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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 i... |
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... |
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 ... |
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... |
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 pri... |
https://en.wikipedia.org/wiki/Gymnasium%20Jur%20Hronec | Gymnázium Jura Hronca (GJH) is a gymnasium (grammar school) located in Bratislava, Slovakia.
The school has a focus on the study of natural sciences, mathematics, and computer sciences. However its affiliation with the International Baccalaureate, an active bi-lingual (English – Slovak) programme and the option to stu... |
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... |
https://en.wikipedia.org/wiki/Linear%20algebraic%20group | In mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation where is the transpose of .
Many Lie groups can be viewed as linear algebraic groups over the... |
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 .
Makin... |
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 algebra... |
https://en.wikipedia.org/wiki/Iwasawa%20theory | In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to a... |
https://en.wikipedia.org/wiki/Oblique | Oblique may refer to:
an alternative name for the character usually called a slash (punctuation) ( / )
Oblique angle, in geometry
Oblique triangle, in geometry
Oblique lattice, in geometry
Oblique leaf base, a characteristic shape of the base of a leaf
Oblique angle, a synonym for Dutch angle, a cinematographic techn... |
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, whi... |
https://en.wikipedia.org/wiki/Solvable | In mathematics, solvable may refer to:
Solvable group, a group that can be constructed by compositions of abelian groups, or equivalently a group whose derived series reaches the trivial group in finitely many steps
Solvable extension, a field extension whose Galois group is a solvable group
Solvable equation, a polyno... |
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 ... |
https://en.wikipedia.org/wiki/Descriptive%20set%20theory | In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the ... |
https://en.wikipedia.org/wiki/Polish%20space | In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicia... |
https://en.wikipedia.org/wiki/Ben%20Roy%20Mottelson | Ben Roy Mottelson (9 July 1926 – 13 May 2022) was an American-Danish nuclear physicist. He won the 1975 Nobel Prize in Physics for his work on the non-spherical geometry of atomic nuclei.
Early life
Mottelson was born in Chicago, Illinois, on 9 July 1926, the son of Georgia (Blum) and Goodman Mottelson, an engineer. H... |
https://en.wikipedia.org/wiki/Sheldon%20Glashow | Sheldon Lee Glashow (, ; born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, emeritus, at Harvard University, and is a member of the board of sponsors for the Bulletin of the ... |
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 'd... |
https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Artin%20theorem | In algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that an (Artinian) semisimple ring R is isomorphic to a product of finitely many -by- matrix rings over division rings , for some integers , both of which are uniquely determined up to ... |
https://en.wikipedia.org/wiki/Normalizing%20constant | In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one.
For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes'... |
https://en.wikipedia.org/wiki/Option%20time%20value | In finance, the time value (TV) (extrinsic or instrumental value) of an option is the premium a rational investor would pay over its current exercise value (intrinsic value), based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market,... |
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 l... |
https://en.wikipedia.org/wiki/Projective%20line | In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity. The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exa... |
https://en.wikipedia.org/wiki/Georges%20de%20Rham | Georges de Rham (; 10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology.
Biography
Georges de Rham was born on 10 September 1903 in Roche, a small village in the canton of Vaud in Switzerland. He was the fifth born of the six children in the family of Léon... |
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 transitio... |
https://en.wikipedia.org/wiki/Lebesgue%20covering%20dimension | In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a
topologically invariant way.
Informal discussion
For ordinary Euclidean spaces, the Lebesgue covering dimension is just the ordinary Euclidean dim... |
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... |
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 fo... |
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... |
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) t... |
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 numbe... |
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).
... |
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 matt... |
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.
... |
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 pro... |
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 po... |
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 ... |
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 +... |
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 t... |
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... |
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 o... |
https://en.wikipedia.org/wiki/Dividing%20a%20circle%20into%20areas | In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method. The greatest possible number of regions, , giving th... |
https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell%20theorem | In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria.
The Rao–Blackwell ... |
https://en.wikipedia.org/wiki/Dirichlet%20L-function | In mathematics, a Dirichlet L-series is a function of the form
where is a Dirichlet character and s a complex variable with real part greater than 1. It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane, and is then called a Diri... |
https://en.wikipedia.org/wiki/Additive%20Schwarz%20method | In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.
Overview
Partial differential equations (PDEs) are used in all sciences t... |
https://en.wikipedia.org/wiki/Gr%C3%BCnwald%E2%80%93Letnikov%20derivative | In mathematics, the Grünwald–Letnikov derivative is a basic extension of the derivative in fractional calculus that allows one to take the derivative a non-integer number of times. It was introduced by Anton Karl Grünwald (1838–1920) from Prague, in 1867, and by Aleksey Vasilievich Letnikov (1837–1888) in Moscow in 186... |
https://en.wikipedia.org/wiki/Shadow%20volume | Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene. They were first proposed by Frank Crow in 1977 as the geometry describing the 3D shape of the region occluded from a light source. A shadow volume divides the virtual world in two: areas that are in shadow and areas that are n... |
https://en.wikipedia.org/wiki/Cross-ratio | In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points , , , on a line, their cross ratio is defined as
where an orientation of the line determines the sign of each dis... |
https://en.wikipedia.org/wiki/Linear%20fractional%20transformation | In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form
The precise definition depends on the nature of , and . In other words, a linear fractional transformation is a transformation that is represented by a fraction whose numerator and denominator are linear... |
https://en.wikipedia.org/wiki/Monopole | Monopole may refer to:
Magnetic monopole, or Dirac monopole, a hypothetical particle that may be loosely described as a magnet with only one pole
Monopole (mathematics), a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle
Monopole, the first term in a multipole e... |
https://en.wikipedia.org/wiki/Ray%20Solomonoff | Ray Solomonoff (July 25, 1926 – December 7, 2009) was the inventor of algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder of algorithmic information theory. He was an originator of the branch of artificial intelligence based on machine lear... |
https://en.wikipedia.org/wiki/Algorithmic%20probability | In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s.
It is used in inductive inference theory and analyses of algorithms. In his general theory... |
https://en.wikipedia.org/wiki/List%20of%20equations | This is a list of equations, by Wikipedia page under appropriate bands of their field.
Eponymous equations
The following equations are named after researchers who discovered them.
Mathematics
Cauchy–Riemann equations
Chapman–Kolmogorov equation
Maurer–Cartan equation
Pell's equation
Poisson's equation
Riccati... |
https://en.wikipedia.org/wiki/Point%20at%20infinity | In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be... |
https://en.wikipedia.org/wiki/Line%20at%20infinity | In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line.
Geometric formulation
In proj... |
https://en.wikipedia.org/wiki/Plane%20at%20infinity | In projective geometry, a plane at infinity is the hyperplane at infinity of a three dimensional projective space or to any plane contained in the hyperplane at infinity of any projective space of higher dimension. This article will be concerned solely with the three-dimensional case.
Definition
There are two approach... |
https://en.wikipedia.org/wiki/Suzuki%20sporadic%20group | In the area of modern algebra known as group theory, the Suzuki group Suz or Sz is a sporadic simple group of order
213 · 37 · 52 · 7 · 11 · 13 = 448345497600 ≈ 4.
History
Suz is one of the 26 Sporadic groups and was discovered by as a rank 3 permutation group on 1782 points with point stabilizer G2(4). It is not ... |
https://en.wikipedia.org/wiki/Higman%E2%80%93Sims%20group | In the area of modern algebra known as group theory, the Higman–Sims group HS is a sporadic simple group of order
29⋅32⋅53⋅7⋅11 = 44352000
≈ 4.
The Schur multiplier has order 2, the outer automorphism group has order 2, and the group 2.HS.2 appears as an involution centralizer in the Harada–Norton group.
History
... |
https://en.wikipedia.org/wiki/McLaughlin%20group | McLaughlin group may refer to:
McLaughlin group (mathematics), a sporadic finite simple group
The McLaughlin Group, a weekly public affairs program broadcast in the United States |
https://en.wikipedia.org/wiki/61%20%28number%29 | 61 (sixty-one) is the natural number following 60 and preceding 62.
In mathematics
61 is the 18th prime number, and a twin prime with 59. It is the sum of two consecutive squares, It is also a centered decagonal number, a centered hexagonal number, and a centered square number.
61 is the fourth cuban prime of the fo... |
https://en.wikipedia.org/wiki/62%20%28number%29 | 62 (sixty-two) is the natural number following 61 and preceding 63.
In mathematics
62 is:
the eighteenth discrete semiprime () and tenth of the form (2.q), where q is a higher prime.
with an aliquot sum of 34; itself a semiprime, within an aliquot sequence of seven composite numbers (62,34,20,22,14,10,8,7,1,0) t... |
https://en.wikipedia.org/wiki/63%20%28number%29 | 63 (sixty-three) is the natural number following 62 and preceding 64.
Mathematics
63 is the sum of the first six powers of 2 (20 + 21 + ... 25). It is the eighth highly cototient number, and the fourth centered octahedral number; after 7 and 25. For five unlabeled elements, there are 63 posets.
Sixty-three is the se... |
https://en.wikipedia.org/wiki/64%20%28number%29 | 64 (sixty-four) is the natural number following 63 and preceding 65.
In mathematics
Sixty-four is the square of 8, the cube of 4, and the sixth-power of 2. It is the smallest number with exactly seven divisors. 64 is the first non-unitary sixth-power prime of the form p6 where p is a prime number.
The aliquot sum of ... |
https://en.wikipedia.org/wiki/65%20%28number%29 | 65 (sixty-five) is the natural number following 64 and preceding 66.
In mathematics
65 is the nineteenth distinct semiprime, (5.13); and the third of the form (5.q), where q is a higher prime.
65 has a prime aliquot sum of 19 within an aliquot sequence of one composite numbers (65,19,1,0) to the prime; as the fir... |
https://en.wikipedia.org/wiki/66%20%28number%29 | 66 (sixty-six) is the natural number following 65 and preceding 67.
Usages of this number include:
In mathematics
66 is:
a sphenic number.
a triangular number.
a hexagonal number.
a semi-meandric number.
a semiperfect number, being a multiple of a perfect number.
an Erdős–Woods number, since it is possible to find s... |
https://en.wikipedia.org/wiki/67%20%28number%29 | 67 (sixty-seven) is the natural number following 66 and preceding 68. It is an odd number.
In mathematics
67 is:
the 19th prime number (the next is 71).
a Chen prime.
an irregular prime.
a lucky prime.
the sum of five consecutive primes (7 + 11 + 13 + 17 + 19).
a Heegner number.
a Pillai prime since 18! + 1 is divis... |
https://en.wikipedia.org/wiki/68%20%28number%29 | 68 (sixty-eight) is the natural number following 67 and preceding 69. It is an even number.
In mathematics
68 is a composite number; a square-prime, of the form (p2, q) where q is a higher prime. It is the eighth of this form and the sixth of the form (22.q).
68 is a Perrin number.
It has an aliquot sum of 58 withi... |
https://en.wikipedia.org/wiki/Algebraic%20equation | In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers.
For example, is an algebraic equation with integer coefficients and
is a multivariate polynomial equation over the rationals.
For... |
https://en.wikipedia.org/wiki/List%20of%20mathematics-based%20methods | This is a list of mathematics-based methods.
Adams' method (differential equations)
Akra–Bazzi method (asymptotic analysis)
Bisection method (root finding)
Brent's method (root finding)
Condorcet method (voting systems)
Coombs' method (voting systems)
Copeland's method (voting systems)
Crank–Nicolson method (numerical... |
https://en.wikipedia.org/wiki/Circular%20segment | In geometry, a circular segment (symbol: ⌓), also known as a disk segment, is a region of a disk which is "cut off" from the rest of the disk by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by a circular arc (of less than π radians by convention) and by the... |
https://en.wikipedia.org/wiki/Brauer%20group | In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer.
The Brauer group arose out of attempts to classify division algebras... |
https://en.wikipedia.org/wiki/Central%20simple%20algebra | In ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A which is simple, and for which the center is exactly K. (Note that not every simple algebra is a central simple algebra over its center: for instance, if K is a field of characte... |
https://en.wikipedia.org/wiki/Piecewise | In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather tha... |
https://en.wikipedia.org/wiki/Closed%20and%20exact%20differential%20forms | In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d, and a closed form is ... |
https://en.wikipedia.org/wiki/Normal%20function | In axiomatic set theory, a function f : Ord → Ord is called normal (or a normal function) if and only if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions:
For every limit ordinal γ (i.e. γ is neither zero nor a successor), ... |
https://en.wikipedia.org/wiki/Fixed-point%20lemma%20for%20normal%20functions | The fixed-point lemma for normal functions is a basic result in axiomatic set theory stating that any normal function has arbitrarily large fixed points (Levy 1979: p. 117). It was first proved by Oswald Veblen in 1908.
Background and formal statement
A normal function is a class function from the class Ord of ordin... |
https://en.wikipedia.org/wiki/Alternating | Alternating may refer to:
Mathematics
Alternating algebra, an algebra in which odd-grade elements square to zero
Alternating form, a function formula in algebra
Alternating group, the group of even permutations of a finite set
Alternating knot, a knot or link diagram for which the crossings alternate under, over,... |
https://en.wikipedia.org/wiki/Bayesian%20statistics | Bayesian statistics ( or ) is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs ab... |
https://en.wikipedia.org/wiki/Finitary | In mathematics and logic, an operation is finitary if it has finite arity, i.e. if it has a finite number of input values. Similarly, an infinitary operation is one with an infinite number of input values.
In standard mathematics, an operation is finitary by definition. Therefore these terms are usually only used in... |
https://en.wikipedia.org/wiki/Trefoil%20knot | In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.
The trefoi... |
https://en.wikipedia.org/wiki/New%20Math | New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s1970s.
Overview
In 1957, the U.S. National Science Foundation funded the development of several new curricula in the... |
https://en.wikipedia.org/wiki/Italian%20National%20Institute%20of%20Statistics | The Italian National Institute of Statistics (; Istat) is the primary source of official statistics in Italy. The institute conducts a variety of activities, including the census of population, economic censuses, and numerous social, economic, and environmental surveys and analyses. Istat is the largest producer of sta... |
https://en.wikipedia.org/wiki/Almost%20periodic%20function | In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Harald Bohr and later generalized by Vyacheslav Stepanov, Hermann Weyl and Abra... |
https://en.wikipedia.org/wiki/Solomonoff%27s%20theory%20of%20inductive%20inference | Solomonoff's theory of inductive inference is a mathematical theory of induction introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior pr... |
https://en.wikipedia.org/wiki/Exact%20differential | In multivariate calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system (hence is a multivariable function whose variab... |
https://en.wikipedia.org/wiki/Teacher%20in%20Space%20Project | The Teacher in Space Project (TISP) was a NASA program announced by Ronald Reagan in 1984 designed to inspire students, honor teachers, and spur interest in mathematics, science, and space exploration. The project would carry teachers into space as Payload Specialists (non-astronaut civilians), who would return to thei... |
https://en.wikipedia.org/wiki/Time%20series | In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and t... |
https://en.wikipedia.org/wiki/Clausen%20function | In mathematics, the Clausen function, introduced by , is a transcendental, special function of a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other forms. It is intimately connected with the polylogarithm, inverse tangent integral, polygamma func... |
https://en.wikipedia.org/wiki/Dawson%20function | In mathematics, the Dawson function or Dawson integral
(named after H. G. Dawson)
is the one-sided Fourier–Laplace sine transform of the Gaussian function.
Definition
The Dawson function is defined as either:
also denoted as or or alternatively
The Dawson function is the one-sided Fourier–Laplace sine transform ... |
https://en.wikipedia.org/wiki/Debye%20function | In mathematics, the family of Debye functions is defined by
The functions are named in honor of Peter Debye, who came across this function (with n = 3) in 1912 when he analytically computed the heat capacity of what is now called the Debye model.
Mathematical properties
Relation to other functions
The Debye functi... |
https://en.wikipedia.org/wiki/Legendre%20form | In mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the name elliptic integrals because the second kind gives the arc length of an ellipse of unit semi-major axis and eccentricity (the ellipse being defined parametr... |
https://en.wikipedia.org/wiki/Carlson%20symmetric%20form | In mathematics, the Carlson symmetric forms of elliptic integrals are a small canonical set of elliptic integrals to which all others may be reduced. They are a modern alternative to the Legendre forms. The Legendre forms may be expressed in terms of the Carlson forms and vice versa.
The Carlson elliptic integrals are... |
https://en.wikipedia.org/wiki/Complete%20Fermi%E2%80%93Dirac%20integral | In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is defined by
This equals
where is the polylogarithm.
Its derivative is
and this derivative relationship is used to define the Fermi-Dirac integral for nonpositive indices j. Differing notation for appear... |
https://en.wikipedia.org/wiki/Incomplete%20Fermi%E2%80%93Dirac%20integral | In mathematics, the incomplete Fermi–Dirac integral for an index j is given by
This is an alternate definition of the incomplete polylogarithm.
See also
Complete Fermi–Dirac integral
External links
GNU Scientific Library - Reference Manual
Special functions |
https://en.wikipedia.org/wiki/Polygamma%20function | In mathematics, the polygamma function of order is a meromorphic function on the complex numbers defined as the th derivative of the logarithm of the gamma function:
Thus
holds where is the digamma function and is the gamma function. They are holomorphic on . At all the nonpositive integers these polygamma functi... |
https://en.wikipedia.org/wiki/Digamma%20function | In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function:
It is the first of the polygamma functions. This function is strictly increasing and strictly concave on , and it asymptotically behaves as
for large arguments () in the sector with some infinitesimally small positiv... |
https://en.wikipedia.org/wiki/Transport%20function | In mathematics and the field of transportation theory, the transport functions J(n,x) are defined by
Note that
See also
Incomplete gamma function
Special functions
Transportation theory |
https://en.wikipedia.org/wiki/Synchrotron%20function | In mathematics the synchrotron functions are defined as follows (for x ≥ 0):
First synchrotron function
Second synchrotron function
where Kj is the modified Bessel function of the second kind.
Use in astrophysics
In astrophysics, x is usually a ratio of frequencies, that is, the frequency over a critical freque... |
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