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https://en.wikipedia.org/wiki/Dynabook | The KiddiComp concept, envisioned by Alan Kay in 1968 while a PhD candidate, and later developed and described as the Dynabook in his 1972 proposal "A personal computer for children of all ages", outlines the requirements for a conceptual portable educational device that would offer similar functionality to that now supplied via a laptop computer or (in some of its other incarnations) a tablet or slate computer with the exception of the requirement for any Dynabook device offering near eternal battery life. Adults could also use a Dynabook, but the target audience was children.
Part of the motivation and funding for the Dynabook project came from the need for portable military maintenance, repair, and operations documentation. Eliminating the need to move large amounts of difficult-to-access paper in a dynamic military theatre provided significant US Department of Defense funding.
Though the hardware required to create a Dynabook is here today, Alan Kay still thinks the Dynabook hasn't been invented yet, because key software and educational curricula are missing. When Microsoft came up with its tablet PC, Kay was quoted as saying "Microsoft's Tablet PC, the first Dynabook-like computer good enough to criticize".
Toshiba also has a line of sub-notebook computers called DynaBooks. In June 2018, Sharp acquired a majority stake in Toshiba's PC business including laptops and tablets sold under the Dynabook brand.
Original concept
Describing the idea as "A Personal Computer For Children of All Ages", Kay wanted the Dynabook concept to embody the learning theories of Jerome Bruner and some of what Seymour Papert— who had studied with developmental psychologist Jean Piaget and who was one of the inventors of the Logo programming language — was proposing. This concept was created two years before the founding of Xerox PARC. The ideas led to the development of the Xerox Alto prototype, which was originally called "the interim Dynabook". It embodied all the elements |
https://en.wikipedia.org/wiki/Cobordism | In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher.
The boundary of an (n + 1)-dimensional manifold W is an n-dimensional manifold ∂W that is closed, i.e., with empty boundary. In general, a closed manifold need not be a boundary: cobordism theory is the study of the difference between all closed manifolds and those that are boundaries. The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions for
piecewise linear and topological manifolds.
A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of M and N, .
Cobordisms are studied both for the equivalence relation that they generate, and as objects in their own right. Cobordism is a much coarser equivalence relation than diffeomorphism or homeomorphism of manifolds, and is significantly easier to study and compute. It is not possible to classify manifolds up to diffeomorphism or homeomorphism in dimensions ≥ 4 – because the word problem for groups cannot be solved – but it is possible to classify manifolds up to cobordism. Cobordisms are central objects of study in geometric topology and algebraic topology. In geometric topology, cobordisms are intimately connected with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories are fundamental extraordinary cohomology theories, and categories of cobordisms are the domains of topological quantum field theories.
Definition
Manifolds
Roughly speaking, an n-dimensional manifold M is a topological space locally (i.e., near each point) homeomorphic to an open subset of Euclid |
https://en.wikipedia.org/wiki/81%20%28number%29 | 81 (eighty-one) is the natural number following 80 and preceding 82.
In mathematics
81 is:
the square of 9 and the second fourth-power of a prime; 34.
with an aliquot sum of 40; within an aliquot sequence of three composite numbers (81,40,50,43,1,0) to the Prime in the 43-aliquot tree.
a perfect totient number like all powers of three.
a heptagonal number.
a centered octagonal number.
a tribonacci number.
an open meandric number.
the ninth member of the Mian-Chowla sequence.
a palindromic number in bases 8 (1218) and 26 (3326).
a Harshad number in bases 2, 3, 4, 7, 9, 10 and 13.
one of three non-trivial numbers (the other two are 1458 and 1729) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
8 + 1 = 9
9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit).
The inverse of 81 is 0. recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,
omitting only the digit b−2.
In astronomy
Messier object M81, a magnitude 8.5 spiral galaxy in the constellation Ursa Major, also known as Bode's Galaxy, and the first of what is known as the M81 Group of galaxies
The New General Catalogue object NGC 81, a spiral galaxy in the constellation Andromeda
In other fields
Eighty-one is also:
The number of squares on a shogi playing board
The year AD 81, 81 BC, or 1981.
The atomic number of thallium
The symbolic number of the Hells Angels Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.
The title of a short film by Stephen Burke: 81
The model number of Sinclair ZX81
The number of the department in France called Tarn
The code for international direct dial phone calls to Japan
"+81" is a song by Japanese metalcore band Crystal Lake.
One of two ISBN Group Identifiers for books published in India
The number of stanzas or chapters in the T |
https://en.wikipedia.org/wiki/82%20%28number%29 | 82 (eighty-two) is the natural number following 81 and preceding 83.
In mathematics
82 is:
the twenty-third semiprime and the twelfth of the form (2.q).
with an aliquot sum of 44, within an aliquot sequence of four composite numbers (82,44,40,50,43,1,0) to the Prime in the 43-aliquot tree.
a companion Pell number.
a happy number.
palindromic in bases 3 (100013), 9 (1019) and 40 (2240).
In science
The atomic number of lead.
The sixth magic number.
Messier 82, a starburst galaxy in the constellation Ursa Major.
The New General Catalogue object NGC 82, a single star in the constellation Andromeda.
In other fields
Eighty-two is also:
The model number of: Mark 82 bomb, a nonguided general-purpose bomb.
The number of the French department Tarn-et-Garonne.
The code for international direct dial phone calls to South Korea.
The ISBN Group Identifier for books published in Norway.
Title of Dennis Smith's book about firefighters, Report from Engine Co. 82.
The year AD 82, 82 BC, or 1982, stylized as '82.
The number of Trip Murphy's (Matt Dillon) car in Herbie: Fully Loaded (2005).
The second studio album by African electropop outfit Just a Band (2009).
The number (*82) to unblock your caller ID for phones that block anonymous incoming calls.
The very significant number that appears at the end of Kurt Vonnegut's book Hocus Pocus.
In sports
Both the NBA and NHL operate 82-game regular seasons.
In Major League Baseball, the number of games a team must win to secure a winning season.
References
Integers |
https://en.wikipedia.org/wiki/83%20%28number%29 | 83 (eighty-three) is the natural number following 82 and preceding 84.
In mathematics
83 is:
the sum of three consecutive primes (23 + 29 + 31).
the sum of five consecutive primes (11 + 13 + 17 + 19 + 23).
the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89.
a Sophie Germain prime.
a safe prime.
a Chen prime.
an Eisenstein prime with no imaginary part and real part of the form 3n − 1.
a highly cototient number.
the number of primes that are right-truncatable.
a super-prime, because 23 is prime.
In science
Chemistry
The atomic number of bismuth (Bi)
Astronomy
Messier object M83, a magnitude 8.5 spiral galaxy in the constellation Hydra, also known as the Southern Pinwheel Galaxy
The New General Catalogue object NGC 83, a magnitude 12.3 elliptical galaxy in the constellation Andromeda
In religion
Judaism
When someone reaches 83 they may celebrate a second bar mitzvah
In music
M83 is the debut album of the French electronic music group M83
83 is a song written by John Mayer in the Room for Squares album.
83 is a Quebec hip-hop group
83 is a song produced by Maximono
In film and television
Gypsy 83 is 2001 film directed by Todd Stephens
Class of '83 is 2004 film directed by Kurt E. Soderling
83 Hours 'Til Dawn is a 1990 film directed by Donald Wrye
83 is the highest UHF channel on older televisions made before the late 1970s (newer televisions only go up to channel 69, due to the frequency spectrum previously assigned to channels 70–83 in the United States being reassigned to cellular phone service there in the late 1970s-early 1980s). As an example, the television station CIVIC-TV managed by the James Woods character Max Renn in the 1983 film Videodrome was on Channel 83.
In other fields
Eighty-three is also:
The year AD 83, 83 BC, or 1983
The TI-83 series, graphing calculators from Texas Instruments
Konsept83 is a Greek graphic design team.
The model number of Bell XP-83
The number of the French |
https://en.wikipedia.org/wiki/84%20%28number%29 | 84 (eighty-four) is the natural number following 83 and preceding 85.
In mathematics
84 is a semiperfect number, being thrice a perfect number, and the sum of the sixth pair of twin primes .
It is the third (or second) dodecahedral number, and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28, 36), which makes it the sixth tetrahedral number.
The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits.
A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.
84 is the limit superior of the largest finite subgroup of the mapping class group of a genus surface divided by .
Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface of genus will contain an automorphism group whose order is classically bound to .
There are 84 zero divisors in the 16-dimensional sedenions .
In astronomy
Messier object M84, a magnitude 11.0 lenticular galaxy in the constellation Virgo
The New General Catalogue object NGC 84, a single star in the constellation Andromeda
In other fields
Eighty-four is also:
The year AD 84, 84 BC, or 1984.
The number of years in the , a cycle used in the past by Celtic peoples, equal to 3 cycles of the Julian Calendar and to 4 Metonic cycles and 1 octaeteris
The atomic number of polonium
The model number of Harpoon missile
WGS 84 - The latest revision of the World Geodetic System, a fixed global reference frame for the Earth.
The house number of 84 Avenue Foch
The number of the French department Vaucluse
The code for international direct dial phone calls to Vietnam
The town of Eighty Four, Pennsylvania
The company 84 Lumber
The ISBN Group Identifier for books published in Spain
A variation of the game 42 played with two sets of dominoes.
The film 84 Charing Cross Road (1987) starring Anne Bancroft and Anthony Hopkins
KKNX Radio 84 in Eugene, Oregon
The B-Side to |
https://en.wikipedia.org/wiki/85%20%28number%29 | 85 (eighty-five) is the natural number following 84 and preceding 86.
In mathematics
85 is:
the product of two prime numbers (5 and 17), and is therefore a semiprime of the form (5.q) where q is prime.
specifically, the 24th Semiprime, it being the fourth of the form (5.q).
together with 86 and 87, forms the second cluster of three consecutive semiprimes; the first comprising 33, 34, 35.
with a prime aliquot sum of 23 in the short aliquot sequence (85,23,1,0).
an octahedral number.
a centered triangular number.
a centered square number.
a decagonal number.
the smallest number that can be expressed as a sum of two squares, with all squares greater than 1, in two ways, 85 = 92 + 22 = 72 + 62.
the length of the hypotenuse of four Pythagorean triangles.
a Smith number in decimal.
In astronomy
Messier object M85 is a magnitude 10.5 lenticular galaxy in the constellation Coma Berenices
NGC 85 is a galaxy in the constellation Andromeda
85 Io is a large main belt asteroid
85 Pegasi is a multiple star system in constellation of Pegasus
85 Ceti is a variable star in the constellation of Cetus
85D/Boethin is a periodic comet
In titles and names
Federalist No. 85, by Alexander Hamilton, the last of The Federalist Papers (1788)
The 85 Ways to Tie a Tie, a book by Thomas Fink and Yong Mao
85 Days: The Last Campaign of Robert Kennedy, a book by Jules Witcover
Live/1975–85, an album of live recordings by Bruce Springsteen (1986)
80–85, a compilation album by Bad Religion (1991)
Cupid & Psyche 85, an album by band Scritti Politti (1985)
45/85 was a television documentary on World War II
Minuscule 85, Papyrus 85, Lectionary 85 are early Greek manuscripts of the New Testament
"85", a 2000 rap single by YoungBloodz, from their album Against Da Grain
85°C, a Taiwanese coffee store chain.
In sports
In U.S. college athletics, schools that are members of NCAA Division I are limited to providing athletic scholarships to a maximum of 85 football players in a |
https://en.wikipedia.org/wiki/86%20%28number%29 | 86 (eighty-six) is the natural number following 85 and preceding 87.
In mathematics
86 is:
nontotient and a noncototient.
the 25th distinct semiprime and the 13th of the form (2.q).
together with 85 and 87, forms the middle semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33, 34, 35.
an Erdős–Woods number, since it is possible to find sequences of 86 consecutive integers such that each inner member shares a factor with either the first or the last member.
a happy number and a self number in base 10.
with an aliquot sum of 46; itself a semiprime, within an aliquot sequence of seven members (86,46,26,16,15,9,4,3,1,0) in the Prime 3-aliquot tree.
It appears in the Padovan sequence, preceded by the terms 37, 49, 65 (it is the sum of the first two of these).
It is conjectured that 86 is the largest n for which the decimal expansion of 2n contains no 0.
86 = (8 × 6 = 48) + (4 × 8 = 32) + (3 × 2 = 6). That is, 86 is equal to the sum of the numbers formed in calculating its multiplicative persistence.
In science
86 is the atomic number of radon.
There are 86 metals on the modern periodic table.
In other fields
In American English, and particularly in the food service industry, 86 has become a slang term referring to an item being out of stock or discontinued, and by extension to a person no longer welcome on the premises.
The number of the French department Vienne. This number is also reflected in the department's postal code and in the name of a local basketball club, Poitiers Basket 86.
+86 is the code for international direct dial phone calls to China.
An art gallery in Ventura, California, displaying art pieces from such artists Billy Childish, Stacy Lande and Derek Hess, most of which include the number *86 hidden or overtly shown in the art, and some of which fall under the genre of lowbrow.
86 is the device number for a lockout relay function in electrical engineering electrical circuit protection schemes.
86 is often |
https://en.wikipedia.org/wiki/87%20%28number%29 | 87 (eighty-seven) is the natural number following 86 and preceding 88.
In mathematics
87 is:
the sum of the squares of the first four primes (87 = 22 + 32 + 52 + 72).
the sum of the sums of the divisors of the first 10 positive integers.
the thirtieth semiprime, and the twenty-sixth distinct semiprime and the eighth of the form (3.q).
together with 85 and 86, forms the last semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33, 34, 35.
with an aliquot sum of 33; itself a semiprime, within an aliquot sequence of five composite numbers (87,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
5! - 4! - 3! - 2! - 1! = 87
the last two decimal digits of Graham's number.
In sports
Cricket in Australia holds 87 as a superstitiously unlucky score and is referred to as "the devil's number". This originates from the fact that 87 is 13 runs short of a century. 187, 287, and so on are also considered unlucky but are not as common as 87 on its own.
In the National Hockey League, Wayne Gretzky scored a league-high 87 goals with the Edmonton Oilers in the 1983–84 NHL season.
In other fields
Eighty-seven is also:
The atomic number of francium.
An answer to a popular puzzle question states 16, 06, 68, 88, xx, 98. The answer is 87 when looked upside down.
The number of years between the signing of the U.S. Declaration of Independence and the Battle of Gettysburg, immortalized in Abraham Lincoln's Gettysburg Address with the phrase "Four Score and Seven Years ago..."
The model number of Junkers Ju 87.
The number of the French department Haute-Vienne.
The code for international direct dial phone calls to Inmarsat and other services.
The 87 photographic filter blocks visible light, allowing only infrared light to pass.
The ISBN Group Identifier for books published in Denmark.
The opus number of the 24 Preludes and Fugues of Dmitri Shostakovich.
In model railroading, the ratio of the popular H0 scale is 1:87. Proto:87 scale claims to offer pre |
https://en.wikipedia.org/wiki/89%20%28number%29 | 89 (eighty-nine) is the natural number following 88 and preceding 90.
In mathematics
89 is:
the 24th prime number, following 83 and preceding 97.
a Chen prime.
a Pythagorean prime.
the smallest Sophie Germain prime to start a Cunningham chain of the first kind of six terms, {89, 179, 359, 719, 1439, 2879}.
an Eisenstein prime with no imaginary part and real part of the form .
a Fibonacci number and thus a Fibonacci prime as well. The first few digits of its reciprocal coincide with the Fibonacci sequence due to the identity
a Markov number, appearing in solutions to the Markov Diophantine equation with other odd-indexed Fibonacci numbers.
M89 is the 10th Mersenne prime.
Although 89 is not a Lychrel number in base 10, it is unusual that it takes 24 iterations of the reverse and add process to reach a palindrome. Among the known non-Lychrel numbers in the first 10000 integers, no other number requires that many or more iterations. The palindrome reached is also unusually large.
There are exactly 1000 prime numbers between 1 and 892.
In science
Eighty-nine is:
The atomic number of actinium.
In astronomy
Messier object M89, a magnitude 11.5 elliptical galaxy in the constellation Virgo.
The New General Catalogue object NGC 89, a magnitude 13.5 peculiar spiral galaxy in the constellation Phoenix and a member of Robert's Quartet.
In sports
The Oklahoma Redhawks, an American minor league baseball team, were formerly known as the Oklahoma 89ers (1962–1997). The number alludes to the Land Run of 1889, when the Unassigned Lands of Oklahoma were opened to white settlement. The team's home of Oklahoma City was founded during this event.
In Rugby, an "89" or eight-nine move is a phase following a scrum, in which the number 8 catches the ball and transfers it to number 9 (scrum half).
The Elite 89 Award is presented by the U.S. NCAA to the participant in each of the NCAA's 89 championship finals with the highest grade point average.
89, a 2017 film about a |
https://en.wikipedia.org/wiki/77%20%28number%29 | 77 (seventy-seven) is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.
In mathematics
77 is:
the 22nd discrete semiprime and the first of the (7.q) family, where q is a higher prime.
with a prime aliquot sum of 19 within an aliquot sequence (77,19,1,0) to the Prime in the 19-aliquot tree. 77 is the second composite member of the 19-aliquot tree with 65
a Blum integer since both 7 and 11 are Gaussian primes.
the sum of three consecutive squares, 42 + 52 + 62.
the sum of the first eight prime numbers.
the number of integer partitions of the number 12.
the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
the number of digits of the 12th perfect number.
It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.
It and 49 are the only 2-digit numbers whose home primes (in base 10) have not been calculated.
In science
The atomic number of iridium
The boiling point of nitrogen (in kelvins)
The temperature, in Fahrenheit, some characteristics of semiconductors are specifically given in a datasheet (77 °F = 25 °C).
In history
During World War II in Sweden at the border with Norway, "77" was used as a shibboleth (password), because the tricky pronunciation in Swedish made it easy to instantly discern whether the speaker was native Swedish, Norwegian, or German.
In religion
In the Islamic tradition, "77" figures prominently. Muhammad is reported to have explained, "Faith has sixty-odd, or seventy-odd branches, the highest and best of which is to declare and believe that there is no god but Allah without any equals or highers and anyone worthy of worship, and the lowest of which is to remove something harmful from a road. Shyness, too, is a branch of faith." While some scholars refrain from clarifying "sixty-odd or seventy-odd", various numbers have been suggested, 77 being the most common. Some have gone s |
https://en.wikipedia.org/wiki/79%20%28number%29 | 79 (seventy-nine) is the natural number following 78 and preceding 80.
In mathematics
79 is:
An odd number.
The smallest number that can not be represented as a sum of fewer than 19 fourth powers.
The 22nd prime number (between and )
An isolated prime without a twin prime, as 77 and 81 are composite.
The smallest prime number p for which the real quadratic field Q[] has class number greater than 1 (namely 3).
A cousin prime with 83.
An emirp in base 10, because the reverse of 79, 97, is also a prime.
A Fortunate prime.
A circular prime.
A prime number that is also a Gaussian prime (since it is of the form ).
A happy prime.
A Higgs prime.
A lucky prime.
A permutable prime, with ninety-seven.
A Pillai prime, because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.
A regular prime.
A right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still prime.
A sexy prime (with 73).
The n value of the Wagstaff prime 201487636602438195784363.
Similarly to how the decimal expansion of 1/89 gives Fibonacci numbers, 1/79 gives Pell numbers, that is,
A Leyland number of the second kind.
In science
The atomic number of the chemical element gold (Au) is 79.
In astronomy
Messier object 79 (M79), a magnitude 8.5 globular cluster in the constellation Lepus
New General Catalogue object 79 (NGC 79), a galaxy in the constellation Andromeda
In other fields
Live Seventy Nine, an album by Hawkwind
The years 79 BC, AD 79 or 1979
The number of the French department Deux-Sèvres
The ASCII code of the capital letter O
References
Integers |
https://en.wikipedia.org/wiki/71%20%28number%29 | 71 (seventy-one) is the natural number following 70 and preceding 72.
In mathematics
Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. It is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.
It is a Pillai prime, since is divisible by 71, but 71 is not one more than a multiple of 9.
It is part of the last known pair (71, 7) of Brown numbers, since .
It is centered heptagonal number.
See also
71 (disambiguation)
References
Integers |
https://en.wikipedia.org/wiki/73%20%28number%29 | 73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.
In mathematics
73 is the 21st prime number, and emirp with 37, the 12th prime number. It is also the eighth twin prime, with 71. It is the largest minimal primitive root in the first 100,000 primes; in other words, if is one of the first one hundred thousand primes, then at least one of the numbers 2, 3, 4, 5, 6, ..., 73 is a primitive root modulo . 73 is also the smallest factor of the first composite generalized Fermat number in decimal: , and the smallest prime congruent to 1 modulo 24, as well as the only prime repunit in octal (1118). It is the fourth star number.
Sheldon prime
Notably, 73 is the only Sheldon prime to contain both "mirror" and "product" properties:
73, as an emirp, has 37 as its dual permutable prime, a mirroring of its base ten digits, 7 and 3. 73 is the 21st prime number, while 37 is the 12th, which is a second mirroring; and
73 has a prime index of 21 = 7 × 3; a product property where the product of its base-10 digits is precisely its index in the sequence of prime numbers.
Arithmetically, from sums of 73 and 37 with their prime indexes, one obtains:
Meanwhile,
In binary 73 is represented as , while 21 in binary is , with 7 and 3 represented as and respectively; all which are palindromic. Of the seven binary digits representing 73, there are three 1s. In addition to having prime factors 7 and 3, the number represents the ternary (base-3) equivalent of the decimal numeral 7, that is to say: .
Other properties
The row sum of Lah numbers of the form with and is equal to . These numbers represent coefficients expressing rising factorials in terms of falling factorials, and vice-versa; equivalently in this case to the number of partitions of into any number of lists, where a list means an ordered subset.
73 requires 115 steps to return to 1 in the Collatz problem, |
https://en.wikipedia.org/wiki/74%20%28number%29 | 74 (seventy-four) is the natural number following 73 and preceding 75.
In mathematics
74 is:
the twenty-first distinct semiprime and the eleventh of the form (2.q), where q is a higher prime.
with an aliquot sum of 40, within an aliquot sequence of three composite numbers (74,40,50,43,1,0) to the Prime in the 43-aliquot tree.
a palindromic number in bases 6 (2026) and 36 (2236).
a nontotient.
the number of collections of subsets of {1, 2, 3} that are closed under union and intersection.
φ(74) = φ(σ(74)).
There are 74 different non-Hamiltonian polyhedra with a minimum number of vertices.
In science
The atomic number of tungsten
In astronomy
Messier object M74, a magnitude 10.5 spiral galaxy in the constellation Pisces.
The New General Catalogue object NGC 74, a galaxy in the constellation Andromeda.
In music
Seventy-four, one of the Number Pieces by John Cage
"Seventy-Four", a song by the American band Bright from the album The Albatross Guest House
In other fields
Seventy-four is also:
The year AD 74, 74 BC, or 1974
Designates the 7400 series of Integrated Chips. 74xx xx=00-4538
A seventy-four was a third-rate warship with 74 guns.
The registry of the U.S. Navy's nuclear aircraft carrier USS John C. Stennis (CVN-74), named after U.S. Senator John C. Stennis
A hurricane or typhoon is a system with sustained winds of at least 74 mph (64 knots).
The number of the French department Haute-Savoie
In the Bible it is the number of people that were in the presence of God on Mount Sinai and saw God without dying "Exodus 24:9-11"
References
Integers |
https://en.wikipedia.org/wiki/75%20%28number%29 | 75 (seventy-five) is the natural number following 74 and preceding 76.
In mathematics
75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number.
It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...
75 is the count of the number of weak orderings on a set of four items.
Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.
In other fields
Seventy-five is:
The atomic number of rhenium
The age limit for Canadian senators
A common name for the Canon de 75 modèle 1897, a French World War I gun
The department number of the city of Paris
The number of balls in a standard game of Bingo in the United States
References
Integers |
https://en.wikipedia.org/wiki/32%20%28number%29 | 32 (thirty-two) is the natural number following 31 and preceding 33.
In mathematics
32 is the fifth power of two (), making it the first non-unitary fifth-power of the form p5 where p is prime. 32 is the totient summatory function over the first 10 integers, and the smallest number with exactly 7 solutions for . The aliquot sum of a power of two () is always one less than the number itself, therefore the aliquot sum of 32 is 31.
The product between neighbor numbers of 23, the dual permutation of the digits of 32 in decimal, is equal to the sum of the first 32 integers: .
32 is the ninth -happy number, while 23 is the sixth. Their sum is 55, which is the tenth triangular number, while their difference is .
32 is also a Leyland number expressible in the form , where:
On the other hand, a regular 32-sided icosidodecagon contains distinct symmetries.
There are collectively 32 uniform colorings to the 11 regular and semiregular tilings.
The product of the five known Fermat primes is equal to the number of sides of the largest regular constructible polygon with a straightedge and compass that has an odd number of sides, with a total of sides numbering
The first 32 rows of Pascal's triangle in binary represent the thirty-two divisors that belong to this number, which is also the number of sides of all odd-sided constructible polygons with simple tools alone (if the monogon is also included).
There are 32 three-dimensional crystallographic point groups and 32 five-dimensional crystal families, and the maximum determinant in a 7 by 7 matrix of only zeroes and ones is 32. In sixteen dimensions, the sedenions generate a non-commutative loop of order 32, and in thirty-two dimensions, there are at least 1,160,000,000 even unimodular lattices (of determinants 1 or −1); which is a marked increase from the twenty-four such Niemeier lattices that exists in twenty-four dimensions, or the single lattice in eight dimensions (these lattices only exist for dimensions ) |
https://en.wikipedia.org/wiki/34%20%28number%29 | 34 (thirty-four) is the natural number following 33 and preceding 35.
In mathematics
34 is the ninth distinct semiprime, with four divisors including 1 and itself. Specifically, 34 is the ninth distinct semiprime, it being the sixth of the form . Its neighbors 33 and 35 are also distinct semiprimes with four divisors each, where 34 is the smallest number to be surrounded by numbers with the same number of divisors it has. This is the first distinct semiprime treble cluster, the next being (85, 86, 87).
The number 34 has an aliquot sum of 20, and is the seventh member in the aliquot sequence (34, 20, 22, 14, 10, 8, 7, 1, 0) that belongs to the prime 7-aliquot tree.
Its reduced totient and Euler totient values are both 16 (or 42 = 24). The sum of all its divisors aside from one equals 53, which is the sixteenth prime number.
There is no solution to the equation φ(x) = 34, making 34 a nontotient. Nor is there a solution to the equation x − φ(x) = 34, making 34 a noncototient.
It is the third Erdős–Woods number, following 22 and 16.
It is the ninth Fibonacci number and a companion Pell number.
Since it is an odd-indexed Fibonacci number, 34 is a Markov number.
34 is also the fourth heptagonal number.
This number is also the magic constant of Queens Problem for .
There are 34 topologically distinct convex heptahedra, excluding mirror images.
34 is the magic constant of a normal magic square, and magic octagram (see accompanying images).
In science
The atomic number of selenium
Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus
The New General Catalogue object NGC 34, a peculiar galaxy in the constellation Cetus
The human vertebral column is made up of up to 34 vertebrae.
Literature
In The Count of Monte Cristo, Number 34 is how Edmond Dantès is referred to during his imprisonment in the Château d'If.
Transportation
34th Street (Manhattan), a major cross-town street in New York City
34th Street station (disambiguation), mult |
https://en.wikipedia.org/wiki/External%20Data%20Representation | External Data Representation (XDR) is a standard data serialization format, for uses such as computer network protocols. It allows data to be transferred between different kinds of computer systems. Converting from the local representation to XDR is called encoding. Converting from XDR to the local representation is called decoding. XDR is implemented as a software library of functions which is portable between different operating systems and is also independent of the transport layer.
XDR uses a base unit of 4 bytes, serialized in big-endian order; smaller data types still occupy four bytes each after encoding. Variable-length types such as string and opaque are padded to a total divisible by four bytes. Floating-point numbers are represented in IEEE 754 format.
History
XDR was developed in the mid 1980s at Sun Microsystems, and first widely published in 1987.
XDR became an IETF standard in 1995.
The XDR data format is in use by many systems, including:
Network File System (protocol)
ZFS File System
NDMP Network Data Management Protocol
Open Network Computing Remote Procedure Call
Legato NetWorker backup software (later sold by EMC)
NetCDF (a scientific data format)
The R language and environment for statistical computing
The HTTP-NG Binary Wire Protocol
The SpiderMonkey JavaScript engine, to serialize/deserialize compiled JavaScript code
The Ganglia distributed monitoring system
The sFlow network monitoring standard
The libvirt virtualization library, API and UI
The Firebird (database server) for Remote Binary Wire Protocol
Stellar Payment Network
XDR data types
boolean
int – 32-bit integer
unsigned int – unsigned 32-bit integer
hyper – 64-bit integer
unsigned hyper – unsigned 64-bit integer
IEEE float
IEEE double
quadruple (new in RFC1832)
enumeration
structure
string
fixed length array
variable length array
union – discriminated union
fixed length opaque data
variable length opaque data
void – zero byte quantity
optional – op |
https://en.wikipedia.org/wiki/Founder%20effect | In population genetics, the founder effect is the loss of genetic variation that occurs when a new population is established by a very small number of individuals from a larger population. It was first fully outlined by Ernst Mayr in 1942, using existing theoretical work by those such as Sewall Wright. As a result of the loss of genetic variation, the new population may be distinctively different, both genotypically and phenotypically, from the parent population from which it is derived. In extreme cases, the founder effect is thought to lead to the speciation and subsequent evolution of new species.
In the figure shown, the original population has nearly equal numbers of blue and red individuals. The three smaller founder populations show that one or the other color may predominate (founder effect), due to random sampling of the original population. A population bottleneck may also cause a founder effect, though it is not strictly a new population.
The founder effect occurs when a small group of migrants—not genetically representative of the population from which they came—establish in a new area. In addition to founder effects, the new population is often very small, so it shows increased sensitivity to genetic drift, an increase in inbreeding, and relatively low genetic variation.
Founder mutation
In genetics, a founder mutation is a mutation that appears in the DNA of one or more individuals which are founders of a distinct population. Founder mutations initiate with changes that occur in the DNA and can be passed down to other generations. Any organism—from a simple virus to something complex like a mammal—whose progeny carry its mutation has the potential to express the founder effect, for instance a goat or a human.
Founder mutations originate in long stretches of DNA on a single chromosome; indeed, the original haplotype is the whole chromosome. As the generations progress, the proportion of the haplotype that is common to all carriers of the mutation is |
https://en.wikipedia.org/wiki/25-pair%20color%20code | The 25-pair color code, originally known as even-count color code, is a color code used to identify individual conductors in twisted-pair wiring for telecommunications.
Color coding
With the development of new generations of telecommunication cables with polyethylene-insulated conductors (PIC) by Bell Laboratories for the Bell System in the 1950s, new methods were developed to mark each individual conductor in cables. Each wire is identified by the combination of two colors, one of which is the major color, and the second the minor color. Major and minor colors are chosen from two different groups of five, resulting in 25 color combinations. The color combinations are applied to the insulation that covers each conductor. Typically, one color is a prominent background color of the insulation, and the other is a tracer, consisting of stripes, rings, or dots, applied over the background. The background color always matches the tracer color of its paired conductor, and vice versa.
The major, or primary group of colors consists of the sequence of white, red, black, yellow, and violet (mnemonics Why Run Backwards, You'll Vomit). The minor, or secondary color is chosen from the sequence blue, orange, green, brown, and slate (mnemonics Bell Operators Give Better Service).
The wire pairs are referenced directly by their color combination, or by the pair number. For example, pair 9 is also called the red-brown pair. In technical tabulations, the colors are often suitably abbreviated.
Violet is the standard name in the telecommunications and electronics industry, but it is sometimes referred to as purple. Similarly, slate is a particular shade of gray. The names of most of the colors were taken from the conventional colors of the rainbow or optical spectrum, and in the electronic color code, which uses the same ten colors, albeit in a different order.
When used for plain old telephone service (POTS), the first wire is known as the tip or A-leg (U.K.) conductor, and is us |
https://en.wikipedia.org/wiki/31%20%28number%29 | 31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.
In mathematics
31 is the 11th prime number. It is a superprime and a self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. It is the third Mersenne prime of the form 2n − 1, and the eighth Mersenne prime exponent, in-turn yielding the maximum positive value for a 32-bit signed binary integer in computing: 2,147,483,647. After 3, it is the second Mersenne prime not to be a double Mersenne prime, while the 31st prime number (127) is the second double Mersenne prime, following 7. On the other hand, the thirty-first triangular number is the perfect number 496, of the form 2(5 − 1)(25 − 1) by the Euclid-Euler theorem. 31 is also a primorial prime like its twin prime (29), as well as both a lucky prime and a happy number like its dual permutable prime in decimal (13).
31 is the number of regular polygons with an odd number of sides that are known to be constructible with compass and straightedge, from combinations of known Fermat primes of the form 22n + 1 (they are 3, 5, 17, 257 and 65537).
31 is the 11th and final consecutive supersingular prime. After 31, the only supersingular primes are 41, 47, 59, and 71.
31 is the first prime centered pentagonal number, the fifth centered triangular number, and a centered decagonal number.
For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals.
At 31, the Mertens function sets a new low of −4, a value which is not subceded until 110.
31 is a repdigit in base 2 (11111) and in base 5 (111).
The cube root of 31 is the value of correct to four significant figures:
The first five Euclid numbers of the form p1 × p2 × p3 × ... × pn + 1 (with pn the nth prime) are prime:
3 = 2 + 1
7 = 2 × 3 + 1
31 = 2 × 3 × 5 + 1
211 = 2 × 3 × 5 × 7 + 1 and
2311 = 2 × 3 × 5 × 7 × 11 + 1
The following term, 30031 = 59 × 509 = 2 × 3 × 5 × 7 × 11 × 13 + 1, i |
https://en.wikipedia.org/wiki/Hilbert%27s%20seventh%20problem | Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers (Irrationalität und Transzendenz bestimmter Zahlen).
Statement of the problem
Two specific equivalent questions are asked:
In an isosceles triangle, if the ratio of the base angle to the angle at the vertex is algebraic but not rational, is then the ratio between base and side always transcendental?
Is always transcendental, for algebraic and irrational algebraic ?
Solution
The question (in the second form) was answered in the affirmative by Aleksandr Gelfond in 1934, and refined by Theodor Schneider in 1935. This result is known as Gelfond's theorem or the Gelfond–Schneider theorem. (The restriction to irrational b is important, since it is easy to see that is algebraic for algebraic a and rational b.)
From the point of view of generalizations, this is the case
of the general linear form in logarithms which was studied by Gelfond and then solved by Alan Baker. It is called the Gelfond conjecture or Baker's theorem. Baker was awarded a Fields Medal in 1970 for this achievement.
See also
Hilbert number or Gelfond–Schneider constant
References
Bibliography
External links
English translation of Hilbert's original address
07 |
https://en.wikipedia.org/wiki/Homeland%20Security%20Advisory%20System | In the United States, the Homeland Security Advisory System (HSAS) was a color-coded terrorism threat advisory scale created in March 2002 under the Bush Administration in response to the September 11 attacks. The different levels triggered specific actions by federal agencies and state and local governments, and they affected the level of security at some airports and other public facilities. It was often called the "terror alert level" by the U.S. media. The system was replaced on April 27, 2011, with a new system called the National Terrorism Advisory System.
History
The system was created by Homeland Security Presidential Directive 3 on March 11, 2002, in response to the September 11 attacks. It was meant to provide a "comprehensive and effective means to disseminate information regarding the risk of terrorist acts to federal, state, and local authorities and to the American people." It was unveiled March 12, 2002, by Tom Ridge, then the Assistant to the President for Homeland Security. However, responsibility for developing, implementing and managing the system was given to the U.S. Attorney General.
In January 2003, the new Department of Homeland Security (DHS) began administering the system. The decision to publicly announce threat conditions is made by the Secretary of Homeland Security in consultation with the Assistant to the President for Homeland Security, according to Homeland Security Presidential Directive-5.
On January 27, 2011, Secretary of Homeland Security Janet Napolitano announced that the Homeland Security Advisory System would be replaced by a new two-level National Terrorism Advisory System in April 2011. Napolitano, who made the announcement at George Washington University, said the color-coded system often presented "little practical information" to the public and that the new system will provide alerts "specific to the threat" and that "they will have a specified end date."
Description
Inspired by the success of the forest fire color |
https://en.wikipedia.org/wiki/Hidden%20node%20problem | In wireless networking, the hidden node problem or hidden terminal problem occurs when a node can communicate with a wireless access point (AP), but cannot directly communicate with other nodes that are communicating with that AP. This leads to difficulties in medium access control sublayer since multiple nodes can send data packets to the AP simultaneously, which creates interference at the AP resulting in no packet getting through.
Although some loss of packets is normal in wireless networking, and the higher layers will resend them, if one of the nodes is transferring a lot of large packets over a long period, the other node may get very little goodput.
Practical protocol solutions exist to the hidden node problem. For example, Request To Send/Clear To Send (RTS/CTS) mechanisms where nodes send short packets to request permission of the access point to send longer data packets. Because responses from the AP are seen by all the nodes, the nodes can synchronize their transmissions to not interfere. However, the mechanism introduces latency, and the overhead can often be greater than the cost, particularly for short data packets.
Background
Hidden nodes in a wireless network are nodes that are out of range of other nodes or a collection of nodes. Consider a physical star topology with an access point with many nodes surrounding it in a circular fashion: each node is within communication range of the AP, but the nodes cannot communicate with each other.
For example, in a wireless network, it is likely that the node at the far edge of the access point's range, which is known as A, can see the access point, but it is unlikely that the same node can communicate with a node on the opposite end of the access point's range, C. These nodes are known as hidden.
Another example would be where A and C are either side of an obstacle that reflects or strongly absorbs radio waves, but nevertheless they can both still see the same AP.
The problem is when nodes A and C start |
https://en.wikipedia.org/wiki/Trinomial%20nomenclature | In biology, trinomial nomenclature refers to names for taxa below the rank of species. These names have three parts. The usage is different in zoology and botany.
In zoology
In zoological nomenclature, a trinomen (), trinominal name, or ternary name refers to the name of a subspecies. Examples are Gorilla gorilla gorilla (Savage, 1847) for the western lowland gorilla (genus Gorilla, species western gorilla), and Bison bison bison (Linnaeus, 1758) for the plains bison (genus Bison, species American bison).
A trinomen is a name with three parts: generic name, specific name and subspecific name. The first two parts alone form the binomen or species name. All three names are typeset in italics, and only the first letter of the generic name is capitalised. No indicator of rank is included: in zoology, subspecies is the only rank below that of species. For example: "Buteo jamaicensis borealis is one of the subspecies of the red-tailed hawk (Buteo jamaicensis)."
In a taxonomic publication, a name is incomplete without an author citation and publication details. This indicates who published the name, in what publication, and the date of the publication. For example: "Phalacrocorax carbo novaehollandiae (Stephens, 1826)" denotes a subspecies of the great cormorant (Phalacrocorax carbo) introduced by James Francis Stephens in 1826 under the subspecies name novaehollandiae ("of New Holland").
If the generic and specific name have already been mentioned in the same paragraph, they are often abbreviated to initial letters. For example, one might write: "The great cormorant Phalacrocorax carbo has a distinct subspecies in Australasia, the black shag P. c. novaehollandiae".
While binomial nomenclature came into being and immediately gained widespread acceptance in the mid-18th century, it was not until the early 20th century that the current unified standard of nomenclature was agreed upon. This became the standard mainly because of tireless promotion by Elliott Coues – eve |
https://en.wikipedia.org/wiki/Index%20set | In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set may be indexed or labeled by means of the elements of a set , then is an index set. The indexing consists of a surjective function from onto , and the indexed collection is typically called an indexed family, often written as .
Examples
An enumeration of a set gives an index set , where is the particular enumeration of .
Any countably infinite set can be (injectively) indexed by the set of natural numbers .
For , the indicator function on is the function given by
The set of all such indicator functions, , is an uncountable set indexed by .
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm that can sample the set efficiently; e.g., on input , can efficiently select a poly(n)-bit long element from the set.
See also
Friendly-index set
References
Mathematical notation
Basic concepts in set theory |
https://en.wikipedia.org/wiki/Comparison%20of%20topologies | In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for comparison of the topologies.
Definition
A topology on a set may be defined as the collection of subsets which are considered to be "open". An alternative definition is that it is the collection of subsets which are considered "closed". These two ways of defining the topology are essentially equivalent because the complement of an open set is closed and vice versa. In the following, it doesn't matter which definition is used.
Let τ1 and τ2 be two topologies on a set X such that τ1 is contained in τ2:
.
That is, every element of τ1 is also an element of τ2. Then the topology τ1 is said to be a coarser (weaker or smaller) topology than τ2, and τ2 is said to be a finer (stronger or larger) topology than τ1.
If additionally
we say τ1 is strictly coarser than τ2 and τ2 is strictly finer than τ1.
The binary relation ⊆ defines a partial ordering relation on the set of all possible topologies on X.
Examples
The finest topology on X is the discrete topology; this topology makes all subsets open. The coarsest topology on X is the trivial topology; this topology only admits the empty set
and the whole space as open sets.
In function spaces and spaces of measures there are often a number of possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships.
All possible polar topologies on a dual pair are finer than the weak topology and coarser than the strong topology.
The complex vector space Cn may be equipped with either its usual (Euclidean) topology, or its Zariski topology. In the latter, a subset V of Cn is closed if and only if it consists of all solutions to some system of polynomial equations. Since any such V also is a closed set in the ordinary sense, but not vice versa, the Zariski topology is strictly weaker than the ordinary one.
Properties |
https://en.wikipedia.org/wiki/Dirichlet%20series | In mathematics, a Dirichlet series is any series of the form
where s is complex, and is a complex sequence. It is a special case of general Dirichlet series.
Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet.
Combinatorial importance
Dirichlet series can be used as generating series for counting weighted sets of objects with respect to a weight which is combined multiplicatively when taking Cartesian products.
Suppose that A is a set with a function w: A → N assigning a weight to each of the elements of A, and suppose additionally that the fibre over any natural number under that weight is a finite set. (We call such an arrangement (A,w) a weighted set.) Suppose additionally that an is the number of elements of A with weight n. Then we define the formal Dirichlet generating series for A with respect to w as follows:
Note that if A and B are disjoint subsets of some weighted set (U, w), then the Dirichlet series for their (disjoint) union is equal to the sum of their Dirichlet series:
Moreover, if (A, u) and (B, v) are two weighted sets, and we define a weight function by
for all a in A and b in B, then we have the following decomposition for the Dirichlet series of the Cartesian product:
This follows ultimately from the simple fact that
Examples
The most famous example of a Dirichlet series is
whose analytic continuation to (apart from a simple pole at ) is the Riemann zeta function.
Provided that is real-valued at all natural numbers , the respective real and imaginary parts of the Dirichlet series have known formulas where we write :
Treating these as formal Dirichlet series for the time being in order to be able to ignore matters of convergence, no |
https://en.wikipedia.org/wiki/Beth%20number | In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the second Hebrew letter (beth). The beth numbers are related to the aleph numbers (), but unless the generalized continuum hypothesis is true, there are numbers indexed by that are not indexed by .
Definition
Beth numbers are defined by transfinite recursion:
where is an ordinal and is a limit ordinal.
The cardinal is the cardinality of any countably infinite set such as the set of natural numbers, so that .
Let be an ordinal, and be a set with cardinality . Then,
denotes the power set of (i.e., the set of all subsets of ),
the set denotes the set of all functions from to {0,1},
the cardinal is the result of cardinal exponentiation, and
is the cardinality of the power set of .
Given this definition,
are respectively the cardinalities of
so that the second beth number is equal to , the cardinality of the continuum (the cardinality of the set of the real numbers), and the third beth number is the cardinality of the power set of the continuum.
Because of Cantor's theorem, each set in the preceding sequence has cardinality strictly greater than the one preceding it. For infinite limit ordinals, λ, the corresponding beth number is defined to be the supremum of the beth numbers for all ordinals strictly smaller than λ:
One can also show that the von Neumann universes have cardinality .
Relation to the aleph numbers
Assuming the axiom of choice, infinite cardinalities are linearly ordered; no two cardinalities can fail to be comparable. Thus, since by definition no infinite cardinalities are between and , it follows that
Repeating this argument (see transfinite induction) yields
for all ordinals .
The continuum hypothesis is equivalent to
The generalized continuum hypothesis says the sequence of beth numbers thus defined is the same as the seque |
https://en.wikipedia.org/wiki/Metaprogramming | Metaprogramming is a programming technique in which computer programs have the ability to treat other programs as their data. It means that a program can be designed to read, generate, analyze or transform other programs, and even modify itself while running. In some cases, this allows programmers to minimize the number of lines of code to express a solution, in turn reducing development time. It also allows programs a greater flexibility to efficiently handle new situations without recompilation.
Metaprogramming can be used to move computations from run-time to compile-time, to generate code using compile time computations, and to enable self-modifying code. The ability of a programming language to be its own metalanguage is called reflection. Reflection is a valuable language feature to facilitate metaprogramming.
Metaprogramming was popular in the 1970s and 1980s using list processing languages such as LISP. LISP hardware machines were popular in the 1980s and enabled applications that could process code. They were frequently used for artificial intelligence applications.
Approaches
Metaprogramming enables developers to write programs and develop code that falls under the generic programming paradigm. Having the programming language itself as a first-class data type (as in Lisp, Prolog, SNOBOL, or Rebol) is also very useful; this is known as homoiconicity. Generic programming invokes a metaprogramming facility within a language by allowing one to write code without the concern of specifying data types since they can be supplied as parameters when used.
Metaprogramming usually works in one of three ways.
The first approach is to expose the internals of the run-time engine to the programming code through application programming interfaces (APIs) like that for the .NET IL emitter.
The second approach is dynamic execution of expressions that contain programming commands, often composed from strings, but can also be from other methods using arguments or conte |
https://en.wikipedia.org/wiki/FIGlet | FIGlet is a computer program that generates text banners, in a variety of typefaces, composed of letters made up of conglomerations of smaller ASCII characters (see ASCII art). The name derives from "Frank, Ian and Glenn's letters".
Being free software, FIGlet is commonly included as part of many Unix-like operating systems (Linux, BSD, etc.) distributions, but it has been ported to other platforms as well. The official FIGlet FTP site includes precompiled ports for the Acorn, Amiga, Apple II, Atari ST, BeOS, Mac, MS-DOS, NeXTSTEP, OS/2, and Microsoft Windows, as well as a reimplementation in Perl (Text::FIGlet). There are third-party reimplementations of FIGlet in Java (including one embedded in the JavE ASCII art editor), JavaScript, PHP, Python, and Go.
Behavior
FIGlet can read from standard input or accept a message as part of the command line. It prints to standard output. Some common arguments (options) are:
-f to select a font file. (font files are available here)
-d to change the directory for fonts.
-c centers the output.
-l left-aligns the output.
-r right-aligns the output.
-t sets the output width to the terminal width.
-w specifies a custom output width.
-k enables kerning, printing each letter of the message individually, instead of merged into the adjacent letters.
Sample usage
An example of output generated by FIGlet is shown below.
[user@hostname ~]$ figlet Wikipedia
__ ___ _ _ _ _
\ \ / (_) | _(_)_ __ ___ __| (_) __ _
\ \ /\ / /| | |/ / | '_ \ / _ \/ _` | |/ _` |
\ V V / | | <| | |_) | __/ (_| | | (_| |
\_/\_/ |_|_|\_\_| .__/ \___|\__,_|_|\__,_|
|_|
The following command:
[user@hostname ~]$ figlet -ct -f roman Wikipedia
generates this output:
oooooo oooooo oooo o8o oooo o8o .o8 o8o
`888. `888. .8' `"' `888 `"' "888 `"'
`88 |
https://en.wikipedia.org/wiki/Voltage%20divider | In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.
Resistor voltage dividers are commonly used to create reference voltages, or to reduce the magnitude of a voltage so it can be measured, and may also be used as signal attenuators at low frequencies. For direct current and relatively low frequencies, a voltage divider may be sufficiently accurate if made only of resistors; where frequency response over a wide range is required (such as in an oscilloscope probe), a voltage divider may have capacitive elements added to compensate load capacitance. In electric power transmission, a capacitive voltage divider is used for measurement of high voltage.
General case
A voltage divider referenced to ground is created by connecting two electrical impedances in series, as shown in Figure 1. The input voltage is applied across the series impedances Z1 and Z2 and the output is the voltage across Z2.
Z1 and Z2 may be composed of any combination of elements such as resistors, inductors and capacitors.
If the current in the output wire is zero then the relationship between the input voltage, Vin, and the output voltage, Vout, is:
Proof (using Ohm's law):
The transfer function (also known as the divider's voltage ratio) of this circuit is:
In general this transfer function is a complex, rational function of frequency.
Examples
Resistive divider
A resistive divider is the case where both impedances, Z1 and Z2, are purely resistive (Figure 2).
Substituting Z1 = R1 and Z2 = R2 into the previous expression gives:
If R1 = R2 then
If Vout = 6 V and V |
https://en.wikipedia.org/wiki/Logical%20possibility | Logical possibility refers to a logical proposition that cannot be disproved, using the axioms and rules of a given system of logic. The logical possibility of a proposition will depend upon the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values. Some assume the system in question is classical propositional logic. Similarly, the criterion for logical possibility is often based on whether or not a proposition is contradictory and as such, is often thought of as the broadest type of possibility.
In modal logic, a logical proposition is possible if it is true in some possible world. The universe of "possible worlds" depends upon the axioms and rules of the logical system in which one is working, but given some logical system, any logically consistent collection of statements is a possible world. The modal diamond operator is used to express possibility: denotes "proposition is possible".
Logical possibility is different from other sorts of subjunctive possibilities. The relationship between modalities (if there is any) is the subject of debate and may depend upon how one views logic, as well as the relationship between logic and metaphysics, for example, many philosophers following Saul Kripke have held that discovered identities such as "Hesperus = Phosphorus" are metaphysically necessary because they pick out the same object in all possible worlds where the terms have a referent. It is logically possible for “Hesperus = Phosphorus” to be false, since denying it does not violate a logical rule such as consistency. Other philosophers are of the view that logical possibility is broader than metaphysical possibility, so that anything which is metaphysically possible is also logically possible.
See also
Modal logic
Paraconsistent logic |
https://en.wikipedia.org/wiki/Test-and-set | In computer science, the test-and-set instruction is an instruction used to write (set) 1 to a memory location and return its old value as a single atomic (i.e., non-interruptible) operation. The caller can then "test" the result to see if the state was changed by the call. If multiple processes may access the same memory location, and if a process is currently performing a test-and-set, no other process may begin another test-and-set until the first process's test-and-set is finished. A central processing unit (CPU) may use a test-and-set instruction offered by another electronic component, such as dual-port RAM; a CPU itself may also offer a test-and-set instruction.
A lock can be built using an atomic test-and-set instruction as follows:
This code assumes that the memory location was initialized to 0 at some point prior to the first test-and-set. The calling process obtains the lock if the old value was 0, otherwise the while-loop spins waiting to acquire the lock. This is called a spinlock. At any point, the holder of the lock can simply set the memory location back to 0 to release the lock for acquisition by another--this does not require any special handling as the holder "owns" this memory location. "Test and test-and-set" is another example.
Maurice Herlihy (1991) proved that test-and-set (1-bit comparand) has a finite consensus number and can solve the wait-free consensus problem for at-most two concurrent processes. In contrast, compare-and-swap (32-bit comparand) offers a more general solution to this problem, and in some implementations compare-double-and-swap (64-bit comparand) is also available for extended utility.
Hardware implementation of test-and-set
DPRAM test-and-set instructions can work in many ways. Here are two variations, both of which describe a DPRAM which provides exactly 2 ports, allowing 2 separate electronic components (such as 2 CPUs) access to every memory location on the DPRAM.
Variation 1
When CPU 1 issues a test-and-set |
https://en.wikipedia.org/wiki/Selection%20bias | Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed. It is sometimes referred to as the selection effect. The phrase "selection bias" most often refers to the distortion of a statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may be false.
Types
Sampling bias
Sampling bias is systematic error due to a non-random sample of a population, causing some members of the population to be less likely to be included than others, resulting in a biased sample, defined as a statistical sample of a population (or non-human factors) in which all participants are not equally balanced or objectively represented. It is mostly classified as a subtype of selection bias, sometimes specifically termed sample selection bias, but some classify it as a separate type of bias.
A distinction of sampling bias (albeit not a universally accepted one) is that it undermines the external validity of a test (the ability of its results to be generalized to the rest of the population), while selection bias mainly addresses internal validity for differences or similarities found in the sample at hand. In this sense, errors occurring in the process of gathering the sample or cohort cause sampling bias, while errors in any process thereafter cause selection bias.
Examples of sampling bias include self-selection, pre-screening of trial participants, discounting trial subjects/tests that did not run to completion and migration bias by excluding subjects who have recently moved into or out of the study area, length-time bias, where slowly developing disease with better prognosis is detected, and lead time bias, where disease is diagnosed earlier participants than in comparison populations, |
https://en.wikipedia.org/wiki/Iron%E2%80%93sulfur%20world%20hypothesis | The iron–sulfur world hypothesis is a set of proposals for the origin of life and the early evolution of life advanced in a series of articles between 1988 and 1992 by Günter Wächtershäuser, a Munich patent lawyer with a degree in chemistry, who had been encouraged and supported by philosopher Karl R. Popper to publish his ideas. The hypothesis proposes that early life may have formed on the surface of iron sulfide minerals, hence the name. It was developed by retrodiction (making a "prediction" about the past) from extant biochemistry (non-extinct, surviving biochemistry) in conjunction with chemical experiments.
Origin of life
Pioneer organism
Wächtershäuser proposes that the earliest form of life, termed the "pioneer organism", originated in a volcanic hydrothermal flow at high pressure and high (100 °C) temperature. It had a composite structure of a mineral base with catalytic transition metal centers (predominantly iron and nickel, but also perhaps cobalt, manganese, tungsten and zinc). The catalytic centers catalyzed autotrophic carbon fixation pathways generating small molecule (non-polymer) organic compounds from inorganic gases (e.g. carbon monoxide, carbon dioxide, hydrogen cyanide and hydrogen sulfide). These organic compounds were retained on or in the mineral base as organic ligands of the transition metal centers with a flow retention time in correspondence with their mineral bonding strength thereby defining an autocatalytic "surface metabolism". The catalytic transition metal centers became autocatalytic by being accelerated by their organic products turned ligands. The carbon fixation metabolism became autocatalytic by forming a metabolic cycle in the form of a primitive sulfur-dependent version of the reductive citric acid cycle. Accelerated catalysts expanded the metabolism and new metabolic products further accelerated the catalysts. The idea is that once such a primitive autocatalytic metabolism was established, its intrinsically synthetic ch |
https://en.wikipedia.org/wiki/S%C3%A9minaire%20de%20G%C3%A9om%C3%A9trie%20Alg%C3%A9brique%20du%20Bois%20Marie | In mathematics, the Séminaire de Géométrie Algébrique du Bois Marie (SGA) was an influential seminar run by Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the IHÉS near Paris. (The name came from the small wood on the estate in Bures-sur-Yvette where the IHÉS was located from 1962.) The seminar notes were eventually published in twelve volumes, all except one in the Springer Lecture Notes in Mathematics series.
Style
The material has a reputation of being hard to read for a number of reasons. More elementary or foundational parts were relegated to the EGA series of Grothendieck and Jean Dieudonné, causing long strings of logical dependencies in the statements. The style is very abstract and makes heavy use of category theory. Moreover, an attempt was made to achieve maximally general statements, while assuming that the reader is aware of the motivations and concrete examples.
First publication
The original notes to SGA were published in fascicles by the IHÉS, most of which went through two or three revisions. These were published as the seminar proceeded, beginning in the early 60's and continuing through most of the decade. They can still be found in large math libraries, but distribution was limited. In the late 60's and early 70's, the original seminar notes were comprehensively revised and rewritten to take into account later developments. In addition, a new volume, SGA 4½, was compiled by Pierre Deligne and published in 1977; it contains simplified and new results by Deligne within the scope of SGA4 as well as some material from SGA5, which had not yet appeared at that time. The revised notes, except for SGA2, were published by Springer in its Lecture Notes in Mathematics series.
After a dispute with Springer, Grothendieck refused the permission for reprints of the series. While these later revisions were more widely distributed than the original |
https://en.wikipedia.org/wiki/Frieder%20Nake | Frieder Nake (born December 16, 1938 in Stuttgart, Germany) is a mathematician, computer scientist, and pioneer of computer art. He is best known internationally for his contributions to the earliest manifestations of computer art, a field of computing that made its first public appearances with three small exhibitions in 1965.
Art career
Nake had his first exhibition at Galerie Wendelin Niedlich in Stuttgart in November, 1965 alongside the artist Georg Nees.
Until 1969, Nake generated in rapid sequence a large number of works that he showed in many exhibitions over the years. He estimates his production at about 300 to 400 works during those years. A few were limited screenprint editions, single pieces and portfolios. The bulk were done as China ink on paper graphics, carried out by a flatbed high precision plotter called the Zuse Graphomat Z64.
Nake participated in the important group shows of the 1960s, such as, most prominently, Cybernetic Serendipity (London, UK, 1968), Tendencies 4: Computers and Visual Research (Zagreb, Yugoslavia, 1968), Ricerca e Progettazione. Proposte per una esposizione sperimentale (35th Venice Biennale, Italy, 1970), Arteonica (São Paulo, Brazil, 1971).
In 1971, he wrote a short and provocative note for Page, the Bulletin of the Computer Arts Society (whose member he was and still is), under the title „There Should Be No Computer-Art“ (Page No. 18, Oct. 1971, p. 1-2. Reprinted in Arie Altena, Lucas van der Velden (eds.): The anthology of computer art. Amsterdam: Sonic Acts 2006, p. 59-60). The note sparked a lively controversial debate among those who had meanwhile started to build an active community of artists, writers, musicians, and designers in the digital domain. His statement was rooted in a moral position. The involvement of computer technology in the Vietnam War and in massive attempts by capital to automate productive processes and, thereby, generate unemployment, should not allow artists to close their eyes and become si |
https://en.wikipedia.org/wiki/David%20Mumford | David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.
Early life
Mumford was born in Worth, West Sussex in England, of an English father and American mother. His father William started an experimental school in Tanzania and worked for the then newly created United Nations.
He attended Phillips Exeter Academy, where he received a Westinghouse Science Talent Search prize for his relay-based computer project. Mumford then went to Harvard University, where he became a student of Oscar Zariski. At Harvard, he became a Putnam Fellow in 1955 and 1956. He completed his PhD in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus. He married Erika, an author and poet, in 1959 and they had four children, Stephen, Peter, Jeremy, and Suchitra. He currently has seven grandchildren.
Work in algebraic geometry
Mumford's work in geometry combined traditional geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic surfaces.
His books Abelian Varieties (with C. P. Ramanujam) and Curves on an Algebraic Surface combined the old and new theories. His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique, the only accessible introduction. They are now available as The Red Book of Varieties and Schemes ().
Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and a study of Goro Shimura's papers from the 1960s.
Mumford's research did much to |
https://en.wikipedia.org/wiki/Newsgroup%20spam | Newsgroup spam is a type of spam where the targets are Usenet newsgroups.
Spamming of Usenet newsgroups pre-dates e-mail spam. The first widely recognized Usenet spam (though not the most famous) was posted on 18 January 1994 by Clarence L. Thomas IV, a sysadmin at Andrews University. Entitled "Global Alert for All: Jesus is Coming Soon", it was a fundamentalist religious tract claiming that "this world's history is coming to a climax." The newsgroup posting bot Serdar Argic also appeared in early 1994, posting tens of thousands of messages to various newsgroups, consisting of identical copies of a political screed relating to the Armenian genocide.
The first "commercial" Usenet spam, and the one which is often (mistakenly) claimed to be the first Usenet spam of any sort, was an advertisement for legal services entitled "Green Card Lottery – Final One?". It was posted on 12 April 1994, by Arizona lawyers Laurence Canter and Martha Siegel, and hawked legal representation for United States immigrants seeking green cards.
Usenet convention defines spamming as "excessive multiple posting", that is, the repeated posting of a message (or substantially similar messages). During the early 1990s there was substantial controversy among Usenet system administrators (news admins) over the use of cancel messages to control spam. A "cancel message" is a directive to news servers to delete a posting, causing it to be inaccessible. Some regarded this as a bad precedent, leaning towards censorship, while others considered it a proper use of the available tools to control the growing spam problem.
A culture of neutrality towards content precluded defining spam on the basis of advertisement or commercial solicitations. The word "spam" was usually taken to mean "excessive multiple posting (EMP)", and other neologisms were coined for other abuses – such as "velveeta" (from the processed cheese product of that name) for "excessive cross-posting". A subset of spam was deemed "cancella |
https://en.wikipedia.org/wiki/Yeast%20artificial%20chromosome | Yeast artificial chromosomes (YACs) are genetically engineered chromosomes derived from the DNA of the yeast, Saccharomyces cerevisiae , which is then ligated into a bacterial plasmid. By inserting large fragments of DNA, from 100–1000 kb, the inserted sequences can be cloned and physically mapped using a process called chromosome walking. This is the process that was initially used for the Human Genome Project, however due to stability issues, YACs were abandoned for the use of bacterial artificial chromosome
The bakers' yeast S. cerevisiae is one of the most important experimental organisms for studying eukaryotic molecular genetics.
Beginning with the initial research of the Rankin et al., Strul et al., and Hsaio et al., the inherently fragile chromosome was stabilized by discovering the necessary autonomously replicating sequence (ARS); a refined YAC utilizing this data was described in 1983 by Murray et al.
The primary components of a YAC are the ARS, centromere , and telomeres from S. cerevisiae. Additionally, selectable marker genes, such as antibiotic resistance and a visible marker, are utilized to select transformed yeast cells. Without these sequences, the chromosome will not be stable during extracellular replication, and would not be distinguishable from colonies without the vector.
Construction
A YAC is built using an initial circular DNA plasmid, which is typically cut into a linear DNA molecule using restriction enzymes; DNA ligase is then used to ligate a DNA sequence or gene of interest into the linearized DNA, forming a single large, circular piece of DNA. The basic generation of linear yeast artificial chromosomes can be broken down into 6 main steps:
Full chromosome III
Chromosome III is the third smallest chromosome in S. cerevisiae; its size was estimated from pulsed-field gel electro- phoresis studies to be 300–360 kb
This chromosome has been the subject of intensive study, not least because it contains the three genetic loci invo |
https://en.wikipedia.org/wiki/36%20%28number%29 | 36 (thirty-six) is the natural number following 35 and preceding 37.
In mathematics
36 is both the square of six, and the eighth triangular number or sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number. Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them; in fact, it is the smallest number with exactly nine divisors, which leads 36 to be the 7th highly composite number. It is the sum of the fourth pair of twin-primes (17 + 19), and the 18th Harshad number in decimal, as it is divisible by the sum of its digits (9).
It is the smallest number with exactly eight solutions (37, 57, 63, 74, 76, 108, 114, 126) to the Euler totient function . Adding up some subsets of its divisors (e.g., 6, 12, and 18) gives 36; hence, it is also the eighth semiperfect number.
This number is the sum of the cubes of the first three positive integers and also the product of the squares of the first three positive integers.
36 is the number of degrees in the interior angle of each tip of a regular pentagram.
The thirty-six officers problem is a mathematical puzzle with no solution.
The number of possible outcomes (not summed) in the roll of two distinct dice.
36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0–9, and the letters, A-Z. See Base 36.
The truncated cube and the truncated octahedron are Archimedean solids with 36 edges.
The number of domino tilings of a 4×4 checkerboard is 36.
Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number.
The sum of the integers from 1 to 36 is 666 (see number of the beast).
Measurements
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https://en.wikipedia.org/wiki/37%20%28number%29 | 37 (thirty-seven) is the natural number following 36 and preceding 38.
In mathematics
37 is the 12th prime number, and the 3rd isolated prime without a twin prime.
37 is the first irregular prime.
The sum of the squares of the first 37 primes is divisible by 37.
Every positive integer is the sum of at most 37 fifth powers (see Waring's problem).
It is the third cuban prime following 7 and 19.
37 is the fifth Padovan prime, after the first four prime numbers 2, 3, 5, and 7.
It is also the fifth lucky prime, after 3, 7, 13, and 31.
37 is the third star number and the fourth centered hexagonal number.
There are exactly 37 complex reflection groups.
The smallest magic square, using only primes and 1, contains 37 as the value of its central cell:
Its magic constant is 37 x 3 = 111, where 3 and 37 are the first and third base-ten unique primes (the second such prime is 11).
In decimal 37 is a permutable prime with 73, which is the 21st prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime. In moonshine theory, whereas all p ⩾ 73 are non-supersingular primes, the smallest such prime is 37.
37 requires twenty-one steps to return to 1 in the Collatz problem, as do adjacent numbers 36 and 38. The two closest numbers to cycle through the elementary {16, 8, 4, 2, 1} Collatz pathway are 5 and 32, whose sum is 37. The trajectories for 3 and 21 both require seven steps to reach 1.
The first two integers that return for the Mertens function (2 and 39) have a difference of 37. Their product (2 × 39) is the twelfth triangular number 78. Their sum is 41, which is the constant term in Euler's lucky numbers that yield prime numbers of the form k2 − k + 41; the largest of which (1601) is a difference of 78 from the second-largest prime (1523) generated by this quadratic polynomial.
In decimal
For a three-digit number that is divisible by 37, a rule of divisibility is that another divisible by 37 can be generated by t |
https://en.wikipedia.org/wiki/39%20%28number%29 | 39 (thirty-nine) is the natural number following 38 and preceding 40.
In mathematics
39 is the 12th distinct semiprime and the 4th in the (3.q) family. It is the last member of the third distinct semiprime pair (38,39).
39 has an aliquot sum of 17, which is a prime. 39 is the 4th member of the 17-aliquot tree within an aliquot sequence of one composite numbers (39,17,1,0) to the Prime in the 17-aliquot tree.
It is a perfect totient number.*39 is the sum of five consecutive primes (3 + 5 + 7 + 11 + 13) and also is the product of the first and the last of those consecutive primes. Among small semiprimes only three other integers (10, 155, and 371) share this attribute. 39 also is the sum of the first three powers of 3 (3 + 3 + 3). Given 39, the Mertens function returns 0.
39 is the smallest natural number which has three partitions into three parts which all give the same product when multiplied: {25, 8, 6}, {24, 10, 5}, {20, 15, 4}.
39 is a Perrin number, coming after 17, 22, 29 (it is the sum of the first two mentioned).
Since the greatest prime factor of 392 + 1 = 1522 is 761, which is more than 39 twice, 39 is a Størmer number.
The F26A graph is a symmetric graph with 39 edges.
In science
The atomic number of yttrium
Astronomy
Messier object Open Cluster M39, a magnitude 5.5 open cluster in the constellation Cygnus
The New General Catalogue object NGC 39, a spiral galaxy in the constellation Andromeda
In religion
The number of the 39 categories of activity prohibited on Shabbat according to Halakha
The number of mentions of work or labor in the Torah
The actual number of lashes given by the Sanhedrin to a person meted the punishment of 40 lashes
The number of books in the Old Testament according to Protestant canon
The number of statements on Anglican Church doctrine, Thirty-Nine Articles
In other fields
Arts and entertainment
In the title of the John Buchan novel and subsequent films (one by Alfred Hitchcock), The Thirty-Nine Steps
The age American com |
https://en.wikipedia.org/wiki/Introduced%20species | An introduced species, alien species, exotic species, adventive species, immigrant species, foreign species, non-indigenous species, or non-native species is a species living outside its native distributional range, but which has arrived there by human activity, directly or indirectly, and either deliberately or accidentally. Non-native species can have various effects on the local ecosystem. Introduced species that become established and spread beyond the place of introduction are considered naturalized. The process of human-caused introduction is distinguished from biological colonization, in which species spread to new areas through "natural" (non-human) means such as storms and rafting. The Latin expression neobiota captures the characteristic that these species are new biota to their environment in terms of established biological network (e.g. food web) relationships. Neobiota can further be divided into neozoa (also: neozoons, sing. neozoon, i.e. animals) and neophyta (plants).
The impact of introduced species is highly variable. Some have a substantial negative effect on a local ecosystem (in which case they are also classified more specifically as an invasive species), while other introduced species may have little or no negative impact (no invasiveness). Some species have been introduced intentionally to combat pests. They are called biocontrols and may be regarded as beneficial as an alternative to pesticides in agriculture for example. In some instances the potential for being beneficial or detrimental in the long run remains unknown. The effects of introduced species on natural environments have gained much scrutiny from scientists, governments, farmers and others.
Terminology
The formal definition of an introduced species from the United States Environmental Protection Agency is "A species that has been intentionally or inadvertently brought into a region or area. Also called an exotic or non-native species".
In the broadest and most widely used sen |
https://en.wikipedia.org/wiki/47%20%28number%29 | 47 (forty-seven) is the natural number following 46 and preceding 48. It is a prime number.
In mathematics
Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, the fourth isolated prime, and the sixth Lucas prime. Forty-seven is a highly cototient number. It is an Eisenstein prime with no imaginary part and real part of the form .
It is a Lucas number. It is also a Keith number because its digits appear as successive terms earlier in the series of Lucas numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, ...
It is the number of trees on 9 unlabeled nodes.
Forty-seven is a strictly non-palindromic number.
Its representation in binary being 101111, 47 is a prime Thabit number, and as such is related to the pair of amicable numbers {17296, 18416}.
In science
47 is the atomic number of silver.
Astronomy
The 47-year cycle of Mars: after 47 years – 22 synodic periods of 780 days each – Mars returns to the same position among the stars and is in the same relationship to the Earth and Sun. The ancient Mesopotamians discovered this cycle.
Messier object M47, a magnitude 4.5 open cluster in the constellation Puppis
47 Tucanae, the second brightest globular cluster in the sky, located in the constellation Tucana.
The New General Catalogue object NGC 47, a barred spiral galaxy in the constellation Cetus. This object is also designated as NGC 58.
In popular culture
Pomona College
Calendar years
47 BC
AD 47
See also
List of highways numbered 47
Other
Telephone dialing country code for Norway
The AK-47, also known as a Kalashnikov rifle, is one of the most widely used military weapons in the world.
The CH-47 Chinook, a helicopter.
47 is the number of the French department Lot-et-Garonne.
The P-47 Thunderbolt was a fighter plane in World War II.
There are Forty-seven Ronin in the famous Japanese story.
There are 47 Prefectures of Japan.
The player protagonist of the Hitman video game franchise is called Agent 47.
References
Inte |
https://en.wikipedia.org/wiki/Tucows | Tucows Inc. is an American-Canadian publicly traded Internet services and telecommunications company headquartered in Toronto, Ontario, Canada, and incorporated in Pennsylvania, United States. The company is composed of three independent businesses: Tucows Domains, Ting Internet, and Wavelo.
Originally founded in 1993 as a shareware and freeware software download site, Tucows shuttered its downloads business in 2021. Tucows Domains is the second-largest domain registrar worldwide and operates OpenSRS, Ascio, and Hover.
In 2012, Tucows launched Ting Mobile, a wireless service provider and used the same brand to launch its fiber Internet provider business Ting Internet in 2015. In 2020, Tucows sold its wireless business to Dish Network, while they continued to operate Ting Internet. The billing platform Tucows built for Ting Mobile was spun off into an independent OSS/BSS SaaS business, Wavelo.
The company was formed in Flint, Michigan, United States, in 1993. The Tucows logo was two cow heads, a play on the homophone "two cows".
Origins
Scott Swedorski, a Flint native, started working as a computer lab manager at Flint's Mott Community College in 1991. By late 1992, Swedorski left Mott College to work at the Genesee County Library System as a system administrator for FALCON (Flint Area Library Cooperative Online Network) and saw a need to bring shareware reviews to the public. In 1993 he formed TUCOWS (The Ultimate Collection Of Winsock Software) leading all editorial, reviews, HTML programming and scripting.
Company history
In the early 1990s, Tucows was hosted on university and public servers (much like Yahoo! and Google were in their early stages). TUCOWS' mission was to provide users with downloads of both freeware and trial versions of shareware. Internet Direct, owned and operated by John Nemanic, Bill Campbell, and Colin Campbell, acquired Tucows in 1996. STI Ventures acquired Tucows in 1999.
The company employed roughly 30 employees in Flint, Michi |
https://en.wikipedia.org/wiki/List%20of%20introduced%20species | A complete list of introduced species for even quite small areas of the world would be dauntingly long. Humans have introduced more different species to new environments than any single document can record. This list is generally for established species with truly wild populations— not kept domestically—that have been seen numerous times, and have breeding populations. While most introduced species can cause a negative impact to new environments they reach, some can have a positive impact, just for conservation purpose.
Australia
Mammals
Platypus in Kangaroo Island
Koala in South Australia
Water buffalo
Cattle
Sheep
Pig
Dromedary
Red deer from Europe
Fallow deer from Europe
Chital
Indian hog deer
Javan rusa
Sambar deer
Donkey
Brumby
Banteng
Goat
Brown hare
Red fox
Dog
Cat
House mouse
Northern palm squirrel - established in Perth
European rabbit from Europe
Rats
Black rat
Brown rat
Birds
Acridotheres tristis (common myna)
Alauda arvensis (Eurasian skylark)
Anas platyrhynchos (mallard)
Cacatua galerita (sulphur-crested cockatoo) - Western Australia from east Australia
Cacatua tenuirostris (long-billed corella) - to coastal areas from inland
Callipepla californica (California quail)
Carduelis carduelis (European goldfinch)
Cereopsis novaehollandiae (Cape Barren goose) - reintroduced onto Australian islands
Chloris chloris (European greenfinch)
Cygnus olor (mute swan)
Dacelo novaeguineae (laughing kookaburra) - artificially expanded range
Dromaius novaehollandiae (emu) - reintroduced onto Australian islands
Columba livia (feral pigeon)
Australian brushturkey in Kangaroo Island
Gallus gallus (red junglefowl)
Gallus varius (green junglefowl) on Cocos (Keeling) Islands
Padda oryzivora (Java sparrow) - Cocos (Keeling) Islands and Christmas Island
Lonchura punctulata (nutmeg mannikin)
Meleagris gallopavo (wild turkey)
Menura novaehollandiae (superb lyrebird) - Tasmania from mainland
Numida meleagris (helmeted guineafowl)
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https://en.wikipedia.org/wiki/Nabla%20symbol | ∇
The nabla symbol
The nabla is a triangular symbol resembling an inverted Greek delta: or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word for a Phoenician harp, and was suggested by the encyclopedist William Robertson Smith to Peter Guthrie Tait in correspondence.
The nabla symbol is available in standard HTML as ∇ and in LaTeX as \nabla. In Unicode, it is the character at code point U+2207, or 8711 in decimal notation, in the Mathematical Operators block.
It is also called del.
History
The differential operator given in Cartesian coordinates on three-dimensional Euclidean space by
was introduced in 1837 by the Irish mathematician and physicist William Rowan Hamilton, who called it ◁. (The unit vectors were originally right versors in Hamilton's quaternions.) The mathematics of ∇ received its full exposition at the hands of P. G. Tait.
After receiving Smith's suggestion, Tait and James Clerk Maxwell referred to the operator as nabla in their extensive private correspondence; most of these references are of a humorous character. C. G. Knott's Life and Scientific Work of Peter Guthrie Tait (p. 145):
It was probably this reluctance on the part of Maxwell to use the term Nabla in serious writings which prevented Tait from introducing the word earlier than he did. The one published use of the word by Maxwell is in the title to his humorous Tyndallic Ode, which is dedicated to the "Chief Musician upon Nabla", that is, Tait.
William Thomson (Lord Kelvin) introduced the term to an American audience in an 1884 lecture; the notes were published in Britain and the U.S. in 1904.
The name is acknowledged, and criticized, by Oliver Heaviside in 1891:
The fictitious vector ∇ given by
is very important. Physical mathematics is very largely the mathematics of ∇. The name Nabla seems, therefore, ludicrously inefficient.
Heaviside and Josiah Willard Gibbs (independently) are credited with the development of the version of v |
https://en.wikipedia.org/wiki/Subbase | In topology, a subbase (or subbasis, prebase, prebasis) for a topological space with topology is a subcollection of that generates in the sense that is the smallest topology containing as open sets. A slightly different definition is used by some authors, and there are other useful equivalent formulations of the definition; these are discussed below.
Definition
Let be a topological space with topology A subbase of is usually defined as a subcollection of satisfying one of the two following equivalent conditions:
The subcollection generates the topology This means that is the smallest topology containing : any topology on containing must also contain
The collection of open sets consisting of all finite intersections of elements of together with the set forms a basis for This means that every proper open set in can be written as a union of finite intersections of elements of Explicitly, given a point in an open set there are finitely many sets of such that the intersection of these sets contains and is contained in
(If we use the nullary intersection convention, then there is no need to include in the second definition.)
For subcollection of the power set there is a unique topology having as a subbase. In particular, the intersection of all topologies on containing satisfies this condition. In general, however, there is no unique subbasis for a given topology.
Thus, we can start with a fixed topology and find subbases for that topology, and we can also start with an arbitrary subcollection of the power set and form the topology generated by that subcollection. We can freely use either equivalent definition above; indeed, in many cases, one of the two conditions is more useful than the other.
Alternative definition
Less commonly, a slightly different definition of subbase is given which requires that the subbase cover In this case, is the union of all sets contained in This means that there can be no confusion regardin |
https://en.wikipedia.org/wiki/Exercise%20physiology | Exercise physiology is the physiology of physical exercise. It is one of the allied health professions, and involves the study of the acute responses and chronic adaptations to exercise. Exercise physiologists are the highest qualified exercise professionals and utilise education, lifestyle intervention and specific forms of exercise to rehabilitate and manage acute and chronic injuries and conditions.
Understanding the effect of exercise involves studying specific changes in muscular, cardiovascular, and neurohumoral systems that lead to changes in functional capacity and strength due to endurance training or strength training. The effect of training on the body has been defined as the reaction to the adaptive responses of the body arising from exercise or as "an elevation of metabolism produced by exercise".
Exercise physiologists study the effect of exercise on pathology, and the mechanisms by which exercise can reduce or reverse disease progression.
History
British physiologist Archibald Hill introduced the concepts of maximal oxygen uptake and oxygen debt in 1922. Hill and German physician Otto Meyerhof shared the 1922 Nobel Prize in Physiology or Medicine for their independent work related to muscle energy metabolism. Building on this work, scientists began measuring oxygen consumption during exercise. Notable contributions were made by Henry Taylor at the University of Minnesota, Scandinavian scientists Per-Olof Åstrand and Bengt Saltin in the 1950s and 60s, the Harvard Fatigue Laboratory, German universities, and the Copenhagen Muscle Research Centre among others.
In some countries it is a Primary Health Care Provider. Accredited Exercise Physiologists (AEP's) are university-trained professionals who prescribe exercise-based interventions to treat various conditions using dose response prescriptions specific to each individual.
Energy expenditure
Humans have a high capacity to expend energy for many hours during sustained exertion. For example, one i |
https://en.wikipedia.org/wiki/Local%20zeta%20function | In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as
where is a non-singular -dimensional projective algebraic variety over the field with elements and is the number of points of defined over the finite field extension of .
Making the variable transformation gives
as the formal power series in the variable .
Equivalently, the local zeta function is sometimes defined as follows:
In other words, the local zeta function with coefficients in the finite field is defined as a function whose logarithmic derivative generates the number of solutions of the equation defining in the degree extension
Formulation
Given a finite field F, there is, up to isomorphism, only one field Fk with
,
for k = 1, 2, ... . Given a set of polynomial equations — or an algebraic variety V — defined over F, we can count the number
of solutions in Fk and create the generating function
.
The correct definition for Z(t) is to set log Z equal to G, so
and Z(0) = 1, since G(0) = 0, and Z(t) is a priori a formal power series.
The logarithmic derivative
equals the generating function
.
Examples
For example, assume all the Nk are 1; this happens for example if we start with an equation like X = 0, so that geometrically we are taking V to be a point. Then
is the expansion of a logarithm (for |t| < 1). In this case we have
To take something more interesting, let V be the projective line over F. If F has q elements, then this has q + 1 points, including the one point at infinity. Therefore, we have
and
for |t| small enough, and therefore
The first study of these functions was in the 1923 dissertation of Emil Artin. He obtained results for the case of a hyperelliptic curve, and conjectured the further main points of the theory as applied to curves. The theory was then developed by F. K. Schmidt and Helmut Hasse. The earliest known nontrivial cases of local zeta functions were implicit in Ca |
https://en.wikipedia.org/wiki/Contact%20%28mathematics%29 | In mathematics, two functions have a contact of order if, at a point , they have the same value and equal derivatives. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp. Contact is a geometric notion; it can be defined algebraically as a valuation.
One speaks also of curves and geometric objects having -th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent. (Here the derivatives are considered with respect to arc length.) An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles, and has second-order contact (same tangent angle and curvature), etc.
Applications
Contact forms are particular differential forms of degree 1 on odd-dimensional manifolds; see contact geometry. Contact transformations are related changes of coordinates, of importance in classical mechanics. See also Legendre transformation.
Contact between manifolds is often studied in singularity theory, where the type of contact are classified, these include the A series (A0: crossing, A1: tangent, A2: osculating, ...) and the umbilic or D-series where there is a high degree of contact with the sphere.
Contact between curves
Two curves in the plane intersecting at a point p are said to have:
0th-order contact if the curves have a simple crossing (not tangent).
1st-order contact if the two curves are tangent.
2nd-order contact if the curvatures of the curves are equal. Such curves are said to be osculating.
3rd-order contact if the derivatives of the curvature are equal.
4th-order contact if the second derivatives of the curvature are equal.
Contact between a cu |
https://en.wikipedia.org/wiki/Formal%20system | A formal system is an abstract structure or formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules.
In 1921, David Hilbert proposed to use the formal system as the foundation for the knowledge in mathematics.
The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation.
Concepts
A formal system has the following:
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules).
Deductive system, deductive apparatus, or proof system, which have rules of inference, which take axioms and infer a theorem, both of which are part of the formal language.
A formal system is said to be recursive (i.e. effective) or recursively enumerable if the set of axioms and the set of inference rules are decidable sets or semidecidable sets, respectively.
Formal language
A formal language is a language that is defined by a formal system. Like languages in linguistics, formal languages generally have two aspects:
the syntax is what the language looks like (more formally: the set of possible expressions that are valid utterances in the language)
the semantics are what the utterances of the language mean (which is formalized in various ways, depending on the type of language in question)
Usually only the syntax of a formal language is considered via the notion of a formal grammar. The two main categories of formal grammar are that of generative grammars, which are sets of rules for how strings in a language can be written, and that of analytic grammars (or reductive grammar), which are sets of rules for how a string can be analyzed to determine whether it is a member of the language.
Deductive system
A deductive system, also called a deductive apparatus, consists of the axioms (or axiom schemata) and rules of in |
https://en.wikipedia.org/wiki/Progress%20Quest | Progress Quest is a video game developed by Eric Fredricksen as a parody of EverQuest and other massively multiplayer online role-playing games. It is loosely considered a zero-player game, in the sense that once the player has set up their artificial character, there is no user interaction at all; the game "plays" itself, with the human player as spectator. The game's source code was released in 2011.
Gameplay
On starting a new game, the player is presented with a few options, such as the choice of race and character class for their player character. Stats are rolled and unrolled to determine Strength, Constitution, Dexterity, Intelligence, Wisdom, and Charisma. Players start off with subpar equipment, eventually earning better weapons, armor, and spells. Almost none of the above-mentioned character statistics and equipment have any effect on gameplay, however. The only exception is the Strength stat, which affects carrying capacity, indirectly influencing the speed of level gain.
After character creation the game runs its course. The game displays the character's stats on the screen, including several progress bars representing how far the player character has advanced in the game. The lengthy, combat free prologue is represented by a set of progress bars, each accompanied by a line of text describing, among other things, the "foreboding vision" the character has. Then the first act begins, and the character is "heading to the killing fields..." where they will start the endless cycle of "executing (number of monsters) (adjective of monsters) (monster type)" or "executing a passing (player character)", only disrupted when their strength is no longer sufficient to carry more items. This forces their return to the market, where they will sell all the loot (each group of monsters drops one monster-specific item of loot, player characters will drop random magic loot) and then spend all their accumulated money to buy equipment. With each group of monsters "executed" |
https://en.wikipedia.org/wiki/%C3%89tale%20cohomology | In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry. This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.
History
Étale cohomology was introduced by , using some suggestions by Jean-Pierre Serre, and was motivated by the attempt to construct a Weil cohomology theory in order to prove the Weil conjectures. The foundations were soon after worked out by Grothendieck together with Michael Artin, and published as and SGA 4. Grothendieck used étale cohomology to prove some of the Weil conjectures (Bernard Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods), and the remaining conjecture, the analogue of the Riemann hypothesis was proved by Pierre Deligne (1974) using ℓ-adic cohomology.
Further contact with classical theory was found in the shape of the Grothendieck version of the Brauer group; this was applied in short order to diophantine geometry, by Yuri Manin. The burden and success of the general theory was certainly both to integrate all this information, and to prove general results such as Poincaré duality and the Lefschetz fixed-point theorem in this context.
Grothendieck originally developed étale cohomology in an extremely general setting, working with concepts such as Grothendieck toposes and Grothendieck universes. With hindsight, much of this machinery proved unnecessary for most practical applications of the étale theory, and gave a simplified exposition of étale cohomology theory. Grothendieck's use of these universes (whose existence cannot be proved in Zermelo–Fraenkel set theory) led |
https://en.wikipedia.org/wiki/Simulation%20%28computer%20science%29 | In theoretical computer science a simulation is a relation between state transition systems associating systems that behave in the same way in the sense that one system simulates the other.
Intuitively, a system simulates another system if it can match all of its moves.
The basic definition relates states within one transition system, but this is easily adapted to relate two separate transition systems by building a system consisting of the disjoint union of the corresponding components.
Formal definition
Given a labelled state transition system (, , →),
where is a set of states, is a set of labels and → is a set of labelled transitions (i.e., a subset of ),
a relation is a simulation if and only if for every pair of states in and all labels α in :
if , then there is such that
Equivalently, in terms of relational composition:
Given two states and in , can be simulated by , written , if and only if there is a simulation such that . The relation is called the simulation preorder, and it is the union of all simulations: precisely when for some simulation .
The set of simulations is closed under union; therefore, the simulation preorder is itself a simulation. Since it is the union of all simulations, it is the unique largest simulation. Simulations are also closed under reflexive and transitive closure; therefore, the largest simulation must be reflexive and transitive. From this follows that the largest simulation — the simulation preorder — is indeed a preorder relation. Note that there can be more than one relation which is both a simulation and a preorder; the term simulation preorder refers to the largest one of them (which is a superset of all the others).
Two states and are said to be similar, written , if and only if can be simulated by and can be simulated by . Similarity is thus the maximal symmetric subset of the simulation preorder, which means it is reflexive, symmetric, and transitive; hence an equivalence relation. However, it |
https://en.wikipedia.org/wiki/F%CF%83%20set | {{DISPLAYTITLE:Fσ set}}
In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in French with F for (French: closed) and σ for (French: sum, union).
The complement of an Fσ set is a Gδ set.
Fσ is the same as in the Borel hierarchy.
Examples
Each closed set is an Fσ set.
The set of rationals is an Fσ set in . More generally, any countable set in a T1 space is an Fσ set, because every singleton is closed.
The set of irrationals is not a Fσ set.
In metrizable spaces, every open set is an Fσ set.
The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set.
The set of all points in the Cartesian plane such that is rational is an Fσ set because it can be expressed as the union of all the lines passing through the origin with rational slope:
where , is the set of rational numbers, which is a countable set.
See also
Gδ set — the dual notion.
Borel hierarchy
P-space, any space having the property that every Fσ set is closed
References
Topology
Descriptive set theory |
https://en.wikipedia.org/wiki/Ivar%20Giaever | Ivar Giaever (, ; born April 5, 1929) is a Norwegian-American engineer and physicist who shared the Nobel Prize in Physics in 1973 with Leo Esaki and Brian Josephson "for their discoveries regarding tunnelling phenomena in solids". Giaever's share of the prize was specifically for his "experimental discoveries regarding tunnelling phenomena in superconductors".
In 1975, he was elected as a member into the National Academy of Engineering for contributions in the discovery and elaboration of electron tunneling into superconductors.
Giaever is a professor emeritus at the Rensselaer Polytechnic Institute and the president of the company Applied Biophysics.
Early life
Giaever earned a degree in mechanical engineering from the Norwegian Institute of Technology in Trondheim in 1952. In 1954, he emigrated from Norway to Canada, where he was employed by the Canadian division of General Electric. He moved to the United States four years later, joining General Electric's Corporate Research and Development Center in Schenectady, New York, in 1958. He has lived in Niskayuna, New York, since then, taking up US citizenship in 1964. While working for General Electric, Giaever earned a Ph.D. degree at the Rensselaer Polytechnic Institute in 1964.
The Nobel Prize
The work that led to Giaever's Nobel Prize was performed at General Electric in 1960. Following on Esaki's discovery of electron tunnelling in semiconductors in 1958, Giaever showed that tunnelling also took place in superconductors, demonstrating tunnelling through a very thin layer of oxide surrounded on both sides by metal in a superconducting or normal state. Giaever's experiments demonstrated the existence of an energy gap in superconductors, one of the most important predictions of the BCS theory of superconductivity, which had been developed in 1957. Giaever's experimental demonstration of tunnelling in superconductors stimulated the theoretical physicist Brian Josephson to work on the phenomenon, leading to |
https://en.wikipedia.org/wiki/Kenneth%20G.%20Wilson | Kenneth Geddes "Ken" Wilson (June 8, 1936 – June 15, 2013) was an American theoretical physicist and a pioneer in leveraging computers for studying particle physics. He was awarded the 1982 Nobel Prize in Physics for his work on phase transitions—illuminating the subtle essence of phenomena like melting ice and emerging magnetism. It was embodied in his fundamental work on the renormalization group.
Life
Wilson was born on June 8, 1936, in Waltham, Massachusetts, the oldest child of Emily Buckingham Wilson and E. Bright Wilson, a prominent chemist at Harvard University, who did
important work on microwave emissions. His mother also trained as a physicist. He attended several schools, including Magdalen College School, Oxford, England,
ending up at the George School in eastern Pennsylvania.
He went on to Harvard College at age 16, majoring in Mathematics and, on two occasions, in 1954 and 1956, ranked among the top five in the William Lowell Putnam Mathematical Competition.
He was also a star on the athletics track, representing Harvard in the Mile. During his summer holidays he worked at the Woods Hole Oceanographic Institution. He earned his PhD from Caltech in 1961, studying under Murray Gell-Mann. He did post-doc work at Harvard and CERN.
He joined Cornell University in 1963 in the Department of Physics as a junior faculty member, becoming a full professor in 1970. He also did research at SLAC during this period. In 1974, he became the James A. Weeks Professor of Physics at Cornell.
In 1982 he was awarded the Nobel Prize in Physics for his work on critical phenomena using the renormalization group.
He was a co-winner of the Wolf Prize in physics in 1980, together with Michael E. Fisher and Leo Kadanoff.
His other awards include the A.C. Eringen Medal, the Franklin Medal, the Boltzmann Medal, and the Dannie Heinemann Prize. He was elected a member of the National Academy of Science and a fellow of the American Academy of Arts and Science, both in 1975, |
https://en.wikipedia.org/wiki/Truckee%E2%80%93Carson%20Irrigation%20District | TCID may also stand for "Tissue Culture Infectious Dose." or "4,5,6,7-Tetrachloro-1H-indene-1,3(2H)-dione"
The Truckee–Carson Irrigation District (TCID) is a political subdivision of the State of Nevada, which operates dams at Lake Tahoe, diversion dams on the Truckee River in Washoe County, and the Lake Lahontan reservoir.
TCD also operates of canals, and of drains, in support of agriculture in Lyon County and Churchill County, western Nevada. The excess irrigation water eventually drains into the endorheic Lake Lahontan Basin.
Endangered species
Diversion of water by the TCID from the Truckee River has caused a reduction in the level of natural Pyramid Lake, resulting in the endemic species of fish that live in it becoming endangered species.
In the mid-1980s the United States Environmental Protection Agency initiated development of the DSSAM Model to analyze effects of variable Truckee River flow rates and water quality upon these endangered fish species.
See also
Derby Dam
Newlands Reclamation Act
References
External links
Water in Nevada
Historic American Engineering Record in Nevada
Irrigation Districts of the United States
Irrigation projects
Local government in Nevada
Agriculture in Nevada
Churchill County, Nevada
Lyon County, Nevada
Washoe County, Nevada |
https://en.wikipedia.org/wiki/Free%20floating%20screed | The free floating screed is a device pioneered in the 1930s that revolutionized the asphalt paving process. The device is designed to spread and smooth out, or screed, the material (e.g. concrete or asphalt) below it.
Description
The screed connects to the tractor portion of the paving machine via its tow arm. Paving material is transferred from the hopper at the front of the tractor to the screed, and augers spread it across the width of the screed. The material then flows out across the width of the screed at the desired depth. A screed operator stands on a platform at the center of the screed and controls the placement of the paving mixture. Adjusting screed settings will change the placement depth and width, as well as amount of material being placed. Many modern screeds can be run in an automatic mode, too.
Because the only connection between the asphalt paver and the screed is the tow arm, the screed can "float" vertically relative to the paver. This allows the paver to traverse uneven ground while the screed floats over the material placed in front of it.
The free floating screed has become standard because of the smoothing or averaging effect it can have on the existing base course. The free floating screed has a number of forces acting on it that, when in equilibrium, allow the depth behind the screed to be constant.
Tow arm pull: the force exerted on the screed by the paver dragging it
Mass: the weight of the screed
Resistance of the head of material: the opposing force exerted on the screed by the pile of material in front of the screed. This force depends in turn on the material's viscosity and mass.
The angle at which the tow arm pull is exerted on the screed also contributes to the motion; its resultant force is either added or subtracted from the mass of the screed.
If each of these forces is constant, altering the angle of the screed to the horizontal (angle of attack) will control the amount of material extruded behind the screed. Increasin |
https://en.wikipedia.org/wiki/273%20%28number%29 | 273 (two hundred [and] seventy-three) is the natural number following 272 and preceding 274.
273 is a sphenic number, a truncated triangular pyramid number and an idoneal number.
There are 273 different ternary trees with five nodes.
In other fields
The zero of the Celsius temperature scale is (to the nearest whole number) 273 kelvins. Thus, absolute zero (0 K) is approximately −273 °C. The freezing temperature of water and the thermodynamic temperature of the triple point of water are both approximately 0 °C or 273 K.
References
Integers |
https://en.wikipedia.org/wiki/Acer%20Inc. | Acer Inc. ( ) is a Taiwanese multinational hardware and electronics corporation specializing in advanced electronics technology, headquartered in Xizhi, New Taipei City. Its products include desktop PCs, laptop PCs (clamshells, 2-in-1s, convertibles and Chromebooks), tablets, servers, storage devices, virtual reality devices, displays, smartphones and peripherals, as well as gaming PCs and accessories under its Predator brand. Acer is the world's 6th-largest PC vendor by unit sales as of September 2022.
In the early 2000s, Acer implemented a new business model, shifting from a manufacturer to a designer, marketer, and distributor of products, while performing production processes via contract manufacturers. Currently, in addition to its core IT products business, Acer also has a new business entity that focuses on the integration of cloud services and platforms, and the development of smartphones and wearable devices with value-added IoT applications.
History
Acer was founded in 1976 by Stan Shih (), his wife Carolyn Yeh, and five others as Multitech in Hsinchu City, Taiwan. The company began with eleven employees and US$25,000 in capital. Initially, it was primarily a distributor of electronic parts and a consultant in the use of microprocessor technologies. It produced the Micro-Professor MPF-I training kit, then two Apple II clones–the Microprofessor II and III–before joining the emerging IBM PC compatible market and becoming a significant PC manufacturer. The company was renamed Acer in 1987.
In 1998, Acer reorganized into five groups: Acer International Service Group, Acer Sertek Service Group, Acer Semiconductor Group, Acer Information Products Group, and Acer Peripherals Group. To dispel complaints from clients that Acer competed with its own products and to alleviate the competitive nature of the branded sales versus contract manufacturing businesses, the company spun off the contract business in 2000, renaming it Wistron Corporation. The restructuring r |
https://en.wikipedia.org/wiki/International%20Air%20Transport%20Association%20code | IATA codes are abbreviations that the International Air Transport Association (IATA) publishes to facilitate air travel. They are typically 1, 2, 3, or 4 character combinations (referred to as unigrams, digrams, trigrams, or tetragrams, respectively) that uniquely identify locations, equipment, companies, and times to standardize international flight operations. All codes within each group follow a pattern (same number of characters, and using either all letters or letter/digit combinations) to reduce the potential for error.
Airport codes
IATA airport codes are trigram letter designations for airports, like "ORY" (Paris-Orly Airport), "CPT" (Cape Town International Airport), OTP (Otopeni International Airport) and "BCN" (Barcelona-El Prat).
Airline designators
IATA airline designators are digram letter/digit codes for airline companies, like "M6" (Amerijet), "NH" (All Nippon Airways), and "4A" (Air Kiribati).
Aircraft type designators
IATA aircraft type designators are trigram letter/digit codes used for aircraft models, like "J41" (British Aerospace Jetstream 41) and "744" (Boeing 747-400).
Country codes
Digram letter codes are used for countries as specified in ISO 3166-1 alpha-2. One additional code is used:
code XU is used to specify part of Russia east of (but not including) the Ural Mountains.
Currency codes
Trigram letter codes are used for currencies as specified in ISO 4217.
IATA time zone codes
IATA time zone is a country or a part of a country, where local time is the same. IATA time zone code is constructed of 2–4 characters (letters and digits) as follows:
ISO 3166-1 alpha-2 country code is always used as first and second characters of time zone code.
If country is not divided into separate time zones – no more characters added. Just 2 characters used.
If country is divided into time zones – 3rd character of time zone code is a digit – number of time zone in country. Note: Russia is divided into 11 time zones, so number of time zone |
https://en.wikipedia.org/wiki/Numeracy | Numeracy is the ability to understand, reason with, and to apply simple numerical concepts. The charity National Numeracy states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the best possible decisions...It’s as much about thinking and reasoning as about 'doing sums'". Basic numeracy skills consist of comprehending fundamental arithmetical operations like addition, subtraction, multiplication, and division. For example, if one can understand simple mathematical equations such as 2 + 2 = 4, then one would be considered to possess at least basic numeric knowledge. Substantial aspects of numeracy also include number sense, operation sense, computation, measurement, geometry, probability and statistics. A numerically literate person can manage and respond to the mathematical demands of life.
By contrast, innumeracy (the lack of numeracy) can have a negative impact. Numeracy has an influence on healthy behaviors, financial literacy, and career decisions. Therefore, innumeracy may negatively affect economic choices, financial outcomes, health outcomes, and life satisfaction. It also may distort risk perception in health decisions. Greater numeracy has been associated with reduced susceptibility to framing effects, less influence of nonnumerical information such as mood states, and greater sensitivity to different levels of numerical risk. Ellen Peters and her colleagues argue that achieving the benefits of numeric literacy, however, may depend on one's numeric self-efficacy or confidence in one's skills.
Representation of numbers
Humans have evolved to mentally represent numbers in two major ways from observation (not formal math). These representations are often thought to be innate (see Numerical cognition), to be shared across human cultures, to be common to multiple species, and not to be the result of individual learning or cultural transmission. They are:
Approximate representation of numerical magni |
https://en.wikipedia.org/wiki/Real%20computation | In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable."
These hypothetical computing machines can be viewed as idealised analog computers which operate on real numbers, whereas digital computers are limited to computable numbers. They may be further subdivided into differential and algebraic models (digital computers, in this context, should be thought of as topological, at least insofar as their operation on computable reals is concerned). Depending on the model chosen, this may enable real computers to solve problems that are inextricable on digital computers (For example, Hava Siegelmann's neural nets can have noncomputable real weights, making them able to compute nonrecursive languages.) or vice versa. (Claude Shannon's idealized analog computer can only solve algebraic differential equations, while a digital computer can solve some transcendental equations as well. However this comparison is not entirely fair since in Claude Shannon's idealized analog computer computations are immediately done; i.e. computation is done in real time. Shannon's model can be adapted to cope with this problem.)
A canonical model of computation over the reals is Blum–Shub–Smale machine (BSS).
If real computation were physically realizable, one could use it to solve NP-complete problems, and even #P-complete problems, in polynomial time. Unlimited precision real numbers in the physical universe are prohibited by the holographic principle and the Bekenstein bound.
See also
Hypercomputation, for other such powerful machines.
References
Further reading
Theory of computation
Hypercomputation |
https://en.wikipedia.org/wiki/Lysis | Lysis ( ) is the breaking down of the membrane of a cell, often by viral, enzymic, or osmotic (that is, "lytic" ) mechanisms that compromise its integrity. A fluid containing the contents of lysed cells is called a lysate. In molecular biology, biochemistry, and cell biology laboratories, cell cultures may be subjected to lysis in the process of purifying their components, as in protein purification, DNA extraction, RNA extraction, or in purifying organelles.
Many species of bacteria are subject to lysis by the enzyme lysozyme, found in animal saliva, egg white, and other secretions. Phage lytic enzymes (lysins) produced during bacteriophage infection are responsible for the ability of these viruses to lyse bacterial cells. Penicillin and related β-lactam antibiotics cause the death of bacteria through enzyme-mediated lysis that occurs after the drug causes the bacterium to form a defective cell wall. If the cell wall is completely lost and the penicillin was used on gram-positive bacteria, then the bacterium is referred to as a protoplast, but if penicillin was used on gram-negative bacteria, then it is called a spheroplast.
Cytolysis
Cytolysis occurs when a cell bursts due to an osmotic imbalance that has caused excess water to move into the cell.
Cytolysis can be prevented by several different mechanisms, including the contractile vacuole that exists in some paramecia, which rapidly pump water out of the cell. Cytolysis does not occur under normal conditions in plant cells because plant cells have a strong cell wall that contains the osmotic pressure, or turgor pressure, that would otherwise cause cytolysis to occur.
Oncolysis
Oncolysis is the destruction of neoplastic cells or of a tumour.
The term is also used to refer to the reduction of any swelling.
Plasmolysis
Plasmolysis is the contraction of cells within plants due to the loss of water through osmosis. In a hypertonic environment, the cell membrane peels off of the cell wall and the vacuole co |
https://en.wikipedia.org/wiki/Bisimulation | In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice versa.
Intuitively two systems are bisimilar if they, assuming we view them as playing a game according to some rules, match each other's moves. In this sense, each of the systems cannot be distinguished from the other by an observer.
Formal definition
Given a labeled state transition system (, , →),
where is a set of states, is a set of labels and → is a set of labelled transitions (i.e., a subset of ),
a bisimulation is a binary relation ,
such that both and its converse are simulations. From this follows that the symmetric closure of a bisimulation is a bisimulation, and that each symmetric simulation is a bisimulation. Thus some authors define bisimulation as a symmetric simulation.
Equivalently, is a bisimulation if and only if for every pair of states in and all labels α in :
if , then there is such that ;
if , then there is such that .
Given two states and in , is bisimilar to , written , if and only if there is a bisimulation such that . This means that the bisimilarity relation is the union of all bisimulations: precisely when for some bisimulation .
The set of bisimulations is closed under union; therefore, the bisimilarity relation is itself a bisimulation. Since it is the union of all bisimulations, it is the unique largest bisimulation. Bisimulations are also closed under reflexive, symmetric, and transitive closure; therefore, the largest bisimulation must be reflexive, symmetric, and transitive. From this follows that the largest bisimulation — bisimilarity — is an equivalence relation.
Alternative definitions
Relational definition
Bisimulation can be defined in terms of composition of relations as follows.
Given a labelled state transition system , a bisimulation relation is a binary relation over (i.e., ⊆ × ) such that
a |
https://en.wikipedia.org/wiki/Semantics%20%28computer%20science%29 | In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs.
Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.
History
In 1967, Robert W. Floyd publishes the paper Assigning meanings to programs; his chief aim is "a rigorous standard for proofs about computer programs, including proofs of correctness, equivalence, and termination". Floyd further writes:
A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It must specify which of the phrases in a syntactically correct program represent commands, and what conditions must be imposed on an interpretation in the neighborhood of each command.
In 1969, Tony Hoare publishes a paper on Hoare logic seeded by Floyd's ideas, now sometimes collectively called axiomatic semantics.
In the 1970s, the terms operational semantics and denotational semantics emerged.
Overview
The field of formal semantics encompasses all of the following:
The definition of semantic models
The relations between different semantic models
The relations between different approaches to meaning
The relation between computation and the underlying mathematical structures from fields such as logic, set theory, model theory, category theory, etc.
It has close links with other areas of computer science such as programming language design, type theory, compilers and interpreters, program verification and model checking.
Approaches
There are many approaches to formal semantics; these belong to three major classe |
https://en.wikipedia.org/wiki/Odra%20%28computer%29 | Odra was a line of computers manufactured in Wrocław, Poland. The name comes from the Odra river that flows through the city of Wrocław.
Overview
The production started in 1959–1960. Models 1001, 1002, 1003, 1013, 1103, 1204 were of original Polish construction. Models 1304 and 1305 were functional counterparts of ICL 1905 and 1906 due to software agreement. The last model was 1325 based on two models by ICL.
The computers were built at the Elwro manufacturing plant, which was closed in 1993.
Odra 1002 was capable of only 100–400 operations per second.
In 1962, Witold Podgórski, an employee of Elwro, managed to create a computer game on a prototype of Odra 1003; it was an adaptation of a variant of Nim, as depicted in the film Last Year at Marienbad. The computer could play a perfect game and was guaranteed to win. The game was never distributed outside of the Elwro company, but its versions appeared elsewhere. It was probably the first Polish computer game in history.
The operating system used by the Odra 1204 is called SODA. It was designed to work on a small computer without magnetic storage and
can run simultaneous loading and execution of programs.
An Odra 1204 computer was used by a team in Leningrad developing an ALGOL 68 compiler in 1976. The Odra 1204 ran the syntax analysis, code generation ran on an IBM System/360.
Up until 30 April 2010 there was still one Odra 1305 working at the railway station in Wrocław Brochów. The system was shut down at 22:00 CEST and replaced with a contemporary computer system.
The Museum of the History of Computers and Information Technology (Muzeum Historii Komputerów i Informatyki) in Katowice, Poland started a project to recommission an Odra 1305 in 2017.
Literature
See also
History of computing in Poland
History of computer hardware in Eastern Bloc countries
References
Early computers
Science and technology in Poland |
https://en.wikipedia.org/wiki/History%20of%20computer%20hardware%20in%20Eastern%20Bloc%20countries | The history of computing hardware in the Eastern Bloc is somewhat different from that of the Western world. As a result of the CoCom embargo, computers could not be imported on a large scale from Western Bloc.
Eastern Bloc manufacturers created copies of Western designs based on intelligence gathering and reverse engineering. This redevelopment led to some incompatibilities with International Electrotechnical Commission (IEC) and IEEE standards, such as spacing integrated circuit pins at of a 25 mm length (colloquially a "metric inch") instead of a standard inch of 25.4 mm. This made Soviet chips unsellable on the world market outside the Comecon, and made test machinery more expensive.
History
By the end of the 1950s most COMECON countries had developed experimental computer designs, yet none of them had managed to create a stable computer industry.
In October 1962 the "Commission for Scientific Problems in Computing" (Комиссия Научные Вопросы Вычислительной Техники, КНВВТ) was founded in Warsaw and modelled after the International Federation for Information Processing.
Computer design and production began to be coordinated between the Comecon countries in 1964, when the Edinaya Sistema mainframe (Unified System, ES, also known as RIAD) was introduced. The project also included plans for the development of a joint Comecon computer network.
Each COMECON country was given a role in the development of the ES: Hungary was responsible for software development, while East Germany improved the design of disk storage devices. The ES-1040 was successfully exported to countries outside the Comecon, including India, Yugoslavia and China. Each country specialized in a model of the ES series: R-10 in the case of Hungary, R-20 in Bulgaria, R-20A in Czechoslovakia, R-30 in Poland and R-40 in East Germany.
Nairi-3, developed at the Armenian Institute for Computers, was the first third-generation computer in the Comecon area, using integrated circuits. Development on the Na |
https://en.wikipedia.org/wiki/Am386 | The Am386 CPU is a 100%-compatible clone of the Intel 80386 design released by AMD in March 1991. It sold millions of units, positioning AMD as a legitimate competitor to Intel, rather than being merely a second source for x86 CPUs (then termed 8086-family).
History and design
While the AM386 CPU was essentially ready to be released prior to 1991, Intel kept it tied up in court. Intel learned of the Am386 when both companies hired employees with the same name who coincidentally stayed at the same hotel, which accidentally forwarded a package for AMD to Intel's employee. AMD had previously been a second-source manufacturer of Intel's Intel 8086, Intel 80186 and Intel 80286 designs, and AMD's interpretation of the contract, made up in 1982, was that it covered all derivatives of them. Intel, however, claimed that the contract only covered the 80286 and prior processors and forbade AMD the right to manufacture 80386 CPUs in 1987. After a few years in the courtrooms, AMD finally won the case and the right to sell their Am386 in March 1991. This also paved the way for competition in the 80386-compatible 32-bit CPU market and so lowered the cost of owning a PC.
While Intel's 386 CPUs had topped out at 33 MHz in 1989, AMD introduced 40 MHz versions of both its 386DX and 386SX out of the gate, extending the lifespan of the architecture. In the following two years the AMD 386DX-40 saw popularity with small manufacturers of PC clones and with budget-minded computer enthusiasts because it offered near-80486 performance at a much lower price than an actual 486. Generally the 386DX-40 performs nearly on par with a 25 MHz 486 due to the 486 needing fewer clock cycles per instruction, thanks to its tighter pipelining (more overlapping of internal processing) in combination with an on-chip CPU cache. However, its 32-bit 40 MHz data bus gave the 386DX-40 comparatively good memory and I/O performance.
Am386DX data
32-bit data bus, can select between either a 32-bit bus or a 16-b |
https://en.wikipedia.org/wiki/Lucas%20number | The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ratio. The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between.
The first few Lucas numbers are
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, ... .
which coincides for example with the number of independent vertex sets for cyclic graphs of length .
Definition
As with the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediately previous terms, thereby forming a Fibonacci integer sequence. The first two Lucas numbers are and , which differs from the first two Fibonacci numbers and . Though closely related in definition, Lucas and Fibonacci numbers exhibit distinct properties.
The Lucas numbers may thus be defined as follows:
(where n belongs to the natural numbers)
All Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff array; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row. Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio.
Extension to negative integers
Using , one can extend the Lucas numbers to negative integers |
https://en.wikipedia.org/wiki/Euler%20product | In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The original such product was given for the sum of all positive integers raised to a certain power as proven by Leonhard Euler. This series and its continuation to the entire complex plane would later become known as the Riemann zeta function.
Definition
In general, if is a bounded multiplicative function, then the Dirichlet series
is equal to
where the product is taken over prime numbers , and is the sum
In fact, if we consider these as formal generating functions, the existence of such a formal Euler product expansion is a necessary and sufficient condition that be multiplicative: this says exactly that is the product of the whenever factors as the product of the powers of distinct primes .
An important special case is that in which is totally multiplicative, so that is a geometric series. Then
as is the case for the Riemann zeta function, where , and more generally for Dirichlet characters.
Convergence
In practice all the important cases are such that the infinite series and infinite product expansions are absolutely convergent in some region
that is, in some right half-plane in the complex numbers. This already gives some information, since the infinite product, to converge, must give a non-zero value; hence the function given by the infinite series is not zero in such a half-plane.
In the theory of modular forms it is typical to have Euler products with quadratic polynomials in the denominator here. The general Langlands philosophy includes a comparable explanation of the connection of polynomials of degree , and the representation theory for .
Examples
The following examples will use the notation for the set of all primes, that is:
The Euler product attached to the Riemann zeta function , also using the sum of the geometric series, is
while for the Liouville function , it is
Using their reciprocals, two Euler produc |
https://en.wikipedia.org/wiki/Howard%20Hughes%20Medical%20Institute | The Howard Hughes Medical Institute (HHMI) is an American non-profit medical research organization based in Chevy Chase, Maryland. It was founded in 1953 by Howard Hughes, an American business magnate, investor, record-setting pilot, engineer, film director, and philanthropist, known during his lifetime as one of the most financially successful individuals in the world. It is one of the largest private funding organizations for biological and medical research in the United States. HHMI spends about $1 million per HHMI Investigator per year, which amounts to annual investment in biomedical research of about $825 million.
The institute has an endowment of $22.6 billion, making it the second-wealthiest philanthropic organization in the United States and the second-best-endowed medical research foundation in the world. HHMI is the former owner of the Hughes Aircraft Company, an American aerospace firm that was divested to various firms over time.
History
The institute was formed with the goal of basic research including trying to understand, in Hughes's words, "the genesis of life itself." Despite its principles, in the early days it was generally viewed as a tax haven for Hughes's huge personal fortune. Hughes was HHMI's sole trustee and he transferred his stock of Hughes Aircraft to the institute, in effect turning the large defense contractor into a tax-exempt charity. For many years the Institute grappled with maintaining its non-profit status; the Internal Revenue Service challenged its "charitable" status which made it tax exempt. Partly in response to such claims, starting in the late 1950s it began funding 47 investigators doing research at eight different institutions; however, it remained a modest enterprise for several decades.
The institute was initially located in Miami, Florida, in 1953. Hughes's internist, Verne Mason, who treated Hughes after his 1946 plane crash, was chairman of the institute's medical advisory committee. By 1975, Hughes was sole |
https://en.wikipedia.org/wiki/Biogeochemical%20cycle | A biogeochemical cycle, or more generally a cycle of matter, is the movement and transformation of chemical elements and compounds between living organisms, the atmosphere, and the Earth's crust. Major biogeochemical cycles include the carbon cycle, the nitrogen cycle and the water cycle. In each cycle, the chemical element or molecule is transformed and cycled by living organisms and through various geological forms and reservoirs, including the atmosphere, the soil and the oceans. It can be thought of as the pathway by which a chemical substance cycles (is turned over or moves through) the biotic compartment and the abiotic compartments of Earth. The biotic compartment is the biosphere and the abiotic compartments are the atmosphere, lithosphere and hydrosphere.
For example, in the carbon cycle, atmospheric carbon dioxide is absorbed by plants through photosynthesis, which converts it into organic compounds that are used by organisms for energy and growth. Carbon is then released back into the atmosphere through respiration and decomposition. Additionally, carbon is stored in fossil fuels and is released into the atmosphere through human activities such as burning fossil fuels. In the nitrogen cycle, atmospheric nitrogen gas is converted by plants into usable forms such as ammonia and nitrates through the process of nitrogen fixation. These compounds can be used by other organisms, and nitrogen is returned to the atmosphere through denitrification and other processes. In the water cycle, the universal solvent water evaporates from land and oceans to form clouds in the atmosphere, and then precipitates back to different parts of the planet. Precipitation can seep into the ground and become part of groundwater systems used by plants and other organisms, or can runoff the surface to form lakes and rivers. Subterranean water can then seep into the ocean along with river discharges, rich with dissolved and particulate organic matter and other nutrients.
There are bio |
https://en.wikipedia.org/wiki/List%20of%20graphical%20methods | This is a list of graphical methods with a mathematical basis.
Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization.
There is also a list of computer graphics and descriptive geometry topics.
Simple displays
Area chart
Box plot
Dispersion fan diagram
Graph of a function
Logarithmic graph paper
Heatmap
Bar chart
Histogram
Line chart
Pie chart
Plotting
Scatterplot
Sparkline
Stemplot
Radar chart
Set theory
Venn diagram
Karnaugh diagram
Descriptive geometry
Isometric projection
Orthographic projection
Perspective (graphical)
Engineering drawing
Technical drawing
Graphical projection
Mohr's circle
Pantograph
Circuit diagram
Smith chart
Sankey diagram
Systems analysis
Binary decision diagram
Control-flow graph
Functional flow block diagram
Information flow diagram
IDEF
N2 chart
Sankey diagram
State diagram
System context diagram
Data-flow diagram
Cartography
Map projection
Orthographic projection (cartography)
Robinson projection
Stereographic projection
Dymaxion map
Topographic map
Craig retroazimuthal projection
Hammer retroazimuthal projection
Biological sciences
Cladogram
Punnett square
Systems Biology Graphical Notation
Physical sciences
Free body diagram
Greninger chart
Phase diagram
Wavenumber-frequency diagram
Bode plot
Nyquist plot
Dalitz plot
Feynman diagram
Carnot Plot
Business methods
Flowchart
Workflow
Gantt chart
Growth-share matrix (often called BCG chart)
Work breakdown structure
Control chart
Ishikawa diagram
Pareto chart (often used to prioritise outputs of an Ishikawa diagram)
Conceptual analysis
Mind mapping
Concept mapping
Conceptual graph
Entity-relationship diagram
Tag cloud, also known as word cloud
Statistics
Autocorrelation plot
Bar chart
Biplot
Box plot
Bullet graph
Chernoff faces
Control chart
Fan chart
Forest plot
Funnel plot
Galbraith plot
Histogram
Mosaic plot
Multidimensional scaling
np-chart
p-chart
Pie chart
Probability plot
Normal probability plot
Poincaré plot
Probability plot |
https://en.wikipedia.org/wiki/Associated%20bundle | In mathematics, the theory of fiber bundles with a structure group (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from to , which are both topological spaces with a group action of . For a fiber bundle F with structure group G, the transition functions of the fiber (i.e., the cocycle) in an overlap of two coordinate systems Uα and Uβ are given as a G-valued function gαβ on Uα∩Uβ. One may then construct a fiber bundle F′ as a new fiber bundle having the same transition functions, but possibly a different fiber.
An example
A simple case comes with the Möbius strip, for which is the cyclic group of order 2, . We can take as any of: the real number line , the interval , the real number line less the point 0, or the two-point set . The action of on these (the non-identity element acting as in each case) is comparable, in an intuitive sense. We could say that more formally in terms of gluing two rectangles and together: what we really need is the data to identify to itself directly at one end, and with the twist over at the other end. This data can be written down as a patching function, with values in G. The associated bundle construction is just the observation that this data does just as well for as for .
Construction
In general it is enough to explain the transition from a bundle with fiber , on which acts, to the associated principal bundle (namely the bundle where the fiber is , considered to act by translation on itself). For then we can go from to , via the principal bundle. Details in terms of data for an open covering are given as a case of descent.
This section is organized as follows. We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle. This then specializes to the case when the specified fibre is a principal homogeneous space for the left action of the group on itself, yielding the associated |
https://en.wikipedia.org/wiki/Measure-preserving%20dynamical%20system | In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
Definition
A measure-preserving dynamical system is defined as a probability space and a measure-preserving transformation on it. In more detail, it is a system
with the following structure:
is a set,
is a σ-algebra over ,
is a probability measure, so that , and ,
is a measurable transformation which preserves the measure , i.e., .
Discussion
One may ask why the measure preserving transformation is defined in terms of the inverse instead of the forward transformation . This can be understood in a fairly easy fashion. Consider a mapping of power sets:
Consider now the special case of maps which preserve intersections, unions and complements (so that it is a map of Borel sets) and also sends to (because we want it to be conservative). Every such conservative, Borel-preserving map can be specified by some surjective map by writing . Of course, one could also define , but this is not enough to specify all such possible maps . That is, conservative, Borel-preserving maps cannot, in general, be written in the form one might consider, for example, the map of the unit interval given by this is the Bernoulli map.
has the form of a pushforward, whereas is generically called a pullback. Almost all properties and behaviors of dynamical systems are defined in terms of the pushforward. For example, the transfer operator is defined in terms of the pushforward of the transformation map ; the measure can now be understood as an invariant measure; it is just t |
https://en.wikipedia.org/wiki/43%20%28number%29 | 43 (forty-three) is the natural number following 42 and preceding 44.
In mathematics
Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is 47. 43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime.
43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 × 3 × 7).
43 is a centered heptagonal number.
Let a = a = 1, and thenceforth a = (a + a + ... + a). This sequence continues 1, 1, 2, 3, 5, 10, 28, 154... . a is the first term of this sequence that is not an integer.
43 is a Heegner number.
43 is the largest prime which divides the order of the Janko group J4.
43 is a repdigit in base 6 (111).
43 is the number of triangles inside the Sri Yantra.
43 is the largest natural number that is not an (original) McNugget number.
43 is the smallest prime number expressible as the sum of 2, 3, 4, or 5 different primes:
43 = 41 + 2
43 = 11 + 13 + 19
43 = 2 + 11 + 13 + 17
43 = 3 + 5 + 7 + 11 + 17.
43 is the smallest number with the property 43 = 4*prime(4) + 3*prime(3). Where prime(n) is the n-th prime number. There are only two numbers with that property, the other one is 127.
When taking the first six terms of the Taylor series for computing e, one obtains
which is also five minus the fifth harmonic number.
Every solvable configuration of the Fifteen puzzle can be solved in no more than 43 multi-tile moves (i.e. when moving two or three tiles at once is counted as one move).
In science
The chemical element with the atomic number 43 is technetium. It has the lowest atomic number of any element that does not possess stable isotopes.
Astronomy
Messier object M43, a magnitude 7.0 H II region in the constellation of Orion, a part of the Orion Nebula, and also sometimes known as de Mairan's Nebula
The New General Catalogue object NGC 43, a barred spiral galaxy in the constellation Andromeda
In sports
In auto racing:
T |
https://en.wikipedia.org/wiki/Cat%20%28Red%20Dwarf%29 | Cat (sometimes The Cat) is a fictional character in the British science fiction sitcom Red Dwarf. He is played by Danny John-Jules. He is a descendant of Dave Lister's pregnant pet house cat Frankenstein, whose descendants evolved into a humanoid form over three million years while Lister was in stasis (suspended animation). As a character he is vain and aloof, and loves to dress in extravagant clothing. He is simply referred to as "Cat" in lieu of a real name.
Fictional history
Television
1980s
The "Cat" first appeared in Red Dwarfs first episode "The End" (1988). The computer of the mining ship Red Dwarf, Holly (Norman Lovett), mentions that after a crisis where all of Red Dwarfs crew had died in a radiation leak, chicken soup machine repairman Dave Lister's (Craig Charles) pregnant cat, along with her unborn kittens, were sealed in the hold while Lister was put into stasis as punishment for keeping an unquarantined cat on board. Lister is left in stasis for three million years until the radiation reaches normal levels. This cat, Frankenstein, is mentioned by the Cat as a story he learnt about at school, describing her as "The holy mother, saved by Cloister the Stupid, who was frozen in time, and who gaveth of his life that we might live ... who shall returneth to lead us to Fuchal, the promised land," with Lister realising that "Cloister the Stupid" refers to Lister. Holly also mentions that the Cat evolved from the cats who have been breeding in the hold for three million years. After reawakening from stasis, Lister, the only known human being in existence, tells Holly to set a course for Fuchal, which is actually the archipelago of Fiji, where Lister had originally intended to take Frankenstein three million years earlier as part of his five-year plan.
In "Waiting for God" (1988), Holly translates a holy book written by the Cat's people for Lister, in which Lister is described as the cats' god "Cloister", and that his plan of buying a farm on Fiji and open |
https://en.wikipedia.org/wiki/44%20%28number%29 | 44 (forty-four) is the natural number following 43 and preceding 45.
In mathematics
Forty-four X is a composite number; a square-prime, of the form (p2,q) and fourth of this form and of the form (22.q), where q is a higher prime.
44 is a repdigit and palindromic number in decimal. It is the tenth 10-happy number, and the fourth octahedral number.
It is the first member of the first cluster of two square-primes; of the form (p2,q), specifically, {(22.11)=44, (32.5)=45}. The next such cluster of two square-primes comprises {(22.29)=116, (32.13)=117}.
44 has an aliquot sum of 40, within an aliquot sequence of three composite numbers (44,40,50,43,1,0) to the prime in the 43-aliquot tree.
Since the greatest prime factor of 442 + 1 = 1937 is 149 and thus more than 44 twice, 44 is a Størmer number. Given Euler's totient function, φ(44) = 20 and φ(69) = 44.
44 is a tribonacci number, preceded by 7, 13, and 24, whose sum it equals.
44 is the number of derangements of 5 items.
There are only 44 kinds of Schwarz triangles, aside from the infinite dihedral family of triangles (p 2 2) with p = {2, 3, 4, ...}.
There are 44 distinct stellations of the truncated cube and truncated octahedron, per Miller's rules.
44 four-dimensional crystallographic point groups of a total 227 contain dual enantiomorphs, or mirror images.
There are forty-four classes of finite simple groups that arise from four general families of such groups:
Two general groups stem from cyclic groups and alternating groups.
Sixteen families of groups stem from simple groups of Lie type.
Twenty-six groups are sporadic.
Sometimes the Tits group is considered a 17th non-strict simple group of Lie type, or a 27th sporadic group, which would yield a total of 45 finite simple groups.
In science
The atomic number of ruthenium
Astronomy
Messier object M44, a magnitude 4.0 open cluster in the constellation Cancer, also known as the Beehive Cluster
The New General Catalogue object NGC 44, a doubl |
https://en.wikipedia.org/wiki/46%20%28number%29 | 46 (forty-six) is the natural number following 45 and preceding 47.
In mathematics
Forty-six is
thirteenth discrete semiprime () and the eighth of the form (2.q), where q is a higher prime.
with an aliquot sum of 26; itself a semiprime, within an aliquot sequence of six composite numbers (46,26,16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
a Wedderburn-Etherington number,
an enneagonal number
a centered triangular number.
the number of parallelogram polyominoes with 6 cells.
It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that cannot be expressed as a sum of two abundant numbers. It is also the sixteenth semiprime.
Since it is possible to find sequences of 46+1 consecutive integers such that each inner member shares a factor with either the first or the last member, 46 is an Erdős–Woods number.
In science
The atomic number of palladium.
The number of human chromosomes.
The approximate molar mass of ethanol (46.07 g mol)
Astronomy
Messier object M46, a magnitude 6.5 open cluster in the constellation Puppis.
The New General Catalogue object NGC 46, a star in the constellation Pisces.
In music
Japanese idol group franchise Sakamichi Series, which consists of Nogizaka46, Keyakizaka46, Hinatazaka46, and Yoshimotozaka46
In sports
Valentino Rossi used 46 as his number in the MotoGP world motorcycle championship.
The number of mountains in the 46 peaks of the Adirondack mountain range. People who have climbed all of them are called "forty-sixers"; there is also an unofficial 47th peak.
The name of a defensive scheme used in American football; see 46 defense.
In religion
The total of books in the Old Testament, Catholic version, if the Book of Lamentations is counted as a book separate from the Book of Jeremiah
In other fields
Forty-six is also:
The code for international direct dial phone calls to Sweden.
The number of samurai, out of 47, who carried out the attack in the his |
https://en.wikipedia.org/wiki/48%20%28number%29 | 48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.
In mathematics
Forty-eight is the double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.
48 is the smallest number with exactly ten divisors, and the first multiple of 12 not to be a sum of twin primes.
The Sum of Odd Anti-Factors of 48 = number * (n/2) where n is an Odd number. So, 48 is an Odd Anti-Factor Hemiperfect Number.
Other such numbers include 6048, 38688, 82132, 975312, etc.
Odd Anti-Factors of 48 = 5, 19
Sum of Odd Anti-Factors = 5 + 19 = 24 = 48 * 1/2
There are 11 solutions to the equation φ(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number.
Since the greatest prime factor of 482 + 1 = 2305 is 461, which is clearly more than twice 48, 48 is a Størmer number.
48 is a Harshad number in base 10. It has 24, 2, 12, and 4 as factors.
In science
The atomic number of cadmium.
The number of Ptolemaic constellations.
The number of symmetries of a cube.
Astronomy
Messier object M48, a magnitude 5.5 open cluster in the constellation Hydra.
The New General Catalogue object NGC 48, a barred spiral galaxy in the constellation Andromeda.
In religion
The prophecies of 48 Jewish prophets and 7 prophetesses were recorded in the Tanakh for posterity.
According to the Mishnah, Torah wisdom is acquired via 48 ways (Pirkei Avoth 6:6).
In Buddhism, Amitabha Buddha had made 48 great vows and promises to provide ultimate salvation to countless beings through countless eons, with benefits said to be available merely by thinking about his name with Nianfo practice. He is thus hailed as "King of Buddhas" through such skillful compassion and became a popular and formal refuge figure in Pureland Buddhism.
In music
Johann Sebastian Bach's Well-Tempered Clavier is informa |
https://en.wikipedia.org/wiki/49%20%28number%29 | 49 (forty-nine) is the natural number following 48 and preceding 50.
In mathematics
Forty-nine is the square of the prime number seven and hence the fourth non-unitary square prime of the form p2
47 has an aliquot sum of 8; itself a prime power, and hence an aliquot sequence of two composite members (49, 8, 7,1,0).
It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these).
Along with the number that immediately derives from it, 77, the only number under 100 not having its home prime known ().
Decimal representation
The sum of the digits of the square of 49 (2401) is the square root of 49.
49 is the first square where the digits are squares. In this case, 4 and 9 are squares.
Reciprocal
The fraction is a repeating decimal with a period of 42:
= (42 digits repeat)
There are 42 (note that this number is the period) positive integers that are less than 49 and coprime to 49. Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a cyclic permutation of the original number:
020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102
020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653
020408163265306122448979591836734693877551 × 4 = 081632653061224489795918367346938775510204
...
The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right:
02
04
08
16
32
64
128
256
512
1024
2048
+ ...
----------------------
020408163265306122448979591836734693877551...0204081632...
because satisfies:
In chemistry
The atomic number of indium.
During the Manhattan Project, plutonium was also often referred to simply as "49". Number 4 was for the last digit in 94 (atomic number of plutonium) and 9 for the last digit in Pu-239, the wea |
https://en.wikipedia.org/wiki/51%20%28number%29 | 51 (fifty-one) is the natural number following 50 and preceding 52.
In mathematics
Fifty-one is
a pentagonal number as well as a centered pentagonal number and an 18-gonal number
the 6th Motzkin number, telling the number of ways to draw non-intersecting chords between any six points on a circle's boundary, no matter where the points may be located on the boundary.
a Perrin number, coming after 22, 29, 39 in the sequence (and the sum of the first two)
a Størmer number, since the greatest prime factor of 512 + 1 = 2602 is 1301, which is substantially more than 51 twice.
There are 51 different cyclic Gilbreath permutations on 10 elements, and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.
Since 51 is the product of the distinct Fermat primes 3 and 17, a regular polygon with 51 sides is constructible with compass and straightedge, the angle is constructible, and the number cos is expressible in terms of square roots.
In other fields
51 is:
The atomic number of antimony
The code for international direct dial phone calls to Peru
The last possible television channel number in the UHF bandplan for American terrestrial television from December 31, 2011, when channels 52–69 were withdrawn, to July 3, 2020, when channels 38–51 were removed from the bandplan.
The number of the laps of the Azerbaijan Grand Prix.
In the 2006 film Cars, 51 was Doc Hudson's number.
The Area 51.
The fire station number in the television series Emergency!.
The number of essays Alexander Hamilton wrote as part of The Federalist Papers defending the US constitution
See also
AD 51, a year in the Julian calendar
List of highways numbered 51
The model number of the P-51 Mustang World War II fighter aircraft
Area 51, a parcel of U.S. military-controlled land in southern Nevada, apparently containing a secret aircraft testing facility
Photo 51, an X-ray image of key importance in elucidating the structure of DNA in the 1950s
Fifty-One Tales, pa |
https://en.wikipedia.org/wiki/52%20%28number%29 | 52 (fifty-two) is the natural number following 51 and preceding 53.
In mathematics
Fifty-two is
a composite number; a square-prime, of the form (p2, q) where q is a higher prime. It is the sixth of this form and the fifth of the form (22.q).
the 5th Bell number, the number of ways to partition a set of 5 objects.
a decagonal number.
with an aliquot sum of 46; within an aliquot sequence of seven composite numbers (52,46,26,16,15, 9,4,3,1,0) to the prime in the 3-aliquot tree. This sequence does not extend above 52 because it is,
an untouchable number, since it is never the sum of proper divisors of any number, and it is a noncototient since it is not equal to x − φ(x) for any x.
a vertically symmetrical number.
In science
The atomic number of tellurium
Astronomy
Messier object M52, a magnitude 8.0 open cluster in the constellation Cassiopeia, also known as NGC 7654.
The New General Catalogue object NGC 52, a spiral galaxy in the constellation Pegasus.
In other fields
Fifty-two is:
The approximate number of weeks in a year. 52 weeks is 364 days, while the tropical year is 365.24 days long. According to ISO 8601, most years have 52 weeks while some have 53.
A significant number in the Maya calendar
On the modern piano, the number of white keys (notes in the C major scale)
The number of cards in a standard deck of playing cards, not counting Jokers or advertisement cards
The name of a practical joke card game 52 Pickup
52 Pick-Up is a film starring Roy Scheider and Ann Margaret
The code for international direct dial phone calls to Mexico
A weekly comic series from DC Comics entitled 52 has 52 issues, with a plot spanning one full year.
The New 52 is a 2011 revamp and relaunch by DC Comics of its entire line of ongoing monthly superhero books.
The number of letters in the English alphabet, if majuscules are distinguished from minuscules
The number of the French department Haute-Marne
52nd Street (disambiguation)
52 Hand Blocks, a variant of the martial art |
https://en.wikipedia.org/wiki/53%20%28number%29 | 53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number.
In mathematics
Fifty-three is the 16th prime number. It is also an Eisenstein prime, an isolated prime, a balanced prime and a Sophie Germain prime.
The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers.
53 cannot be expressed as the sum of any integer and its decimal digits, making 53 a self number.
53 is the smallest prime number that does not divide the order of any sporadic group.
In science
The atomic number of iodine
Astronomy
Messier object M53, a magnitude 8.5 globular cluster in the constellation Coma Berenices
The New General Catalogue object NGC 53, a magnitude 12.6 barred spiral galaxy in the constellation Tucana
In other fields
Fifty-three is:
The racing number of Herbie, a fictional Volkswagen Beetle with a mind of his own, first appearing in the 1968 film The Love Bug
The code for international direct dial phone calls to Cuba
53 Days is a northeastern USA rock band
53 Days a novel by Georges Perec
In How the Grinch Stole Christmas!, and its animated TV special adaptation the Grinch says he's put up with the Whos' Christmas cheer for 53 years.
Fictional 53rd Precinct in the Bronx was found in the TV comedy "Car 54, Where Are You?"
"53rd & 3rd" a song by the Ramones
The number of Hail Mary beads on a standard, five decade Catholic Rosary (the Dominican Rosary).
The number of bytes in an Asynchronous Transfer Mode packet.
UDP and TCP port number for the Domain Name System protocol.
53-TET (53 tone, equal temperament) is a musical temperament that has a fifth that is closer to pure than our current system.
53 More Things To Do In Zero Gravity is a book mentioned in The Hitchhiker's Guide to the Galaxy
Sports
The maximum number of players on a National Football League roster
Most points by a rookie in an NBA playoff game, by Philadelphia's Wilt Chamberlain, 1960
Most field goals (three-game serie |
https://en.wikipedia.org/wiki/54%20%28number%29 | 54 (fifty-four) is the natural number following 53 and preceding 55.
In mathematics
54 is an abundant number and a semiperfect number, like all other multiples of 6.
It is twice the third power of three, 3 + 3 = 54, and hence is a Leyland number.
54 is the smallest number that can be written as the sum of three positive squares in more than two different ways: = = = 54.
It is a 19-gonal number,
In base 10, 54 is a Harshad number.
The Holt graph has 54 edges.
The sine of an angle of 54 degrees is half the golden ratio.
The number of primes ≤ 28.
A Lehmer-Comtet number.
54 is the only non-trivial Neon Number in Power 9: 549 = 3,904,305,912,313,344; 3 + 9 + 0 + 4 + 3 + 0 + 5 + 9 + 1 + 2 + 3 + 1 + 3 + 3 + 4 + 4 = 54
In science
The atomic number of xenon is 54.
Astronomy
Messier object M54, a magnitude 8.5 globular cluster in the constellation Sagittarius
The New General Catalogue object NGC 54, a spiral galaxy in the constellation Cetus
The number of years in three Saros cycles of eclipses of the sun and moon is known as a Triple Saros or exeligmos (Greek: "turn of the wheel").
In sports
Fewest points in an NBA playoff game: Chicago (96), Utah (54), June 7, 1998
The New York Rangers won the Stanley Cup in 1994, 54 years after their previous Cup win. It is the longest drought in the trophy's history.
For years car number 54 was driven by NASCAR's Lennie Pond. More recently, it is known as the Nationwide Series car number for Kyle Busch.
A score of 54 on a par 72 course in golf is colloquially referred to as a perfect round. This score has never been achieved in competition.
The number used when a player is defeated 3 games in a row in racquetball.
In other fields
54 is also:
+54 The code for international direct dial phone calls to Argentina
A broadcast television channel number
54, a 1998 film about Studio 54 starring Ryan Phillippe, Mike Myers, and Salma Hayek
54, a novel by the Wu Ming collective of authors
In the title of a 1960s television show |
https://en.wikipedia.org/wiki/55%20%28number%29 | 55 (fifty-five) is the natural number following 54 and preceding 56.
Mathematics
55 is
the fifteenth discrete semiprime () and the second with 5 as the lowest non-unitary factor thus of the form (5.q), where q is a higher prime.
with an aliquot sum of 17; a prime, within an aliquot sequence of one composite number (55, 17, 1,0) to the Prime 17 in the 17-aliquot tree.
a triangular number (the sum of the consecutive numbers 1 to 10), and a doubly triangular number.
the 10th Fibonacci number. It is the largest Fibonacci number to also be a triangular number.
a square pyramidal number (the sum of the squares of the integers 1 to 5) as well as a heptagonal number, and a centered nonagonal number.
in base 10, a Kaprekar number.
the product of 5 and 11, 5 being the prime index of 11.
the first number to be a sum of more than one pair of numbers which mirror each other (23 + 32 and 14 + 41).
Science
The atomic number of caesium.
Astronomy
Messier object M55, a magnitude 7.0 globular cluster in the constellation Sagittarius
The New General Catalogue object NGC 55, a magnitude 7.9 barred spiral galaxy in the constellation Sculptor
Music
The name of a song by Kasabian. The song was released as a B side to Club Foot and was recorded live when the band performed at London's Brixton Academy.
"55", a song by Mac Miller
"I Can't Drive 55", a song by Sammy Hagar
"Ol' '55", a song by Tom Waits
Ol' 55 (band), an Australian rock band.
Primer 55 an American band
Station 55, an album released in 2005 by Cristian Vogel
55 Cadillac, an album by Andrew W.K.
Transportation
In the United States, the National Maximum Speed Law prohibited speed limits higher than from 1974 to 1987
Film
55 Days at Peking a film starring Charlton Heston and David Niven
Years
AD 55
55 BC
1755
1855
1955
Other uses
Gazeta 55, an Albanian newspaper
Agitation and Propaganda against the State, also known as Constitution law 55, a law during Communist Albania.
The code for internati |
https://en.wikipedia.org/wiki/56%20%28number%29 | 56 (fifty-six) is the natural number following 55 and preceding 57.
Mathematics
56 is:
The sum of the first six triangular numbers (making it a tetrahedral number).
The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter.
The sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17)
a tetranacci number and as a multiple of 7 and 8, a pronic number. Interestingly it is one of a few pronic numbers whose digits in decimal also are successive (5 and 6).
a refactorable number, since 8 is one of its 8 divisors.
The sum of the sums of the divisors of the first 8 positive integers.
A semiperfect number, since 56 is twice a perfect number.
A partition number – the number of distinct ways 11 can be represented as the sum of natural numbers.
An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member.
The only known number n such that , where φ(m) is Euler's totient function and σ(n) is the sum of the divisor function, see .
The maximum determinant in an 8 by 8 matrix of zeroes and ones.
The number of polygons formed by connecting all the 8 points on the perimeter of a two-times-two-square by straight lines.
Plutarch states that the Pythagoreans associated a polygon of 56 sides with Typhon and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using a compass and straightedge, a close approximation has recently been discovered which it is claimed might have been used at Stonehenge, and it is constructible if the use of an angle trisector is allowed since 56 = 23 × 7.
Science, technology, and biology
The atomic number of barium.
In humans, olfactory receptors are categorized in 56 families.
The maximum speed of analog data transmission over a POTS in the 20th century was 56 kbit/s.
|
https://en.wikipedia.org/wiki/57%20%28number%29 | 57 (fifty-seven) is the natural number following 56 and preceding 58.
In mathematics
Fifty-seven is the sixteenth discrete semiprime (specifically, the sixth distinct semiprime of the form , where is a higher prime). It also forms the fourth discrete semiprime pair with 58.
57 is the third Blum integer since its two prime factors (3 and 19) are both Gaussian primes. 57 has an aliquot sum of 23, which makes it the tenth number to contain a prime aliquot sum. This also makes 57 the first composite member of the 23-aliquot tree (..., 57, 23, 1, 0). The only other numbers to generate an aliquot sum of 57 are 99, 159, 343, 559, and 703; where 343 is the cube of 7, and 703 the sum of the first thirty-seven nonzero integers. Fifty seven is also a repdigit in base-7 (111).
57 is the fifth Leyland number, as it can be written in the form:
57 is the number of compositions of 10 into distinct parts.
57 is the seventh fine number, equivalently the number of ordered rooted trees with seven nodes having root of even degree.
57 is also the number of nodes in a regular octagon when all of its diagonals are drawn, and the first non-trivial icosagonal (20-gonal) number.
In geometry, there are:
57 non-prismatic uniform star polyhedra in 3-space, including four Kepler-Poinsot star polyhedra that are regular.
57 vertices and hemi-dodecahedral facets in the 57-cell, a 4-dimensional abstract regular polytope.
57 uniform prismatic 5-polytopes in the fifth dimension based on four different finite prismatic families, and inclusive of one special non-Wythoffian figure: the grand antiprism prism.
57 uniform prismatic 6-polytopes in the sixth dimension, as prisms of all non-prismatic uniform 5-polytopes.
The split Lie algebra E has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional.
57 lies between prime numbers 53 and 61, which are the only two prime numbers less than 71 that do not divide the order of |
https://en.wikipedia.org/wiki/58%20%28number%29 | 58 (fifty-eight) is the natural number following 57 and preceding 59.
In mathematics
Fifty-eight is the 17th discrete semiprime and the 9th with 2 as the lowest non-unitary factor; thus of the form (2.q), where q is a higher prime.
Fifty-eight is the first member of a cluster of two semiprimes (57, 58), the next such cluster is (118, 119).
Fifty-eight has an aliquot sum of 32 within an aliquot sequence of two composite numbers (58, 32, 13, 1, 0) in the 13-aliquot tree.
Fifty-eight is an 11-gonal number, after 30 (and 11). It is also a Smith number,
and given 58, the Mertens function returns zero.
58 is the smallest integer whose square root has a continued fraction with period 7.
58 is equal to the sum of the first seven consecutive prime numbers: This is a difference of 1 from the 17th prime number and 7th super-prime, 59.
There is no solution to the equation x – φ(x) = 58, making 58 a noncototient. However, the sum of the totient function for the first thirteen integers is 58.
The regular icosahedron produces 58 distinct stellations, the most of any other Platonic solid, which collectively produce 62 stellations.
Coxeter groups
With regard to Coxeter groups and uniform polytopes in higher dimensional spaces, there are:
58 distinct uniform polytopes in the fifth dimension that are generated from symmetries of three Coxeter groups, they are the A5 simplex group, B5 cubic group, and the D5 demihypercubic group;
58 fundamental Coxeter groups that generate uniform polytopes in the seventh dimension, with only four of these generating uniform non-prismatic figures.
There exist 58 total paracompact Coxeter groups of ranks four through ten, with realizations in dimensions three through nine. These solutions all contain infinite facets and vertex figures, in contrast from compact hyperbolic groups that contain finite elements; there are no other such groups with higher or lower ranks.
In science
The atomic number of cerium, a lanthanide.
Astronomy
Messier |
https://en.wikipedia.org/wiki/59%20%28number%29 | 59 (fifty-nine) is the natural number following 58 and preceding 60.
In mathematics
Fifty-nine is the 17th prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary part and real part of the form . Since is divisible by 59 but 59 is not one more than a multiple of 15, 59 is a Pillai prime.
It is also a highly cototient number.
There are 59 stellations of the regular icosahedron, inclusive of the icosahedron.
59 is one of the factors that divides the smallest composite Euclid number. In this case 59 divides the Euclid number 13# + 1 = 2 × 3 × 5 × 7 × 11 × 13 + 1 = 59 × 509 = 30031.
59 is the highest integer a single symbol may represent in the Sexagesimal system.
As 17 is prime, 59 is a super-prime.
The number 59 takes 3 iterations of the "reverse and add" process to form the palindrome 1111. All smaller integers (1 through 58) take either one or two iterations to form a palindrome through this process.
In science
The atomic number of praseodymium, a lanthanide.
Astronomy
Messier object M59, a magnitude 11.5 galaxy in the constellation Virgo.
The New General Catalogue object NGC 59, a magnitude 12.4 spiral galaxy in the constellation Cetus.
In music
Beethoven's Opus 59 consists of the three so-called Razumovsky Quartets
59, an album by Puffy AmiYumi
The 1960s song "The 59th Street Bridge Song (Feelin' Groovy)" was popularized by Simon & Garfunkel and Harpers Bizarre
The '59 Sound, an album by The Gaslight Anthem; includes the song of the same name
The album 14:59 by Sugar Ray
"11:59", a song by Blondie from Parallel Lines
.59 is a song by from beatmania IIDX 2nd Style and Dance Dance Revolution 4thMIX
'59 is the sixth track on the album Ignition! by Brian Setzer
59 is an area code of Andheri, Mumbai. Used by Vivian Divine in various songs with Gully Gang.
In sports
Satchel Paige became the oldest Major League B |
https://en.wikipedia.org/wiki/Logical%20effort | The method of logical effort, a term coined by Ivan Sutherland and Bob Sproull in 1991, is a straightforward technique used to estimate delay in a CMOS circuit. Used properly, it can aid in selection of gates for a given function (including the number of stages necessary) and sizing gates to achieve the minimum delay possible for a circuit.
Derivation of delay in a logic gate
Delay is expressed in terms of a basic delay unit, τ = 3RC, the delay of an inverter driving an identical inverter without any additional capacitance added by interconnects or other loads; the unitless number associated with this is known as the normalized delay.
(Some authors prefer define the basic delay unit as the fanout of 4 delay—the delay of one inverter driving 4 identical inverters).
The absolute delay is then simply defined as the product of the normalized delay of the gate, d, and τ:
In a typical 600-nm process τ is about 50 ps. For a 250-nm process, τ is about 20 ps. In modern 45 nm processes the delay is approximately 4 to 5 ps.
The normalized delay in a logic gate can be expressed as a summation of two primary terms: normalized parasitic delay, p (which is an intrinsic delay of the gate and can be found by considering the gate driving no load), and stage effort, f (which is dependent on the load as described below). Consequently,
The stage effort is divided into two components: a logical effort, g, which is the ratio of the input capacitance of a given gate to that of an inverter capable of delivering the same output current (and hence is a constant for a particular class of gate and can be described as capturing the intrinsic properties of the gate), and an electrical effort, h, which is the ratio of the input capacitance of the load to that of the gate. Note that "logical effort" does not take the load into account and hence we have the term "electrical effort" which takes the load into account. The stage effort is then simply:
Combining these equations yields a basic equa |
https://en.wikipedia.org/wiki/Electric%20Sheep | Electric Sheep is a volunteer computing project for animating and evolving fractal flames, which are in turn distributed to the networked computers, which display them as a screensaver.
Process
The process is transparent to the casual user, who can simply install the software as a screensaver. Alternatively, the user may become more involved with the project, manually creating a fractal flame file for upload to the server where it is rendered into a video file of the animated fractal flame. As the screensaver entertains the user, their computer is also used for rendering commercial projects, sales of which keep the servers and developers running.
There are about 500,000 active users (monthly uniques).
According to Mitchell Whitelaw in his Metacreation: Art and Artificial Life, "On the screen they are luminous, twisting, elastic shapes, abstract tangles and loops of glowing filaments."
The name "Electric Sheep" is taken from the title of Philip K. Dick's novel Do Androids Dream of Electric Sheep?. The title mirrors the nature of the project: computers (androids) who have started running the screensaver begin rendering (dreaming) the fractal movies (sheep).
The sheep motif is carried over into other aspects of the project: the 100 or so sheep stored on the server at any time is referred to as 'the flock'; creating a new fractal by interpolating or combining the sheep's fractal code with that of another sheep is called mating/breeding; changes to the code are called mutations, etc.
The parameters that generate these movies (sheep) can be created in a few ways: they can be created and submitted by members of the electricsheep mailing list, members of the mailing list can download the parameters of existing sheep and tweak them, or sheep can be mated together automatically by the server or manually by server admins (nicknamed shepherds).
Users may vote on sheep that they like or dislike, and this voting is used for the genetic algorithm which generates new shee |
https://en.wikipedia.org/wiki/List%20of%20interface%20bit%20rates | This is a list of interface bit rates, is a measure of information transfer rates, or digital bandwidth capacity, at which digital interfaces in a computer or network can communicate over various kinds of buses and channels. The distinction can be arbitrary between a computer bus, often closer in space, and larger telecommunications networks. Many device interfaces or protocols (e.g., SATA, USB, SAS, PCIe) are used both inside many-device boxes, such as a PC, and one-device-boxes, such as a hard drive enclosure. Accordingly, this page lists both the internal ribbon and external communications cable standards together in one sortable table.
Factors limiting actual performance, criteria for real decisions
Most of the listed rates are theoretical maximum throughput measures; in practice, the actual effective throughput is almost inevitably lower in proportion to the load from other devices (network/bus contention), physical or temporal distances, and other overhead in data link layer protocols etc. The maximum goodput (for example, the file transfer rate) may be even lower due to higher layer protocol overhead and data packet retransmissions caused by line noise or interference such as crosstalk, or lost packets in congested intermediate network nodes. All protocols lose something, and the more robust ones that deal resiliently with very many failure situations tend to lose more maximum throughput to get higher total long term rates.
Device interfaces where one bus transfers data via another will be limited to the throughput of the slowest interface, at best. For instance, SATA revision 3.0 (6 Gbit/s) controllers on one PCI Express 2.0 (5 Gbit/s) channel will be limited to the 5 Gbit/s rate and have to employ more channels to get around this problem. Early implementations of new protocols very often have this kind of problem. The physical phenomena on which the device relies (such as spinning platters in a hard drive) will also impose limits; for instance, no spin |
https://en.wikipedia.org/wiki/Yamaha%20DSP-1 | The Yamaha DSP-1 is a processor of early home theater surround sound equipment, produced in 1985. The DSP-1 (referred to by Yamaha as a Digital Soundfield Processor) allowed owners to synthesize up to 6-channels of surround sound from 2 channel stereo sound via a complex digital signal processor (DSP). Much like today's home theater receivers the DSP-1 offered sixteen "sound fields" created through the DSP including a jazz club, a cathedral, a concert hall, and a stadium. However, unlike today's integrated amps and receivers, these soundfield modes were highly editable, allowing the owner to customize the effect to his or her own personal taste. The DSP-1 also included an analog Dolby Surround decoder as well as other effects such as real-time echo and pitch change.
Most of the DSP-1's controls are on the unit's remote control. The reason, as mentioned in the manual, being that it was felt that adjustments should be done at the listening position. This can make it difficult for collectors to find a complete functioning unit, although there is at least one provider of aftermarket remote controls with duplicate programming for the DSP-1 if needed. In Dolby Surround mode, only 4 channels are active, with just the front main channels and rear surround channels operating, the forward surround channels being muted.
Yamaha has kept the DSP prefix for many of its home DSP and audio amp/receiver products.
See also
AMD TrueAudio
E-mu 20K
External links
Yamaha
Yamaha DSP Demo from late 1980s
Yamaha DSP Demo from early 1990s
Alternate Yamaha DSP Demo from early 1990s
DSP-1
Audio electronics |
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