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Bernoulli polynomials Summary Bernoulli_polynomial In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bernoulli polynomials Summary Bernoulli_polynomial For the Bernoulli polynomials, the number of crossings of the x-axis in the unit interval does not go up with the degree. In the limit of large degree, they approach, when appropriately scaled, the sine and cosine functions. A similar set of polynomials, based on a gen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bernoulli scheme Summary Bernoulli_automorphism In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynam... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bernoulli scheme Summary Bernoulli_automorphism This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bernstein–Sato polynomial Summary Bernstein–Sato_polynomial In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by Joseph Bernstein (1971) and Mikio Sato and Takuro Shintani (1972, 1974), Sato (1990). It is also known as the b-function, the b-polynom... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bernstein–Zelevinsky classification Summary Bernstein–Zelevinsky_classification In mathematics, the Bernstein–Zelevinsky classification, introduced by Bernstein and Zelevinsky (1977) and Zelevinsky (1980), classifies the irreducible complex smooth representations of a general linear group over a local field in terms of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Berry–Robbins problem Summary Berry–Robbins_problem In mathematics, the Berry–Robbins problem asks whether there is a continuous map from configurations of n points in R3 to the flag manifold U(n)/Tn that is compatible with the action of the symmetric group on n points. It was posed by Berry and Robbins (1997) and solv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Besicovitch inequality Summary Besicovitch_inequality In mathematics, the Besicovitch inequality is a geometric inequality relating volume of a set and distances between certain subsets of its boundary. The inequality was first formulated by Abram Besicovitch.Consider the n-dimensional cube n {\displaystyle ^{n}} with... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Besicovitch inequality Summary Besicovitch_inequality The Besicovitch inequality asserts that The inequality can be generalized in the following way. Given an n-dimensional Riemannian manifold M with connected boundary and a smooth map f: M → n {\displaystyle f:M\rightarrow ^{n}} , such that the restriction of f to th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Besov space Summary Besov_space In mathematics, the Besov space (named after Oleg Vladimirovich Besov) B p , q s ( R ) {\displaystyle B_{p,q}^{s}(\mathbf {R} )} is a complete quasinormed space which is a Banach space when 1 ≤ p, q ≤ ∞. These spaces, as well as the similarly defined Triebel–Lizorkin spaces, serve to gen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel polynomials Summary Bessel_polynomials In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The definition favored by mathematicians is given by the series: 101 y n ( x ) = ∑ k = 0 n ( n + k ) ! ( n − k ) ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel polynomials Summary Bessel_polynomials k ! ( x 2 ) k . {\displaystyle y_{n}(x)=\sum _{k=0}^{n}{\frac {(n+k)!}{(n-k)!k! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel polynomials Summary Bessel_polynomials }}\,\left({\frac {x}{2}}\right)^{k}.} Another definition, favored by electrical engineers, is sometimes known as the reverse Bessel polynomials: 8: 15 θ n ( x ) = x n y n ( 1 / x ) = ∑ k = 0 n ( n + k ) ! ( n − k ) ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel polynomials Summary Bessel_polynomials k ! x n − k 2 k . {\displaystyle \theta _{n}(x)=x^{n}\,y_{n}(1/x)=\sum _{k=0}^{n}{\frac {(n+k)!}{(n-k)!k! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel polynomials Summary Bessel_polynomials }}\,{\frac {x^{n-k}}{2^{k}}}.} The coefficients of the second definition are the same as the first but in reverse order. For example, the third-degree Bessel polynomial is y 3 ( x ) = 15 x 3 + 15 x 2 + 6 x + 1 {\displaystyle y_{3}(x)=15x^{3}+15x^{2}+6x+1} while the third-de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel potential Summary Bessel_potential In mathematics, the Bessel potential is a potential (named after Friedrich Wilhelm Bessel) similar to the Riesz potential but with better decay properties at infinity. If s is a complex number with positive real part then the Bessel potential of order s is the operator ( I − Δ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bessel–Maitland function Summary Bessel–Maitland_function In mathematics, the Bessel–Maitland function, or Wright generalized Bessel function, is a generalization of the Bessel function, introduced by Edward Maitland Wright (1934). The word "Maitland" in the name of the function seems to be the result of confusing Edwa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Beurling–Lax theorem Summary Beurling–Lax_theorem In mathematics, the Beurling–Lax theorem is a theorem due to Beurling (1949) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space H 2 ( D , C ) {\displaystyle H^{2}(\mathbb {D} ,\mathbb {C} )} . It states that each such space is of the for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bhatia–Davis inequality Summary Bhatia–Davis_inequality In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ2 of any bounded probability distribution on the real line. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bianchi classification Summary Bianchi_classification In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized family of Lie algebras. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bing–Borsuk conjecture Summary Bing–Borsuk_conjecture In mathematics, the Bing–Borsuk conjecture states that every n {\displaystyle n} -dimensional homogeneous absolute neighborhood retract space is a topological manifold. The conjecture has been proved for dimensions 1 and 2, and it is known that the 3-dimensional ver... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Birch and Swinnerton-Dyer conjecture Summary BSD_conjecture In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely reco... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Birch and Swinnerton-Dyer conjecture Summary BSD_conjecture The modern formulation of the conjecture relates arithmetic data associated with an elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian gr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Birkhoff–Grothendieck theorem Summary Grothendieck_splitting_principle In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over C P 1 {\displaystyle \mathbb {CP} ^{1}} is a direct sum of holomorphic line ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Birman–Wenzl algebra Summary Birman–Wenzl_algebra In mathematics, the Birman–Murakami–Wenzl (BMW) algebra, introduced by Joan Birman and Hans Wenzl (1989) and Jun Murakami (1987), is a two-parameter family of algebras C n ( ℓ , m ) {\displaystyle \mathrm {C} _{n}(\ell ,m)} of dimension 1 ⋅ 3 ⋅ 5 ⋯ ( 2 n − 1 ) {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bishop-Gromov inequality Summary Bishop-Gromov_inequality In mathematics, the Bishop–Gromov inequality is a comparison theorem in Riemannian geometry, named after Richard L. Bishop and Mikhail Gromov. It is closely related to Myers' theorem, and is the key point in the proof of Gromov's compactness theorem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bishop–Phelps theorem Summary Bishop–Phelps_theorem In mathematics, the Bishop–Phelps theorem is a theorem about the topological properties of Banach spaces named after Errett Bishop and Robert Phelps, who published its proof in 1961. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bismut connection Summary Bismut_connection In mathematics, the Bismut connection ∇ {\displaystyle \nabla } is the unique connection on a complex Hermitian manifold that satisfies the following conditions, It preserves the metric ∇ g = 0 {\displaystyle \nabla g=0} It preserves the complex structure ∇ J = 0 {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bismut connection Summary Bismut_connection Further let ∇ {\displaystyle \nabla } be the Levi-Civita connection. Define first a tensor T {\displaystyle T} such that T ( Z , X , Y ) = − 1 2 ⟨ Z , J ( ∇ X J ) Y ⟩ {\displaystyle T(Z,X,Y)=-{\frac {1}{2}}\langle Z,J(\nabla _{X}J)Y\rangle } . This tensor is anti-symmetric in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bismut connection Summary Bismut_connection In concrete terms, the new connection is given by Γ β γ α − 1 2 J δ α ∇ β J γ δ {\displaystyle \Gamma _{\beta \gamma }^{\alpha }-{\frac {1}{2}}J_{~\delta }^{\alpha }\nabla _{\beta }J_{~\gamma }^{\delta }} with Γ β γ α {\displaystyle \Gamma _{\beta \gamma }^{\alpha }} being th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bismut connection Summary Bismut_connection Denote the anti-symmetrization as T ( Z , X , Y ) + cyc~in~ X , Y , Z = T ( Z , X , Y ) + S ( Z , X , Y ) {\displaystyle T(Z,X,Y)+{\textrm {cyc~in~}}X,Y,Z=T(Z,X,Y)+S(Z,X,Y)} , with S {\displaystyle S} given explicitly as S ( Z , X , Y ) = − 1 2 ⟨ X , J ( ∇ Y J ) Z ⟩ − 1 2 ⟨ Y... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bismut connection Summary Bismut_connection S ( Z , X , J Y ) + S ( J Z , X , Y ) = − 1 2 ⟨ J X , ( − ( ∇ J Y J ) Z − ( J ∇ Z J ) Y + ( J ∇ Y J ) Z + ( ∇ J Z J ) Y ) ⟩ = − 1 2 ⟨ J X , R e ( ( 1 − i J ) ) ⟩ . {\displaystyle {\begin{aligned}S(Z,X,JY)+S(JZ,X,Y)&=-{\frac {1}{2}}\langle JX,{\big (}-(\nabla _{JY}J)Z-(J\nabl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bloch group Summary Bloch_group In mathematics, the Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic geometry and algebraic K-theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Blumberg theorem Summary Blumberg_theorem In mathematics, the Blumberg theorem states that for any real function f: R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } there is a dense subset D {\displaystyle D} of R {\displaystyle \mathbb {R} } such that the restriction of f {\displaystyle f} to D {\displaystyle D} i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner integral Summary Bochner_integral In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner–Kodaira–Nakano identity Summary Bochner–Kodaira–Nakano_identity In mathematics, the Bochner–Kodaira–Nakano identity is an analogue of the Weitzenböck identity for hermitian manifolds, giving an expression for the antiholomorphic Laplacian of a vector bundle over a hermitian manifold in terms of its complex conj... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bochner–Martinelli formula Summary Bochner–Martinelli_formula In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced by Enzo Martinelli (1938) and Salomon Bochner (1943). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bockstein spectral sequence Summary Bockstein_spectral_sequence In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod p coefficients and the homology reduced mod p. It is named after Meyer Bockstein. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bogomolov conjecture Summary Bogomolov_conjecture In mathematics, the Bogomolov conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin-Mumford conjecture in arithmetic geometry. The conjecture was proved by Emmanuel Ullmo and Shou-Wu Zhang in 19... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bogomolov–Miyaoka–Yau inequality Summary Bogomolov–Miyaoka–Yau_inequality In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality c 1 2 ≤ 3 c 2 {\displaystyle c_{1}^{2}\leq 3c_{2}} between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bohr compactification Summary Bohr_compactification In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G. Its importance lies in the reduction of the theory of uniformly almost periodic functions on G to the theory of conti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bolza surface Summary Bolza_surface In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by Oskar Bolza (1887)), is a compact Riemann surface of genus 2 {\displaystyle 2} with the highest possible order of the conformal automorphism group in this genus, namely G L 2 ( 3 ) {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bolza surface Summary Bolza_surface The Bolza surface is the smooth completion of the affine curve. Of all genus 2 {\displaystyle 2} hyperbolic surfaces, the Bolza surface maximizes the length of the systole (Schmutz 1993). As a hyperelliptic Riemann surface, it arises as the ramified double cover of the Riemann sphere... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bombieri norm Summary Bombieri_norm In mathematics, the Bombieri norm, named after Enrico Bombieri, is a norm on homogeneous polynomials with coefficient in R {\displaystyle \mathbb {R} } or C {\displaystyle \mathbb {C} } (there is also a version for non homogeneous univariate polynomials). This norm has many remarkabl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bombieri–Vinogradov theorem Summary Bombieri–Vinogradov_theorem In mathematics, the Bombieri–Vinogradov theorem (sometimes simply called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averaged over a range of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bombieri–Vinogradov theorem Summary Bombieri–Vinogradov_theorem This result is a major application of the large sieve method, which developed rapidly in the early 1960s, from its beginnings in work of Yuri Linnik two decades earlier. Besides Bombieri, Klaus Roth was working in this area. In the late 1960s and early 197... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bony–Brezis theorem Summary Bony–Brezis_theorem In mathematics, the Bony–Brezis theorem, due to the French mathematicians Jean-Michel Bony and Haïm Brezis, gives necessary and sufficient conditions for a closed subset of a manifold to be invariant under the flow defined by a vector field, namely at each point of the cl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boole polynomials Summary Boole_polynomials In mathematics, the Boole polynomials sn(x) are polynomials given by the generating function ∑ s n ( x ) t n / n ! = ( 1 + t ) x 1 + ( 1 + t ) λ {\displaystyle \displaystyle \sum s_{n}(x)t^{n}/n!={\frac {(1+t)^{x}}{1+(1+t)^{\lambda }}}} (Roman 1984, 4.5), (Jordan 1939, sectio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean prime ideal theorem Summary Boolean_prime_ideal_theorem In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement for filters on sets is known as the ultrafilter lemma. Other theorems are obtained by considering differe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Boolean prime ideal theorem Summary Boolean_prime_ideal_theorem Although the various prime ideal theorems may appear simple and intuitive, they cannot be deduced in general from the axioms of Zermelo–Fraenkel set theory without the axiom of choice (abbreviated ZF). Instead, some of the statements turn out to be equival... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel fixed-point theorem Summary Borel_fixed-point_theorem In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie–Kolchin theorem. The result was proved by Armand Borel (1956). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borell–Brascamp–Lieb inequality Summary Borell–Brascamp–Lieb_inequality In mathematics, the Borell–Brascamp–Lieb inequality is an integral inequality due to many different mathematicians but named after Christer Borell, Herm Jan Brascamp and Elliott Lieb. The result was proved for p > 0 by Henstock and Macbeath in 1953... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borel–Carathéodory theorem Summary Borel–Carathéodory_theorem In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borromean rings Summary Borromean_rings In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the three is cut or removed. Most common... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borromean rings Summary Borromean_rings They have been used in Christian symbolism as a sign of the Trinity, and in modern commerce as the logo of Ballantine beer, giving them the alternative name Ballantine rings. Physical instances of the Borromean rings have been made from linked DNA or other molecules, and they hav... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borromean rings Summary Borromean_rings It is impossible to realize them using circles in three-dimensional space, but it has been conjectured that they may be realized by copies of any non-circular simple closed curve in space. In knot theory, the Borromean rings can be proved to be linked by counting their Fox n-colo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borsuk–Ulam theorem Summary Borsuk-Ulam_Theorem In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Borsuk–Ulam theorem Summary Borsuk-Ulam_Theorem The same is true for any circle. This assumes the temperature varies continuously in space, which is, however, not always the case.The case n = 2 {\displaystyle n=2} is often illustrated by saying that at any moment, there is always a pair of antipodal points on the Earth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bott cannibalistic class Summary Bott_cannibalistic_class In mathematics, the Bott cannibalistic class, introduced by Raoul Bott (1962), is an element θ k ( V ) {\displaystyle \theta _{k}(V)} of the representation ring of a compact Lie group that describes the action of the Adams operation ψ k {\displaystyle \psi ^{k}}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bott periodicity theorem Summary Bott_periodicity_theorem In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bott residue formula Summary Bott_residue_formula In mathematics, the Bott residue formula, introduced by Bott (1967), describes a sum over the fixed points of a holomorphic vector field of a compact complex manifold. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bourbaki–Witt theorem Summary Bourbaki–Witt_theorem In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed point theorem for partially ordered sets. It states that if X is a non-empty chain complete poset, and f: X → X {\displaystyle f:X\to X} such that ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brascamp–Lieb inequality Summary Brascamp–Lieb_inequality In mathematics, the Brascamp–Lieb inequality is either of two inequalities. The first is a result in geometry concerning integrable functions on n-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . It generalizes the Loomis–Whitney inequality and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer group Summary Brauer_group 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 attem... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Nesbitt theorem Summary Brauer–Nesbitt_theorem In mathematics, the Brauer–Nesbitt theorem can refer to several different theorems proved by Richard Brauer and Cecil J. Nesbitt in the representation theory of finite groups. In modular representation theory, the Brauer–Nesbitt theorem on blocks of defect zero stat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Nesbitt theorem Summary Brauer–Nesbitt_theorem Let G {\displaystyle G} be a group and E {\displaystyle E} be some field. If ρ i: G → G L n ( E ) , i = 1 , 2 {\displaystyle \rho _{i}:G\to GL_{n}(E),i=1,2} are two finite-dimensional semisimple representations such that the characteristic polynomials of ρ 1 ( g ) {... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Siegel theorem Summary Brauer–Siegel_theorem In mathematics, the Brauer–Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel. It attempts to generalise the results known on the cla... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Siegel theorem Summary Brauer–Siegel_theorem {\displaystyle {\frac {}{\log |D_{i}|}}\to 0{\text{ as }}i\to \infty .} Assuming that, and the algebraic hypothesis that Ki is a Galois extension of Q, the conclusion is that log ( h i R i ) log | D i | → 1 as i → ∞ {\displaystyle {\frac {\log(h_{i}R_{i})}{\log {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Siegel theorem Summary Brauer–Siegel_theorem If one assumes that all the degrees {\displaystyle } are bounded above by a uniform constant N, then one may drop the assumption of normality - this is what is actually proved in Brauer's paper. This result is ineffective, as indeed was the result on quadratic fields... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Suzuki theorem Summary Brauer–Suzuki_theorem In mathematics, the Brauer–Suzuki theorem, proved by Brauer & Suzuki (1959), Suzuki (1962), Brauer (1964), states that if a finite group has a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order, then the group has a center of orde... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Suzuki–Wall theorem Summary Brauer–Suzuki–Wall_theorem In mathematics, the Brauer–Suzuki–Wall theorem, proved by Brauer, Suzuki & Wall (1958), characterizes the one-dimensional unimodular projective groups over finite fields. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Clifford invariant Summary Clifford_invariant In mathematics, the Brauer–Wall group or super Brauer group or graded Brauer group for a field F is a group BW(F) classifying finite-dimensional graded central division algebras over the field. It was first defined by Terry Wall (1964) as a generalization of the Brauer grou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bretherton equation Summary Bretherton_equation In mathematics, the Bretherton equation is a nonlinear partial differential equation introduced by Francis Bretherton in 1964: u t t + u x x + u x x x x + u = u p , {\displaystyle u_{tt}+u_{xx}+u_{xxxx}+u=u^{p},} with p {\displaystyle p} integer and p ≥ 2. {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bretherton equation Summary Bretherton_equation The original equation studied by Bretherton has quadratic nonlinearity, p = 2. {\displaystyle p=2.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bretherton equation Summary Bretherton_equation Nayfeh treats the case p = 3 {\displaystyle p=3} with two different methods: Whitham's averaged Lagrangian method and the method of multiple scales.The Bretherton equation is a model equation for studying weakly-nonlinear wave dispersion. It has been used to study the int... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Browder–Minty theorem Summary Browder–Minty_theorem In mathematics, the Browder–Minty theorem (sometimes called the Minty–Browder theorem) states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. Th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brown measure Summary Brown_measure In mathematics, the Brown measure of an operator in a finite factor is a probability measure on the complex plane which may be viewed as an analog of the spectral counting measure (based on algebraic multiplicity) of matrices. It is named after Lawrence G. Brown. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bruhat decomposition Summary Bruhat_decomposition In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Weak Bruhat order Summary Bruhat_order In mathematics, the Bruhat order (also called strong order or strong Bruhat order or Chevalley order or Bruhat–Chevalley order or Chevalley–Bruhat order) is a partial order on the elements of a Coxeter group, that corresponds to the inclusion order on Schubert varieties. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brumer bound Summary Brumer_bound In mathematics, the Brumer bound is a bound for the rank of an elliptic curve, proved by Brumer (1992). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brunn–Minkowski theorem Summary Brunn–Minkowski_theorem In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Buckmaster equation Summary Buckmaster_equation In mathematics, the Buckmaster equation is a second-order nonlinear partial differential equation, named after John D. Buckmaster, who derived the equation in 1977. The equation models the surface of a thin sheet of viscous liquid. The equation was derived earlier by S. H... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Burkill integral Summary Burkill_integral In mathematics, the Burkill integral is an integral introduced by Burkill (1924a, 1924b) for calculating areas. It is a special case of the Kolmogorov integral. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Burnside ring Summary Burnside_ring In mathematics, the Burnside ring of a finite group is an algebraic construction that encodes the different ways the group can act on finite sets. The ideas were introduced by William Burnside at the end of the nineteenth century. The algebraic ring structure is a more recent develop... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Burr–Erdős conjecture Summary Burr–Erdős_conjecture In mathematics, the Burr–Erdős conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erdős, and is one of many conjectures named after Erdős; it states that the Ramsey number of graphs in any sparse ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bussgang theorem Summary Bussgang_theorem In mathematics, the Bussgang theorem is a theorem of stochastic analysis. The theorem states that the cross-correlation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butcher group Summary Butcher_group In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta meth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Butcher group Summary Butcher_group Connes & Kreimer (1999) pointed out that the Butcher group is the group of characters of the Hopf algebra of rooted trees that had arisen independently in their own work on renormalization in quantum field theory and Connes' work with Moscovici on local index theorems. This Hopf alge... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calderón–Zygmund theory Summary Calderón–Zygmund_theory In mathematics, the Calderón–Zygmund lemma is a fundamental result in Fourier analysis, harmonic analysis, and singular integrals. It is named for the mathematicians Alberto Calderón and Antoni Zygmund. Given an integrable function f: Rd → C, where Rd denotes Eucl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calkin correspondence Summary Calkin_correspondence In mathematics, the Calkin correspondence, named after mathematician John Williams Calkin, is a bijective correspondence between two-sided ideals of bounded linear operators of a separable infinite-dimensional Hilbert space and Calkin sequence spaces (also called rear... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Calogero–Degasperis–Fokas equation Summary Calogero–Degasperis–Fokas_equation In mathematics, the Calogero–Degasperis–Fokas equation is the nonlinear partial differential equation u t = u x x x − 1 8 u x 3 + u x ( A e u + B e − u ) . {\displaystyle \displaystyle u_{t}=u_{xxx}-{\frac {1}{8}}u_{x}^{3}+u_{x}\left(Ae^{u}+B... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cameron–Martin formula Summary Cameron–Martin_formula In mathematics, the Cameron–Martin theorem or Cameron–Martin formula (named after Robert Horton Cameron and W. T. Martin) is a theorem of measure theory that describes how abstract Wiener measure changes under translation by certain elements of the Cameron–Martin Hi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor function Summary Cantor_function In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Though it is continuous everywhere an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor function Summary Cantor_function Thus, in one sense the function seems very much like a constant one which cannot grow, and in another, it does indeed monotonically grow. It is also called the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor–Vitali function, the Devil's st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor dust Summary Cantor_set In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.Through consideration of this set, Cantor and oth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cantor dust Summary Cantor_set Cantor mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace topology). By... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carathéodory kernel theorem Summary Carathéodory_kernel_theorem In mathematics, the Carathéodory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carathéodory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carathéodory metric Summary Carathéodory_metric In mathematics, the Carathéodory metric is a metric defined on the open unit ball of a complex Banach space that has many similar properties to the Poincaré metric of hyperbolic geometry. It is named after the Greek mathematician Constantin Carathéodory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Caristi fixed-point theorem Summary Caristi_fixed-point_theorem In mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed-point theorem for maps of a complete metric space into itself. Caristi's fixed-point theorem modifies the ε {\displaystyle \va... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carleson–Jacobs theorem Summary Carleson–Jacobs_theorem In mathematics, the Carleson–Jacobs theorem, introduced by Carleson and Jacobs (1972), describes the best approximation to a continuous function on the unit circle by a function in a Hardy space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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