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https://en.wikipedia.org/wiki/Adsorption | Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid (the absorbate) is dissolved by or permeates a liquid or solid (the absorbent). Adsorption is a surface phenomenon and the adsorbate does not penetrate through the surface and into the bulk of the adsorbent, while absorption involves transfer of the absorbate into the volume of the material, although adsorption does often precede absorption. The term sorption encompasses both adsorption and absorption, and desorption is the reverse of sorption.
Like surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent or metallic) of the constituent atoms of the material are fulfilled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding). It may also occur due to electrostatic attraction. The nature of the adsorption can affect the structure of the adsorbed species. For example, polymer physisorption from solution can result in squashed structures on a surface.
Adsorption is present in many natural, physical, biological and chemical systems and is widely used in industrial applications such as heterogeneous catalysts, activated charcoal, capturing and using waste heat to provide cold water for air conditioning and other process requirements (adsorption chillers), synthetic resins, increasing storage capacity of carbide-derived carbons and water purification. Adsorption, ion exchange and chromatography are |
https://en.wikipedia.org/wiki/Somatic%20cell | In cellular biology, a somatic cell (), or vegetal cell, is any biological cell forming the body of a multicellular organism other than a gamete, germ cell, gametocyte or undifferentiated stem cell. Somatic cells compose the body of an organism and divide through the process of binary fission and mitotic division.
In contrast, gametes are cells that fuse during sexual reproduction and germ cells are cells that give rise to gametes. Stem cells also can divide through mitosis, but are different from somatic in that they differentiate into diverse specialized cell types.
In mammals, somatic cells make up all the internal organs, skin, bones, blood and connective tissue, while mammalian germ cells give rise to spermatozoa and ova which fuse during fertilization to produce a cell called a zygote, which divides and differentiates into the cells of an embryo. There are approximately 220 types of somatic cell in the human body.
Theoretically, these cells are not germ cells (the source of gametes); they transmit their mutations, to their cellular descendants (if they have any), but not to the organism's descendants. However, in sponges, non-differentiated somatic cells form the germ line and, in Cnidaria, differentiated somatic cells are the source of the germline. Mitotic cell division is only seen in diploid somatic cells. Only some cells like germ cells take part in reproduction.
Evolution
As multicellularity was theorized to be evolved many times, so did sterile somatic cells. The evolution of an immortal germline producing specialized somatic cells involved the emergence of mortality, and can be viewed in its simplest version in volvocine algae. Those species with a separation between sterile somatic cells and a germline are called Weismannists. Weismannist development is relatively rare (e.g., vertebrates, arthropods, Volvox), as many species have the capacity for somatic embryogenesis (e.g., land plants, most algae, and numerous invertebrates).
Genetics and chrom |
https://en.wikipedia.org/wiki/Veronica%20%28search%20engine%29 | Veronica was a search engine system for the Gopher protocol, released in November 1992 by Steven Foster and Fred Barrie at the University of Nevada, Reno.
During its existence, Veronica was a constantly updated database of the names of almost every menu item on thousands of Gopher servers. The Veronica database could be searched from most major Gopher menus. Although the original Veronica database is no longer accessible, various local Veronica installations and at least one complete rewrite ("Veronica-2") still exist.
Naming
The search engine was named after the character Veronica Lodge from Archie Comics, an intentional analogy with the naming of the Archie search engine, a search engine for FTP servers. A backronym for Veronica is "Very Easy Rodent-Oriented Net-wide Index to Computer Archives".
See also
Archie – a search engine for finding FTP files.
Jughead – an alternative search engine system for the Gopher protocol.
WAIS – another client-server text searching system of the same era.
References
External links
local-veronica source
Search Veronica-2 an actively indexed re-implementation of Veronica.
Gopher (protocol)
Internet protocols
Internet search engines
Internet Standards
Unix Internet software |
https://en.wikipedia.org/wiki/G%C3%B6del%20numbering | In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was developed by Kurt Gödel for the proof of his incompleteness theorems. ()
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.
Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
Simplified overview
Gödel noted that each statement within a system can be represented by a natural number (its Gödel number). The significance of this was that properties of a statement – such as its truth or falsehood – would be equivalent to determining whether its Gödel number had certain properties. The numbers involved might be very large indeed, but this is not a barrier; all that matters is that such numbers can be constructed.
In simple terms, he devised a method by which every formula or statement that can be formulated in the system gets a unique number, in such a way that formulas and Gödel numbers can be mechanically converted back and forth. There are many ways this can be done. A simple example is the way in which English is stored as a sequence of numbers in computers using ASCII. Since ASCII codes are in the range 0 to 127, it is sufficient to pad them to 3 decimal digits and then to concatenate them:
The word is represented by .
The logical formula is represented by .
Gödel's encoding
Gödel used a system based on prime factorization. He first assigned a unique natural number to each basic symbol in the formal language of arithmetic wit |
https://en.wikipedia.org/wiki/Swarm%20behaviour | Swarm behaviour, or swarming, is a collective behaviour exhibited by entities, particularly animals, of similar size which aggregate together, perhaps milling about the same spot or perhaps moving en masse or migrating in some direction. It is a highly interdisciplinary topic.
As a term, swarming is applied particularly to insects, but can also be applied to any other entity or animal that exhibits swarm behaviour. The term flocking or murmuration can refer specifically to swarm behaviour in birds, herding to refer to swarm behaviour in tetrapods, and shoaling or schooling to refer to swarm behaviour in fish. Phytoplankton also gather in huge swarms called blooms, although these organisms are algae and are not self-propelled the way animals are. By extension, the term "swarm" is applied also to inanimate entities which exhibit parallel behaviours, as in a robot swarm, an earthquake swarm, or a swarm of stars.
From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities. From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination. Swarm behaviour is also studied by active matter physicists as a phenomenon which is not in thermodynamic equilibrium, and as such requires the development of tools beyond those available from the statistical physics of systems in thermodynamic equilibrium. In this regard, swarming has been compared to the mathematics of superfluids, specifically in the context of starling flocks (murmuration).
Swarm behaviour was first simulated on a computer in 1986 with the simulation program boids. This program simulates simple agents (boids) that are allowed to move according to a set of basic rules. The model was originally designed to mimic the flocking behaviour of birds, but it can be applied also to schooling fish and other swarming entities.
Models
In recent |
https://en.wikipedia.org/wiki/IBM%207040 | The IBM 7040 was a historic but short-lived model of transistor computer built in the 1960s.
History
It was announced by IBM in December 1961, but did not ship until April 1963. A later member of the IBM 700/7000 series of scientific computers, it was a scaled-down version of the IBM 7090. It was not fully compatible with the 7090. Some 7090 features, including index registers, character instructions and floating point, were extra-cost options. It also featured a different input/output architecture, based on the IBM 1414 data synchronizer, allowing more modern IBM peripherals to be used. A model designed to be compatible with the 7040 with more performance was announced as the 7044 at the same time.
Peter Fagg headed the development of the 7040 under executive Bob O. Evans.
A number of IBM 7040 and 7044 computers were shipped, but it was eventually made obsolete by the IBM System/360 family, announced in 1964. The schedule delays caused by IBM's multiple incompatible architectures provided motivation for the unified System/360 family.
The 7040 proved popular for use at universities, due to its comparatively low price. For example, one was installed in May 1965 at Columbia University.
One of the first in Canada was at the University of Waterloo, bought by professor J. Wesley Graham. A team of students was frustrated with the slow performance of the Fortran compiler. In the summer of 1965 they wrote the WATFOR compiler for their 7040, which became popular with many newly formed computer science departments.
IBM also offered the 7040 (or 7044) as an input-output processor attached to a 7090, in a configuration known as the 7090/7040 Direct Coupled System (DCS). Each computer was slightly modified to be able to interrupt the other.
IBM used similar numbers for a model of its eServer pSeries 690 RS/6000 architecture much later. The 7040-681, for example, was withdrawn in 2005.
See also
List of IBM products
IBM mainframe
History of IBM
References
External lin |
https://en.wikipedia.org/wiki/Windows%20Server%202003 | Windows Server 2003, codenamed "Whistler Server", is the second version of the Windows Server operating system produced by Microsoft. It is part of the Windows NT family of operating systems and was released to manufacturing on March 28, 2003 and generally available on April 24, 2003. Windows Server 2003 is the successor to the Server editions of Windows 2000 and the predecessor to Windows Server 2008. An updated version, Windows Server 2003 R2, was released to manufacturing on December 6, 2005. Windows Server 2003 is based on Windows 2000.
Windows Server 2003's kernel has also been used in Windows XP 64-bit Edition and Windows XP Professional x64 Edition, and was the starting point for the development of Windows Vista.
Windows Server 2003 is the final version of Windows Server that supports processors without ACPI. Its successor, Windows Server 2008, requires a processor with ACPI in any supported architecture (x86, x64 and Itanium).
As of July 2016, 18% of organizations used servers that were running Windows Server 2003.
Overview
Windows Server 2003 is the follow-up to Windows 2000 Server, incorporating compatibility and other features from Windows XP. Unlike Windows 2000, Windows Server 2003's default installation has none of the server components enabled, to reduce the attack surface of new machines. Windows Server 2003 includes compatibility modes to allow older applications to run with greater stability. It was made more compatible with Windows NT 4.0 domain-based networking. Windows Server 2003 brought in enhanced Active Directory compatibility and better deployment support to ease the transition from Windows NT 4.0 to Windows Server 2003 and Windows XP Professional.
Windows Server 2003 is the first server edition of Windows to support the IA64 and x64 architectures.
The product went through several name changes during the course of development. When first announced in 2000, it was known by its codename "Whistler Server"; it was named "Windows 2002 Serv |
https://en.wikipedia.org/wiki/10 | 10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
Anthropology
Usage and terms
A collection of ten items (most often ten years) is called a decade.
The ordinal adjective is decimal; the distributive adjective is denary.
Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten.
To reduce something by one tenth is to decimate. (In ancient Rome, the killing of one in ten soldiers in a cohort was the punishment for cowardice or mutiny; or, one-tenth of the able-bodied men in a village as a form of retribution, thus causing a labor shortage and threat of starvation in agrarian societies.)
Other
The number of kingdoms in Five Dynasties and Ten Kingdoms period.
The house number of 10 Downing Street.
The number of Provinces in Canada.
Number of dots in a tetractys.
The number of the French department Aube.
In mathematics
Ten is the fifth composite number. It is also the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it. It is the second discrete semiprime (), as well as the second member of the discrete semiprime family. Ten is the only number whose sum and difference of its prime divisors yield prime numbers ( and ). In general, powers of 10 contain divisors, where is the number of digits: 10 has 22 = 4 divisors, 100 has 32 = 9 divisors, 1,000 has 42 = 16 divisors, 10,000 has 52 = 25 divisors, and so forth. Ten is the smallest number whose status as a possible friendly number is unknown.
As important sums,
the sum of the first four positive integers.
, the sum of the first three prime numbers, and the smallest semiprime that is the sum of all the distinct prime numbers from its lower factor through its higher factor.
, the smallest number that can be written as the sum o |
https://en.wikipedia.org/wiki/Dozen | A dozen (commonly abbreviated doz or dz) is a grouping of twelve.
The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year. Twelve is convenient because it has a maximal number of divisors among the numbers up to its double, a property only true of 1, 2, 6, 12, 60, 360, and 2520.
The use of twelve as a base number, known as the duodecimal system (also as dozenal), originated in Mesopotamia (see also sexagesimal). Twelve dozen (122 = 144) are known as a gross; and twelve gross (123 = 1,728, the duodecimal 1,000) are called a great gross, a term most often used when shipping or buying items in bulk. A great hundred, also known as a small gross, is 120 or ten dozen.
Dozen may also be used to express a moderately large quantity as in "several dozen" (e.g., dozens of people came to the party).
Varying by country, some products are packaged or sold by the dozen, often foodstuff (a dozen eggs).
Etymology
The English word dozen comes from the old form douzaine, a French word meaning "a group of twelve" ("Assemblage de choses de même nature au nombre de douze" (translation: A group of twelve things of the same nature), as defined in the eighth edition of the Dictionnaire de l'Académie française). This French word is a derivation from the cardinal number douze ("twelve", from Latin duodĕcim) and the collective suffix -aine (from Latin -ēna), a suffix also used to form other words with similar meanings such as quinzaine (a group of fifteen), vingtaine (a group of twenty), centaine (a group of one hundred), etc. These French words have synonymous cognates in Spanish: docena, quincena, veintena, centena, etc. English dozen, French douzaine, Catalan dotzena, Portuguese "dúzia", Persian dowjin "دوجین", Arabic durzen "درزن", Turkish "düzine", Hindi darjan "दर्जन", German Dutzend, Dutch dozijn, Italian dozzina and Polish tuzin, are also used as indefinite quanti |
https://en.wikipedia.org/wiki/12%20%28number%29 | 12 (twelve) is the natural number following 11 and preceding 13. Twelve is a superior highly composite number, divisible by the numbers 2, 3, 4, and 6.
It is the number of years required for an orbital period of Jupiter. It is central to many systems of timekeeping, including the Western calendar and units of time of day and frequently appears in the world's major religions.
Name
Twelve is the largest number with a single-syllable name in English. Early Germanic numbers have been theorized to have been non-decimal: evidence includes the unusual phrasing of eleven and twelve, the former use of "hundred" to refer to groups of 120, and the presence of glosses such as "tentywise" or "ten-count" in medieval texts showing that writers could not presume their readers would normally understand them that way. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance.
Derived from Old English, and are first attested in the 10th-century Lindisfarne Gospels' Book of John. It has cognates in every Germanic language (e.g. German ), whose Proto-Germanic ancestor has been reconstructed as , from ("two") and suffix or of uncertain meaning. It is sometimes compared with the Lithuanian , although is used as the suffix for all numbers from 11 to 19 (analogous to "-teen"). Every other Indo-European language instead uses a form of "two"+"ten", such as the Latin . The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" (from the Latin word) is also used in some contexts, particularly base-12 numeration. Similarly, a group of twelve things is usually a "dozen" but may also be referred to as a "dodecad" or "duodecad". The adjective referring to a group of twelve is "duodecuple".
As with eleven, the earliest forms of twelve are often considered to be connected with Proto-Germanic or ("to leave"), with the implicit meaning that "two is left" after having already counted to ten. The Lithuanian suffix is also considered to |
https://en.wikipedia.org/wiki/11%20%28number%29 | 11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.
Name
"Eleven" derives from the Old English , which is first attested in Bede's late 9th-century Ecclesiastical History of the English People. It has cognates in every Germanic language (for example, German ), whose Proto-Germanic ancestor has been reconstructed as , from the prefix (adjectival "one") and suffix , of uncertain meaning. It is sometimes compared with the Lithuanian , though is used as the suffix for all numbers from 11 to 19 (analogously to "-teen").
The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as . This was formerly thought to be derived from Proto-Germanic ("ten"); it is now sometimes connected with or ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.
In languages
While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it is the first compound number in many other languages: Chinese , Korean or .
In mathematics
Eleven is the fifth prime number, and the first two-digit numeric palindrome in decimal. It forms a twin prime with 13, and it is the first member of the second prime quadruplet (11, 13, 17, 19). 11 is the first prime exponent that does not yield a Mersenne prime, where , which is composite. On the other hand, the eleventh prime number 31 is the third Mersenne prime, while the thirty-first prime number 127 is not only a Mersenne prime but also the second double Mersenne prime. 11 is also the fifth Heegner number, meaning that the ring of integers of the field has the property of unique factorization and class number 1. 11 is the first prime repunit in decimal (and simply, the first repunit), as well as the second unique prime in base ten. It is the first st |
https://en.wikipedia.org/wiki/3 | 3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious or cultural significance in many societies.
Evolution of the Arabic digit
The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३.
The Indian digits spread to the Caliphate in the 9th century. The bottom stroke was dropped around the 10th century in the western parts of the Caliphate, such as the Maghreb and Al-Andalus, when a distinct variant ("Western Arabic") of the digit symbols developed, including modern Western 3. In contrast, the Eastern Arabs retained and enlarged that stroke, rotating the digit once more to yield the modern ("Eastern") Arabic digit "٣".
In most modern Western typefaces, the digit 3, like the other decimal digits, has the height of a capital letter, and sits on the baseline. In typefaces with text figures, on the other hand, the glyph usually has the height of a lowercase letter "x" and a descender: "". In some French text-figure typefaces, though, it has an ascender instead of a descender.
A common graphic variant of the digit three has a flat top, similar to the letter Ʒ (ezh). This form is sometimes used to prevent falsifying a 3 as an 8. It is found on UPC-A barcodes and standard 52-card decks.
Mathematics
3 is the second smallest prime number an |
https://en.wikipedia.org/wiki/7 | 7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube.
As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week. It is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky.
Evolution of the Arabic digit
In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase vertically inverted (ᒉ). The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs developed the digit from a form that looked something like 6 to one that looked like an uppercase V. Both modern Arab forms influenced the European form, a two-stroke form consisting of a horizontal upper stroke joined at its right to a stroke going down to the bottom left corner, a line that is slightly curved in some font variants. As is the case with the European digit, the Cham and Khmer digit for 7 also evolved to look like their digit 1, though in a different way, so they were also concerned with making their 7 more different. For the Khmer this often involved adding a horizontal line to the top of the digit. This is analogous to the horizontal stroke through the middle that is sometimes used in handwriting in the Western world but which is almost never used in computer fonts. This horizontal stroke is, however, important to distinguish the glyph for seven from the glyph for one in writing that uses a long upstroke in the glyph for 1. In some Greek dialects of the early 12th century the longer line diagonal was drawn in a rather semicircular transverse line.
On seven-segment displays, |
https://en.wikipedia.org/wiki/4 | 4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.
Evolution of the Hindu-Arabic digit
Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The Arabs' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross.
While the shape of the character for the digit 4 has an ascender in most modern typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in .
On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top: .
Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".
Mathematics
Four is the smallest composite number, its proper divisors being and . Four is the sum and product of two with itself: , the only number such that , which also makes four the smallest and only even squared prime number and hence the first squared prime of the form , where is a prime. Four, as the first composite number, has a prime aliquot sum of 3; and as such it is pa |
https://en.wikipedia.org/wiki/6 | 6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.
In mathematics
Six is the smallest positive integer which is neither a square number nor a prime number. It is the second smallest composite number after four, equal to the sum and the product of its three proper divisors (, and ). As such, 6 is the only number that is both the sum and product of three consecutive positive numbers. It is the smallest perfect number, which are numbers that are equal to their aliquot sum, or sum of their proper divisors. It is also the largest of the four all-Harshad numbers (1, 2, 4, and 6).
6 is a pronic number and the only semiprime to be. It is the first discrete biprime (2 × 3) which makes it the first member of the (2 × q) discrete biprime family, where q is a higher prime. All primes above 3 are of the form 6n ± 1 for n ≥ 1.
As a perfect number:
6 is related to the Mersenne prime 3, since . (The next perfect number is 28.)
6 is the only even perfect number that is not the sum of successive odd cubes.
6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one other number; the square number, .
Six is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist; sixty (10 × 6) and ninety (15 × 6) are the next two.
All integers that are multiples of 6 are pseudoperfect (all multiples of a pseudoperfect number are pseudoperfect). Six is also the smallest Granville number, or -perfect number.
Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". Six is a congruent number.
6 is the second primary pseudoperfect number, and harmonic divisor number. It is also the second superior highly composite number, and the last to also be a primorial.
There are 6 non-equivalent ways in which 100 can be expressed as the sum of two prime numbers: (3 + 97), (11 + 89), |
https://en.wikipedia.org/wiki/8 | 8 (eight) is the natural number following 7 and preceding 9.
Etymology
English eight, from Old English , æhta, Proto-Germanic *ahto is a direct continuation of Proto-Indo-European *oḱtṓ(w)-, and as such cognate with Greek and Latin octo-, both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary.
The adjective octuple (Latin octu-plus) may also be used as a noun, meaning "a set of eight items"; the diminutive octuplet is mostly used to refer to eight siblings delivered in one birth.
The Semitic numeral is based on a root *θmn-, whence Akkadian smn-, Arabic ṯmn-, Hebrew šmn- etc.
The Chinese numeral, written (Mandarin: bā; Cantonese: baat), is from Old Chinese *priāt-, ultimately from Sino-Tibetan b-r-gyat or b-g-ryat which also yielded Tibetan brgyat.
It has been argued that, as the cardinal number is the highest number of items that can universally be cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar.
The Turkic words for "eight" are from a Proto-Turkic stem *sekiz, which has been suggested as originating as a negation of eki "two", as in "without two fingers" (i.e., "two short of ten; two fingers are not being held up");
this same principle is found in Finnic *kakte-ksa, which conveys a meaning of "two before (ten)". The Proto-Indo-European reconstruction *oḱtṓ(w)- itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four".
Proponents of this "quaternary hypothesis" adduce the numeral , which might be built on the stem new-, meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight).
Evolution of the Arabic digit
The modern digit 8, like all modern Arabic numerals other than zero, originates with the Brahmi numerals.
The Brahmi digit for e |
https://en.wikipedia.org/wiki/Lucky%20number | In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers).
The term was introduced in 1956 in a paper by Gardiner, Lazarus, Metropolis and Ulam. In the same work they also suggested calling another sieve, "the sieve of Josephus Flavius" because of its similarity with the counting-out game in the Josephus problem.
Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. Twin lucky numbers and twin primes also appear to occur with similar frequency. However, if Ln denotes the n-th lucky number, and pn the n-th prime, then Ln > pn for all sufficiently large n.
Because of their apparent similarities with the prime numbers, some mathematicians have suggested that some of their common properties may also be found in other sets of numbers generated by sieves of a certain unknown form, but there is little theoretical basis for this conjecture.
The sieving process
Continue removing the nth remaining numbers, where n is the next number in the list after the last surviving number. Next in this example is 9.
One way that the application of the procedure differs from that of the Sieve of Eratosthenes is that for n being the number being multiplied on a specific pass, the first number eliminated on the pass is the n-th remaining number that has not yet been eliminated, as opposed to the number 2n. That is to say, the list of numbers this sieve counts through is different on each pass (for example 1, 3, 7, 9, 13, 15, 19... on the third pass), whereas in the Sieve of Eratosthenes, the sieve always counts through the entire original list (1, 2 |
https://en.wikipedia.org/wiki/John%20the%20Ripper | John the Ripper is a free password cracking software tool. Originally developed for the Unix operating system, it can run on fifteen different platforms (eleven of which are architecture-specific versions of Unix, DOS, Win32, BeOS, and OpenVMS). It is among the most frequently used password testing and breaking programs as it combines a number of password crackers into one package, autodetects password hash types, and includes a customizable cracker. It can be run against various encrypted password formats including several crypt password hash types most commonly found on various Unix versions (based on DES, MD5, or Blowfish), Kerberos AFS, and Windows NT/2000/XP/2003 LM hash. Additional modules have extended its ability to include MD4-based password hashes and passwords stored in LDAP, MySQL, and others.
Sample output
Here is a sample output in a Debian environment.
$ cat pass.txt
user:AZl.zWwxIh15Q
$ john -w:password.lst pass.txt
Loaded 1 password hash (Traditional DES [24/32 4K])
example (user)
guesses: 1 time: 0:00:00:00 100% c/s: 752 trying: 12345 - pookie
The first line is a command to expand the data stored in the file "pass.txt". The next line is the contents of the file, i.e. the user (AZl) and the hash associated with that user (zWwxIh15Q). The third line is the command for running John the Ripper utilizing the "-w" flag. "password.lst" is the name of a text file full of words the program will use against the hash, pass.txt makes another appearance as the file we want John to work on.
Then we see output from John working. Loaded 1 password hash — the one we saw with the "cat" command — and the type of hash John thinks it is (Traditional DES). We also see that the attempt required one guess at a time of 0 with a 100% guess rate.
Attack types
One of the modes John can use is the dictionary attack. It takes text string samples (usually from a file, called a wordlist, containing words found in a dictionary or real passwords cracked before), e |
https://en.wikipedia.org/wiki/15%20%28number%29 | 15 (fifteen) is the natural number following 14 and preceding 16.
Mathematics
15 is:
The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; its proper divisors are , , and , so the first of the form (3.q), where q is a higher prime.
a deficient number, a lucky number, a bell number (i.e., the number of partitions for a set of size 4), a pentatope number, and a repdigit in binary (1111) and quaternary (33). In hexadecimal, and higher bases, it is represented as F.
with an aliquot sum of 9; within an aliquot sequence of three composite numbers (15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
the second member of the first cluster of two discrete semiprimes (14, 15); the next such cluster is (21, 22).
a triangular number, a hexagonal number, and a centered tetrahedral number.
the number of partitions of 7.
the smallest number that can be factorized using Shor's quantum algorithm.
the magic constant of the unique order-3 normal magic square.
the number of supersingular primes.
the smallest positive number that can be expressed as the difference of two positive squares in more than one way: or (see image).
Furthermore,
15's prime factors, (3 and 5), form the first twin-prime pair.
The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers.
In decimal, 15 contains the digits 1 and 5 and is the result of adding together the integers from 1 to 5 (1 + 2 + 3 + 4 + 5 = 15). The only other number with this property (in decimal) is 27.
There are 15 truncatable primes that are both right-truncatable and left-truncatable:
2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397
There are 15 perfect matchings of the complete graph K6 and 15 rooted binary trees with four labeled leaves, both of these being among the types of objects counted by double factorials.
With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by t |
https://en.wikipedia.org/wiki/16%20%28number%29 | 16 (sixteen) is the natural number following 15 and preceding 17. 16 is the ninth composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and .
16 is the first non-unitary fourth-power prime of the form p4
The aliquot sum of a 2-power (2n) is always one less than the 2-power itself therefore the aliquot sum of 16 is 15, within an aliquot sequence of four composite members (16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
In English speech, the numbers 16 and 60 are sometimes confused, as they sound very similar.
Sixteen is the fourth power of two. For this reason, 16 was used in weighing light objects in several cultures. The British have 16 ounces in one pound; the Chinese used to have 16 liangs in one jin. In old days, weighing was done with a beam balance to make equal splits. It would be easier to split a heap of grains into sixteen equal parts through successive divisions than to split into ten parts. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and 5 lower beads to represent the 1s, the 7 beads can represent a hexadecimal digit from 0 to 15 in each column.
Mathematics
Sixteen is an even number and the square of four.
Sixteen is the fourth power of two.
Sixteen is the only integer that equals mn and nm, for some unequal integers m and n (, , or vice versa). It has this property because . It is also equal to 32 (see tetration).
Sixteen is the base of the hexadecimal number system, which is used extensively in computer science.
Sixteen is the largest known integer , for which is prime.
It is the first Erdős–Woods number.
There are 16 partially ordered sets with four unlabeled elements.
16 is the only number that can be both the perimeter and area of the same |
https://en.wikipedia.org/wiki/20%20%28number%29 | 20 (twenty; Roman numeral XX) is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.
In mathematics
Twenty is a pronic number, as it is the product of consecutive integers, namely 4 and 5. It is the third composite number to be the product of a squared prime and a prime, and also the second member of the 22 × q family in this form.
20 has an aliquot sum of 22; a semiprime, within an aliquot sequence of four composite numbers (20, 22, 14, 10, 8) that belong to the prime 7-aliquot tree.
20 is the smallest primitive abundant number.
20 is the third tetrahedral number.
20 is the basis for vigesimal number systems.
20 is the number of parallelogram polyominoes with 5 cells.
20 is the number of moves (quarter or half turns) required to optimally solve a Rubik's Cube in the worst case.
20 is the length of a side of the fifth smallest right triangle that forms a primitive Pythagorean triple, (20,21,29). This is the second Pythagorean triple that can be formed using Pell numbers where and are one unit apart.
20 is the smallest non-trivial decimal neon number equal to the sum of its digits when raised to the thirteenth power (2013 = 8192 × 1013).
There are twenty edge-to-edge 2-uniform tilings by convex regular polygons, which are uniform tessellations of the plane containing 2 orbits of vertices.
The largest number of faces a Platonic solid can have is twenty faces, which make up a regular icosahedron. A dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. There are a total of 20 regular and semiregular polyhedra, aside from the infinite family of semiregular prisms and antiprisms that exists in the third dimension: the 5 Platonic solids, and 15 Archimedean solids (including chiral forms of the snub cube and snub dodecahedron). There are also four uniform compound polyhedra that contain twenty polyhedra (UC13, UC14, UC19, UC33), which is the most any |
https://en.wikipedia.org/wiki/Parabolic%20antenna | A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves. The most common form is shaped like a dish and is popularly called a dish antenna or parabolic dish. The main advantage of a parabolic antenna is that it has high directivity. It functions similarly to a searchlight or flashlight reflector to direct radio waves in a narrow beam, or receive radio waves from one particular direction only. Parabolic antennas have some of the highest gains, meaning that they can produce the narrowest beamwidths, of any antenna type. In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used, so parabolic antennas are used in the high frequency part of the radio spectrum, at UHF and microwave (SHF) frequencies, at which the wavelengths are small enough that conveniently-sized reflectors can be used.
Parabolic antennas are used as high-gain antennas for point-to-point communications, in applications such as microwave relay links that carry telephone and television signals between nearby cities, wireless WAN/LAN links for data communications, satellite communications, and spacecraft communication antennas. They are also used in radio telescopes.
The other large use of parabolic antennas is for radar antennas, which need to transmit a narrow beam of radio waves to locate objects like ships, airplanes, and guided missiles. They are also often used for weather detection. With the advent of home satellite television receivers, parabolic antennas have become a common feature of the landscapes of modern countries.
The parabolic antenna was invented by German physicist Heinrich Hertz during his discovery of radio waves in 1887. He used cylindrical parabolic reflectors with spark-excited dipole antennas at their foci for both transmitting and receiving during his historic experiments.
Design
The operating principle of a pa |
https://en.wikipedia.org/wiki/17%20%28number%29 | 17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.
Seventeen is the sum of the first four prime numbers.
In mathematics
Seventeen is the seventh prime number, which makes it the fourth super-prime, as seven is itself prime. It forms a twin prime with 19, a cousin prime with 13, and a sexy prime with both 11 and 23. Seventeen is the only prime number which is the sum of four consecutive primes (2, 3, 5, and 7), as any other four consecutive primes that are added always generate an even number divisible by two. It is one of six lucky numbers of Euler which produce primes of the form , and the sixth Mersenne prime exponent, which yields 131,071. It is also the minimum possible number of givens for a sudoku puzzle with a unique solution. 17 can be written in the form and ; and as such, it is a Leyland prime and Leyland prime of the second kind:
17 is the third Fermat prime, as it is of the form with . On the other hand, the seventeenth Jacobsthal–Lucas number — that is part of a sequence which includes four Fermat primes (except for 3) — is the fifth and largest known Fermat prime: 65,537. It is one more than the smallest number with exactly seventeen divisors, 65,536 = 216. Since seventeen is a Fermat prime, regular heptadecagons can be constructed with a compass and unmarked ruler. This was proven by Carl Friedrich Gauss and ultimately led him to choose mathematics over philology for his studies.
Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other natural numbers with this property. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch notes it when writing that the Pythagoreans "utterly abominate" 17, which "bars them off from each other and disjoins them".
17 is the minimum number of vertices on a graph such that, if the edges are colored with three different colors, there is bound to be a monochromatic triangle; see Ramsey's theo |
https://en.wikipedia.org/wiki/19%20%28number%29 | 19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
Mathematics
is the eighth prime number, and forms a sexy prime with 13, a twin prime with 17, and a cousin prime with 23. It is the third full reptend prime in decimal, the fifth central trinomial coefficient, and the seventh Mersenne prime exponent. 19 is the second Keith number, and more specifically the first Keith prime. It is also the second octahedral number, after 6.
R19 is the second base-10 repunit prime, short for the number 1111111111111111111.
19 is the maximum number of fourth powers needed to sum up to any natural number, and in the context of Waring's problem, 19 is the fourth value of g(k).
The sum of the squares of the first 19 primes is divisible by 19.
19 is the sixth Heegner number. 67 and 163, respectively the 19th and 38th prime numbers, are the two largest Heegner numbers, of nine total.
19 is the third centered triangular number as well as the third centered hexagonal number.
The 19th triangular number is 190, equivalently the sum of the first 19 non-zero integers, that is also the sixth centered nonagonal number.
19 is the first number in an infinite sequence of numbers in decimal whose digits start with 1 and have trailing 9's, that form triangular numbers containing trailing zeroes in proportion to 9s present in the original number; i.e. 19900 is the 199th triangular number, and 1999000 is the 1999th.
Like 19, 199 and 1999 are also both prime, as are 199999 and 19999999. In fact, a number of the form 19n, where n is the number of nines that terminate in the number, is prime for:
n = {1, 2, 3, 5, 7, 26, 27, 53, 147, 236, 248, 386, 401}.
19, alongside 109, 1009, and 10009, are all prime (with 109 also full reptend), and form part of a sequence of numbers where inserting a digit inside the previous term produces the next smallest prime possible, up to scale, with the composite number 9 as root. 100019 is the next such smallest pr |
https://en.wikipedia.org/wiki/18%20%28number%29 | 18 (eighteen) is the natural number following 17 and preceding 19.
In mathematics
Eighteen is the tenth composite number, its divisors being 1, 2, 3, 6 and 9. Three of these divisors (3, 6 and 9) add up to 18, hence 18 is a semiperfect number. Eighteen is the first inverted square-prime of the form p·q2.
In base ten, it is a Harshad number.
It is an abundant number, as the sum of its proper divisors is greater than itself (1+2+3+6+9 = 21). It is known to be a solitary number, despite not being coprime to this sum.
It is the number of one-sided pentominoes.
It is the only number where the sum of its written digits in base 10 (1+8 = 9) is equal to half of itself (18/2 = 9).
It is a Fine number.
In science
Chemistry
Eighteen is the atomic number of argon.
Group 18 of the periodic table is called the noble gases.
The 18-electron rule is a rule of thumb in transition metal chemistry for characterising and predicting the stability of metal complexes.
In religion and literature
The Hebrew word for "life" is (chai), which has a numerical value of 18. Consequently, the custom has arisen in Jewish circles to give donations and monetary gifts in multiples of 18 as an expression of blessing for long life.
In Judaism, in the Talmud; Pirkei Avot (5:25), Rabbi Yehudah ben Teime gives the age of 18 as the appropriate age to get married ("Ben shmonah esra lechupah", at eighteen years old to the Chupah (marriage canopy)). (See Coming of age, Age of majority).
Shemoneh Esrei (sh'MOH-nuh ES-ray) is a prayer that is the center of any Jewish religious service. Its name means "eighteen". The prayer is also known as the Amidah.
In Ancient Roman custom the number 18 can symbolise a blood relative.
Joseph Heller's novel Catch-22 was originally named Catch-18 because of the Hebrew meaning of the number, but was amended to the published title to avoid confusion with another war novel, Mila 18.
There are 18 chapters in the Bhagavad Gita, which is contained in the Mahabharata |
https://en.wikipedia.org/wiki/Primary%20production | In ecology, primary production is the synthesis of organic compounds from atmospheric or aqueous carbon dioxide. It principally occurs through the process of photosynthesis, which uses light as its source of energy, but it also occurs through chemosynthesis, which uses the oxidation or reduction of inorganic chemical compounds as its source of energy. Almost all life on Earth relies directly or indirectly on primary production. The organisms responsible for primary production are known as primary producers or autotrophs, and form the base of the food chain. In terrestrial ecoregions, these are mainly plants, while in aquatic ecoregions algae predominate in this role. Ecologists distinguish primary production as either net or gross, the former accounting for losses to processes such as cellular respiration, the latter not.
Overview
Primary production is the production of chemical energy in organic compounds by living organisms. The main source of this energy is sunlight but a minute fraction of primary production is driven by lithotrophic organisms using the chemical energy of inorganic molecules.Regardless of its source, this energy is used to synthesize complex organic molecules from simpler inorganic compounds such as carbon dioxide () and water (H2O). The following two equations are simplified representations of photosynthesis (top) and (one form of) chemosynthesis (bottom):
+ H2O + light → CH2O + O2
+ O2 + 4 H2S → CH2O + 4 S + 3 H2O
In both cases, the end point is a polymer of reduced carbohydrate, (CH2O)n, typically molecules such as glucose or other sugars. These relatively simple molecules may be then used to further synthesise more complicated molecules, including proteins, complex carbohydrates, lipids, and nucleic acids, or be respired to perform work. Consumption of primary producers by heterotrophic organisms, such as animals, then transfers these organic molecules (and the energy stored within them) up the food web, fueling all of the Earth' |
https://en.wikipedia.org/wiki/R-S-T%20system | The R-S-T system is used by amateur radio operators, shortwave listeners, and other radio hobbyists to exchange information about the quality of a radio signal being received. The code is a three digit number, with one digit each for conveying an assessment of the signal's readability, strength, and tone. The code was developed in 1934 by Amateur radio operator Arthur W. Braaten, W2BSR, and was similar to that codified in the ITU Radio Regulations, Cairo, 1938.
Readability
The R stands for "Readability". Readability is a qualitative assessment of how easy or difficult it is to correctly copy the information being sent during the transmission. In a Morse code telegraphy transmission, readability refers to how easy or difficult it is to distinguish each of the characters in the text of the message being sent; in a voice transmission, readability refers to how easy or difficult it is for each spoken word to be understood correctly. Readability is measured on a scale of 1 to 5.
Unreadable
Barely readable, occasional words distinguishable
Readable with considerable difficulty
Readable with practically no difficulty
Perfectly readable
Strength
The S stands for "Strength". Strength is an assessment of how powerful the received signal is at the receiving location. Although an accurate signal strength meter can determine a quantitative value for signal strength, in practice this portion of the RST code is a qualitative assessment, often made based on the S meter of the radio receiver at the location of signal reception. "Strength" is measured on a scale of 1 to 9.
Faint—signals barely perceptible
Very weak signals
Weak signals
Fair signals
Fairly good signals
Good signals
Moderately strong signals
Strong signals
Extremely strong signals
For a quantitative assessment, quality HF receivers are calibrated so that S9 on the S-meter corresponds to a signal of 50 μV at the antenna standard terminal impedance 50 ohms. One "S" difference should correspond t |
https://en.wikipedia.org/wiki/Ten-code | Ten-codes, officially known as ten signals, are brevity codes used to represent common phrases in voice communication, particularly by law enforcement and in citizens band (CB) radio transmissions. The police version of ten-codes is officially known as the APCO Project 14 Aural Brevity Code.
The codes, developed during 1937–1940 and expanded in 1974 by the Association of Public-Safety Communications Officials-International (APCO), allow brevity and standardization of message traffic. They have historically been widely used by law enforcement officers in North America, but in 2006, due to the lack of standardization, the U.S. federal government recommended they be discontinued in favor of everyday language.
History
APCO first proposed Morse code brevity codes in the June 1935 issue of The APCO Bulletin, which were adapted from the procedure symbols of the U.S. Navy, though these procedures were for communications in Morse code, not voice.
In August 1935, the APCO Bulletin published a recommendation that the organization issue a handbook that described standard operating procedures, including:
A standard message form for use by all police departments.
A simple code for service dispatches relating to corrections, repetitions, etc.
A standard arrangement of the context of messages, (for example, name and description of missing person might be transmitted as follows: Name, age, height, weight, physical characteristics, clothing; if car used, the license, make, description and motor number. This information would actually be transmitted in the text of the message as follows: John Brown 28-5-9-165 medium build brown eyes dark hair dark suit light hat Mich. 35 lic. W 2605 Ford S 35 blue red wheels 2345678 may go to Indiana).
A standard record system for logging the operation of the station.
Other important records in accordance with the uniform crime reporting system sponsored by the International Association of Chiefs of Police.
The development of the APCO Ten Sig |
https://en.wikipedia.org/wiki/List%20%28abstract%20data%20type%29 | In computer science, a list or sequence is an abstract data type that represents a finite number of ordered values, where the same value may occur more than once. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence; the (potentially) infinite analog of a list is a stream. Lists are a basic example of containers, as they contain other values. If the same value occurs multiple times, each occurrence is considered a distinct item.
The name list is also used for several concrete data structures that can be used to implement abstract lists, especially linked lists and arrays. In some contexts, such as in Lisp programming, the term list may refer specifically to a linked list rather than an array. In class-based programming, lists are usually provided as instances of subclasses of a generic "list" class, and traversed via separate iterators.
Many programming languages provide support for list data types, and have special syntax and semantics for lists and list operations. A list can often be constructed by writing the items in sequence, separated by commas, semicolons, and/or spaces, within a pair of delimiters such as parentheses '()', brackets '[]', braces '{}', or angle brackets '<>'. Some languages may allow list types to be indexed or sliced like array types, in which case the data type is more accurately described as an array.
In type theory and functional programming, abstract lists are usually defined inductively by two operations: nil that yields the empty list, and cons, which adds an item at the beginning of a list.
Operations
Implementation of the list data structure may provide some of the following operations:
a constructor for creating an empty list;
an operation for testing whether or not a list is empty;
an operation for prepending an entity to a list
an operation for appending an entity to a list
an operation for determining the first component (or the "head") of a list
an operation for r |
https://en.wikipedia.org/wiki/Filoviridae | Filoviridae () is a family of single-stranded negative-sense RNA viruses in the order Mononegavirales. Two members of the family that are commonly known are Ebola virus and Marburg virus. Both viruses, and some of their lesser known relatives, cause severe disease in humans and nonhuman primates in the form of viral hemorrhagic fevers.
All filoviruses are classified by the US as select agents, by the World Health Organization as Risk Group 4 Pathogens (requiring Biosafety Level 4-equivalent containment), by the National Institutes of Health/National Institute of Allergy and Infectious Diseases as Category A Priority Pathogens, and by the Centers for Disease Control and Prevention as Category A Bioterrorism Agents, and are listed as Biological Agents for Export Control by the Australia Group.
Use of term
The family Filoviridae is a virological taxon that was defined in 1982 and emended in 1991, 1998, 2000, 2005, 2010 and 2011. The family currently includes the six virus genera Cuevavirus, Dianlovirus, Ebolavirus, Marburgvirus, Striavirus, and Thamnovirus and is included in the order Mononegavirales. The members of the family (i.e. the actual physical entities) are called filoviruses or filovirids. The name Filoviridae is derived from the Latin noun filum (alluding to the filamentous morphology of filovirions) and the taxonomic suffix -viridae (which denotes a virus family).
Note
According to the rules for taxon naming established by the International Committee on Taxonomy of Viruses (ICTV), the name Filoviridae is always to be capitalized, italicized, never abbreviated, and to be preceded by the word "family". The names of its members (filoviruses or filovirids) are to be written in lower case, are not italicized, and used without articles.
Life cycle
The filovirus life cycle begins with virion attachment to specific cell-surface receptors, followed by fusion of the virion envelope with cellular membranes and the concomitant release of the virus nucleocapsid int |
https://en.wikipedia.org/wiki/Object-modeling%20technique | The object-modeling technique (OMT) is an object modeling approach for software modeling and designing. It was developed around 1991 by Rumbaugh, Blaha, Premerlani, Eddy and Lorensen as a method to develop object-oriented systems and to support object-oriented programming. OMT describes object model or static structure of the system.
OMT was developed as an approach to software development. The purposes of modeling according to Rumbaugh are:
testing physical entities before building them (simulation),
communication with customers,
visualization (alternative presentation of information), and
reduction of complexity.
OMT has proposed three main types of models:
Object model: The object model represents the static and most stable phenomena in the modeled domain. Main concepts are classes and associations with attributes and operations. Aggregation and generalization (with multiple inheritance) are predefined relationships.
Dynamic model: The dynamic model represents a state/transition view on the model. Main concepts are states, transitions between states, and events to trigger transitions. Actions can be modeled as occurring within states. Generalization and aggregation (concurrency) are predefined relationships.
Functional model: The functional model handles the process perspective of the model, corresponding roughly to data flow diagrams. Main concepts are process, data store, data flow, and actors.
OMT is a predecessor of the Unified Modeling Language (UML). Many OMT modeling elements are common to UML.
Functional Model in OMT:
In brief, a functional model in OMT defines the function of the whole internal processes in a model with the help of "Data Flow Diagrams (DFDs)". It details how processes are performed independently.
References
Further reading
James Rumbaugh, Michael Blaha, William Premerlani, Frederick Eddy, William Lorensen (1994). Object-Oriented Modeling and Design. Prentice Hall.
Terry Quatrani, Michael Jesse Chonoles (1996). Succeeding |
https://en.wikipedia.org/wiki/Highly%20composite%20number |
A highly composite number or antiprime is a positive integer with more divisors than any smaller positive integer has. A related concept is that of a largely composite number, a positive integer which has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually composite numbers; however, all further terms are.
Ramanujan wrote a paper on highly composite numbers in 1915.
The mathematician Jean-Pierre Kahane suggested that Plato must have known about highly composite numbers as he deliberately chose such a number, 5040 (= 7!), as the ideal number of citizens in a city.
Examples
The initial or smallest 40 highly composite numbers are listed in the table below . The number of divisors is given in the column labeled d(n). Asterisks indicate superior highly composite numbers.
The divisors of the first 19 highly composite numbers are shown below.
The table below shows all 72 divisors of 10080 by writing it as a product of two numbers in 36 different ways.
The 15,000th highly composite number can be found on Achim Flammenkamp's website. It is the product of 230 primes:
where is the sequence of successive prime numbers, and all omitted terms (a22 to a228) are factors with exponent equal to one (i.e. the number is ). More concisely, it is the product of seven distinct primorials:
where is the primorial .
Prime factorization
Roughly speaking, for a number to be highly composite it has to have prime factors as small as possible, but not too many of the same. By the fundamental theorem of arithmetic, every positive integer n has a unique prime factorization:
where are prime, and the exponents are positive integers.
Any factor of n must have the same or lesser multiplicity in each prime:
So the number of divisors of n is:
Hence, for a highly composite number n,
the k given prime numbers pi must be precisely the first k prime numbers (2, 3, 5, ... |
https://en.wikipedia.org/wiki/Thirty-year%20rule | The "thirty-year rule" is the informal name given to laws in the United Kingdom, the Republic of Ireland, and the Commonwealth of Australia that provide that certain government documents will be released publicly thirty years after they were created.
Some other countries' national archives also adhere to a thirty-year rule for the release of government documents.
United Kingdom
In the United Kingdom, the Public Records Act 1958 stated that:
The closure period was reduced from fifty to thirty years by an amending act of 1967, passed during Harold Wilson's government. Among those who had repeatedly urged the scrapping of the fifty-year rule was the historian A. J. P. Taylor.
There were two elements to the rule: the first required that records be transferred from government departments to the Public Record Office (now The National Archives) after thirty years unless specific exemptions were given (by the Lord Chancellor's Advisory Council on Public Records); the second that they would be opened to public access at the same time unless their release was deemed likely to cause "damage to the country's image, national security or foreign relations".
Significant changes were made to the rules as a consequence of the Freedom of Information Act 2000 (FOIA) (which came into full effect on 1 January 2005). FOIA essentially removed the second of the thirty-year rules (the access one), and replaced it with provisions allowing citizens to request a wide range of information before any time limit has expired; and also removed some of the exemptions which had previously applied at the thirty-year point. After thirty years, records are transferred to The National Archives, and are reviewed under FOIA to see if they should be opened. The only rationale for keeping them closed within The National Archives is if a FOIA exemption applies.
As a result of that change, releases now occur monthly, rather than annually, and include more recent events, rather than only those over thirt |
https://en.wikipedia.org/wiki/Menger%20sponge | In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.
Construction
The construction of a Menger sponge can be described as follows:
Begin with a cube.
Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes.
Remove the smaller cube in the middle of each face, and remove the smaller cube in the center of the more giant cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).
Repeat steps two and three for each of the remaining smaller cubes, and continue to iterate ad infinitum.
The second iteration gives a level-2 sponge, the third iteration gives a level-3 sponge, and so on. The Menger sponge itself is the limit of this process after an infinite number of iterations.
Properties
The th stage of the Menger sponge, , is made up of smaller cubes, each with a side length of (1/3)n. The total volume of is thus . The total surface area of is given by the expression . Therefore, the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues so that the limit is neither a solid nor a surface; it has a topological dimension of 1 and is accordingly identified as a curve.
Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross-section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry. The number of these hexagrams, in d |
https://en.wikipedia.org/wiki/Quotient%20of%20a%20formal%20language | In mathematics and computer science, the right quotient (or simply quotient) of a language with respect to language is the language consisting of strings w such that wx is in for some string x in Formally:
In other words, we take all the strings in that have a suffix in , and remove this suffix.
Similarly, the left quotient of with respect to is the language consisting of strings w such that xw is in for some string x in . Formally:
In other words, we take all the strings in that have a prefix in , and remove this prefix.
Note that the operands of are in reverse order: the first operand is and is second.
Example
Consider
and
Now, if we insert a divider into an element of , the part on the right is in only if the divider is placed adjacent to a b (in which case i ≤ n and j = n) or adjacent to a c (in which case i = 0 and j ≤ n). The part on the left, therefore, will be either or ; and can be written as
Properties
Some common closure properties of the quotient operation include:
The quotient of a regular language with any other language is regular.
The quotient of a context free language with a regular language is context free.
The quotient of two context free languages can be any recursively enumerable language.
The quotient of two recursively enumerable languages is recursively enumerable.
These closure properties hold for both left and right quotients.
See also
Brzozowski derivative
References
Formal languages |
https://en.wikipedia.org/wiki/Underclocking | Underclocking, also known as downclocking, is modifying a computer or electronic circuit's timing settings to run at a lower clock rate than is specified. Underclocking is used to reduce a computer's power consumption, increase battery life, reduce heat emission, and it may also increase the system's stability, lifespan/reliability and compatibility. Underclocking may be implemented by the factory, but many computers and components may be underclocked by the end user.
Types
CPU underclocking
For microprocessors, the purpose is generally to decrease the need for heat dissipation devices or decrease the electrical power consumption. This can provide increased system stability in high-heat environments, or can allow a system to run with a lower airflow (and therefore quieter) cooling fan or without one at all. For example, a Pentium 4 processor normally clocked at 3.4 GHz can be "underclocked" to 2 GHz and can then be safely run with reduced fan speeds. This invariably comes at the expense of some system performance. However, the proportional performance reduction is usually less than the proportional reduction in clock speed because performance is often limited by other bottlenecks: the hard disk, GPU, disk controller, Internet, network, etc. Underclocking refers to alterations of the timing of a synchronous circuit in order to lower a device's energy needs. Deliberate underclocking involves limiting a processor's speed, which may affect the speed of operations, but may or may not make a device noticeably less able, depending on other hardware and desired use.
Many computers and other devices allow for underclocking. Manufacturers add underclocking options for many reasons. Underclocking can help with excessive heat buildup, because lower performance will not generate as much heat inside the device. It can also lower the amount of energy needed to run the device. Laptop computers and other battery-operated devices often have underclocking settings, so that batterie |
https://en.wikipedia.org/wiki/Outline%20of%20sustainable%20agriculture | The following outline is provided as an overview of and topical guide to sustainable agriculture:
Sustainable agriculture – applied science that integrates three main goals, environmental health, economic profitability, and social and economic equity. These goals have been defined by various philosophies, policies, and practices, from the vision of farmers and consumers. Perspectives and approaches are very diverse. The following topics intend to help understand sustainable agriculture.
Introduction
Agroecology
Alan Chadwick
Biodynamic agriculture
Ecoagriculture
French intensive gardening
Horticulture
John D. Hamaker
Lady Eve Balfour
Organic farming
Polyculture
Resilience (ecology)
Rudolf Steiner
Sustainability
Branches of sustainable agriculture
Fisheries management – protecting fishery resources in an effort to maintain sustainable fisheries
Sustainable farming
Sustainable forest management
Sustainable gardening
Sustainable farming
Sustainable farming
Natural farming
Masanobu Fukuoka
Perennial foods
Achillea millefolium
Asparagus
Blitum bonus-henricus
Breadfruit
Cassava
Crambe maritima
Fruit
Herb
Nut (fruit)
Olericulture
Perennial vegetable
Rhubarb
Sacred herbs
Shrub
Sium sisarum
Sorrel
Taro
Sustainable forestry management
Sustainable forest management
Coppicing
Forest gardening
Pollarding
Short rotation coppice
Woodland
Sustainable landscaping
Sustainable landscaping
A Sand County Almanac
Aldo Leopold
Biodiversity
Calvert Vaux
Central Park
Ecology
Ecosystem
Food miles
Frederick Law Olmsted
John Muir
Land ethic
Sierra Club
Soil food web
Approaches in sustainable agriculture
Hydroculture
Hydroculture
Aeroponics
Aquaponics
Hydroponics
Integrated pest control
Apiaceae
Asteraceae
Bee
Beneficial insects
Beneficial weed
Biological pest control
Bumblebee
Chrysopidae
Coccinellidae
Companion planting
Hoverfly
Ichneumonoidea
Insectary plant
Integrated pest management
List of be |
https://en.wikipedia.org/wiki/Non-renewable%20resource | A non-renewable resource (also called a finite resource) is a natural resource that cannot be readily replaced by natural means at a pace quick enough to keep up with consumption. An example is carbon-based fossil fuels. The original organic matter, with the aid of heat and pressure, becomes a fuel such as oil or gas. Earth minerals and metal ores, fossil fuels (coal, petroleum, natural gas) and groundwater in certain aquifers are all considered non-renewable resources, though individual elements are always conserved (except in nuclear reactions, nuclear decay or atmospheric escape).
Conversely, resources such as timber (when harvested sustainably) and wind (used to power energy conversion systems) are considered renewable resources, largely because their localized replenishment can occur within time frames meaningful to humans as well.
Earth minerals and metal ores
Earth minerals and metal ores are examples of non-renewable resources. The metals themselves are present in vast amounts in Earth's crust, and their extraction by humans only occurs where they are concentrated by natural geological processes (such as heat, pressure, organic activity, weathering and other processes) enough to become economically viable to extract. These processes generally take from tens of thousands to millions of years, through plate tectonics, tectonic subsidence and crustal recycling.
The localized deposits of metal ores near the surface which can be extracted economically by humans are non-renewable in human time-frames. There are certain rare earth minerals and elements that are more scarce and exhaustible than others. These are in high demand in manufacturing, particularly for the electronics industry.
Fossil fuels
Natural resources such as coal, petroleum(crude oil) and natural gas take thousands of years to form naturally and cannot be replaced as fast as they are being consumed. Eventually it is considered that fossil-based resources will become too costly to harvest and |
https://en.wikipedia.org/wiki/Mizar%20system | The Mizar system consists of a formal language for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in this language, and a library of formalized mathematics, which can be used in the proof of new theorems. The system is maintained and developed by the Mizar Project, formerly under the direction of its founder Andrzej Trybulec.
In 2009 the Mizar Mathematical Library was the largest coherent body of strictly formalized mathematics in existence.
History
The Mizar Project was started around 1973 by Andrzej Trybulec as an attempt to reconstruct mathematical vernacular so it can be checked by a computer. Its current goal, apart from the continual development of the Mizar System, is the collaborative creation of a large library of formally verified proofs, covering most of the core of modern mathematics. This is in line with the influential QED manifesto.
Currently the project is developed and maintained by research groups at Białystok University, Poland, the University of Alberta, Canada, and Shinshu University, Japan. While the Mizar proof checker remains proprietary, the Mizar Mathematical Library—the sizable body of formalized mathematics that it verified—is licensed open-source.
Papers related to the Mizar system regularly appear in the peer-reviewed journals of the mathematic formalization academic community. These include Studies in Logic, Grammar and Rhetoric, Intelligent Computer Mathematics, Interactive Theorem Proving, Journal of Automated Reasoning and the Journal of Formalized Reasoning.
Mizar language
The distinctive feature of the Mizar language is its readability. As is common in mathematical text, it relies on classical logic and a declarative style. Mizar articles are written in ordinary ASCII, but the language was designed to be close enough to the mathematical vernacular that most mathematicians could read and understand Mizar articles without special training. Yet, the language |
https://en.wikipedia.org/wiki/List%20of%20numbers | This is a list of notable numbers and articles about notable numbers. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities which could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the interesting number paradox.
The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorised with the standard convention of types of numbers.
This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number).
Natural numbers
The natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for counting and often have ethno-cultural significance (see below). Beyond this, natural numbers are widely used as a building block for other number systems including the integers, rational numbers and real numbers. Natural numbers are those used for counting (as in "there are six (6) coins on the table") and ordering (as in "this is the third (3rd) largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers". Defined by the Peano axioms, the natural numbers form an infinitely large set. Often referred to as "the naturals", the natural numbers are usually symbolised by a boldface (or blackboard bold , Unicode ).
The incl |
https://en.wikipedia.org/wiki/Quotient%20rule | In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let , where both and are differentiable and The quotient rule states that the derivative of is
It is provable in many ways by using other derivative rules.
Examples
Example 1: Basic example
Given , let , then using the quotient rule:
Example 2: Derivative of tangent function
The quotient rule can be used to find the derivative of as follows:
Reciprocal rule
The reciprocal rule is a special case of the quotient rule in which the numerator . Applying the quotient rule gives
Note that utilizing the chain rule yields the same result.
Proofs
Proof from derivative definition and limit properties
Let Applying the definition of the derivative and properties of limits gives the following proof, with the term added and subtracted to allow splitting and factoring in subsequent steps without affecting the value:The limit evaluation is justified by the differentiability of , implying continuity, which can be expressed as .
Proof using implicit differentiation
Let so that
The product rule then gives
Solving for and substituting back for gives:
Proof using the reciprocal rule or chain rule
Let
Then the product rule gives
To evaluate the derivative in the second term, apply the reciprocal rule, or the power rule along with the chain rule:
Substituting the result into the expression gives
Proof by logarithmic differentiation
Let Taking the absolute value and natural logarithm of both sides of the equation gives
Applying properties of the absolute value and logarithms,
Taking the logarithmic derivative of both sides,
Solving for and substituting back for gives:
Note: Taking the absolute value of the functions is necessary for the logarithmic differentiation of functions that may have negative values, as logarithms are only real-valued for positive arguments. This works because , which justifies taking t |
https://en.wikipedia.org/wiki/Pest%20%28organism%29 | A pest is any organism harmful to humans or human concerns. The term is particularly used for creatures that damage crops, livestock, and forestry or cause a nuisance to people, especially in their homes. Humans have modified the environment for their own purposes and are intolerant of other creatures occupying the same space when their activities impact adversely on human objectives. Thus, an elephant is unobjectionable in its natural habitat but a pest when it tramples crops.
Some animals are disliked because they bite or sting; snakes, wasps, ants, bed bugs, fleas and ticks belong in this category. Others enter the home; these include houseflies, which land on and contaminate food, beetles, which tunnel into the woodwork, and other animals that scuttle about on the floor at night, like cockroaches, which are often associated with unsanitary conditions.
Agricultural and horticultural crops are attacked by a wide variety of pests, the most important being insects, mites, nematodes and gastropod molluscs. The damage they do results both from the direct injury they cause to the plants and from the indirect consequences of the fungal, bacterial or viral infections they transmit. Plants have their own defences against these attacks but these may be overwhelmed, especially in habitats where the plants are already stressed, or where the pests have been accidentally introduced and may have no natural enemies. The pests affecting trees are predominantly insects, and many of these have also been introduced inadvertently and lack natural enemies, and some have transmitted novel fungal diseases with devastating results.
Humans have traditionally performed pest control in agriculture and forestry by the use of pesticides; however, other methods exist such as mechanical control, and recently developed biological controls.
Concept
A pest is any living thing, whether animal, plant, or fungus, which humans consider troublesome to themselves, their possessions, or the environ |
https://en.wikipedia.org/wiki/21%20%28number%29 | 21 (twenty-one) is the natural number following 20 and preceding 22.
The current century is the 21st century AD, under the Gregorian calendar.
In mathematics
Twenty-one is the fifth distinct semiprime, and the second of the form where is a higher prime.
As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite member of the 11-aliquot tree, following 18. 21 is the first member of the second cluster of two discrete semiprimes (21, 22), where the next such cluster is (38, 39). 21 is the smallest natural number that is not close to a power of two , where the range of nearness is . 21 is a Harshad number in base ten, and a repdigit in quaternary (1114).
While 21 is the sixth triangular number, it is also the sum of the divisors of the first five positive integers:
21 is the fifth Motzkin number, and the eighth Fibonacci number, equal to the sum of the preceding terms in the sequence, 8 and 13. It is the smallest non-trivial example in decimal of a Fibonacci number whose digits are Fibonacci numbers and whose digit sum is also a Fibonacci number. It is also an octagonal number, and a Padovan number (preceded by the terms (9, 12, 16), where it is the sum of the first two of these). 21 is a Blum integer, since it is a semiprime with both its prime factors being Gaussian primes.
While the twenty-first prime number 73 is the largest member of Bhargava's definite quadratic 17–integer matrix representative of all prime numbers,
the twenty-first composite number 33 is the largest member of a like definite quadratic 9–integer matrix
representative of all odd numbers.
21 is also a positive integer that has the following property (see brief proof below):
Note that a necessary condition for is that for any coprime to , and must satisfy the condition above, therefore at least one of and must only have factor 2 and 5.
Let denot |
https://en.wikipedia.org/wiki/Open%20Firmware | Open Firmware is a standard defining the interfaces of a computer firmware system, formerly endorsed by the Institute of Electrical and Electronics Engineers (IEEE). It originated at Sun Microsystems where it was known as OpenBoot, and has been used by multiple vendors including Sun, Apple, IBM and ARM.
Open Firmware allows a system to load platform-independent drivers directly from a PCI device, improving compatibility.
Open Firmware may be accessed through its command line interface, which uses the Forth programming language.
History
Open Firmware was described by IEEE standard as IEEE 1275-1994. This standard was not reaffirmed by the Open Firmware Working Group (OFWG) since 1998, and was therefore officially withdrawn by IEEE in May 2005.
Features
Open Firmware defines a standard way to describe the hardware configuration of a system, called the device tree. This helps the operating system to better understand the configuration of the host computer, relying less on user configuration and hardware polling. For example, Open Firmware is essential for reliably identifying slave I2C devices like temperature sensors for hardware monitoring, whereas the alternative solution of performing a blind probe of the I2C bus, as has to be done by software like lm_sensors on generic hardware, is known to result in serious hardware issues under certain circumstances.
Open Firmware Forth Code may be compiled into FCode, a bytecode which is independent of instruction set architecture. A PCI card may include a program, compiled to FCode, which runs on any Open Firmware system. In this way, it can provide boot-time diagnostics, configuration code, and device drivers. FCode is also very compact, so that a disk driver may require only one or two kilobytes. Therefore, many of the same I/O cards can be used on Sun systems and Macintoshes that used Open Firmware. FCode implements ANS Forth and a subset of the Open Firmware library.
Being based upon an interactive programming la |
https://en.wikipedia.org/wiki/QED%20manifesto | The QED manifesto was a proposal for a computer-based database of all mathematical knowledge, strictly formalized and with all proofs having been checked automatically. (Q.E.D. means in Latin, meaning "which was to be demonstrated.")
Overview
The idea for the project arose in 1993, mainly under the impetus of Robert Boyer. The goals of the project, tentatively named QED project or project QED, were outlined in the QED manifesto, a document first published in 1994, with input from several researchers. Explicit authorship was deliberately avoided. A dedicated mailing list was created, and two scientific conferences on QED took place, the first one in 1994 at Argonne National Laboratories and the second in 1995 in Warsaw organized by the Mizar group.
The project seems to have dissolved by 1996, never having produced more than discussions and plans. In a 2007 paper, Freek Wiedijk identifies two reasons for the failure of the project. In order of importance:
Very few people are working on formalization of mathematics. There is no compelling application for fully mechanized mathematics.
Formalized mathematics does not yet resemble real, traditional mathematics. This is partly due to the complexity of mathematical notation, and partly to the limitations of existing theorem provers and proof assistants; the paper finds that the major contenders, Mizar, HOL, and Coq, have serious shortcomings in their abilities to express mathematics.
Nonetheless, QED-style projects are regularly proposed. The Mizar Mathematical Library formalizes a large portion of undergraduate mathematics, and was considered the largest such library in 2007. Similar projects include the Metamath proof database and the mathlib library written in Lean.
In 2014 the Twenty years of the QED Manifesto workshop was organized as part of the Vienna Summer of Logic.
See also
Formalism (mathematics)
Mathematical knowledge management
POPLmark, a more modest project in programming language theory
Refer |
https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon%20equation | The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. It is a quantized version of the relativistic energy–momentum relation . Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Its theoretical relevance is similar to that of the Dirac equation. Electromagnetic interactions can be incorporated, forming the topic of scalar electrodynamics, but because common spinless particles like the pions are unstable and also experience the strong interaction (with unknown interaction term in the Hamiltonian) the practical utility is limited.
The equation can be put into the form of a Schrödinger equation. In this form it is expressed as two coupled differential equations, each of first order in time. The solutions have two components, reflecting the charge degree of freedom in relativity. It admits a conserved quantity, but this is not positive definite. The wave function cannot therefore be interpreted as a probability amplitude. The conserved quantity is instead interpreted as electric charge, and the norm squared of the wave function is interpreted as a charge density. The equation describes all spinless particles with positive, negative, and zero charge.
Any solution of the free Dirac equation is, for each of its four components, a solution of the free Klein–Gordon equation. The Klein–Gordon equation does not form the basis of a consistent quantum relativistic one-particle theory. There is no known such theory for particles of any spin. For full reconciliation of quantum mechanics with special relativity, quantum field theory is needed, in which the Klein–Gordon equation reemerges as the equation obeyed by the components of all free quantum fields. In quantum field theory, the solutions of the free (noninteracting) versions of the original |
https://en.wikipedia.org/wiki/Empty%20sum | In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero.
The natural way to extend non-empty sums is to let the empty sum be the additive identity.
Let , , , ... be a sequence of numbers, and let
be the sum of the first m terms of the sequence. This satisfies the recurrence
provided that we use the following natural convention: .
In other words, a "sum" with only one term evaluates to that one term, while a "sum" with no terms evaluates to 0.
Allowing a "sum" with only 1 or 0 terms reduces the number of cases to be considered in many mathematical formulas. Such "sums" are natural starting points in induction proofs, as well as in algorithms. For these reasons, the "empty sum is zero" extension is standard practice in mathematics and computer programming (assuming the domain has a zero element).
For the same reason, the empty product is taken to be the multiplicative identity.
For sums of other objects (such as vectors, matrices, polynomials), the value of an empty summation is taken to be its additive identity.
Examples
Empty linear combinations
In linear algebra, a basis of a vector space V is a linearly independent subset B such that every element of V is a linear combination of B.
The empty sum convention allows the zero-dimensional vector space V={0} to have a basis, namely the empty set.
See also
Empty product
Iterated binary operation
Empty function
References
Operations on numbers
0 (number) |
https://en.wikipedia.org/wiki/Glutinous%20rice | Glutinous rice (Oryza sativa var. glutinosa; also called sticky rice, sweet rice or waxy rice) is a type of rice grown mainly in Southeast and East Asia, and the northeastern regions of South Asia, which has opaque grains, very low amylose content, and is especially sticky when cooked. It is widely consumed across Asia.
It is called glutinous () in the sense of being glue-like or sticky, and not in the sense of containing gluten (which it does not). While often called sticky rice, it differs from non-glutinous strains of japonica rice, which also become sticky to some degree when cooked. There are numerous cultivars of glutinous rice, which include japonica, indica and tropical japonica strains.
History
In China, glutinous rice has been grown for at least 2,000 years. However, researchers believe that glutinous rice distribution appears to have been culturally influenced and closely associated with the early southward migration and distribution of the Tai ethnic groups, particularly the Lao people along the Mekong River basin originating from Southern China. Along the Greater Mekong Sub-region, the Lao have been cultivating glutinous rice for approximately 4000–6000 years.
The history of rice cultivation in Thailand dates back over 5,000 years. Different types of rice have been cultivated in various regions during different historical periods, including glutinous rice, large-grain rice, and slender grain rice. Through archaeological research, Japanese scholars found that fortified grain was likely the glutinous-lowland variety of glutinous rice, and large-grain rice was likely glutinous rice that thrives at high altitudes. Meanwhile, slender grain rice is non-glutinous. Sticky rice has been a staple food in all regions from north to south since about 3,000 years ago, and it has played an essential role in the country's food culture.
Cultivation
Glutinous rice is grown in Laos, Thailand, Cambodia, Vietnam, Malaysia, Indonesia, Myanmar, Nepal, Bangladesh, Bhutan |
https://en.wikipedia.org/wiki/Reflexive%20space | In the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space (TVS) for which the canonical evaluation map from into its bidual (which is the strong dual of the strong dual of ) is an isomorphism of TVSs.
Since a normable TVS is reflexive if and only if it is semi-reflexive, every normed space (and so in particular, every Banach space) is reflexive if and only if the canonical evaluation map from into its bidual is surjective;
in this case the normed space is necessarily also a Banach space.
In 1951, R. C. James discovered a Banach space, now known as James' space, that is reflexive but is nevertheless isometrically isomorphic to its bidual (any such isomorphism is thus necessarily the canonical evaluation map).
Reflexive spaces play an important role in the general theory of locally convex TVSs and in the theory of Banach spaces in particular. Hilbert spaces are prominent examples of reflexive Banach spaces. Reflexive Banach spaces are often characterized by their geometric properties.
Definition
Definition of the bidual
Suppose that is a topological vector space (TVS) over the field (which is either the real or complex numbers) whose continuous dual space, separates points on (that is, for any there exists some such that ).
Let and both denote the strong dual of which is the vector space of continuous linear functionals on endowed with the topology of uniform convergence on bounded subsets of ;
this topology is also called the strong dual topology and it is the "default" topology placed on a continuous dual space (unless another topology is specified).
If is a normed space, then the strong dual of is the continuous dual space with its usual norm topology.
The bidual of denoted by is the strong dual of ; that is, it is the space
If is a normed space, then is the continuous dual space of the Banach space with its usual norm topology.
Definitions of the evaluation map |
https://en.wikipedia.org/wiki/Der%20Spiegel | (, ) is a German weekly news magazine published in Hamburg. With a weekly circulation of about 724,000 copies in 2022, it is one of the largest such publications in Europe. It was founded in 1947 by John Seymour Chaloner, a British army officer, and Rudolf Augstein, a former Wehrmacht radio operator who was recognized in 2000 by the International Press Institute as one of the fifty World Press Freedom Heroes. Typically, the magazine has a content to advertising ratio of 2:1.
is known in German-speaking countries mostly for its investigative journalism. It has played a key role in uncovering many political scandals such as the Spiegel affair in 1962 and the Flick affair in the 1980s. According to The Economist, is one of continental Europe's most influential magazines. The news website by the same name was launched in 1994 under the name Spiegel Online with an independent editorial staff. Today, the content is created by a shared editorial team and the website uses the same media brand as the printed magazine.
History
The first edition of was published in Hanover on Saturday, 4 January 1947. Its release was initiated and sponsored by the British occupational administration and preceded by a magazine titled Diese Woche (German: This Week), which had first been published in November 1946. After disagreements with the British, the magazine was handed over to Rudolf Augstein as chief editor, and was renamed . From the first edition in January 1947, Augstein held the position of editor-in-chief, which he retained until his death on 7 November 2002.
After 1950, the magazine was owned by Rudolf Augstein and John Jahr; Jahr's share merged with Richard Gruner's in 1965 to form the publishing company Gruner + Jahr. In 1969, Augstein bought out Gruner + Jahr for DM 42 million and became the sole owner of . In 1971, Gruner + Jahr bought back a 25% share in the magazine. In 1974, Augstein restructured the company to make the employees shareholders. All employees with more |
https://en.wikipedia.org/wiki/Brook%20Taylor | Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem and the Taylor series, which are important for their use in mathematical analysis.
Life and work
Brook Taylor was born in Edmonton (former Middlesex). Taylor was the son of John Taylor, MP of Patrixbourne, Kent and Olivia Tempest, the daughter of Sir Nicholas Tempest, Baronet of Durham.
He entered St John's College, Cambridge, as a fellow-commoner in 1701, and took degrees in LL.B. in 1709 and LL.D. in 1714. Taylor studied mathematics under John Machin and John Keill, leading to Taylor obtaining a solution to the problem of "center of oscillation." Taylor's solution remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli.
Taylor's Methodus Incrementorum Directa et Inversa (1715) ("Direct and Indirect Methods of Incrementation") added a new branch to higher mathematics, called "calculus of finite differences". Taylor used this development to determine the form of movement in vibrating strings. Taylor also wrote the first satisfactory investigation of astronomical refraction. The same work contains the well-known Taylor's theorem, the importance of which remained unrecognized until 1772, when Joseph-Louis Lagrange realized its usefulness and termed it "the main foundation of differential calculus".
In Taylor's 1715 essay Linear Perspective, Taylor set forth the principles of perspective in a more understandable form, but the work suffered from brevity and obscurity problems which plagued most of his writings, meaning the essay required further explanation in the treatises of Joshua Kirby (1754) and Daniel Fournier (1761).
Taylor was elected as a fellow in the Royal Society in 1712. In the same year, Taylor sat on the committee for adjudicating the claims of Sir Isaac Newton and Gottfried Leibniz. He acted as secretary to the society from 13 January 1714 to 21 October 1718.
From 1715 onward, Taylor's |
https://en.wikipedia.org/wiki/Canadian%20Trusted%20Computer%20Product%20Evaluation%20Criteria | The Canadian Trusted Computer Product Evaluation Criteria (CTCPEC) is a computer security standard published in 1993 by the Communications Security Establishment to provide an evaluation criterion on IT products. It is a combination of the TCSEC (also called Orange Book) and the European ITSEC approaches.
CTCPEC led to the creation of the Common Criteria standard.
The Canadian System Security Centre, part of the Communications Security Establishment was founded in 1988 to establish a Canadian computer security standard.
The Centre published a draft of the standard in April 1992. The final version was published in January 1993.
References
External links
Computer security standards |
https://en.wikipedia.org/wiki/Declarative%20programming | In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow.
Many languages that apply this style attempt to minimize or eliminate side effects by describing what the program must accomplish in terms of the problem domain, rather than describing how to accomplish it as a sequence of the programming language primitives (the how being left up to the language's implementation). This is in contrast with imperative programming, which implements algorithms in explicit steps.
Declarative programming often considers programs as theories of a formal logic, and computations as deductions in that logic space. Declarative programming may greatly simplify writing parallel programs.
Common declarative languages include those of database query languages (e.g., SQL, XQuery), regular expressions, logic programming (e.g. Prolog, Datalog, answer set programming), functional programming, and configuration management systems.
The term is often used in contrast to imperative programming, which dictates the transformation steps of its state explicitly.
Definition
Declarative programming is often defined as any style of programming that is not imperative. A number of other common definitions attempt to define it by simply contrasting it with imperative programming. For example:
A high-level program that describes what a computation should perform.
Any programming language that lacks side effects (or more specifically, is referentially transparent)
A language with a clear correspondence to mathematical logic.
These definitions overlap substantially.
Declarative programming is a non-imperative style of programming in which programs describe their desired results without explicitly listing commands or steps that must be performed. Functional and logic programming languages are characterized by a declarative programming style. |
https://en.wikipedia.org/wiki/Invariance%20of%20domain | Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space .
It states:
If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and .
The theorem and its proof are due to L. E. J. Brouwer, published in 1912.
The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.
Notes
The conclusion of the theorem can equivalently be formulated as: " is an open map".
Normally, to check that is a homeomorphism, one would have to verify that both and its inverse function are continuous;
the theorem says that if the domain is an subset of and the image is also in then continuity of is automatic.
Furthermore, the theorem says that if two subsets and of are homeomorphic, and is open, then must be open as well.
(Note that is open as a subset of and not just in the subspace topology.
Openness of in the subspace topology is automatic.)
Both of these statements are not at all obvious and are not generally true if one leaves Euclidean space.
It is of crucial importance that both domain and image of are contained in Euclidean space .
Consider for instance the map defined by
This map is injective and continuous, the domain is an open subset of , but the image is not open in
A more extreme example is the map defined by because here is injective and continuous but does not even yield a homeomorphism onto its image.
The theorem is also not generally true in infinitely many dimensions. Consider for instance the Banach Lp space of all bounded real sequences.
Define as the shift
Then is injective and continuous, the domain is open in , but the image is not.
Consequences
An important consequence of the domain invariance theorem is that cannot be homeomorphic to if
Indeed, no non-empty open subset of can be homeomorphic to any open subset of in this case.
Generalizations
The domain invariance theorem may be generalized to manifo |
https://en.wikipedia.org/wiki/Royal%20Swedish%20Academy%20of%20Engineering%20Sciences | The Royal Swedish Academy of Engineering Sciences or Kungliga Ingenjörsvetenskapsakademien (IVA), founded on 24 October 1919 by King Gustaf V, is one of the royal academies in Sweden. The academy is an independent organisation, which promotes contact and exchange between business, research, and government, in Sweden and internationally. It is the world's oldest academy of engineering sciences.(OECD Reviews of Innovation Policy: Sweden 2012).
Leadership
The King is the patron of the academy.
The following people have been presidents of IVA since its foundation in 1919:
1919–1940: Axel F. Enström
1941–1959: Edy Velander
1960–1970: Sven Brohult
1971–1982: Gunnar Hambraeus
1982–1994: Hans G. Forsberg
1995–2000: Kurt Östlund
1999–2001: (temporary) Enrico Deiaco
2001–2008: Lena Treschow Torell
2008–2017: Björn O. Nilsson
2017–2023: Tuula Teeri
Academy member
Each year, outstanding scientists and engineers from universities and industries are elected into membership of IVA. Currently, the academy has 1000 Swedish and 300 foreign members. Foreign members are non-resident and non-citizen of Sweden. All new members are nominated by existing members.
Focus areas
The academy focuses on twelve areas of engineering sciences:
Mechanical Engineering
Electrical Engineering
Building and Construction
Chemical Engineering
Mining and Materials
Management
Basic and Interdisciplinary Engineering Sciences
Forest Technology
Economics
Biotechnology
Education and Research Policy
Information Technology
Each focus area is addressed by a committee with a representative chair.
Awards
The academy awards several prizes, medals and scholarships:
Large Gold Medal (since 1924)
Gold Medal (since 1921)
Brinell medal (Brinellmedaljen, since 1936, and named after Johan August Brinell)
Gold Plaque (since 1951)
Honorary Sign (since 1919)
Axel F. Enstrom Medal (1959–1981)
Prize for science in journalism (since 2015)
Hans Werthén Fonden
The King Carl XVI Gustafs 50-years-old Foun |
https://en.wikipedia.org/wiki/Winsock | In computing, the Windows Sockets API (WSA), later shortened to Winsock, is an application programming interface (API) that defines how Windows network application software should access network services, especially TCP/IP. It defines a standard interface between a Windows TCP/IP client application (such as an FTP client or a web browser) and the underlying TCP/IP protocol stack. The nomenclature is based on the Berkeley sockets API used in BSD for communications between programs.
Background
Early Microsoft operating systems, both MS-DOS and Microsoft Windows, offered limited networking capability, chiefly based on NetBIOS. In particular, Microsoft did not offer support for the TCP/IP protocol stack at that time. A number of university groups and commercial vendors, including the PC/IP group at MIT, FTP Software, Sun Microsystems, Ungermann-Bass, and Excelan, introduced TCP/IP products for MS-DOS, often as part of a hardware/software bundle. When Windows 2.0 was released, these vendors were joined by others such as Distinct and NetManage in offering TCP/IP for Windows.
The drawback faced by all of these vendors was that each of them used their own API (Application Programming Interface). Without a single standard programming model, it was difficult to persuade independent software developers to create networking applications which would work with any vendor's underlying TCP/IP implementation. Add to this the fact that end users were wary of getting locked into a single vendor and it became clear that some standardization was needed.
The Windows Sockets project had its origins in a Birds Of A Feather session held at Interop '91 in San Jose on October 10, 1991. It is based on socket specifications created by NetManage and which it put into public domain at this meeting. At the time the NetManage socket was the only 100% DLL based, multi-threaded product for Windows 3.0 available. The first edition of the specification was authored by Martin Hall, Mark Towfiq of Mi |
https://en.wikipedia.org/wiki/Structural%20induction | Structural induction is a proof method that is used in mathematical logic (e.g., in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction over natural numbers and can be further generalized to arbitrary Noetherian induction. Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinary mathematical induction.
Structural induction is used to prove that some proposition holds for all of some sort of recursively defined structure, such as
formulas, lists, or trees. A well-founded partial order is defined on the structures ("subformula" for formulas, "sublist" for lists, and "subtree" for trees). The structural induction proof is a proof that the proposition holds for all the minimal structures and that if it holds for the immediate substructures of a certain structure , then it must hold for also. (Formally speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all .)
A structurally recursive function uses the same idea to define a recursive function: "base cases" handle each minimal structure and a rule for recursion. Structural recursion is usually proved correct by structural induction; in particularly easy cases, the inductive step is often left out. The length and ++ functions in the example below are structurally recursive.
For example, if the structures are lists, one usually introduces the partial order "<", in which whenever list is the tail of list . Under this ordering, the empty list is the unique minimal element. A structural induction proof of some proposition then consists of two parts: A proof that is true and a proof that if is true for some list , and if is the tail of list , then must also be true.
Eventually, there may exist more than one base case |
https://en.wikipedia.org/wiki/Radioisotope%20thermoelectric%20generator | A radioisotope thermoelectric generator (RTG, RITEG), sometimes referred to as a radioisotope power system (RPS), is a type of nuclear battery that uses an array of thermocouples to convert the heat released by the decay of a suitable radioactive material into electricity by the Seebeck effect. This type of generator has no moving parts. Because they don't need solar energy, RTGs are ideal for remote and harsh environments for extended periods of time, and because they have no moving parts, there is no risk of parts wearing out or malfunctioning.
RTGs are usually the most desirable power source for unmaintained situations that need a few hundred watts (or less) of power for durations too long for fuel cells, batteries, or generators to provide economically, and in places where solar cells are not practical. RTGs have been used as power sources in satellites, space probes, and uncrewed remote facilities such as a series of lighthouses built by the Soviet Union inside the Arctic Circle.
Safe use of RTGs requires containment of the radioisotopes long after the productive life of the unit. The expense of RTGs tends to limit their use to niche applications in rare or special situations.
History
The RTG was invented in 1954 by Mound Laboratories scientists Kenneth (Ken) C. Jordan (1921-2008) and John Birden (1918-2011). They were inducted into the National Inventors Hall of Fame in 2013. Jordan and Birden worked on an Army Signal Corps contract (R-65-8- 998 11-SC-03-91) beginning on 1 January 1957, to conduct research on radioactive materials and thermocouples suitable for the direct conversion of heat to electrical energy using polonium-210 as the heat source. RTGs were developed in the US during the late 1950s by Mound Laboratories in Miamisburg, Ohio, under contract with the United States Atomic Energy Commission. The project was led by Dr. Bertram C. Blanke.
The first RTG launched into space by the United States was SNAP 3B in 1961 powered by 96 grams of plutoni |
https://en.wikipedia.org/wiki/3DNow%21 | 3DNow! is a deprecated extension to the x86 instruction set developed by Advanced Micro Devices (AMD). It adds single instruction multiple data (SIMD) instructions to the base x86 instruction set, enabling it to perform vector processing of floating-point vector operations using vector registers, which improves the performance of many graphics-intensive applications. The first microprocessor to implement 3DNow! was the AMD K6-2, which was introduced in 1998. When the application was appropriate, this raised the speed by about 2–4 times.
However, the instruction set never gained much popularity, and AMD announced in August 2010 that support for 3DNow! would be dropped in future AMD processors, except for two instructions (the PREFETCH and PREFETCHW instructions). These two instructions are also available in Bay-Trail Intel processors.
History
3DNow! was developed at a time when 3D graphics were becoming mainstream in PC multimedia and games. Realtime display of 3D graphics depended heavily on the host CPU's floating-point unit (FPU) to perform floating-point calculations, a task in which AMD's K6 processor was easily outperformed by its competitor, the Intel Pentium II.
As an enhancement to the MMX instruction set, the 3DNow! instruction-set augmented the MMX SIMD registers to support common arithmetic operations (add/subtract/multiply) on single-precision (32-bit) floating-point data. Software written to use AMD's 3DNow! instead of the slower x87 FPU could execute up to four times faster, depending on the instruction mix.
Versions
3DNow!
The first implementation of 3DNow! technology contains 21 new instructions that support SIMD floating-point operations. The 3DNow! data format is packed, single-precision, floating-point. The 3DNow! instruction set also includes operations for SIMD integer operations, data prefetch, and faster MMX-to-floating-point switching. Later, Intel would add similar (but incompatible) instructions to the Pentium III, known as SSE (Str |
https://en.wikipedia.org/wiki/Instructions%20per%20cycle | In computer architecture, instructions per cycle (IPC), commonly called instructions per clock, is one aspect of a processor's performance: the average number of instructions executed for each clock cycle. It is the multiplicative inverse of cycles per instruction.
Explanation
While early generations of CPUs carried out all the steps to execute an instruction sequentially, modern CPUs can do many things in parallel. As it is impossible to just keep doubling the speed of the clock, instruction pipelining and superscalar processor design have evolved so CPUs can use a variety of execution units in parallel - looking ahead through the incoming instructions in order to optimise them. This leads to the instructions per cycle completed being much higher than 1 and is responsible for much of the speed improvements in subsequent CPU generations.
Calculation of IPC
The calculation of IPC is done through running a set piece of code, calculating the number of machine-level instructions required to complete it, then using high-performance timers to calculate the number of clock cycles required to complete it on the actual hardware. The final result comes from dividing the number of instructions by the number of CPU clock cycles.
The number of instructions per second and floating point operations per second for a processor can be derived by multiplying the number of instructions per cycle with the clock rate (cycles per second given in Hertz) of the processor in question. The number of instructions per second is an approximate indicator of the likely performance of the processor.
The number of instructions executed per clock is not a constant for a given processor; it depends on how the particular software being run interacts with the processor, and indeed the entire machine, particularly the memory hierarchy. However, certain processor features tend to lead to designs that have higher-than-average IPC values; the presence of multiple arithmetic logic units (an ALU is |
https://en.wikipedia.org/wiki/Direct%20limit | In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category. The way they are put together is specified by a system of homomorphisms (group homomorphism, ring homomorphism, or in general morphisms in the category) between those smaller objects. The direct limit of the objects , where ranges over some directed set , is denoted by . (This is a slight abuse of notation as it suppresses the system of homomorphisms that is crucial for the structure of the limit.)
Direct limits are a special case of the concept of colimit in category theory. Direct limits are dual to inverse limits, which are a special case of limits in category theory.
Formal definition
We will first give the definition for algebraic structures like groups and modules, and then the general definition, which can be used in any category.
Direct limits of algebraic objects
In this section objects are understood to consist of underlying sets equipped with a given algebraic structure, such as groups, rings, modules (over a fixed ring), algebras (over a fixed field), etc. With this in mind, homomorphisms are understood in the corresponding setting (group homomorphisms, etc.).
Let be a directed set. Let be a family of objects indexed by and be a homomorphism for all with the following properties:
is the identity of , and
for all .
Then the pair is called a direct system over .
The direct limit of the direct system is denoted by and is defined as follows. Its underlying set is the disjoint union of the 's modulo a certain :
Here, if and , then if and only if there is some with and such that .
Intuitively, two elements in the disjoint union are equivalent if and only if they "eventually become equal" in the direct system. An equivalent formulation that highlights the duality to the inverse limit is th |
https://en.wikipedia.org/wiki/Megaphone | A megaphone, speaking-trumpet, bullhorn, blowhorn, or loudhailer is usually a portable or hand-held, cone-shaped acoustic horn used to amplify a person's voice or other sounds and direct it in a given direction. The sound is introduced into the narrow end of the megaphone, by holding it up to the face and speaking into it, and the sound waves radiate out the wide end. A megaphone increases the volume of sound by increasing the acoustic impedance seen by the vocal cords, matching the impedance of the vocal cords to the air, so that more sound power is radiated. It also serves to direct the sound waves in the direction the horn is pointing. It somewhat distorts the sound of the voice because the frequency response of the megaphone is greater at higher sound frequencies.
Since the 1960s the voice-powered acoustic megaphone described above has been replaced by the electric megaphone, which uses a microphone, an electrically-powered amplifier and a folded horn loudspeaker to amplify the voice.
History
The initial inventor of the speaking trumpet is a subject of historical controversy. There have been references to speakers in Ancient Greece (5th Century B.C.) wearing masks with cones protruding from the mouth in order to amplify their voices in theatres. Hellenic architects may have also consciously utilized acoustic physics in their design of theatre amphitheaters.
A drawing by Louis Nicolas (right) on page 14 of the Codex canadensis, circa 1675 to 1682, shows a Native American chief named Iscouakité using a megaphone made of birch bark. The text of the illustration says that he is addressing his soldiers through a birch bark tube.
Both Samuel Morland and Athanasius Kircher have been credited with inventing megaphones around the same time in the 17th century. Morland, in a work published in 1655, wrote about his experimentation with different horns. His largest megaphone consisted of over 20 feet of copper tube and could reportedly project a person's voice a m |
https://en.wikipedia.org/wiki/Mechanical%20puzzle | A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day is the Rubik's Cube, invented by the Hungarian architect Ernő Rubik in 1974. The puzzles are typically designed for a single player, where the goal is for the player to see through the principle of the object, rather than accidentally coming up with the right solution through trial and error. With this in mind, they are often used as an intelligence test or in problem solving training.
History
The oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC.
The game consists of a square divided into 14 parts, and the aim was to create different shapes from these pieces. This is not easy to do. (see Ostomachion loculus Archimedius)
In Iran "puzzle-locks" were made as early as the 17th century AD.
The next known occurrence of puzzles is in Japan. In 1742 there is a mention of a game called "Sei Shona-gon Chie No-Ita" in a book. Around the year 1800 the Tangram puzzle from China became popular, and 20 years later it had spread through Europe and America.
The company Richter from Rudolstadt began producing large amounts of Tangram-like puzzles of different shapes, the so-called "Anker-puzzles" in about 1891.
In 1893, Angelo John Lewis, using the pen name "Professor Hoffman", wrote a book called Puzzles; Old and New. It contained, among other things, more than 40 descriptions of puzzles with secret opening mechanisms. This book grew into a reference work for puzzle games and modern copies exist for those interested.
The beginning of the 20th century was a time in which puzzles were greatly fashionable and the first patents for puzzles were recorded.
With the invention of modern polymers manufacture of many puzzles became easier and cheape |
https://en.wikipedia.org/wiki/Disentanglement%20puzzle | Disentanglement puzzles (also called entanglement puzzles, tanglement puzzles, tavern puzzles or topological puzzles) are a type or group of mechanical puzzle that involves disentangling one piece or set of pieces from another piece or set of pieces. Several subtypes are included under this category, the names of which are sometimes used synonymously for the group: wire puzzles; nail puzzles; ring-and-string puzzles; et al. Although the initial object is disentanglement, the reverse problem of reassembling the puzzle can be as hard as—or even harder than—disentanglement. There are several different kinds of disentanglement puzzles, though a single puzzle may incorporate several of these features.
Wire-and-string puzzles
Wire-and-string puzzles usually consist of:
one piece of string, ribbon or similar, which may form a closed loop or which may have other pieces like balls fixed to its end.
one or several pieces of stiff wire
sometimes additional pieces like wooden ball through which the string is threaded.
One can distinguish three subgroups of wire-and-string puzzles:
Closed string subgroup: The pieces of string consist of one closed loop, as in the Baguenaudier puzzle. Usually the string has to be disentangled from the wire.
Unclosed loose string subgroup: The pieces of string are not closed, and are not attached to the wire. In this case the ends of the string are fitted with a ball, cube or similar which stops the string from slipping out too easily. Usually the string has to be disentangled from the wire. Sometimes other tasks have to be completed instead, such as shifting a ring or ball from one end of the string to another end.
Unclosed fixed string subgroup: The pieces of string are not closed, but are somewhere on its length attached to the wire. In these puzzles the string is not to be disentangled from the wire. One possible task may be to shift a ring or ball from one end of the string to another end.
One particularly difficult puzzle was |
https://en.wikipedia.org/wiki/Burr%20puzzle | A burr puzzle is an interlocking puzzle consisting of notched sticks, combined to make one three-dimensional, usually symmetrical unit.
These puzzles are traditionally made of wood, but versions made of plastic or metal can also be found. Quality burr puzzles are usually precision-made for easy sliding and accurate fitting of the pieces.
In recent years the definition of "burr" is expanding, as puzzle designers use this name for puzzles not necessarily of stick-based pieces.
History
The term "burr" is first mentioned in a 1928 book by Edwin Wyatt, but the text implies that it was commonly used before. The term is attributed to the finished shape of many of these puzzles, resembling a seed burr.
The origin of burr puzzles is unknown. The first known record appears in a 1698 engraving used as a frontispiece page of Chambers's Cyclopaedia. Later records can be found in German catalogs from the late 18th century and early 19th century. There are claims of the burr being a Chinese invention, like other classic puzzles such as the Tangram. In Kerala, India, these wooden puzzles are called edakoodam(ഏടാകൂടം).
Six-piece burr
The six-piece burr, also called "Puzzle Knot" or "Chinese Cross", is the most well-known and presumably the oldest of the burr puzzles. This is actually a family of puzzles, all sharing the same finished shape and basic shape of the pieces. The earliest US patent for a puzzle of this kind dates back to 1917.
For many years, the six-piece burr was very common and popular, but was considered trite and uninteresting by enthusiasts. Most of the puzzles made and sold were very similar to one another and most of them included a "key" piece, an unnotched stick that slides easily out. In the late 1970s, however, the six-piece burr regained the attention of inventors and collectors, thanks largely to a computer analysis conducted by the mathematically trained puzzle designer Bill Cutler which was published by Martin Gardner in his Mathematical Games column |
https://en.wikipedia.org/wiki/Crypt | A crypt (from Greek κρύπτη (krypte) crypta "vault") is a stone chamber beneath the floor of a church or other building. It typically contains coffins, sarcophagi, or religious relics.
Originally, crypts were typically found below the main apse of a church, such as at the Abbey of Saint-Germain en Auxerre, but were later located beneath chancel, naves and transepts as well. Occasionally churches were raised high to accommodate a crypt at the ground level, such as St Michael's Church in Hildesheim, Germany.
Etymology
The word "crypt" developed as an alternative form of the Latin "vault" as it was carried over into Late Latin, and came to refer to the ritual rooms found underneath church buildings. It also served as a vault for storing important and/or sacred items.
The word "crypta", however, is also the female form of crypto "hidden". The earliest known origin of both is in the Ancient Greek κρύπτω, the first person singular indicative of the verb "to conceal, to hide".
Development
First known in the early Christian period, in particular North Africa at Chlef and Djemila in Algeria, and Byzantium at Saint John Studio in Constantinople where Christian churches have been built over mithraea, the mithraeum has often been adapted to serve as a crypt.
The famous crypt at Old St. Peter's Basilica, Rome, developed about the year 600, as a means of affording pilgrims a view of Saint Peter's tomb, which lay according to the Roman fashion, directly below the high altar. The tomb was made accessible through an underground passageway beneath the sanctuary from where pilgrims could enter at one stair, pass by the tomb and exit without interrupting the clerical community's service at the altar directly above.
The Visigothic crypt (the Crypt of San Antolín) in Palencia Cathedral (Spain), was built during the reign of Wamba to preserve the remains of the martyr Saint Antoninus of Pamiers, a Visigothic-Gallic nobleman brought from Narbonne to Visigothic Hispania in 672 or 673 |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein%20constant | The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein.
By definition it is:
Equivalent forms
It can be proven that the following forms all sum to the same constant:
where σ0(n) = d(n) is the divisor function, a multiplicative function that equals the number of positive divisors of the number n. To prove the equivalence of these sums, note that they all take the form of Lambert series and can thus be resummed as such.
Irrationality
Erdős in 1948 showed that the constant E is an irrational number. Later, Borwein provided an alternative proof.
Despite its irrationality, the binary representation of the Erdős–Borwein constant may be calculated efficiently.
Applications
The Erdős–Borwein constant comes up in the average case analysis of the heapsort algorithm, where it controls the constant factor in the running time for converting an unsorted array of items into a heap.
References
External links
Mathematical constants
Irrational numbers
Borwein constant |
https://en.wikipedia.org/wiki/B%20cell | B cells, also known as B lymphocytes, are a type of white blood cell of the lymphocyte subtype. They function in the humoral immunity component of the adaptive immune system. B cells produce antibody molecules which may be either secreted or inserted into the plasma membrane where they serve as a part of B-cell receptors. When a naïve or memory B cell is activated by an antigen, it proliferates and differentiates into an antibody-secreting effector cell, known as a plasmablast or plasma cell. Additionally, B cells present antigens (they are also classified as professional antigen-presenting cells (APCs)) and secrete cytokines. In mammals, B cells mature in the bone marrow, which is at the core of most bones. In birds, B cells mature in the bursa of Fabricius, a lymphoid organ where they were first discovered by Chang and Glick, which is why the 'B' stands for bursa and not bone marrow as commonly believed.
B cells, unlike the other two classes of lymphocytes, T cells and natural killer cells, express B cell receptors (BCRs) on their cell membrane. BCRs allow the B cell to bind to a foreign antigen, against which it will initiate an antibody response. B cell receptors are extremely specific, with all BCRs on a B cell recognizing the same epitope.
Development
B cells develop from hematopoietic stem cells (HSCs) that originate from bone marrow. HSCs first differentiate into multipotent progenitor (MPP) cells, then common lymphoid progenitor (CLP) cells. From here, their development into B cells occurs in several stages (shown in image to the right), each marked by various gene expression patterns and immunoglobulin H chain and L chain gene loci arrangements, the latter due to B cells undergoing V(D)J recombination as they develop.
B cells undergo two types of selection while developing in the bone marrow to ensure proper development, both involving B cell receptors (BCR) on the surface of the cell. Positive selection occurs through antigen-independent signalling inv |
https://en.wikipedia.org/wiki/Cytotoxic%20T%20cell | A cytotoxic T cell (also known as TC, cytotoxic T lymphocyte, CTL, T-killer cell, cytolytic T cell, CD8+ T-cell or killer T cell) is a T lymphocyte (a type of white blood cell) that kills cancer cells, cells that are infected by intracellular pathogens (such as viruses or bacteria), or cells that are damaged in other ways.
Most cytotoxic T cells express T-cell receptors (TCRs) that can recognize a specific antigen. An antigen is a molecule capable of stimulating an immune response and is often produced by cancer cells, viruses, bacteria or intracellular signals. Antigens inside a cell are bound to class I MHC molecules, and brought to the surface of the cell by the class I MHC molecule, where they can be recognized by the T cell. If the TCR is specific for that antigen, it binds to the complex of the class I MHC molecule and the antigen, and the T cell destroys the cell.
In order for the TCR to bind to the class I MHC molecule, the former must be accompanied by a glycoprotein called CD8, which binds to the constant portion of the class I MHC molecule. Therefore, these T cells are called CD8+ T cells.
The affinity between CD8 and the MHC molecule keeps the TC cell and the target cell bound closely together during antigen-specific activation. CD8+ T cells are recognized as TC cells once they become activated and are generally classified as having a pre-defined cytotoxic role within the immune system. However, CD8+ T cells also have the ability to make some cytokines, such as TNF-α and IFN-γ, with antitumour and antimicrobial effects.
Development
The immune system must recognize millions of potential antigens. There are fewer than 30,000 genes in the human body, so it is impossible to have one gene for every antigen. Instead, the DNA in millions of white blood cells in the bone marrow is shuffled to create cells with unique receptors, each of which can bind to a different antigen. Some receptors bind to tissues in the human body itself, so to prevent the body fro |
https://en.wikipedia.org/wiki/T%20helper%20cell | The T helper cells (Th cells), also known as CD4+ cells or CD4-positive cells, are a type of T cell that play an important role in the adaptive immune system. They aid the activity of other immune cells by releasing cytokines. They are considered essential in B cell antibody class switching, breaking cross-tolerance in dendritic cells, in the activation and growth of cytotoxic T cells, and in maximizing bactericidal activity of phagocytes such as macrophages and neutrophils. CD4+ cells are mature Th cells that express the surface protein CD4. Genetic variation in regulatory elements expressed by CD4+ cells determines susceptibility to a broad class of autoimmune diseases.
Structure and function
Th cells contain and release cytokines to aid other immune cells. Cytokines are small protein mediators that alter the behavior of target cells that express receptors for those cytokines. These cells help polarize the immune response depending on the nature of the immunological insult (for example; virus vs. extracellular bacterium vs. intracellular bacterium vs. helminth vs. fungus vs. protist).
Mature Th cells express the surface protein CD4 and are referred to as CD4+ T cells. CD4+ T cells are generally treated as having a pre-defined role as helper T cells within the immune system. For example, when an antigen-presenting cell displays a peptide antigen on MHC class II proteins, a CD4+ cell will aid those cells through a combination of cell to cell interactions (e.g. CD40 (protein) and CD40L) and through cytokines.
Th cells are not a monolithic immunological entity because they are diverse in terms of function and their interaction with partner cells. In general, mature naive T cells are stimulated by professional antigen presenting cells to acquire an effector module. These are defined by the presence of a lineage-determining (or lineage-specifying) transcription factor (also called master regulator, though the term has been criticized for being too reductive). The l |
https://en.wikipedia.org/wiki/Shugart%20Associates | Shugart Associates (later Shugart Corporation) was a computer peripheral manufacturer that dominated the floppy disk drive market in the late 1970s and is famous for introducing the -inch "Minifloppy" floppy disk drive. In 1979 it was one of the first companies to introduce a hard disk drive form factor compatible with a floppy disk drive, the SA1000 form factor compatible with the 8-inch floppy drive form factor.
Founded in 1973, Shugart Associates was purchased in 1977 by Xerox, which then exited the business in 1985 and 1986, selling the brand name and the 8-inch floppy product line (in March 1986) to Narlinger Group, which ultimately ceased operations circa 1991.
History
Beginnings
Alan Shugart, after a distinguished career at IBM and a few years at Memorex, decided to strike out on his own in 1973; after gathering venture capital, he started Shugart Associates. The original business plan was to build a small-business system (similar to the IBM 3740) dealing with the development of various major components, including floppy disk drives and printers. After two years, Shugart had exhausted his startup money and had no product to show for it. The board then wanted to focus on the floppy disk drive, but Shugart wished to continue the original plan. Official company documents state that Shugart quit, but he himself claims that he was fired by the venture capitalists. Shugart went on with Finis Conner to found Shugart Technology in 1979, which was later renamed to Seagate Technology in response to a legal challenge by Xerox.
The -inch floppy disk drive was introduced by Shugart in September 1976 as the Shugart SA-400 Minifloppy (Shugart's trademarked brand name) at an OEM price of $390 for the drive and $45 for ten diskettes. The SA-400 and related models became the company's best selling products, with shipments of up to 4000 drives per day.
The original SA-400 was single-sided with 35-tracks and used FM (single density) recording. It could be used on either har |
https://en.wikipedia.org/wiki/Reinhard%20Selten | Reinhard Justus Reginald Selten (; 5 October 1930 – 23 August 2016) was a German economist, who won the 1994 Nobel Memorial Prize in Economic Sciences (shared with John Harsanyi and John Nash). He is also well known for his work in bounded rationality and can be considered one of the founding fathers of experimental economics.
Biography
Selten was born in Breslau (Wrocław) in Lower Silesia, now in Poland, to a Jewish father, Adolf Selten (a blind bookseller; d. 1942), and Protestant mother, Käthe Luther. Reinhard Selten was raised as Protestant.
After a brief family exile in Saxony and Austria, Selten returned to Hesse, Germany after the war and, in high school, read an article in Fortune magazine about game theory by the business writer John D. McDonald. He recalled later, he would occupy his "mind with problems of elementary geometry and algebra" while walking back and forth to school during that time. He studied mathematics at Goethe University Frankfurt and obtained his diploma in 1957. He then worked as scientific assistant to Heinz Sauermann until 1967. In 1959, he married with Elisabeth Langreiner. They had no children. In 1961, he also received his doctorate in Frankfurt in mathematics with a thesis on the evaluation of n-person games.
He was a visiting professor at Berkeley and taught from 1969 to 1972 at the Free University of Berlin and, from 1972 to 1984, at the University of Bielefeld. He then accepted a professorship at the University of Bonn. There he built the BonnEconLab, a laboratory for experimental economic research, where he was active even after his retirement.
Selten was professor emeritus at the University of Bonn, Germany, and held several honorary doctoral degrees. He had been an Esperantist since 1959 and met his wife through the Esperanto movement. He was a member and co-founder of the International Academy of Sciences San Marino.
For the 2009 European Parliament election, he was the top candidate for the German wing of Europe – De |
https://en.wikipedia.org/wiki/Enumeration | An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.
Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements.
Combinatorics
In combinatorics, enumeration means counting, i.e., determining the exact number of elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There are flourishing subareas in many branches of mathematics concerned with enumerating in this sense objects of special kinds. For instance, in partition enumeration and graph enumeration the objective is to count partitions or graphs that meet certain conditions.
Set theory
In set theory, the notion of enumeration has a broader sense, and does not require the set being enumerated to be finite.
Listing
When an enumeration is used in an ordered list context, we impose some sort of ordering structure requirement on the index set. While we can make the requirements on the ordering quite lax in order to allow for great generality, the most natural and common prerequisite is that the index set be well-ordered. According to this characterization, an ordered enumeration is defined to be a surjection (an onto relationship) with a well-ordered domain. This definitio |
https://en.wikipedia.org/wiki/Algebraic%20enumeration | Algebraic enumeration is a subfield of enumeration that deals with finding exact formulas for the number of combinatorial objects of a given type, rather than estimating this number asymptotically. Methods of finding these formulas include generating functions and the solution of recurrence relations.
References
Enumerative combinatorics |
https://en.wikipedia.org/wiki/Time%20Sharing%20Option | Time Sharing Option (TSO) is an interactive time-sharing environment for IBM mainframe operating systems, including OS/360 MVT, OS/VS2 (SVS), MVS, OS/390, and z/OS.
Use
In computing, time-sharing is a design technique that allows many people to use a computer system concurrently and independently—without interfering with each other. Each TSO user is isolated; it appears to each one that they are the only user of the system.
TSO is most commonly used by mainframe system administrators and programmers. It provides:
A text editor
Batch job support, including completion notification
Debuggers for some programming languages used on System/360 and later IBM mainframes
Support for other vendors' end-user applications, for example for querying IMS and DB2 databases
TSO interacts with users in either a line-by-line mode or in a full screen, menu-driven mode. In the line-by-line mode, the user enters commands by typing them in at the keyboard; in turn, the system interprets the commands, and then displays responses on the terminal screen. But most mainframe interaction is actually via ISPF, which allows for customized menu-driven interaction. This combination is called TSO/ISPF. TSO can also provide a Unix-style environment on OS/390 and z/OS via the UNIX System Services command shell, with or without ISPF.
TSO commands can be embedded in REXX execs or CLISTs, which can run interactively or in batch.
TSO eliminated the need to punch cards on a keypunch machine, and send card decks to the computer room to be read by a card reading machine.
History
When it was originally introduced in 1971, IBM considered time-sharing an "optional feature", as compared to standard batch processing, and hence offered TSO as an option for OS/360 MVT. With the introduction of MVS in 1974, IBM made it a standard component of their top-end mainframe operating system. TSO/E ("Time Sharing Option/Extensions") is a set of extensions to the original TSO. TSO/E is a base element of z/OS. Befo |
https://en.wikipedia.org/wiki/Electric%20power%20distribution | Electric power distribution is the final stage in the delivery of electricity. Electricity is carried from the transmission system to individual consumers. Distribution substations connect to the transmission system and lower the transmission voltage to medium voltage ranging between and with the use of transformers. Primary distribution lines carry this medium voltage power to distribution transformers located near the customer's premises. Distribution transformers again lower the voltage to the utilization voltage used by lighting, industrial equipment and household appliances. Often several customers are supplied from one transformer through secondary distribution lines. Commercial and residential customers are connected to the secondary distribution lines through service drops. Customers demanding a much larger amount of power may be connected directly to the primary distribution level or the subtransmission level.
The transition from transmission to distribution happens in a power substation, which has the following functions:
Circuit breakers and switches enable the substation to be disconnected from the transmission grid or for distribution lines to be disconnected.
Transformers step down transmission voltages, or more, down to primary distribution voltages. These are medium voltage circuits, usually .
From the transformer, power goes to the busbar that can split the distribution power off in multiple directions. The bus distributes power to distribution lines, which fan out to customers.
Urban distribution is mainly underground, sometimes in common utility ducts. Rural distribution is mostly above ground with utility poles, and suburban distribution is a mix.
Closer to the customer, a distribution transformer steps the primary distribution power down to a low-voltage secondary circuit, usually 120/240 V in the US for residential customers. The power comes to the customer via a service drop and an electricity meter. The final circuit in an urban system |
https://en.wikipedia.org/wiki/Meiobenthos | Meiobenthos, also called meiofauna, are small benthic invertebrates that live in marine or freshwater environments, or both. The term meiofauna loosely defines a group of organisms by their sizelarger than microfauna but smaller than macrofaunarather than by their taxonomy. This fauna includes both animals that turns into macrofauna later in life, and those small enough to belong to the meiobenthos their entire life. In marine environments there can be thousands individuals in 10 cm3 of sediment, and counts animals like nematodes, copepods, rotifers, tardigrades and ostracods, but protists like ciliates and foraminifers within the size range of the meiobethos are also often included. In practice, the term usually includes organisms that can pass through a 1 mm mesh but are retained by a 45 μm mesh, though exact dimensions may vary. Whether an organism will pass through a 1 mm mesh also depends upon whether it is alive or dead at the time of sorting.
The term meiobenthos was first coined in 1942 by Molly Mare, but organisms that fit into the modern meiofauna category have been studied since the 18th century.
Meiofaunal taxa
Collecting the meiobenthos
Meiofauna are most commonly encountered in sedimentary environments in both marine and freshwater environments, from the littoral to the deep-sea. They can also be found on hard substrates living on algae, the phytal environment, and sessile animals (barnacles, mussel beds, etc.).
Sampling methodologies
Sampling the meiobenthos is dependent upon the environment and whether quantitative or qualitative samples are required. In the sedimentary environment, the methodology used also depends on the physical morphology of the sediment. For qualititative sampling within the littoral zone, for both coarse and fine sediment, a bucket and spade will work. In the sub-littoral and deep water, some form of grab (like the Van Veen grab sampler) is required, although a fine mesh (about 0.25 mm or less) would work also.
For the qu |
https://en.wikipedia.org/wiki/Tilde | The tilde () or , is a grapheme with a number of uses . The name of the character came into English from Spanish, which in turn came from the Latin titulus, meaning "title" or "superscription". Its primary use is as a diacritic (accent) in combination with a base letter but, for historical reasons, it is also used in standalone form within a variety of contexts.
History
Use by medieval scribes
The tilde was originally written over an omitted letter or several letters as a scribal abbreviation, or "mark of suspension" and "mark of contraction", shown as a straight line when used with capitals. Thus, the commonly used words Anno Domini were frequently abbreviated to Ao Dñi, with an elevated terminal with a suspension mark placed over the "n". Such a mark could denote the omission of one letter or several letters. This saved on the expense of the scribe's labor and the cost of vellum and ink. Medieval European charters written in Latin are largely made up of such abbreviated words with suspension marks and other abbreviations; only uncommon words were given in full.
The text of the Domesday Book of 1086, relating for example, to the manor of Molland in Devon (see adjacent picture), is highly abbreviated as indicated by numerous tildes.
The text with abbreviations expanded is as follows:
Role of mechanical typewriters
On typewriters designed for languages that routinely use diacritics (accent marks), there are two possible solutions. Keys can be dedicated to precomposed characters or alternatively a dead key mechanism can be provided. With the latter, a mark is made when a dead key is typed, but unlike normal keys, the paper carriage does not move on and thus the next letter to be typed is printed under that accent. Typewriters for Spanish typically have a dedicated key for Ñ/ñ but, as Portuguese uses Ã/ã and Õ/õ, a single dead-key (rather than take two keys to dedicate) is the most practical solution.
The tilde symbol did not exist independently as a movable t |
https://en.wikipedia.org/wiki/Transaction%20processing | In computer science, transaction processing is information processing that is divided into individual, indivisible operations called transactions. Each transaction must succeed or fail as a complete unit; it can never be only partially complete.
For example, when you purchase a book from an online bookstore, you exchange money (in the form of credit) for a book. If your credit is good, a series of related operations ensures that you get the book and the bookstore gets your money. However, if a single operation in the series fails during the exchange, the entire exchange fails. You do not get the book and the bookstore does not get your money. The technology responsible for making the exchange balanced and predictable is called transaction processing. Transactions ensure that data-oriented resources are not permanently updated unless all operations within the transactional unit complete successfully. By combining a set of related operations into a unit that either completely succeeds or completely fails, one can simplify error recovery and make one's application more reliable.
Transaction processing systems consist of computer hardware and software hosting a transaction-oriented application that performs the routine transactions necessary to conduct business. Examples include systems that manage sales order entry, airline reservations, payroll, employee records, manufacturing, and shipping.
Since most, though not necessarily all, transaction processing today is interactive, the term is often treated as synonymous with online transaction processing.
Description
Transaction processing is designed to maintain a system's Integrity (typically a database or some modern filesystems) in a known, consistent state, by ensuring that interdependent operations on the system are either all completed successfully or all canceled successfully.
For example, consider a typical banking transaction that involves moving $700 from a customer's savings account to a customer's check |
https://en.wikipedia.org/wiki/Mis%C3%A8re | Misère (French for "destitution"), misere, bettel, betl, or (German for "beggar"; equivalent terms in other languages include , and ) is a bid in various card games, and the player who bids misère undertakes to win no tricks or as few as possible, usually at no trump, in the round to be played. This does not allow sufficient variety to constitute a game in its own right, but it is the basis of such trick-avoidance games as Hearts, and provides an optional contract for most games involving an auction. The term or category may also be used for some card game of its own with the same aim, like Black Peter.
A misère bid usually indicates an extremely poor hand, hence the name. An open or lay down misère, or misère ouvert is a 500 bid where the player is so sure of losing every trick that they undertake to do so with their cards placed face-up on the table. Consequently, 'lay down misère' is Australian gambling slang for a predicted easy victory.
In Skat, the bidding can result in a null game, where the bidder wins only if they lose every trick. (Conversely, the opponents win by forcing the bidder to take a trick.) In Swedish Whist, by contrast, a null game is one in which both teams try to take the fewest tricks. This variation is known as ramsch in Skat.
In Spades, bidding for no tricks is known as bidding nil, which if successful gives the bidder a bonus.
The word is first recorded in this sense in the rules for the game "Boston" in the late 18th century. It cannot be played in 6 hand 500.
Misère game
A misère game or bettel game is a game that is played according to its conventional rules, except that it is "played to lose"; that is, the winner is the one who loses according to the normal game rules. Or, if the game is for more than two players, the one who wins according to the normal game rules loses. Such games generally have rulesets that normally encourage players to win; for example, most variations of checkers (draughts) require players to make a |
https://en.wikipedia.org/wiki/Rural%20area | In general, a rural area or a countryside is a geographic area that is located outside towns and cities. Typical rural areas have a low population density and small settlements. Agricultural areas and areas with forestry typically are described as rural. Different countries have varying definitions of rural for statistical and administrative purposes.
In rural areas, because of their unique economic and social dynamics, and relationship to land-based industry such as agriculture, forestry and resource extraction, the economics are very different from cities and can be subject to boom and bust cycles and vulnerability to extreme weather or natural disasters, such as droughts. These dynamics alongside larger economic forces encouraging to urbanization have led to significant demographic declines, called rural flight, where economic incentives encourage younger populations to go to cities for education and access to jobs, leaving older, less educated and less wealthy populations in the rural areas. Slower economic development results in poorer services like healthcare and education and rural infrastructure. This cycle of poverty in some rural areas, means that three quarters of the global population in poverty live in rural areas according to the Food and Agricultural Organization.
Some communities have successfully encouraged economic development in rural areas, with some policies such as giving increased access to electricity or internet, proving very successful on encouraging economic activities in rural areas. Historically development policies have focused on larger extractive industries, such as mining and forestry. However, recent approaches more focused on sustainable development are more aware of economic diversification in these communities.
Regional definitions
North America
Canada
In Canada, the Organization for Economic Co-operation and Development defines a "predominantly rural region" as having more than 50% of the population living in rural communit |
https://en.wikipedia.org/wiki/Whitehead%20problem | In group theory, a branch of abstract algebra, the Whitehead problem is the following question:
Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory.
Refinement
Assume that A is an abelian group such that every short exact sequence
must split if B is also abelian. The Whitehead problem then asks: must A be free? This splitting requirement is equivalent to the condition Ext1(A, Z) = 0. Abelian groups A satisfying this condition are sometimes called Whitehead groups, so Whitehead's problem asks: is every Whitehead group free? It should be mentioned that if this condition is strengthened by requiring that the exact sequence
must split for any abelian group C, then it is well known that this is equivalent to A being free.
Caution: The converse of Whitehead's problem, namely that every free abelian group is Whitehead, is a well known group-theoretical fact. Some authors call Whitehead group only a non-free group A satisfying Ext1(A, Z) = 0. Whitehead's problem then asks: do Whitehead groups exist?
Shelah's proof
Saharon Shelah showed that, given the canonical ZFC axiom system, the problem is independent of the usual axioms of set theory. More precisely, he showed that:
If every set is constructible, then every Whitehead group is free;
If Martin's axiom and the negation of the continuum hypothesis both hold, then there is a non-free Whitehead group.
Since the consistency of ZFC implies the consistency of both of the following:
The axiom of constructibility (which asserts that all sets are constructible);
Martin's axiom plus the negation of the continuum hypothesis,
Whitehead's problem cannot be resolved in ZFC.
Discussion
J. H. C. Whitehead, motivated by the second Cousin problem, first posed the problem in the 1950s. Stein answered the question in the affirmative for countable groups. Progress for larger groups was slow, and the problem was considered an important one in algebra for some years.
Shelah's resul |
https://en.wikipedia.org/wiki/Eating | Eating (also known as consuming) is the ingestion of food. In the natural biological world, this is typically to provide a heterotrophic organism with energy and nutrients and to allow for growth. Animals and other heterotrophs must eat in order to survive — carnivores eat other animals, herbivores eat plants, omnivores consume a mixture of both plant and animal matter, and detritivores eat detritus. Fungi digest organic matter outside their bodies as opposed to animals that digest their food inside their bodies.
For humans, eating is more complex, but is typically an activity of daily living. Physicians and dieticians consider a healthful diet essential for maintaining peak physical condition. Some individuals may limit their amount of nutritional intake. This may be a result of a lifestyle choice: as part of a diet or as religious fasting. Limited consumption may be due to hunger or famine. Overconsumption of calories may lead to obesity and the reasons behind it are myriad but its prevalence has led some to declare an "obesity epidemic".
Eating practices among humans
Many homes have a large kitchen area devoted to preparation of meals and food, and may have a dining room, dining hall, or another designated area for eating.
Most societies also have restaurants, food courts, and food vendors so that people may eat when away from home, when lacking time to prepare food, or as a social occasion. At their highest level of sophistication, these places become "theatrical spectacles of global cosmopolitanism and myth." At picnics, potlucks, and food festivals, eating is in fact the primary purpose of a social gathering. At many social events, food and beverages are made available to attendees.
People usually have two or three meals a day. Snacks of smaller amounts may be consumed between meals. Doctors in the UK recommend three meals a day (with between 400 and 600 kcal per meal), with four to six hours between. Having three well-balanced meals (described as: half o |
https://en.wikipedia.org/wiki/Software%20company | A software company is an organisation — owned either by the state or private — established for profit whose primary products are various forms of software, software technology, distribution, and software product development. They make up the software industry.
Types
There are a number of different types of software companies:
There are companies selling available to use commercial off-the-shelf (COTS) products, such as Microsoft's Outlook, Word and Excel, Adobe Systems's Acrobat, Illustrator and other designing tools, or Google apps like Chrome.
Many companies provide Software Development services, and have a structure to develop custom software for other companies and businesses.
Companies producing specialized commercial off-the-shelf software, such as Panorama, Hyperion, and Siebel Systems
Companies providing Software as a Service (SaaS), such as Google's email service Gmail, Voice and Maps, and companies like Salesforce and Zendesk.
Technology that mobilizes social media such as Facebook, LinkedIn, Instagram, Twitter and Parler.
There are also other types of SaaS products, of companies providing IT infrastructure services and Cloud Computing services, such as Amazon Web Services (AWS), Microsoft Azure Cloud Services, and GoDaddy hosting services.
API as a Service, that allows third party developers to interact with a companies software, such as Google Geo Location API, Google Calendar API, etc.
Companies producing software components, such as Syncfusion, DevExpress, Telerik, Nevron and Dundas
Application Service Provider such as Salesforce
Companies producing bespoke software for vertical industries or particular geographical regions
Independent software vendors (ISVs) that build, develop and sell consumer or enterprise software that is consumed by end users
All of these may be categorized in one or many of the following:
contractual - when the software company is contracted to deliver some particular software from outside (software outsourcing)
product d |
https://en.wikipedia.org/wiki/Order%20of%20operations | In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.
These rules are formalized with a ranking of the operators. The rank of an operator is called its precedence, and an operation with a higher precedence is performed before operations with lower precedence. Calculators generally perform operations with the same precedence from left to right, but some programming languages and calculators adopt different conventions.
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, in the expression , the multiplication is performed before addition, and the expression has the value , and not . When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of their base. Thus and .
These conventions exist to avoid notational ambiguity while allowing notation to remain brief. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, forces addition to precede multiplication, while forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in .
These rules are meaningful only when the usual notation (called infix notation) is used. When functional or Polish notation are used for all operations, the order of operations results from the notation itself.
Internet memes sometimes present ambiguous infix expressions that cause disputes and increase web traffic. Most of these ambiguous expressions involve mixed division and multiplication, where there is no general |
https://en.wikipedia.org/wiki/Packing%20problems | Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.
In a bin packing problem, you are given:
A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem.
A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly.
Usually the packing must be without overlaps between goods and other goods or the container walls. In some variants, the aim is to find the configuration that packs a single container with the maximal packing density. More commonly, the aim is to pack all the objects into as few containers as possible. In some variants the overlapping (of objects with each other and/or with the boundary of the container) is allowed but should be minimized.
Packing in infinite space
Many of these problems, when the container size is increased in all directions, become equivalent to the problem of packing objects as densely as possible in infinite Euclidean space. This problem is relevant to a number of scientific disciplines, and has received significant attention. The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales. Many other shapes have received attention, including ellipsoids, Platonic and Archimedean solids including tetrahedra, tripods (uni |
https://en.wikipedia.org/wiki/Carrion | Carrion (), also known as a carcass, is the decaying flesh of dead animals.
Overview
Carrion is an important food source for large carnivores and omnivores in most ecosystems. Examples of carrion-eaters (or scavengers) include crows, vultures, condors, hawks, eagles, hyenas, Virginia opossum, Tasmanian devils, coyotes and Komodo dragons. Many invertebrates, such as the carrion and burying beetles, as well as maggots of calliphorid flies (such as one of the most important species in Calliphora vomitoria) and flesh-flies, also eat carrion, playing an important role in recycling nitrogen and carbon in animal remains.
Carrion begins to decay at the moment of the animal's death, and it will increasingly attract insects and breed bacteria. Not long after the animal has died, its body will begin to exude a foul odor caused by the presence of bacteria and the emission of cadaverine and putrescine.
Some plants and fungi smell like decomposing carrion and attract insects that aid in reproduction. Plants that exhibit this behavior are known as carrion flowers. Stinkhorn mushrooms are examples of fungi with this characteristic.
Sometimes carrion is used to describe an infected carcass that is diseased and should not be touched. An example of carrion being used to describe dead and rotting bodies in literature may be found in William Shakespeare's play Julius Caesar (III.i):
Cry 'Havoc,' and let slip the dogs of war;
That this foul deed shall smell above the earth
With carrion men, groaning for burial.
Another example can be found in Daniel Defoe's Robinson Crusoe when the title character kills an unknown bird for food but finds "its flesh was carrion, and fit for nothing".
Consumption by humans
In Noahide law
The thirty-count laws of Ulla (Talmudist) include the prohibition of humans consuming carrion. This count is in addition to the standard seven law count and has been recently published from the Judeo-Arabic writing of Shmuel ben Hophni Gaon after having been lost |
https://en.wikipedia.org/wiki/Negative%20feedback | Negative feedback (or balancing feedback) occurs when some function of the output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances. A classic example of negative feedback is a heating system thermostat — when the temperature gets high enough, the heater is turned OFF. When the temperature gets too cold, the heat is turned back ON. In each case the "feedback" generated by the thermostat "negates" the trend.
The opposite tendency — called positive feedback — is when a trend is positively reinforced, creating amplification, such as the squealing "feedback" loop that can occur when a mic is brought too close to a speaker which is amplifying the very sounds the mic is picking up, or the runaway heating and ultimate meltdown of a nuclear reactor.
Whereas positive feedback tends to lead to instability via exponential growth, oscillation or chaotic behavior, negative feedback generally promotes stability. Negative feedback tends to promote a settling to equilibrium, and reduces the effects of perturbations. Negative feedback loops in which just the right amount of correction is applied with optimum timing, can be very stable, accurate, and responsive.
Negative feedback is widely used in mechanical and electronic engineering, and also within living organisms, and can be seen in many other fields from chemistry and economics to physical systems such as the climate. General negative feedback systems are studied in control systems engineering.
Negative feedback loops also play an integral role in maintaining the atmospheric balance in various systems on Earth. One such feedback system is the interaction between solar radiation, cloud cover, and planet temperature.
General description
In many physical and biological systems, qualitatively different influences can oppose each other. For example, in biochemistry, one set of chemicals drives the syst |
https://en.wikipedia.org/wiki/Subtyping | In programming language theory, subtyping (also called subtype polymorphism or inclusion polymorphism) is a form of type polymorphism. A subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements (typically subroutines or functions), written to operate on elements of the supertype, can also operate on elements of the subtype.
If S is a subtype of T, the subtyping relation (written as , , or ) means that any term of type S can safely be used in any context where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how "safely be used" and "any context" are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms.
Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming.
Functional programming languages often allow the subtyping of records. Consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in which a useful notion of subtyping may be defined and studied. Because the resulting calculus allows terms to have more than one type, it is no longer a "simple" type theory. Since functional programming languages, by definition, support function literals, which can also be stored in records, records types with subtyping provide some of the features of object-oriented programming. Typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. In a theoretical setting, i |
https://en.wikipedia.org/wiki/Project%20Coast | Project Coast was a 1980s top-secret chemical and biological weapons (CBW) program instituted by the apartheid-era government of South Africa. Project Coast was the successor to a limited postwar CBW program, which mainly produced the lethal agents CX powder and mustard gas, as well as non-lethal tear gas for riot control purposes. The program was headed by the cardiologist Wouter Basson, who was also the personal physician of South African Prime Minister P. W. Botha.
History
From 1975 onwards, the South African Defence Force (SADF) found itself embroiled in conventional battles in Angola as a result of the South African Border War. The perception that its enemies had access to battlefield chemical and biological weapons (CBW) led South Africa to begin expanding its own program, initially as a defensive measure and by carrying out research on vaccines. As the years went on, research shifted to offensive uses. In 1981, President P. W. Botha ordered the SADF to develop CBW technology for use against South Africa's enemies. In response, the head of the South African Medical Service division, which was responsible for defensive CBW capabilities, hired Wouter Basson, a cardiologist, to visit other countries and report back on their respective CBW capabilities. He returned with the recommendation that South Africa's program be expanded. In 1983, Project Coast was formed, with Basson at its head. To hide the program and its procurement of CBW-related substances, Project Coast formed four front companies: Delta G Scientific Company, Roodeplaat Research Laboratories, Protechnik and Infladel. Ben Raubenheimer was appointed as CEO.
Project Coast created a progressively larger variety of lethal offensive CBW toxins and biotoxins, in addition to the defensive measures. Initially, they were intended for use by the military in combat as a last resort. To that end, they copied Soviet techniques and designed devices that looked like ordinary objects but had the capability to poiso |
https://en.wikipedia.org/wiki/Magic%20star | An n-pointed magic star is a star polygon with Schläfli symbol {n/2} in which numbers are placed at each of the n vertices and n intersections, such that the four numbers on each line sum to the same magic constant. A normal magic star contains the integers from 1 to 2n with no numbers repeated. The magic constant of an n-pointed normal magic star is M = 4n + 2.
No star polygons with fewer than 5 points exist, and the construction of a normal 5-pointed magic star turns out to be impossible. It can be proven that there exists no 4-pointed star that will satisfy the conditions here. The smallest examples of normal magic stars are therefore 6-pointed. Some examples are given below. Notice that for specific values of n, the n-pointed magic stars are also known as magic hexagrams (n = 6), magic heptagrams (n = 7), etc.
See also
Magic square
References
External links
Marian Trenkler's Magic Stars
Gianni Sarcone's Magic Star
Magic shapes
Star symbols |
https://en.wikipedia.org/wiki/Order%20topology | In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets.
If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays"
for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals
together with the above rays form a base for the order topology. The open sets in X are the sets that are a union of (possibly infinitely many) such open intervals and rays.
A topological space X is called orderable or linearly orderable if there exists a total order on its elements such that the order topology induced by that order and the given topology on X coincide. The order topology makes X into a completely normal Hausdorff space.
The standard topologies on R, Q, Z, and N are the order topologies.
Induced order topology
If Y is a subset of X, X a totally ordered set, then Y inherits a total order from X. The set Y therefore has an order topology, the induced order topology. As a subset of X, Y also has a subspace topology. The subspace topology is always at least as fine as the induced order topology, but they are not in general the same.
For example, consider the subset Y = {–1} ∪ {1/n}n∈N in the rationals. Under the subspace topology, the singleton set {–1} is open in Y, but under the induced order topology, any open set containing –1 must contain all but finitely many members of the space.
An example of a subspace of a linearly ordered space whose topology is not an order topology
Though the subspace topology of Y = {–1} ∪ {1/n}n∈N in the section above is shown to be not generated by the induced order on Y, it is nonetheless an order topology on Y; indeed, in the subspace topology every point is isolated (i.e., singleton {y} is open in Y for every y in Y), so the subspace topology is the discrete topology on Y (the topology in which eve |
https://en.wikipedia.org/wiki/Trophallaxis | Trophallaxis () is the transfer of food or other fluids among members of a community through mouth-to-mouth (stomodeal) or anus-to-mouth (proctodeal) feeding. Along with nutrients, trophallaxis can involve the transfer of molecules such as pheromones, organisms such as symbionts, and information to serve as a form of communication. Trophallaxis is used by some birds, gray wolves, vampire bats, and is most highly developed in eusocial insects such as ants, wasps, bees, and termites.
Etymology
Tropho- (prefix or suffix) is derived from the Greek trophé, meaning 'nourishment'. The Greek 'allaxis' means 'exchange'. The word was introduced by the entomologist William Morton Wheeler in 1918.
Evolutionary significance
Trophallaxis was used in the past to support theories on the origin of sociality in insects. The Swiss psychologist and entomologist Auguste Forel also believed that food sharing was key to ant society and he used an illustration of it as the frontispiece for his book The Social World of the Ants Compared with that of Man. Proctodeal trophallaxis allowed termites to transfer cellulolytic flagellates that made the digestion of wood possible and efficient. Besides sociality, trophallaxis has evolved within many species as a method of nourishment for adults and/or juveniles, kin survival, transfer of symbionts, transfer of immunity, colony recognition and foraging communication. Trophallaxis has even evolved as a parasitic strategy in some species to obtain food from their host. Trophallaxis can also result in the spreading of chemicals, such as pheromones, throughout a colony, which is significant in social colony functioning.
Species have evolved anatomy to allow them to participate in trophallaxis, such as the proventriculus in the crops of Formica fusca ants. This structure acts as a valve to enhance food storage capacity. Likewise, the honey bee Apis mellifera is able to protrude their proboscis and sip nectar from the open mandibles of the donor be |
https://en.wikipedia.org/wiki/Triangular%20number | A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in the triangular arrangement with dots on each side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers, starting with the 0th triangular number, is
Formula
The triangular numbers are given by the following explicit formulas:
where is notation for a binomial coefficient. It represents the number of distinct pairs that can be selected from objects, and it is read aloud as " plus one choose two".
The first equation can be illustrated using a visual proof. For every triangular number , imagine a "half-rectangle" arrangement of objects corresponding to the triangular number, as in the figure below. Copying this arrangement and rotating it to create a rectangular figure doubles the number of objects, producing a rectangle with dimensions , which is also the number of objects in the rectangle. Clearly, the triangular number itself is always exactly half of the number of objects in such a figure, or: . The example follows:
This formula can be proven formally using mathematical induction. It is clearly true for :
Now assume that, for some natural number , . Adding to this yields
so if the formula is true for , it is true for . Since it is clearly true for , it is therefore true for , , and ultimately all natural numbers by induction.
The German mathematician and scientist, Carl Friedrich Gauss, is said to have found this relationship in his early youth, by multiplying pairs of numbers in the sum by the values of each pair . However, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans in the 5th century BC. The two formulas were described by the Irish monk Dicuil in abou |
https://en.wikipedia.org/wiki/Square%20number | In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).
In the real number system, square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example, so 9 is a square number.
A positive integer that has no square divisors except 1 is called square-free.
For a non-negative integer , the th square number is , with being the zeroth one. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square, for example,
.
Starting with 1, there are square numbers up to and including , where the expression represents the floor of the number .
Examples
The squares smaller than 602 = 3600 are:
02 = 0
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
212 = 441
222 = 484
232 = 529
242 = 576
252 = 625
262 = 676
272 = 729
282 = 784
292 = 841
302 = 900
312 = 961
322 = 1024
332 = 1089
342 = 1156
352 = 1225
362 = 1296
372 = 1369
382 = 1444
392 = 1521
402 = 1600
412 = 1681
422 = 176 |
https://en.wikipedia.org/wiki/Relative%20atomic%20mass | Relative atomic mass (symbol: A; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant (symbol: m) is defined as being of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 redefinition of the SI base units.
For a single given sample, the relative atomic mass of a given element is the weighted arithmetic mean of the masses of the individual atoms (including all its isotopes) that are present in the sample. This quantity can vary significantly between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced combinations of isotopic abundances in varying ratios. For example, due to a different mixture of stable carbon-12 and carbon-13 isotopes, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.
The more common, and more specific quantity known as standard atomic weight (A) is an application of the relative atomic mass values obtained from many different samples. It is sometimes interpreted as the expected range of the relative atomic mass values for the atoms of a given element from all terrestrial sources, with the various sources being taken from Earth. "Atomic weight" is often loosely and incorrectly used as a synonym for standard atomic weight (incorrectly because standard atomic weights are not from a single sample). Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.
Additionally, the continued use of the term "atomic weight" (for any element) as opposed to "relative atomic mass" has attracted considerable controversy since at least the 196 |
https://en.wikipedia.org/wiki/Host%20%28biology%29 | In biology and medicine, a host is a larger organism that harbours a smaller organism; whether a parasitic, a mutualistic, or a commensalist guest (symbiont). The guest is typically provided with nourishment and shelter. Examples include animals playing host to parasitic worms (e.g. nematodes), cells harbouring pathogenic (disease-causing) viruses, or a bean plant hosting mutualistic (helpful) nitrogen-fixing bacteria. More specifically in botany, a host plant supplies food resources to micropredators, which have an evolutionarily stable relationship with their hosts similar to ectoparasitism. The host range is the collection of hosts that an organism can use as a partner.
Symbiosis
Symbiosis spans a wide variety of possible relationships between organisms, differing in their permanence and their effects on the two parties. If one of the partners in an association is much larger than the other, it is generally known as the host. In parasitism, the parasite benefits at the host's expense. In commensalism, the two live together without harming each other, while in mutualism, both parties benefit.
Most parasites are only parasitic for part of their life cycle. By comparing parasites with their closest free-living relatives, parasitism has been shown to have evolved on at least 233 separate occasions. Some organisms live in close association with a host and only become parasitic when environmental conditions deteriorate.
A parasite may have a long-term relationship with its host, as is the case with all endoparasites. The guest seeks out the host and obtains food or another service from it, but does not usually kill it. In contrast, a parasitoid spends a large part of its life within or on a single host, ultimately causing the host's death, with some of the strategies involved verging on predation. Generally, the host is kept alive until the parasitoid is fully grown and ready to pass on to its next life stage. A guest's relationship with its host may be intermitten |
https://en.wikipedia.org/wiki/Umbral%20calculus | In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to "prove" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively.
Short history
In the 1930s and 1940s, Eric Temple Bell attempted to set the umbral calculus on a rigorous footing.
In the 1970s, Steven Roman, Gian-Carlo Rota, and others developed the umbral calculus by means of linear functionals on spaces of polynomials. Currently, umbral calculus refers to the study of Sheffer sequences, including polynomial sequences of binomial type and Appell sequences, but may encompass systematic correspondence techniques of the calculus of finite differences.
The 19th-century umbral calculus
The method is a notational procedure used for deriving identities involving indexed sequences of numbers by pretending that the indices are exponents. Construed literally, it is absurd, and yet it is successful: identities derived via the umbral calculus can also be properly derived by more complicated methods that can be taken literally without logical difficulty.
An example involves the Bernoulli polynomials. Consider, for example, the ordinary binomial expansion (which contains a binomial coefficient):
and the remarkably similar-looking relation on the Bernoulli polynomials:
Compare also the ordinary derivative
to a very similar-looking relation on the Bernoulli polynomials:
These similarities allow one to construct umbral proofs, which, on the surface, cannot be correct, but seem to work anyway. Thus, for example, by pretending that the subscript n − k is an exponent:
and then differentiating, one gets the desired result:
In the above, the variable b is an "umbra" (Latin for shadow).
See also Faulhaber's formula.
Umbral Taylor |
https://en.wikipedia.org/wiki/Linear%20form | In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers).
If is a vector space over a field , the set of all linear functionals from to is itself a vector space over with addition and scalar multiplication defined pointwise. This space is called the dual space of , or sometimes the algebraic dual space, when a topological dual space is also considered. It is often denoted , or, when the field is understood, ; other notations are also used, such as , or When vectors are represented by column vectors (as is common when a basis is fixed), then linear functionals are represented as row vectors, and their values on specific vectors are given by matrix products (with the row vector on the left).
Examples
The constant zero function, mapping every vector to zero, is trivially a linear functional. Every other linear functional (such as the ones below) is surjective (that is, its range is all of ).
Indexing into a vector: The second element of a three-vector is given by the one-form That is, the second element of is
Mean: The mean element of an -vector is given by the one-form That is,
Sampling: Sampling with a kernel can be considered a one-form, where the one-form is the kernel shifted to the appropriate location.
Net present value of a net cash flow, is given by the one-form where is the discount rate. That is,
Linear functionals in Rn
Suppose that vectors in the real coordinate space are represented as column vectors
For each row vector there is a linear functional defined by
and each linear functional can be expressed in this form.
This can be interpreted as either the matrix product or the dot product of the row vector and the column vector :
Trace of a square matrix
The trace of a square matrix is the sum of all elements on its main diagonal. Matrices can be multiplied by scalars and two mat |
https://en.wikipedia.org/wiki/Very-long-baseline%20interferometry | Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. The distance between the radio telescopes is then calculated using the time difference between the arrivals of the radio signal at different telescopes. This allows observations of an object that are made simultaneously by many radio telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.
Data received at each antenna in the array include arrival times from a local atomic clock, such as a hydrogen maser. At a later time, the data are correlated with data from other antennas that recorded the same radio signal, to produce the resulting image. The resolution achievable using interferometry is proportional to the observing frequency. The VLBI technique enables the distance between telescopes to be much greater than that possible with conventional interferometry, which requires antennas to be physically connected by coaxial cable, waveguide, optical fiber, or other type of transmission line. The greater telescope separations are possible in VLBI due to the development of the closure phase imaging technique by Roger Jennison in the 1950s, allowing VLBI to produce images with superior resolution.
VLBI is best known for imaging distant cosmic radio sources, spacecraft tracking, and for applications in astrometry. However, since the VLBI technique measures the time differences between the arrival of radio waves at separate antennas, it can also be used "in reverse" to perform Earth rotation studies, map movements of tectonic plates very precisely (within millimetres), and perform other types of geodesy. Using VLBI in this manner requires large numbers of time difference measurements from distant sources (such as quasars) observed with a global network of antennas over a |
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