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Boas–Buck polynomials Summary Boas–Buck_polynomials In mathematics, Boas–Buck polynomials are sequences of polynomials Φ n ( r ) ( z ) {\displaystyle \Phi _{n}^{(r)}(z)} defined from analytic functions B {\displaystyle B} and C {\displaystyle C} by generating functions of the form C ( z t r B ( t ) ) = ∑ n ≥ 0 Φ n ( r ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner space Summary Bochner_space In mathematics, Bochner spaces are a generalization of the concept of L p {\displaystyle L^{p}} spaces to functions whose values lie in a Banach space which is not necessarily the space R {\displaystyle \mathbb {R} } or C {\displaystyle \mathbb {C} } of real or complex numbers. The s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner space Summary Bochner_space Almost all standard results on L p {\displaystyle L^{p}} spaces do hold on Bochner spaces too; in particular, the Bochner spaces L p ( X ) {\displaystyle L^{p}(X)} are Banach spaces for 1 ≤ p ≤ ∞ . {\displaystyle 1\leq p\leq \infty .} Bochner spaces are named for the mathematician Sa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner formula Summary Bochner_formula In mathematics, Bochner's formula is a statement relating harmonic functions on a Riemannian manifold ( M , g ) {\displaystyle (M,g)} to the Ricci curvature. The formula is named after the American mathematician Salomon Bochner. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner theorem Summary Bochner's_theorem In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier transform of a positive finite Borel measure on the real line. More generally in harmonic analysis, Bochner's theorem asserts that under Fourier transform a continuous positive-definite func... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner's tube theorem Summary Bochner's_tube_theorem In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in C n {\displaystyle \mathbb {C} ^{n}} can be extended to the convex hull of this domain. Theorem Let ω ⊂ R n {\displaystyle \omega \subset \ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Edge-of-the-wedge theorem Summary Edge-of-the-wedge_theorem In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bondy's theorem Summary Bondy's_theorem In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boole's rule Summary Boole's_rule In mathematics, Boole's rule, named after George Boole, is a method of numerical integration. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel summation Summary Borel_summability In mathematics, Borel summation is a summation method for divergent series, introduced by Émile Borel (1899). It is particularly useful for summing divergent asymptotic series, and in some sense gives the best possible sum for such series. There are several variations of this m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel's lemma Summary Borel's_lemma In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel–de Siebenthal theory Summary Borel–de_Siebenthal_theory In mathematics, Borel–de Siebenthal theory describes the closed connected subgroups of a compact Lie group that have maximal rank, i.e. contain a maximal torus. It is named after the Swiss mathematicians Armand Borel and Jean de Siebenthal who developed the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borwein's algorithm Summary Borwein's_algorithm In mathematics, Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/π. They devised several other algorithms. They published the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bour's minimal surface Summary Bour's_minimal_surface In mathematics, Bour's minimal surface is a two-dimensional minimal surface, embedded with self-crossings into three-dimensional Euclidean space. It is named after Edmond Bour, whose work on minimal surfaces won him the 1861 mathematics prize of the French Academy o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brandt matrix Summary Brandt_matrix In mathematics, Brandt matrices are matrices, introduced by Brandt (1943), that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra. Eichler (1955) calculated the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brandt matrix Summary Brandt_matrix Fix an integer m. Let ej denote the number of units in the right order of Ij and let Bij denote the number of α in Ij−1Ii with reduced norm N(α) equal to mN(Ii)/N(Ij). The Brandt matrix B(m) is the H×H matrix with entries Bij. Up to conjugation by a permutation matrix it is independe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brandt semigroup Summary Brandt_semigroup In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also inverse semigroups. They are built in the same way as completely 0-simple semigroups: Let G be a group and I , J {\displays... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brandt semigroup Summary Brandt_semigroup Define a matrix P {\displaystyle P} of dimension | I | × | J | {\displaystyle |I|\times |J|} with entries in G 0 = G ∪ { 0 } . {\displaystyle G^{0}=G\cup \{0\}.} Then, it can be shown that every 0-simple semigroup is of the form S = ( I × G 0 × J ) {\displaystyle S=(I\times G^{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brandt semigroup Summary Brandt_semigroup As Brandt semigroups are also inverse semigroups, the construction is more specialized and in fact, I = J (Howie 1995). Thus, a Brandt semigroup has the form S = ( I × G 0 × I ) {\displaystyle S=(I\times G^{0}\times I)} with the operation ( i , a , j ) ∗ ( k , b , n ) = ( i , a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brenke polynomials Summary Brenke_polynomials In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and Brenke–Chihara polynomials are the Brenke polynomials that are also orthogonal polynomials. Brenke (1945) introduced sequences of Brenke polynomials Pn, which are special cases of ge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brenke polynomials Summary Brenke_polynomials Brenke observed that Hermite polynomials and Laguerre polynomials are examples of Brenke polynomials, and asked if there are any other sequences of orthogonal polynomials of this form. Geronimus (1947) found some further examples of orthogonal Brenke polynomials. Chihara (1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brewer sum Summary Brewer_sum In mathematics, Brewer sums are finite character sum introduced by Brewer (1961, 1966) related to Jacobsthal sums. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bring's curve Summary Bring's_curve In mathematics, Bring's curve (also called Bring's surface and, by analogy with the Klein quartic, the Bring sextic) is the curve in P 4 {\displaystyle \mathbb {P} ^{4}} cut out by the homogeneous equations v + w + x + y + z = v 2 + w 2 + x 2 + y 2 + z 2 = v 3 + w 3 + x 3 + y 3 + z 3... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bring's curve Summary Bring's_curve {\displaystyle k=1,2,3.} The automorphism group of the curve is the symmetric group S5 of order 120, given by permutations of the 5 coordinates. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bring's curve Summary Bring's_curve This is the largest possible automorphism group of a genus 4 complex curve. The curve can be realized as a triple cover of the sphere branched in 12 points, and is the Riemann surface associated to the small stellated dodecahedron. It has genus 4. The full group of symmetries (includ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brown's representability theorem Summary Brown_representability In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brownian Motion Mathematics Brownian_diffusion > Mathematics In mathematics, Brownian motion is described by the Wiener process, a continuous-time stochastic process named in honor of Norbert Wiener. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brown–Peterson cohomology Summary Brown-Peterson_cohomology In mathematics, Brown–Peterson cohomology is a generalized cohomology theory introduced by Edgar H. Brown and Franklin P. Peterson (1966), depending on a choice of prime p. It is described in detail by Douglas Ravenel (2003, Chapter 4). Its representing spectr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Buchsbaum ring Summary Weak_sequence In mathematics, Buchsbaum rings are Noetherian local rings such that every system of parameters is a weak sequence. A sequence ( a 1 , ⋯ , a r ) {\displaystyle (a_{1},\cdots ,a_{r})} of the maximal ideal m {\displaystyle m} is called a weak sequence if m ⋅ ( ( a 1 , ⋯ , a i − 1 ): a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Budan's Theorem Summary Budan's_Theorem In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan de Boislaurent. A similar theorem was published independently by Joseph Fourier i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Burnside theorem Summary Burnside's_theorem In mathematics, Burnside's theorem in group theory states that if G is a finite group of order p a q b {\displaystyle p^{a}q^{b}} where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence each non-Abelian finite simple group has order d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Busemann's theorem Summary Busemann's_theorem In mathematics, Busemann's theorem is a theorem in Euclidean geometry and geometric tomography. It was first proved by Herbert Busemann in 1949 and was motivated by his theory of area in Finsler spaces. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bäcklund transform Summary Bäcklund_transform In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential equations and their solutions. They are an important tool in soliton theory and integrable systems. A Bäcklund transfor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bäcklund transform Summary Bäcklund_transform A Bäcklund transform which relates solutions of the same equation is called an invariant Bäcklund transform or auto-Bäcklund transform. If such a transform can be found, much can be deduced about the solutions of the equation especially if the Bäcklund transform contains a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bézout's lemma Summary Bézout's_lemma In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout, is the following theorem: Here the greatest common divisor of 0 and 0 is taken to be 0. The integers x and y are called Bézout coefficients for (a, b); they are not unique. A pair of Bézout ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bézout's lemma Summary Bézout's_lemma As an example, the greatest common divisor of 15 and 69 is 3, and 3 can be written as a combination of 15 and 69 as 3 = 15 × (−9) + 69 × 2, with Bézout coefficients −9 and 2. Many other theorems in elementary number theory, such as Euclid's lemma or the Chinese remainder theorem, r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bôcher's theorem Summary Bôcher's_theorem In mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Capelli's identity Summary Capelli_identity In mathematics, Capelli's identity, named after Alfredo Capelli (1887), is an analogue of the formula det(AB) = det(A) det(B), for certain matrices with noncommuting entries, related to the representation theory of the Lie algebra g l n {\displaystyle {\mathfrak {gl}}_{n}} . ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carathéodory existence theorem Summary Carathéodory's_existence_theorem In mathematics, Carathéodory's existence theorem says that an ordinary differential equation has a solution under relatively mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carathéodory's theorem (conformal mapping) Summary Carathéodory's_theorem_(conformal_mapping) In mathematics, Carathéodory's theorem is a theorem in complex analysis, named after Constantin Carathéodory, which extends the Riemann mapping theorem. The theorem, first proved in 1913, states that any conformal mapping send... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleman linearization Summary Carleman_linearization In mathematics, Carleman linearization (or Carleman embedding) is a technique to transform a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system. It was introduced by the Swedish mathematician Torsten Carleman in 1932. Carleman l... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleman's equation Summary Carleman's_equation In mathematics, Carleman's equation is a Fredholm integral equation of the first kind with a logarithmic kernel. Its solution was first given by Torsten Carleman in 1922. The equation is ∫ a b ln | x − t | y ( t ) d t = f ( x ) {\displaystyle \int _{a}^{b}\ln |x-t|\,y(t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carmichael's totient function conjecture Summary Carmichael's_totient_function_conjecture In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number of integers less than and coprime to n. It states that, for every n there is at... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan criterion Summary Cartan's_criterion In mathematics, Cartan's criterion gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on g {\displaystyle {\mat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Theory of equivalence Summary Cartan's_equivalence_method In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Theory of equivalence Summary Cartan's_equivalence_method (His techniques were later developed more fully by many others, such as D. C. Spencer and Shiing-Shen Chern.) The equivalence method is an essentially algorithmic procedure for determining when two geometric structures are identical. For Cartan, the primary geom... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan's lemma Summary Cartan's_lemma In mathematics, Cartan's lemma refers to a number of results named after either Élie Cartan or his son Henri Cartan: In exterior algebra: Suppose that v1, ..., vp are linearly independent elements of a vector space V and w1, ..., wp are such that v 1 ∧ w 1 + ⋯ + v p ∧ w p = 0 {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan's theorems A and B Summary Cartan's_theorems_A_and_B In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan's theorems A and B Summary Cartan's_theorems_A_and_B The analogue of Theorem B in this context is as follows (Hartshorne 1977, Theorem III.3.7): These theorems have many important applications. For instance, they imply that a holomorphic function on a closed complex submanifold, Z, of a Stein manifold X can be e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartan's theorems A and B Summary Cartan's_theorems_A_and_B quasi-coherent sheaves F on a noetherian scheme X), then X is Stein (resp. affine); see (Serre 1956) (resp. (Serre 1957) and (Hartshorne 1977, Theorem III.3.7)). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cartier duality Summary Cartier_dual In mathematics, Cartier duality is an analogue of Pontryagin duality for commutative group schemes. It was introduced by Pierre Cartier (1962). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Casey's theorem Summary Casey's_theorem In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Castelnuovo's contraction theorem Summary Castelnuovo's_contraction_theorem In mathematics, Castelnuovo's contraction theorem is used in the classification theory of algebraic surfaces to construct the minimal model of a given smooth algebraic surface. More precisely, let X {\displaystyle X} be a smooth projective surf... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Catalan's constant Summary Catalan's_constant In mathematics, Catalan's constant G, is defined by G = β ( 2 ) = ∑ n = 0 ∞ ( − 1 ) n ( 2 n + 1 ) 2 = 1 1 2 − 1 3 2 + 1 5 2 − 1 7 2 + 1 9 2 − ⋯ , {\displaystyle G=\beta (2)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cauchy integral formula Summary Cauchy's_integral_formula In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cayley's Ω process Summary Cayley's_Ω_process In mathematics, Cayley's Ω process, introduced by Arthur Cayley (1846), is a relatively invariant differential operator on the general linear group, that is used to construct invariants of a group action. As a partial differential operator acting on functions of n2 variable... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Charlier polynomials Summary Charlier_polynomials In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier. They are given in terms of the generalized hypergeometric function by C n ( x ; μ ) = 2 F 0 ( − n , − x ; − ; − 1 / μ ) = ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Charlier polynomials Summary Charlier_polynomials They satisfy the orthogonality relation ∑ x = 0 ∞ μ x x ! C n ( x ; μ ) C m ( x ; μ ) = μ − n e μ n ! δ n m , μ > 0. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Charlier polynomials Summary Charlier_polynomials {\displaystyle \sum _{x=0}^{\infty }{\frac {\mu ^{x}}{x! }}C_{n}(x;\mu )C_{m}(x;\mu )=\mu ^{-n}e^{\mu }n!\delta _{nm},\quad \mu >0.} They form a Sheffer sequence related to the Poisson process, similar to how Hermite polynomials relate to the Brownian motion. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev distance Summary Maximum_metric In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev's sum inequality Summary Chebyshev's_sum_inequality In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if a 1 ≥ a 2 ≥ ⋯ ≥ a n {\displaystyle a_{1}\geq a_{2}\geq \cdots \geq a_{n}\quad } and b 1 ≥ b 2 ≥ ⋯ ≥ b n , {\displaystyle \quad b_{1}\geq b_{2}\geq \cdots \geq b_{n},} t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choi's theorem on completely positive maps Summary Choi's_theorem_on_completely_positive_maps In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. An infinite-dimensional algebraic generalization of Choi's theore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choquet theory Summary Choquet_theory In mathematics, Choquet theory, named after Gustave Choquet, is an area of functional analysis and convex analysis concerned with measures which have support on the extreme points of a convex set C. Roughly speaking, every vector of C should appear as a weighted average of extreme ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choquet theory Summary Choquet_theory The two ends of a line segment determine the points in between: in vector terms the segment from v to w consists of the λv + (1 − λ)w with 0 ≤ λ ≤ 1. The classical result of Hermann Minkowski says that in Euclidean space, a bounded, closed convex set C is the convex hull of its ext... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chow's theorem Summary Chow's_theorem In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow: Chow's theorem: The theorem that asserts that any analytic subvariety in projective space is actually algebraic. Chow–Rashevskii theorem: In sub-Riemannian geometry, the theorem that asserts tha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chrystal's equation Summary Chrystal's_equation In mathematics, Chrystal's equation is a first order nonlinear ordinary differential equation, named after the mathematician George Chrystal, who discussed the singular solution of this equation in 1896. The equation reads as ( d y d x ) 2 + A x d y d x + B y + C x 2 = 0 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Church numerals Summary Church_encoding In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Church numerals Summary Church_encoding Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clarke's generalized Jacobian Summary Clarke's_generalized_Jacobian In mathematics, Clarke's generalized Jacobian is a generalization of the Jacobian matrix of a smooth function to non-smooth functions. It was introduced by Clarke (1983). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clarkson's inequalities Summary Clarkson's_inequalities In mathematics, Clarkson's inequalities, named after James A. Clarkson, are results in the theory of Lp spaces. They give bounds for the Lp-norms of the sum and difference of two measurable functions in Lp in terms of the Lp-norms of those functions individually. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clausen's formula Summary Clausen's_formula In mathematics, Clausen's formula, found by Thomas Clausen (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states 2 F 1 2 = 3 F 2 {\displaystyle \;_{2}F_{1}\left^{2}=\;_{3}F_{2}\left} In particular it gives conditi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford theory Summary Clifford_theory In mathematics, Clifford theory, introduced by Alfred H. Clifford (1937), describes the relation between representations of a group and those of a normal subgroup. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Green's conjecture Summary Clifford's_theorem_on_special_divisors In mathematics, Clifford's theorem on special divisors is a result of William K. Clifford (1878) on algebraic curves, showing the constraints on special linear systems on a curve C. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohn's theorem Summary Cohn's_theorem In mathematics, Cohn's theorem states that a nth-degree self-inversive polynomial p ( z ) {\displaystyle p(z)} has as many roots in the open unit disk D = { z ∈ C: | z | < 1 } {\displaystyle D=\{z\in \mathbb {C} :|z|<1\}} as the reciprocal polynomial of its derivative. Cohn's theor... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohn's theorem Summary Cohn's_theorem The coefficients of self-inversive polynomials satisfy the relations. p k = ω p ¯ n − k , 0 ⩽ k ⩽ n . {\displaystyle p_{k}=\omega {\bar {p}}_{n-k},\qquad 0\leqslant k\leqslant n.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohn's theorem Summary Cohn's_theorem In the case where ω = 1 , {\displaystyle \omega =1,} a self-inversive polynomial becomes a complex-reciprocal polynomial (also known as a self-conjugate polynomial). If its coefficients are real then it becomes a real self-reciprocal polynomial. The formal derivative of p ( z ) {\d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cohn's theorem Summary Cohn's_theorem {\displaystyle q(z)=p'(z)=p_{1}+2p_{2}z+\cdots +np_{n}z^{n-1}.} Therefore, Cohn's theorem states that both p ( z ) {\displaystyle p(z)} and the polynomial q ∗ ( z ) = z n − 1 q ¯ n − 1 ( 1 / z ¯ ) = z n − 1 p ¯ ′ ( 1 / z ¯ ) = n p ¯ n + ( n − 1 ) p ¯ n − 1 z + ⋯ + p ¯ 1 z n − 1 {\d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Costa's minimal surface Summary Costa's_minimal_surface In mathematics, Costa's minimal surface, is an embedded minimal surface discovered in 1982 by the Brazilian mathematician Celso José da Costa. It is also a surface of finite topology, which means that it can be formed by puncturing a compact surface. Topologically... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Costa's minimal surface Summary Costa's_minimal_surface The Costa surface evolves from a torus, which is deformed until the planar end becomes catenoidal. Defining these surfaces on rectangular tori of arbitrary dimensions yields the Costa surface. Its discovery triggered research and discovery into several new surface... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coxeter matroid Summary Coxeter_matroid In mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond to the case when P is a maximal parabolic subgroup of a symmetric group W. They were introduced by Gelfand and Serga... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cramer's paradox Summary Cramer's_paradox In mathematics, Cramer's paradox or the Cramer–Euler paradox is the statement that the number of points of intersection of two higher-order curves in the plane can be greater than the number of arbitrary points that are usually needed to define one such curve. It is named after... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cramer's paradox Summary Cramer's_paradox It is the result of a naive understanding or a misapplication of two theorems: Bézout's theorem states that the number of points of intersection of two algebraic curves is equal to the product of their degrees, provided that certain necessary conditions are met. In particular, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cramer's paradox Summary Cramer's_paradox However, because these points belong to both curves, they do not define a unique curve of this degree. The resolution of the paradox is that the n ( n + 3 ) / 2 {\displaystyle n(n+3)/2} bound on the number of points needed to define a curve only applies to points in general pos... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cutler's bar notation Summary Cutler's_bar_notation In mathematics, Cutler's bar notation is a notation system for large numbers, introduced by Mark Cutler in 2004. The idea is based on iterated exponentiation in much the same way that exponentiation is iterated multiplication. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dihedral group of order 6 Summary Symmetric_group_of_degree_3 In mathematics, D3 (sometimes alternatively denoted by D6) is the dihedral group of degree 3 and order 6. It equals the symmetric group S3. It is also the smallest non-abelian group.This page illustrates many group concepts using this group as example. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Danzer's configuration Summary Danzer's_configuration In mathematics, Danzer's configuration is a self-dual configuration of 35 lines and 35 points, having 4 points on each line and 4 lines through each point. It is named after the German geometer Ludwig Danzer and was popularised by Branko Grünbaum. The Levi graph of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Danzer's configuration Summary Danzer's_configuration Every middle layer graph is Hamiltonian.Danzer's configuration DCD(4) is the fourth term of an infinite series of ( ( 2 n − 1 n ) n ) {\displaystyle ({\tbinom {2n-1}{n}}_{n})} configurations DCD(n), where DCD(1) is the trivial configuration (11), DCD(2) is the trila... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Darboux function Summary Darboux's_theorem_(analysis) In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interva... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
De Gua's theorem Summary De_Gua's_theorem In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-ang... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completion (order theory) Summary Completion_(order_theory) In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers int... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completion (order theory) Summary Completion_(order_theory) Otherwise, that cut defines a unique irrational number which, loosely speaking, fills the "gap" between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than or equal to the cut. An irrat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Completion (order theory) Summary Completion_(order_theory) See also completeness (order theory). It is straightforward to show that a Dedekind cut among the real numbers is uniquely defined by the corresponding cut among the rational numbers. Similarly, every cut of reals is identical to the cut produced by a specific... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dedekind sum Summary Dedekind_sum In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have subsequently been much studied in number theo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Degen's eight-square identity Summary Degen's_eight-square_identity In mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which is a sum of eight squares, is itself the sum of eight squares. Namely: First discovered by Carl Ferdinand Degen around 1818, the identity was indep... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Degen's eight-square identity Summary Degen's_eight-square_identity In algebraic terms the identity means that the norm of product of two octonions equals the product of their norms: ‖ a b ‖ = ‖ a ‖ ‖ b ‖ {\displaystyle \left\|ab\right\|=\left\|a\right\|\left\|b\right\|} . Similar statements are true for quaternions (E... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Degen's eight-square identity Summary Degen's_eight-square_identity However, in the 1960s, H. Zassenhaus, W. Eichhorn, and A. Pfister (independently) showed there can be a non-bilinear identity for 16 squares. Note that each quadrant reduces to a version of Euler's four-square identity: and similarly for the other thre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Degen's eight-square identity Summary Degen's_eight-square_identity The eight-square identity can be written in the form of a product of two inner products of 8-dimensional vectors, yielding again an inner product of 8-dimensional vectors: (a·a)(b·b) = (a×b)·(a×b). This defines the octonion multiplication rule a×b, whi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dehn's lemma Summary Dehn's_lemma In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear map of the disk which is an embedding and is identical to the original on the boundary ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Deligne cohomology Summary Deligne_cohomology In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold. It was introduced by Pierre Deligne in unpublished work in about 1972 as a cohomology theory for algebraic varieties that includes both ordinary cohomology and intermedia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Deligne–Lusztig theory Summary Deligne–Lusztig_theory In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by Pierre Deligne and George Lusztig (1976). Lusztig (1985) used these representations to fin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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