remained current in Byzantium as late as 1310. According to Pliny the Elder, a Roman pound () of cassia, cinnamon (), cost up to 1,500 , the wage of fifty months' labour. Diocletian's Edict on Maximum Prices from 301 AD gives a price of 125 for a pound of cassia, while an agricultural labourer earned 25 per day. Cinnamon was too expensive to be commonly used on funeral pyres in Rome, but the Emperor Nero is said to have burned a year's worth of the city's supply at the funeral for his wife Poppaea Sabina in AD 65. Middle Ages Through the Middle Ages, the source of cinnamon remained a mystery to the Western world. From reading Latin writers who quoted Herodotus, Europeans had learned that cinnamon came up the Red Sea to the trading ports of Egypt, but where it came from was less than clear. When the Sieur de Joinville accompanied his king, Louis IX of France to Egypt on the Seventh Crusade in 1248, he reported—and believed—what he had been told: that cinnamon was fished up in nets at the source of the Nile out at the edge of the world (i.e., Ethiopia). Marco Polo avoided precision on the topic. The first mention that the spice grew in the area of India was in Maimonides's Mishneh Torah, about 1180. The first mention that the spice grew specifically in Sri Lanka was in Zakariya al-Qazwini's ("Monument of Places and History of God's Bondsmen") about 1270. This was followed shortly thereafter by John of Montecorvino in a letter of about 1292. Indonesian rafts transported cinnamon directly from the Moluccas to East Africa (see also Rhapta), where local traders then carried it north to Alexandria in Egypt. Venetian traders from Italy held a monopoly on the spice trade in Europe, distributing cinnamon from Alexandria. The disruption of this trade by the rise of other Mediterranean powers, such as the Mamluk sultans and the Ottoman Empire, was one of many factors that led Europeans to search more widely for other routes to Asia. Early modern period During the 1500s, Ferdinand Magellan was searching for spices on behalf of Spain; in the Philippines, he found , which was closely related to C. zeylanicum, the cinnamon found in Sri Lanka. This cinnamon eventually competed with Sri Lankan cinnamon, which was controlled by the Portuguese. In 1638, Dutch traders established a trading post in Sri Lanka, took control of the manufactories by 1640, and expelled the remaining Portuguese by 1658. "The shores of the island are full of it," a Dutch captain reported, "and it is the best in all the Orient. When one is downwind of the island, one can still smell cinnamon eight leagues out to sea." The Dutch East India Company continued to overhaul the methods of harvesting in the wild and eventually began to cultivate its own trees. In 1767, Lord Brown of the British East India Company established the Anjarakkandy Cinnamon Estate near Anjarakkandy in the Kannur district of Kerala, India. It later became Asia's largest cinnamon estate. The British took control of Ceylon from the Dutch in 1796. Cultivation Cinnamon is an evergreen tree characterized by oval-shaped leaves, thick bark and a berry fruit. When harvesting the spice, the bark and leaves are the primary parts of the plant used. However, in Japan, the more pungent roots are harvested in order to produce nikki (ニッキ) which is a product distinct from cinammon (シナモン shinamon). Cinnamon is cultivated by growing the tree for two years, then coppicing it, i.e., cutting the stems at ground level. The following year, about a dozen new shoots form from the roots, replacing those that were cut. A number of pests such as Colletotrichum gloeosporioides, Diplodia species and Phytophthora cinnamomi (stripe canker) can affect the growing plants. The stems must be processed immediately after harvesting while the inner bark is still wet. The cut stems are processed by scraping off the outer bark, then beating the branch evenly with a hammer to loosen the inner bark, which is then pried off in long rolls. Only of the inner bark is used; the outer, woody portion is discarded, leaving metre-long cinnamon strips that curl into rolls ("quills") on drying. The processed bark dries completely in four to six hours, provided it is in a well-ventilated and relatively warm environment. Once dry, the bark is cut into lengths for sale. A less than ideal drying environment encourages the proliferation of pests in the bark, which may then require treatment by fumigation with sulphur dioxide. In 2011, the European Union approved the use of sulphur dioxide at a concentration of up to for the treatment of C. verum bark harvested in Sri Lanka. Species A number of species are often sold as cinnamon: Cinnamomum cassia (cassia or Chinese cinnamon, the most common commercial type in the USA) C. burmanni (Korintje, Padang cassia, or Indonesian cinnamon) C. loureiroi (Saigon cinnamon, Vietnamese cassia, or Vietnamese cinnamon) C. verum (Sri Lanka cinnamon, Ceylon cinnamon or Cinnamomum zeylanicum) C. citriodorum (Malabar cinnamon) Cassia induces a strong, spicy flavour and is often used in baking, especially associated with cinnamon rolls, as it handles baking conditions well. Among cassia, Chinese cinnamon is generally medium to light reddish-brown in colour, hard and woody in texture, and thicker ( thick), as all of the layers of bark are used. Ceylon cinnamon, using only the thin inner bark, has a lighter brown colour and a finer, less dense, and more crumbly texture. It is subtle and more aromatic in flavour than cassia and it loses much of its flavour during cooking. The barks of the species are easily distinguished when whole, both in macroscopic and microscopic characteristics. Ceylon cinnamon sticks (quills) have many thin layers and can easily be made into powder using a coffee or spice grinder, whereas cassia sticks are much harder. Indonesian cinnamon is often sold in neat quills made up of one thick layer, capable of damaging a spice or coffee grinder. Saigon cinnamon (C. loureiroi) and Chinese cinnamon (C. cassia) are always sold as broken pieces of thick bark, as the bark is not supple enough to be rolled into quills. The powdered bark is harder to distinguish, but if it is treated with tincture of iodine (a test for starch), little effect is visible with pure Ceylon cinnamon; however, when Chinese cinnamon is present, a deep-blue tint is produced. Grading The Sri Lankan grading system divides the cinnamon quills into four groups: Alba, less than in diameter Continental, less than in diameter Mexican, less than in diameter Hamburg, less than in diameter These groups are further divided into specific grades. For example, Mexican is divided into M00000 special, M000000 and M0000, depending on quill diameter and number of quills per kilogram. Any pieces of bark less than long are categorized as quillings. Featherings are the inner bark of twigs and twisted shoots. Chips are trimmings of quills, outer and inner bark that cannot be separated, or the bark of small twigs. Production In 2021, four countries accounted for 98% of the world's cinnamon production, a total of 226,753 tonnes: China, Indonesia, Vietnam, and Sri Lanka. Counterfeit True cinnamon from C. verum bark can be mixed with cassia (C. cassia) as counterfeit and falsely marketed as authentic cinnamon. In one analysis, authentic Ceylon cinnamon bark contained 12-143 mg/kg of coumarin a phenolic typically low in content in true cinnamon but market samples contained coumarin with levels as high as 3462 mg/kg, indicating probable contamination with cassia in the counterfeit cinnamon. ConsumerLab.com found the same problem in a 2020 analysis; "a supplement that contained the highest amount of coumarin was labeled as Ceylon cinnamon". Food uses Cinnamon bark is used as a spice. It is principally employed in cookery as a condiment and flavouring material. It is used in the preparation of chocolate, especially in Mexico. Cinnamon is often used in savoury dishes of chicken and lamb. In the United States and Europe, cinnamon and sugar are often used to flavour cereals, bread-based dishes such as toast, and fruits, especially apples; a cinnamon and sugar mixture (cinnamon sugar) is sold separately for such purposes. It is also used in Portuguese and Turkish cuisine for both sweet and savoury dishes. Cinnamon can also be used in pickling, and in Christmas drinks such as eggnog. Cinnamon powder has long been an important spice in enhancing the flavour of Persian cuisine, used in a variety of thick soups, drinks and sweets. Cinnamon is a common ingredient in Jewish cuisine across various communities. In Sephardic cooking, it is incorporated into vegetable stews and desserts such as tishpishti and travados, both of which are soaked in honey. In Ashkenazi cuisine, cinnamon features in dishes like honey cakes, and kugels. It is also one of "four sibling spices" (rempah empat beradik) essential in Malay cuisine along with clove, star anise and cardamom. Nutrient composition Ground cinnamon is 11% water, 81% carbohydrates (including 53% dietary fiber), 4% protein and 1% fat. Characteristics Texture Ceylon cinnamon may be crushed into small pieces by hand while Indonesian cinnamon requires a powerful blender. Flavour, aroma and taste The flavour of cinnamon is due to the aromatic essential oils that makes up 0.5 to 1% of its composition. Cinnamon bark can be macerated, then extracted in 80% ethanol, to a tincture. Cinnamon essential oil can be prepared by roughly pounding the bark, macerating it in sea water, and then quickly distilling the whole. It is of a golden-yellow colour, with the characteristic odour of cinnamon and a very hot aromatic taste. Cinnamon oil nanoemulsion can be made with polysorbate 80, cinnamon essential oil, and water, by ultrasonic emulsification. Cinnamon oil macroemulsion can be made with a dispersing emulsifying homogenizer. The pungent taste and scent come from cinnamaldehyde, about 90% of the essential oil from cinnamon bark. Cinnamaldehyde decomposes, in high humidity and high temperatures, to styrene, and, by reaction with oxygen as it ages, it darkens in colour and forms resinous compounds. Cinnamon constituents include some 80 aromatic compounds, including eugenol, found in the oil from leaves or bark of cinnamon trees. Alcohol flavorant Cinnamon is used as a flavoring in cinnamon liqueur, such as cinnamon-flavored whiskey in the United States, and , a cinnamon brandy in Greece. Health-related research Cinnamon has a long history of use in traditional medicine as a digestive aid. However, contemporary studies are unable to find evidence of any significant medicinal or therapeutic effect. Reviews of clinical trials reported lowering of fasting plasma glucose and inconsistent effects on hemoglobin A1C (HbA1c, an indicator of chronically elevated plasma glucose). Four of the reviews reported a decrease in fasting plasma glucose, only two reported lower HbA1c, and one reported no change to either measure. The Cochrane review noted that trial durations were limited to 4 to 16 weeks, and that no trials reported on changes to quality of life, morbidity or mortality rate. The Cochrane authors' conclusion was: "There is insufficient evidence to support the use of cinnamon for type 1 or type 2 diabetes mellitus." Citing the Cochrane review, the U.S. National Center for Complementary and Integrative Health stated: "Studies done in people don't support using cinnamon for any health condition." However, the results of the studies are difficult to interpret because it is often unclear what type of cinnamon and what part of the plant were used. A meta-analysis of cinnamon supplementation trials with lipid measurements reported lower total cholesterol and triglycerides, but no significant changes in LDL-cholesterol or HDL-cholesterol. Another reported no change to body weight or insulin resistance. Toxicity A systematic review of adverse events as a result of cinnamon use reported gastrointestinal disorders and allergic reactions as the most frequently reported side effects. In 2008, the European Food Safety Authority considered the toxicity of coumarin, a component of cinnamon, and confirmed a maximum recommended tolerable daily intake (TDI) of 0.1 mg of coumarin per kg of body weight. Coumarin is known to cause liver and kidney damage in high concentrations and metabolic effect in humans with CYP2A6 polymorphism. Based on this assessment, the European Union set a guideline for maximum coumarin content in foodstuffs of 50 mg per kg of dough in seasonal foods, and 15 mg per kg in everyday baked foods. The maximum recommended TDI of 0.1 mg of coumarin per kg of body weight equates to 5 mg of coumarin (or 5.6 g C. verum with 0.9 mg coumarin per gram) for a body weight of 50 kg. C as shown in the table below: Due to the variable amount of coumarin in C. cassia, usually well over 1.0 mg of coumarin per g of cinnamon and sometimes up to 12 times that, C. cassia has a low safe-intake-level upper limit to adhere to the above TDI. In contrast, C. verum has only trace amounts of coumarin. In March 2024, the US Food and Drug Administration recommended a voluntary recall on 6 brands of cinnamon due to contamination with lead, after an investigation stemming from 500 reports of child lead poisoning across the US. The FDA determined that cinnamon was adulterated with lead chromate. Gallery See also Canella, a plant known as "wild cinnamon" or "white cinnamon" Cinnamomea, a Neo-Latin adjective meaning 'cinnamon-coloured' Cinnamon challenge List of culinary herbs and spices Notes References Further reading Wijesekera R. O. B., Ponnuchamy S., Jayewardene A. L., "Cinnamon" (1975) monograph published by CISIR, Colombo, Sri Lanka External links "In pictures: Sri Lanka's spice of life". BBC News. Antifungals Cinnamomum Incense material Medicinal plants Non-timber forest products Spices Indian spices Sri Lankan spices	Cinnamon	[ "Physics" ]	3,992	[ "Incense material", "Materials", "Matter" ]
53,497	https://en.wikipedia.org/wiki/Optical%20illusion	In visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; their categorization is difficult because the underlying cause is often not clear but a classification proposed by Richard Gregory is useful as an orientation. According to that, there are three main classes: physical, physiological, and cognitive illusions, and in each class there are four kinds: Ambiguities, distortions, paradoxes, and fictions. A classical example for a physical distortion would be the apparent bending of a stick half immersed in water; an example for a physiological paradox is the motion aftereffect (where, despite movement, position remains unchanged). An example for a physiological fiction is an afterimage. Three typical cognitive distortions are the Ponzo, Poggendorff, and Müller-Lyer illusion. Physical illusions are caused by the physical environment, e.g. by the optical properties of water. Physiological illusions arise in the eye or the visual pathway, e.g. from the effects of excessive stimulation of a specific receptor type. Cognitive visual illusions are the result of unconscious inferences and are perhaps those most widely known. Pathological visual illusions arise from pathological changes in the physiological visual perception mechanisms causing the aforementioned types of illusions; they are discussed e.g. under visual hallucinations. Optical illusions, as well as multi-sensory illusions involving visual perception, can also be used in the monitoring and rehabilitation of some psychological disorders, including phantom limb syndrome and schizophrenia. Physical visual illusions A familiar phenomenon and example for a physical visual illusion is when mountains appear to be much nearer in clear weather with low humidity (Foehn) than they are. This is because haze is a cue for depth perception, signalling the distance of far-away objects (Aerial perspective). The classical example of a physical illusion is when a stick that is half immersed in water appears bent. This phenomenon was discussed by Ptolemy () and was often a prototypical example for an illusion. Physiological visual illusions Physiological illusions, such as the afterimages following bright lights, or adapting stimuli of excessively longer alternating patterns (contingent perceptual aftereffect), are presumed to be the effects on the eyes or brain of excessive stimulation or interaction with contextual or competing stimuli of a specific type—brightness, color, position, tile, size, movement, etc. The theory is that a stimulus follows its individual dedicated neural path in the early stages of visual processing and that intense or repetitive activity in that or interaction with active adjoining channels causes a physiological imbalance that alters perception. The Hermann grid illusion and Mach bands are two illusions that are often explained using a biological approach. Lateral inhibition, where in receptive fields of the retina receptor signals from light and dark areas compete with one another, has been used to explain why we see bands of increased brightness at the edge of a color difference when viewing Mach bands. Once a receptor is active, it inhibits adjacent receptors. This inhibition creates contrast, highlighting edges. In the Hermann grid illusion, the gray spots that appear at the intersections at peripheral locations are often explained to occur because of lateral inhibition by the surround in larger receptive fields. However, lateral inhibition as an explanation of the Hermann grid illusion has been disproved. More recent empirical approaches to optical illusions have had some success in explaining optical phenomena with which theories based on lateral inhibition have struggled. Cognitive illusions Cognitive illusions are assumed to arise by interaction with assumptions about the world, leading to "unconscious inferences", an idea first suggested in the 19th century by the German physicist and physician Hermann Helmholtz. Cognitive illusions are commonly divided into ambiguous illusions, distorting illusions, paradox illusions, or fiction illusions. Ambiguous illusions are pictures or objects that elicit a perceptual "switch" between the alternative interpretations. The Necker cube is a well-known example; other instances are the Rubin vase and the "squircle", based on Kokichi Sugihara's ambiguous cylinder illusion. Distorting or geometrical-optical illusions are characterized by distortions of size, length, position or curvature. A striking example is the Café wall illusion. Other examples are the famous Müller-Lyer illusion and Ponzo illusion. Paradox illusions (or impossible object illusions) are generated by objects that are paradoxical or impossible, such as the Penrose triangle or impossible staircase seen, for example, in M. C. Escher's Ascending and Descending and Waterfall. The triangle is an illusion dependent on a cognitive misunderstanding that adjacent edges must join. Fictions are when a figure is perceived even though it is not in the stimulus, like with the Kanizsa triangle, using illusory contours. Explanation of cognitive illusions Perceptual organization To make sense of the world it is necessary to organize incoming sensations into information which is meaningful. Gestalt psychologists believe one way this is done is by perceiving individual sensory stimuli as a meaningful whole. Gestalt organization can be used to explain many illusions including the rabbit–duck illusion where the image as a whole switches back and forth from being a duck then being a rabbit and why in the figure–ground illusion the figure and ground are reversible. In addition, gestalt theory can be used to explain the illusory contours in the Kanizsa's triangle. A floating white triangle, which does not exist, is seen. The brain has a need to see familiar simple objects and has a tendency to create a "whole" image from individual elements. Gestalt means "form" or "shape" in German. However, another explanation of the Kanizsa's triangle is based in evolutionary psychology and the fact that in order to survive it was important to see form and edges. The use of perceptual organization to create meaning out of stimuli is the principle behind other well-known illusions including impossible objects. The brain makes sense of shapes and symbols putting them together like a jigsaw puzzle, formulating that which is not there to that which is believable. The gestalt principles of perception govern the way different objects are grouped. Good form is where the perceptual system tries to fill in the blanks in order to see simple objects rather than complex objects. Continuity is where the perceptual system tries to disambiguate which segments fit together into continuous lines. Proximity is where objects that are close together are associated. Similarity is where objects that are similar are seen as associated. Some of these elements have been successfully incorporated into quantitative models involving optimal estimation or Bayesian inference. The double-anchoring theory, a popular but recent theory of lightness illusions, states that any region belongs to one or more frameworks, created by gestalt grouping principles, and within each frame is independently anchored to both the highest luminance and the surround luminance. A spot's lightness is determined by the average of the values computed in each framework. Depth and motion perception Illusions can be based on an individual's ability to see in three dimensions even though the image hitting the retina is only two dimensional. The Ponzo illusion is an example of an illusion which uses monocular cues of depth perception to fool the eye. But even with two-dimensional images, the brain exaggerates vertical distances when compared with horizontal distances, as in the vertical–horizontal illusion where the two lines are exactly the same length. In the Ponzo illusion the converging parallel lines tell the brain that the image higher in the visual field is farther away, therefore, the brain perceives the image to be larger, although the two images hitting the retina are the same size. The optical illusion seen in a diorama/false perspective also exploits assumptions based on monocular cues of depth perception. The M.C. Escher painting Waterfall exploits rules of depth and proximity and our understanding of the physical world to create an illusion. Like depth perception, motion perception is responsible for a number of sensory illusions. Film animation is based on the illusion that the brain perceives a series of slightly varied images produced in rapid succession as a moving picture. Likewise, when we are moving, as we would be while riding in a vehicle, stable surrounding objects may appear to move. We may also perceive a large object, like an airplane, to move more slowly than smaller objects, like a car, although the larger object is actually moving faster. The phi phenomenon is yet another example of how the brain perceives motion, which is most often created by blinking lights in close succession. The ambiguity of direction of motion due to lack of visual references for depth is shown in the spinning dancer illusion. The spinning dancer appears to be moving clockwise or counterclockwise depending on spontaneous activity in the brain where perception is subjective. Recent studies show on the fMRI that there are spontaneous fluctuations in cortical activity while watching this illusion, particularly the parietal lobe because it is involved in perceiving movement. Color and brightness constancies Perceptual constancies are sources of illusions. Color constancy and brightness constancy are responsible for the fact that a familiar object will appear the same color regardless of the amount of light or color of light reflecting from it. An illusion of color difference or luminosity difference can be created when the luminosity or color of the area surrounding an unfamiliar object is changed. The luminosity of the object will appear brighter against a black field (that reflects less light) than against a white field, even though the object itself did not change in luminosity. Similarly, the eye will compensate for color contrast depending on the color cast of the surrounding area. In addition to the gestalt principles of perception, water-color illusions contribute to the formation of optical illusions. Water-color illusions consist of object-hole effects and coloration. Object-hole effects occur when boundaries are prominent where there is a figure and background with a hole that is 3D volumetric in appearance. Coloration consists of an assimilation of color radiating from a thin-colored edge lining a darker chromatic contour. The water-color illusion describes how the human mind perceives the wholeness of an object such as top-down processing. Thus, contextual factors play into perceiving the brightness of an object. Object Just as it perceives color and brightness constancies, the brain has the ability to understand familiar objects as having a consistent shape or size. For example, a door is perceived as a rectangle regardless of how the image may change on the retina as the door is opened and closed. Unfamiliar objects, however, do not always follow the rules of shape constancy and may change when the perspective is changed. The Shepard tables illusion is an example of an illusion based on distortions in shape constancy. Future perception Researcher Mark Changizi of Rensselaer Polytechnic Institute in New York has a more imaginative take on optical illusions, saying that they are due to a neural lag which most humans experience while awake. When light hits the retina, about one-tenth of a second goes by before the brain translates the signal into a visual perception of the world. Scientists have known of the lag, yet they have debated how humans compensate, with some proposing that our motor system somehow modifies our movements to offset the delay. Changizi asserts that the human visual system has evolved to compensate for neural delays by generating images of what will occur one-tenth of a second into the future. This foresight enables humans to react to events in the present, enabling humans to perform reflexive acts like catching a fly ball and to maneuver smoothly through a crowd.<ref name="Bryner">Key to All-Optical Illusions Discovered , Jeanna Bryner, Senior Writer, LiveScience.com 6/2/08. His research on this topic is detailed in the May/June 2008 issue of the journal Cognitive Science.</ref> In an interview with ABC Changizi said, "Illusions occur when our brains attempt to perceive the future, and those perceptions don't match reality." For example, an illusion called the Hering illusion looks like bicycle spokes around a central point, with vertical lines on either side of this central, so-called vanishing point. The illusion tricks us into thinking we are looking at a perspective picture, and thus according to Changizi, switches on our future-seeing abilities. Since we are not actually moving and the figure is static, we misperceive the straight lines as curved ones. Changizi said: Evolution has seen to it that geometric drawings like this elicit in us premonitions of the near future. The converging lines toward a vanishing point (the spokes) are cues that trick our brains into thinking we are moving forward—as we would in the real world, where the door frame (a pair of vertical lines) seems to bow out as we move through it—and we try to perceive what that world will look like in the next instant. Pathological visual illusions (distortions) A pathological visual illusion is a distortion of a real external stimulus and is often diffuse and persistent. Pathological visual illusions usually occur throughout the visual field, suggesting global excitability or sensitivity alterations. Alternatively visual hallucination is the perception of an external visual stimulus where none exists. Visual hallucinations are often from focal dysfunction and are usually transient. Types of visual illusions include oscillopsia, halos around objects, illusory palinopsia (visual trailing, light streaking, prolonged indistinct afterimages), akinetopsia, visual snow, micropsia, macropsia, teleopsia, pelopsia, metamorphopsia, dyschromatopsia, intense glare, blue field entoptic phenomenon, and purkinje trees. These symptoms may indicate an underlying disease state and necessitate seeing a medical practitioner. Etiologies associated with pathological visual illusions include multiple types of ocular disease, migraines, hallucinogen persisting perception disorder, head trauma, and prescription drugs. If a medical work-up does not reveal a cause of the pathological visual illusions, the idiopathic visual disturbances could be analogous to the altered excitability state seen in visual aura with no migraine headache. If the visual illusions are diffuse and persistent, they often affect the patient's quality of life. These symptoms are often refractory to treatment and may be caused by any of the aforementioned etiologies, but are often idiopathic. There is no standard treatment for these visual disturbances. Connections to psychological disorders The rubber hand illusion (RHI) The rubber hand illusion (RHI), a multi-sensory illusion involving both visual perception and touch, has been used to study how phantom limb syndrome affects amputees over time. Amputees with the syndrome actually responded to RHI more strongly than controls, an effect that was often consistent for both the sides of the intact and the amputated arm. However, in some studies, amputees actually had stronger responses to RHI on their intact arm, and more recent amputees responded to the illusion better than amputees who had been missing an arm for years or more. Researchers believe this is a sign that the body schema, or an individual's sense of their own body and its parts, progressively adapts to the post-amputation state. Essentially, the amputees were learning to no longer respond to sensations near what had once been their arm. As a result, many have suggested the use of RHI as a tool for monitoring an amputee's progress in reducing their phantom limb sensations and adjusting to the new state of their body. Other research used RHI in the rehabilitation of amputees with prosthetic limbs. After prolonged exposure to RHI, the amputees gradually stopped feeling a dissociation between the prosthetic (which resembled the rubber hand) and the rest of their body. This was thought to be because they adjusted to responding to and moving a limb that did not feel as connected to the rest of their body or senses. RHI may also be used to diagnose certain disorders related to impaired proprioception or impaired sense of touch in non-amputees. Illusions and schizophrenia Schizophrenia, a mental disorder often marked by hallucinations, also decreases a person's ability to perceive high-order optical illusions. This is because schizophrenia impairs one's capacity to perform top-down processing and a higher-level integration of visual information beyond the primary visual cortex, V1. Understanding how this specifically occurs in the brain may help in understanding how visual distortions, beyond imaginary hallucinations, affect schizophrenic patients. Additionally, evaluating the differences between how schizophrenic patients and unaffected individuals see illusions may enable researchers to better identify where specific illusions are processed in the visual streams. One study on schizophrenic patients found that they were extremely unlikely to be fooled by a three dimensional optical illusion, the hollow face illusion, unlike non affected volunteers. Based on fMRI data, researchers concluded that this resulted from a disconnection between their systems for bottom-up processing of visual cues and top-down interpretations of those cues in the parietal cortex. In another study on the motion-induced blindness (MIB) illusion (pictured right), schizophrenic patients continued to perceive stationary visual targets even when observing distracting motion stimuli, unlike non schizophrenic controls, who experienced motion induced blindness. The schizophrenic test subjects demonstrated impaired cognitive organization, meaning they were less able to coordinate their processing of motion cues and stationary image cues. In art Artists who have worked with optical illusions include M. C. Escher, Bridget Riley, Salvador Dalí, Giuseppe Arcimboldo, Patrick Bokanowski, Marcel Duchamp, Jasper Johns, Oscar Reutersvärd, Victor Vasarely and Charles Allan Gilbert. Contemporary artists who have experimented with illusions include Jonty Hurwitz, Sandro del Prete, Octavio Ocampo, Dick Termes, Shigeo Fukuda, Patrick Hughes, István Orosz, Rob Gonsalves, Gianni A. Sarcone, Ben Heine and Akiyoshi Kitaoka. Optical illusion is also used in film by the technique of forced perspective. Op art is a style of art that uses optical illusions to create an impression of movement, or hidden images and patterns. Trompe-l'œiluses realistic imagery to create the optical illusion that depicted objects exist in three dimensions. Tourists attractions employing large-scale illusory art allowing visitors to photograph themselves in fantastic scenes have opened in several Asian countries, such as the Trickeye Museum and Hong Kong 3D Museum. Cognitive processes hypothesis The hypothesis claims that visual illusions occur because the neural circuitry in our visual system evolves, by neural learning, to a system that makes very efficient interpretations of usual 3D scenes based in the emergence of simplified models in our brain that speed up the interpretation process but give rise to optical illusions in unusual situations. In this sense, the cognitive processes hypothesis can be considered a framework for an understanding of optical illusions as the signature of the empirical statistical way vision has evolved to solve the inverse problem. Research indicates that 3D vision capabilities emerge and are learned jointly with the planning of movements. That is, as depth cues are better perceived, individuals can develop more efficient patterns of movement and interaction within the 3D environment around them. After a long process of learning, an internal representation of the world emerges that is well-adjusted to the perceived data coming from closer objects. The representation of distant objects near the horizon is less "adequate". In fact, it is not only the Moon that seems larger when we perceive it near the horizon. In a photo of a distant scene, all distant objects are perceived as smaller than when we observe them directly using our vision. Gallery See also Notes References Further reading David Cycleback. 2018. Understanding Human Minds and Their Limits''. Publisher Bookboon.com Optical phenomena Articles containing video clips	Optical illusion	[ "Physics" ]	4,143	[ "Optical phenomena", "Physical phenomena", "Optical illusions" ]
53,507	https://en.wikipedia.org/wiki/Group%20object	In category theory, a branch of mathematics, group objects are certain generalizations of groups that are built on more complicated structures than sets. A typical example of a group object is a topological group, a group whose underlying set is a topological space such that the group operations are continuous. Definition Formally, we start with a category C with finite products (i.e. C has a terminal object 1 and any two objects of C have a product). A group object in C is an object G of C together with morphisms m : G × G → G (thought of as the "group multiplication") e : 1 → G (thought of as the "inclusion of the identity element") inv : G → G (thought of as the "inversion operation") such that the following properties (modeled on the group axioms – more precisely, on the definition of a group used in universal algebra) are satisfied m is associative, i.e. m (m × idG) = m (idG × m) as morphisms G × G × G → G, and where e.g. m × idG : G × G × G → G × G; here we identify G × (G × G) in a canonical manner with (G × G) × G. e is a two-sided unit of m, i.e. m (idG × e) = p1, where p1 : G × 1 → G is the canonical projection, and m (e × idG) = p2, where p2 : 1 × G → G is the canonical projection inv is a two-sided inverse for m, i.e. if d : G → G × G is the diagonal map, and eG : G → G is the composition of the unique morphism G → 1 (also called the counit) with e, then m (idG × inv) d = eG and m (inv × idG) d = eG. Note that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying "elements" of the group object – categories in general do not have elements of their objects. Another way to state the above is to say G is a group object in a category C if for every object X in C, there is a group structure on the morphisms Hom(X, G) from X to G such that the association of X to Hom(X, G) is a (contravariant) functor from C to the category of groups. Examples Each set G for which a group structure (G, m, u, −1) can be defined can be considered a group object in the category of sets. The map m is the group operation, the map e (whose domain is a singleton) picks out the identity element u of G, and the map inv assigns to every group element its inverse. eG : G → G is the map that sends every element of G to the identity element. A topological group is a group object in the category of topological spaces with continuous functions. A Lie group is a group object in the category of smooth manifolds with smooth maps. A Lie supergroup is a group object in the category of supermanifolds. An algebraic group is a group object in the category of algebraic varieties. In modern algebraic geometry, one considers the more general group schemes, group objects in the category of schemes. A localic group is a group object in the category of locales. The group objects in the category of groups (or monoids) are the abelian groups. The reason for this is that, if inv is assumed to be a homomorphism, then G must be abelian. More precisely: if A is an abelian group and we denote by m the group multiplication of A, by e the inclusion of the identity element, and by inv the inversion operation on A, then (A, m, e, inv) is a group object in the category of groups (or monoids). Conversely, if (A, m, e, inv) is a group object in one of those categories, then m necessarily coincides with the given operation on A, e is the inclusion of the given identity element on A, inv is the inversion operation and A with the given operation is an abelian group. See also Eckmann–Hilton argument. The strict 2-group is the group object in the category of small categories. Given a category C with finite coproducts, a cogroup object is an object G of C together with a "comultiplication" m: G → G G, a "coidentity" e: G → 0, and a "coinversion" inv: G → G that satisfy the dual versions of the axioms for group objects. Here 0 is the initial object of C. Cogroup objects occur naturally in algebraic topology. See also Hopf algebras can be seen as a generalization of group objects to monoidal categories. Groupoid object References Group theory Objects (category theory)	Group object	[ "Mathematics" ]	1,065	[ "Mathematical structures", "Objects (category theory)", "Group theory", "Fields of abstract algebra", "Category theory" ]
53,539	https://en.wikipedia.org/wiki/Soyuz%20programme	The Soyuz programme ( , ; , meaning "Union") is a human spaceflight programme initiated by the Soviet Union in the early 1960s. The Soyuz spacecraft was originally part of a Moon landing project intended to put a Soviet cosmonaut on the Moon. It was the third Soviet human spaceflight programme after the Vostok (1961–1963) and Voskhod (1964–1965) programmes. The programme consists of the Soyuz capsule and the Soyuz rocket and is now the responsibility of the Russian Roscosmos. After the retirement of the Space Shuttle in 2011, Soyuz was the only way for humans to get to the International Space Station (ISS) until 30 May 2020, when Crew Dragon flew to the ISS for the first time with astronauts. Soyuz rocket The launch vehicles used in the Soyuz expendable launch system are manufactured at the Progress State Research and Production Rocket Space Center (TsSKB-Progress) in Samara, Russia. As well as being used in the Soyuz programme as the launcher for the crewed Soyuz spacecraft, Soyuz launch vehicles are now also used to launch robotic Progress supply spacecraft to the International Space Station and commercial launches marketed and operated by TsSKB-Progress and the Starsem company. Currently Soyuz vehicles are launched from the Baikonur Cosmodrome in Kazakhstan and the Plesetsk Cosmodrome in northwest Russia and, since 2011, Soyuz launch vehicles are also being launched from the Guiana Space Centre in French Guiana. The Spaceport's new Soyuz launch site has been handling Soyuz launches since 21 October 2011, the date of the first launch. As of December 2019, 19 Guiana Soyuz launches had been made from French Guiana Space Centre, all successful. The Soyuz rocket family is one of the most dependable and widely utilized launch vehicles in the history of space travel. It has been in operation for nearly six decades, having been developed by the Soviet Union and presently run by Russia. The Soyuz rockets have played an important role in both crewed and uncrewed space missions, launching people to the International Space Station (ISS) and delivering satellites and scientific payloads. Soyuz spacecraft The basic Soyuz spacecraft design was the basis for many projects, many of which were never developed. Its earliest form was intended to travel to the Moon without employing a huge booster like the Saturn V or the Soviet N-1 by repeatedly docking with upper stages that had been put in orbit using the same rocket as the Soyuz. This and the initial civilian designs were done under the Soviet Chief Designer Sergei Pavlovich Korolev, who did not live to see the craft take flight. Several military derivatives took precedence in the Soviet design process, though they never came to pass. A Soyuz spacecraft consists of three parts (from front to back): a spheroid orbital module a small aerodynamic reentry module a cylindrical service module with solar panels attached There have been many variants of the Soyuz spacecraft, including: Sever early crewed spacecraft proposal to replace Vostok (1959) L1-1960 crewed circumlunar spacecraft proposal (1960); evolved into the Soyuz-A design L4-1960 crewed lunar orbiter proposal (1960) L1-1962 crewed lunar flyby spacecraft proposal (1962); early design led to Soyuz OS-1962 space station proposal (1962) Soyuz-A 7K-9K-11K circumlunar complex proposal (1963) Soyuz 7K crewed spacecraft concept; cancelled in 1964 in favor of the LK-1 Soyuz 9K proposed orbital tug; cancelled in 1964 when the Soyuz 7K and Soyuz P were cancelled Soyuz 11K proposed fuel tanker; cancelled in 1964 when the Soyuz 7K and Soyuz P were cancelled L3-1963 crewed lunar lander proposal (1963) L4-1963 crewed lunar orbiter proposal; modified 7K (1963) Soyuz 7K-OK (1967–1970) Soyuz 7K-L1 Zond (1967–1970) Soyuz 7K-L3 LOK (1971–1972) Soyuz 7K-OKS (1971); also known as 7KT-OK Soyuz 7K-T or "ferry" (1973–1981) Soyuz 7K-T-AF (1973); 7K-T modified for space station flight with Orion 2 space telescope Soyuz 7K-T/A9 (1974–1978); 7K-T modified for flights to military Almaz space stations Soyuz 7K-TM (1974–1976) 7K-MF6 (1976); 7K-TM modified for space station flight with MKF-6 camera Soyuz-T (1976–1986) Zarya planned 'Super Soyuz' replacement for Soyuz and Progress (1985) Alpha Lifeboat rescue spacecraft based on Zarya (1995); cancelled in favor of a modified Soyuz TM Big Soyuz enlarged version of Soyuz reentry vehicle (2008) Soyuz-TM (1986–2003) Soyuz TMA (2003–2012) Soyuz-ACTS (2006) Soyuz TMA-M (2010–2016) Soyuz MS (since 2016) Military Soyuz (P, PPK, R, 7K-VI Zvezda, and OIS) Soyuz P crewed satellite interceptor proposal (1962); cancelled in 1964 in favor of the Istrebitel Sputnikov program Soyuz R command-reconnaissance spacecraft proposal (1962); cancelled in 1966 and replaced by Almaz Soyuz 7K-TK transport spacecraft proposal for delivering cosmonauts to Soyuz R military stations (1966); cancelled in 1970 in favor of the TKS spacecraft Soyuz PPK revised version of Soyuz P (1964) Soyuz 7K-VI Zvezda space station proposal (1964) Soyuz-VI crewed combat spacecraft proposal; cancelled in 1965 Soyuz OIS (1967) Soyuz OB-VI space station proposal (1967) Soyuz 7K-S military transport proposal (1974) Soyuz 7K-ST concept for Soyuz T and TM (1974) Derivatives The Zond spacecraft was designed to take a crew around the Moon, but never achieved the required degree of safety or political need. Zond 5 did circle the Moon in September 1968, with two tortoises and other life forms, and returned safely to Earth although in an atmospheric entry which probably would have killed human travelers. The Progress series of robotic cargo ships for the Salyut, Mir, and ISS use the engine section, orbital module, automatic navigation, docking mechanism, and overall layout of the Soyuz spacecraft, but are incapable of reentry. While not a direct derivative, the Chinese Shenzhou spacecraft follows the basic template originally pioneered by Soyuz. Soyuz crewed flights Soviet human spaceflight missions started in 1961 and ended in 1991 with the dissolution of the Soviet Union. The Russian human spaceflight missions program started in 1991 and continues to this day. Soyuz crewed missions were the only spacecraft visiting the International Space Station, starting from when the Space Shuttle program ended in 2011, until the launch of Crew Dragon Demo-2 on 30 May 2020. The International Space Station always has at least one Soyuz spacecraft docked at all times for use as an escape craft. Soyuz uncrewed flights Kosmos 133 - launch failure Kosmos 140 - reentry damage Kosmos 186 Kosmos 188 Kosmos 212 Kosmos 213 Kosmos 238 Soyuz 2 - failed to dock Kosmos 379 Kosmos 396 Kosmos 434 Kosmos 496 Kosmos 573 Kosmos 613 Kosmos 638 Kosmos 656 Kosmos 670 Kosmos 672 Kosmos 772 - partial fail Soyuz 20 Kosmos 869 Kosmos 1001 Kosmos 1074 Soyuz 34 Soyuz T-1 Soyuz TM-1 Soyuz MS-14 Soyuz MS-23 Gallery See also Shenzhou, a Chinese spacecraft influenced by Soyuz Space Shuttle Buran (spacecraft) List of spaceflight-related accidents and incidents References Human spaceflight programs Crewed space program of Russia Crewed space program of the Soviet Union Projects established in 1963 1963 establishments in the Soviet Union	Soyuz programme	[ "Engineering" ]	1,642	[ "Space programs", "Human spaceflight programs" ]

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