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Grace–Walsh–Szegő theorem Summary Grace–Walsh–Szegő_theorem In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Graham–Rothschild theorem Summary Graham–Rothschild_theorem In mathematics, the Graham–Rothschild theorem is a theorem that applies Ramsey theory to combinatorics on words and combinatorial cubes. It is named after Ronald Graham and Bruce Lee Rothschild, who published its proof in 1971. Through the work of Graham, Roth... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grassmannian variety Summary Grassmannian_manifold In mathematics, the Grassmannian Gr(k, V ) is a space that parameterizes all k-dimensional linear subspaces of the n-dimensional vector space V. For example, the Grassmannian Gr(1, V ) is the space of lines through the origin in V, so it is the same as the projective s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grassmannian variety Summary Grassmannian_manifold The earliest work on a non-trivial Grassmannian is due to Julius Plücker, who studied the set of projective lines in projective 3-space, equivalent to Gr(2, R4) and parameterized them by what are now called Plücker coordinates. Hermann Grassmann later introduced the co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grauert-Riemenschneider conjecture Summary Grauert–Riemenschneider_vanishing_theorem In mathematics, the Grauert–Riemenschneider vanishing theorem is an extension of the Kodaira vanishing theorem on the vanishing of higher cohomology groups of coherent sheaves on a compact complex manifold, due to Grauert and Riemensch... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Griess algebra Summary Griess_algebra In mathematics, the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 that has the Monster group M as its automorphism group. It is named after mathematician R. L. Griess, who constructed it in 1980 and subsequently used it in 1982 t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Griewank function Summary Griewank_function In mathematics, the Griewank function is often used in testing of optimization. It is defined as follows: 1 + 1 4000 ∑ i = 1 n x i 2 − ∏ i = 1 n cos ( x i i ) {\displaystyle 1+{\frac {1}{4000}}\sum _{i=1}^{n}x_{i}^{2}-\prod _{i=1}^{n}\cos \left({\frac {x_{i}}{\sqrt {i}}}\ri... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gromov boundary Summary Gromov_boundary In mathematics, the Gromov boundary of a δ-hyperbolic space (especially a hyperbolic group) is an abstract concept generalizing the boundary sphere of hyperbolic space. Conceptually, the Gromov boundary is the set of all points at infinity. For instance, the Gromov boundary of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taubes's Gromov invariant Summary Taubes's_Gromov_invariant In mathematics, the Gromov invariant of Clifford Taubes counts embedded (possibly disconnected) pseudoholomorphic curves in a symplectic 4-manifold, where the curves are holomorphic with respect to an auxiliary compatible almost complex structure. (Multiple co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taubes's Gromov invariant Summary Taubes's_Gromov_invariant Much of the analytical complexity connected to this invariant comes from properly counting multiply covered pseudoholomorphic curves so that the result is invariant of the choice of almost complex structure. The crux is a topologically defined index for pseudo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Taubes's Gromov invariant Summary Taubes's_Gromov_invariant ECH is a symplectic field theory-like invariant; namely, it is the homology of a chain complex generated by certain combinations of Reeb orbits of a contact form on Y, and whose differential counts certain embedded pseudoholomorphic curves and multiply covered... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gross–Koblitz formula Summary Gross–Koblitz_formula In mathematics, the Gross–Koblitz formula, introduced by Gross and Koblitz (1979) expresses a Gauss sum using a product of values of the p-adic gamma function. It is an analog of the Chowla–Selberg formula for the usual gamma function. It implies the Hasse–Davenport r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck existence theorem Summary Grothendieck_existence_theorem In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), gives conditions that enable one to lift infinitesimal deformations of a scheme to a deformation, and to lift schemes over infinitesimal neighborhoods o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck group Summary Grothendieck_group In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed from M in the most universal way, in the sense that any abelian group containing a homomorphic image of M will also conta... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck constant Summary Grothendieck_constant In mathematics, the Grothendieck inequality states that there is a universal constant K G {\displaystyle K_{G}} with the following property. If Mij is an n × n (real or complex) matrix with | ∑ i , j M i j s i t j | ≤ 1 {\displaystyle {\Big |}\sum _{i,j}M_{ij}s_{i}t_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck conjecture Summary Grothendieck_conjecture In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Galois–Teichmüller theory Summary Galois–Teichmüller_theory In mathematics, the Grothendieck–Teichmüller group GT is a group closely related to (and possibly equal to) the absolute Galois group of the rational numbers. It was introduced by Vladimir Drinfeld (1990) and named after Alexander Grothendieck and Oswald Teich... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grünwald–Letnikov derivative Summary Grünwald–Letnikov_derivative 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... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gudermannian function Summary Transcendent_angle In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called the gudermannian of ψ {\textstyle \psi } and denoted gd ψ {\textstyle \operatorname {gd} \psi } . The Gudermannian ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gudermannian function Summary Transcendent_angle {\textstyle m=1.} The real Gudermannian function is typically defined for − ∞ < ψ < ∞ {\textstyle -\infty <\psi <\infty } to be the integral of the hyperbolic secant ϕ = gd ψ ≡ ∫ 0 ψ sech t d t = arctan ( sinh ψ ) . {\displaystyle \phi =\operatorname {gd} \psi \e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gudermannian function Summary Transcendent_angle The real inverse Gudermannian function can be defined for − 1 2 π < ϕ < 1 2 π {\textstyle -{\tfrac {1}{2}}\pi <\phi <{\tfrac {1}{2}}\pi } as the integral of the secant ψ = gd − 1 ϕ = ∫ 0 ϕ sec t d t = arsinh ( tan ϕ ) . {\displaystyle \psi =\operatorname {gd} ^{-... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gudermannian function Summary Transcendent_angle {\displaystyle \psi =\operatorname {lam} \phi .} In the context of geodesy and navigation for latitude ϕ {\textstyle \phi } , k gd − 1 ϕ {\displaystyle k\operatorname {gd} ^{-1}\phi } (scaled by arbitrary constant k {\textstyle k} ) was historically called the meridion... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
H-derivative Summary H-derivative In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
HM-GM-AM-QM inequalities Summary HM-GM-AM-QM_inequalities In mathematics, the HM-GM-AM-QM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that x 1 , x 2 , … , x n {\disp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Britton's Lemma Summary Britton's_Lemma In mathematics, the HNN extension is an important construction of combinatorial group theory. Introduced in a 1949 paper Embedding Theorems for Groups by Graham Higman, Bernhard Neumann, and Hanna Neumann, it embeds a given group G into another group G' , in such a way that two g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar transform Summary Rademacher_function In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar transform Summary Rademacher_function Haar used these functions to give an example of an orthonormal system for the space of square-integrable functions on the unit interval . The study of wavelets, and even the term "wavelet", did not come until much later. As a special case of the Daubechies wavelet, the Haar wa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar transform Summary Rademacher_function The Haar wavelet is also the simplest possible wavelet. The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haar transform Summary Rademacher_function This property can, however, be an advantage for the analysis of signals with sudden transitions (discrete signals), such as monitoring of tool failure in machines.The Haar wavelet's mother wavelet function ψ ( t ) {\displaystyle \psi (t)} can be described as ψ ( t ) = { 1 0 ≤ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadamard derivative Summary Hadamard_derivative In mathematics, the Hadamard derivative is a concept of directional derivative for maps between Banach spaces. It is particularly suited for applications in stochastic programming and asymptotic statistics. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elementwise division Summary Elementwise_division In mathematics, the Hadamard product (also known as the element-wise product, entrywise product: ch. 5 or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements. This operation... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadwiger–Finsler inequality Summary Hadwiger–Finsler_inequality In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths a, b and c and area T, then | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jordan decomposition theorem Summary Jordan_decomposition_theorem In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that for any measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} and any signed measure μ {\displaystyle \mu } defined on the σ {\displaystyle \si... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hahn polynomials Summary Hahn_polynomials In mathematics, the Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev in 1875 (Chebyshev 1907) and rediscovered by Wolfgang Hahn (Hahn 1949). The Hahn class is a name for special... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hahn polynomials Summary Hahn_polynomials {\displaystyle Q_{n}(x;\alpha ,\beta ,N)={}_{3}F_{2}(-n,-x,n+\alpha +\beta +1;\alpha +1,-N+1;1).\ } Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties. If α = β = 0 {\displaystyle \alpha =\beta =0} , these polynomials are i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hahn–Exton q-Bessel function Summary Hahn–Exton_q-Bessel_function In mathematics, the Hahn–Exton q-Bessel function or the third Jackson q-Bessel function is a q-analog of the Bessel function, and satisfies the Hahn-Exton q-difference equation (Swarttouw (1992)). This function was introduced by Hahn (1953) in a special ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hales–Jewett theorem Summary Hales–Jewett_theorem In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure; it is impossi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hall algebra Summary Hall_polynomial In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed by Steinitz (1901) but forgotten until it was rediscovered by Philip Hall (1959), both of whom published no more than brief... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hall-Littlewood polynomials Summary Hall–Littlewood_polynomials In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter t and a partition λ. They are Schur functions when t is 0 and monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials. They wer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Halpern–Läuchli theorem Summary Halpern–Läuchli_theorem In mathematics, the Halpern–Läuchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for set theory in which the Boolean prime ideal theorem is true but the axiom of choice is false. It is often called... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamburger moment problem Summary Hamburger_moment_problem In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution functi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial In mathematics, the Hamiltonian cycle polynomial of an n×n-matrix is a polynomial in its entries, defined as ham ( A ) = ∑ σ ∈ H n ∏ i = 1 n a i , σ ( i ) {\displaystyle \operatorname {ham} (A)=\sum _{\sigma \in H_{n}}\prod _{i=1}^{n}a_{i,\sigma (i)}} ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial Hence if it's possible to polynomial-time assign weights from a field of characteristic 2 to a digraph's arcs that make its weighted adjacency matrix unitary and having a non-zero Hamiltonian cycle polynomial then the digraph is Hamiltonian. Therefore th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial For k = 1 {\displaystyle k=1} the latter statement can be re-formulated as the # 2 {\displaystyle _{2}} P-completeness of computing, for a given unitary n×n-matrix U {\displaystyle U} over a field of characteristic 2, the n×n-matrix H ( U ) {\displaystyl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial . + a n 2 ) ham ( U ) {\displaystyle \operatorname {ham} \left({\begin{matrix}U&{Ua}\\a^{T}&1\end{matrix}}\right)=(a_{1}^{2}+...+a_{n}^{2})\operatorname {ham} (U)} where a {\displaystyle a} is an arbitrary n-vector (what can be interpreted as the polyn... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial Besides, in characteristic 2 for square matrices X, Y ham ( X Y Y X ) {\displaystyle \operatorname {ham} \left({\begin{matrix}X&Y\\Y&X\end{matrix}}\right)} is the square of the sum, over all the pairs of non-equal indexes i,j, of the i,j-th entry of Y ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian cycle polynomial Summary Hamiltonian_cycle_polynomial These two types of transformation don't compress the matrix, but keep its size unchanged. However, in a number of cases their application allows to reduce the matrix's size by some of the above-mentioned compression operators. Hence there is a variety of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fourier–Bessel transform Summary Fourier–Bessel_transform In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fourier–Bessel transform Summary Fourier–Bessel_transform The Hankel transform is an integral transform and was first developed by the mathematician Hermann Hankel. It is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite int... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haran's diamond theorem Summary Haran's_diamond_theorem In mathematics, the Haran diamond theorem gives a general sufficient condition for a separable extension of a Hilbertian field to be Hilbertian. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hardy–Littlewood maximal operator Summary Hardy-Littlewood_maximal_inequality In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hardy–Littlewood zeta-function conjectures Summary Hardy–Littlewood_zeta-function_conjectures In mathematics, the Hardy–Littlewood zeta-function conjectures, named after Godfrey Harold Hardy and John Edensor Littlewood, are two conjectures concerning the distances between zeros and the density of zeros of the Riemann z... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hardy–Ramanujan theorem Summary Hardy–Ramanujan_theorem In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω(n) of distinct prime factors of a number n is log(log(n)). Roughly speaking, this means that most numbers have about this number of d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hardy–Littlewood circle method Summary Hardy-Littlewood_method In mathematics, the Hardy–Ramanujan–Littlewood circle method is a technique of analytic number theory. It is named for G. H. Hardy, S. Ramanujan, and J. E. Littlewood, who developed it in a series of papers on Waring's problem. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Distributional character Summary Distributional_character In mathematics, the Harish-Chandra character, named after Harish-Chandra, of a representation of a semisimple Lie group G on a Hilbert space H is a distribution on the group G that is analogous to the character of a finite-dimensional representation of a compact... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Harish-Chandra isomorphism Summary Harish-Chandra_isomorphism In mathematics, the Harish-Chandra isomorphism, introduced by Harish-Chandra (1951), is an isomorphism of commutative rings constructed in the theory of Lie algebras. The isomorphism maps the center Z ( U ( g ) ) {\displaystyle {\mathcal {Z}}(U({\mathfrak {g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cas (mathematics) Summary Hartley_kernel In mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions to real-valued functions. It was proposed as an alternative to the Fourier transform by Ralph V. L. Hartley in 1942, and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hartogs–Rosenthal theorem Summary Hartogs–Rosenthal_theorem In mathematics, the Hartogs–Rosenthal theorem is a classical result in complex analysis on the uniform approximation of continuous functions on compact subsets of the complex plane by rational functions. The theorem was proved in 1931 by the German mathematici... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hartree equation Hartree equation in mathematics Hartree_equation > Hartree equation in mathematics In mathematics, the Hartree equation, named after Douglas Hartree, is i ∂ t u + ∇ 2 u = V ( u ) u {\displaystyle i\,\partial _{t}u+\nabla ^{2}u=V(u)u} in R d + 1 {\displaystyle \mathbb {R} ^{d+1}} where V ( u ) = ± | x |... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse derivative Summary Hasse_derivative In mathematics, the Hasse derivative is a generalisation of the derivative which allows the formulation of Taylor's theorem in coordinate rings of algebraic varieties. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse invariant of a quadratic form Summary Hasse_invariant_of_a_quadratic_form In mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt. The quadratic form Q may be taken as a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse invariant of an algebra Summary Hasse_invariant_of_an_algebra In mathematics, the Hasse invariant of an algebra is an invariant attached to a Brauer class of algebras over a field. The concept is named after Helmut Hasse. The invariant plays a role in local class field theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse–Weil zeta function Summary Hasse–Weil_L-function In mathematics, the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex plane defined in terms of the number of points on the variety after reducing modulo each prime number p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hasse-Witt matrix Summary Hasse-Witt_matrix In mathematics, the Hasse–Witt matrix H of a non-singular algebraic curve C over a finite field F is the matrix of the Frobenius mapping (p-th power mapping where F has q elements, q a power of the prime number p) with respect to a basis for the differentials of the first kin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hausdorff convergence Summary Hausdorff_metric In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hausdorff convergence Summary Hausdorff_metric The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hausdorff maximal principle Summary Hausdorff_maximal_principle In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hausdorff moment problem Summary Hausdorff_moment_problem In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1, m2, ...) be the sequence of moments m n = ∫ 0 1 x n d μ ( x ) {\displaystyle m_{n}=\int _{0}^{1}x^{n}\,d\mu (x)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hausdorff moment problem Summary Hausdorff_moment_problem In the indeterminate moment problem case, there are infinite measures corresponding to the same prescribed moments and they consist of a convex set. The set of polynomials may or may not be dense in the associated Hilbert spaces if the moment problem is indeterm... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hawaiian earring Summary Hawaiian_earring In mathematics, the Hawaiian earring H {\displaystyle \mathbb {H} } is the topological space defined by the union of circles in the Euclidean plane R 2 {\displaystyle \mathbb {R} ^{2}} with center ( 1 n , 0 ) {\displaystyle \left({\tfrac {1}{n}},0\right)} and radius 1 n {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hawaiian earring Summary Hawaiian_earring Therefore, H {\displaystyle \mathbb {H} } does not have a simply connected covering space and is usually given as the simplest example of a space with this complication. The Hawaiian earring looks very similar to the wedge sum of countably infinitely many circles; that is, the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haynsworth inertia additivity formula Summary Haynsworth_inertia_additivity_formula In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heawood number Summary Heawood_number In mathematics, the Heawood number of a surface is an upper bound for the number of colors that suffice to color any graph embedded in the surface. In 1890 Heawood proved for all surfaces except the sphere that no more than H ( S ) = ⌊ 7 + 49 − 24 e ( S ) 2 ⌋ = ⌊ 7 + 1 + 48 g ( S )... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heawood number Summary Heawood_number Franklin proved that the chromatic number of a graph embedded in the Klein bottle can be as large as 6 {\displaystyle 6} , but never exceeds 6 {\displaystyle 6} . Later it was proved in the works of Gerhard Ringel, J. W. T. Youngs, and other contributors that the complete graph wit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hecke algebra Summary Classical_Hecke_algebra In mathematics, the Hecke algebra is the algebra generated by Hecke operators. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heine-Cantor theorem Summary Heine–Cantor_theorem In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if f: M → N {\displaystyle f\colon M\to N} is a continuous function between two metric spaces M {\displaystyle M} and N {\displaystyle N} , and M {\displaystyle M} is compac... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heine–Stieltjes polynomials Summary Heine–Stieltjes_polynomials In mathematics, the Heine–Stieltjes polynomials or Stieltjes polynomials, introduced by T. J. Stieltjes (1885), are polynomial solutions of a second-order Fuchsian equation, a differential equation all of whose singularities are regular. The Fuchsian equat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heinz mean Summary Heinz_mean In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: H x ( A , B ) = A x B 1 − x + A 1 − x B x 2 , {\displaystyle \operatorname {H} _{x}(A,B)={\frac {A^{x}B^{1-x}+A^{1-x}B^{x}}{2}},} with 0 ≤ x ≤ 1/2. For different valu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heisenberg group Summary Heisenberg_group In mathematics, the Heisenberg group H {\displaystyle H} , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form ( 1 a c 0 1 b 0 0 1 ) {\displaystyle {\begin{pmatrix}1&a&c\\0&1&b\\0&0&1\\\end{pmatrix}}} under the operation of matrix multiplica... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hellinger integral Summary Hellinger_integral In mathematics, the Hellinger integral is an integral introduced by Hellinger (1909) that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paraxial Helmholtz equation Summary Paraxial_Helmholtz_equation In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation where ∇2 is the Laplace operator, k2 is the eigenvalue, and f is the (eigen)function. When the equation is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Henstock integral Summary Henstock_integral In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced ), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral – is one of a numb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Henstock integral Summary Henstock_integral Denjoy was interested in a definition that would allow one to integrate functions like f ( x ) = 1 x sin ( 1 x 3 ) . {\displaystyle f(x)={\frac {1}{x}}\sin \left({\frac {1}{x^{3}}}\right).} This function has a singularity at 0, and is not Lebesgue integrable. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Henstock integral Summary Henstock_integral However, it seems natural to calculate its integral except over the interval and then let ε, δ → 0. Trying to create a general theory, Denjoy used transfinite induction over the possible types of singularities, which made the definition quite complicated. Other definitions w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Henstock integral Summary Henstock_integral It took a while to understand that the Perron and Denjoy integrals are actually identical. Later, in 1957, the Czech mathematician Jaroslav Kurzweil discovered a new definition of this integral elegantly similar in nature to Riemann's original definition which he named the ga... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Herbrand quotient Summary Herbrand_quotient In mathematics, the Herbrand quotient is a quotient of orders of cohomology groups of a cyclic group. It was invented by Jacques Herbrand. It has an important application in class field theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Herbrand–Ribet theorem Summary Herbrand–Ribet_theorem In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity if and only if ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Herglotz–Zagier function Summary Herglotz–Zagier_function In mathematics, the Herglotz–Zagier function, named after Gustav Herglotz and Don Zagier, is the function F ( x ) = ∑ n = 1 ∞ { Γ ′ ( n x ) Γ ( n x ) − log ( n x ) } 1 n . {\displaystyle F(x)=\sum _{n=1}^{\infty }\left\{{\frac {\Gamma ^{\prime }(nx)}{\Gamma (n... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hermite constant Summary Hermite_constant In mathematics, the Hermite constant, named after Charles Hermite, determines how long a shortest element of a lattice in Euclidean space can be. The constant γn for integers n > 0 is defined as follows. For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) =... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hermite polynomials Summary Hermite_form In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; comb... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hermite–Hadamard inequality Summary Hermite–Hadamard_inequality In mathematics, the Hermite–Hadamard inequality, named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality, states that if a function ƒ: → R is convex, then the following chain of inequalities hold: f ( a + b 2 ) ≤ 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Heronian mean Summary Heronian_mean In mathematics, the Heronian mean H of two non-negative real numbers A and B is given by the formula It is named after Hero of Alexandria. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Herzog–Schönheim conjecture Summary Herzog–Schönheim_conjecture In mathematics, the Herzog–Schönheim conjecture is a combinatorial problem in the area of group theory, posed by Marcel Herzog and Jochanan Schönheim in 1974.Let G {\displaystyle G} be a group, and let A = { a 1 G 1 , … , a k G k } {\displaystyle A=\{a_{1}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hessian group Summary Hessian_group In mathematics, the Hessian group is a finite group of order 216, introduced by Jordan (1877) who named it for Otto Hesse. It may be represented as the group of affine transformations with determinant 1 of the affine plane over the field of 3 elements. It has a normal subgroup that i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hessian determinant Summary Hessian_determinant In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was develo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Higman group Summary Higman_group In mathematics, the Higman group, introduced by Graham Higman (1951), was the first example of an infinite finitely presented group with no non-trivial finite quotients. The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. Higman (1974) late... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hilbert cube Summary Hilbert_cube In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hilbert metric Summary Hilbert_metric In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert (1895) as a generalization of Cayley's formula for the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hilbert projection theorem Summary Hilbert_projection_theorem In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector x {\displaystyle x} in a Hilbert space H {\displaystyle H} and every nonempty closed convex C ⊆ H , {\displaystyle C\subseteq H,} there exist... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hilbert's reciprocity law Summary Hilbert_symbol In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from K× × K× to the group of nth roots of unity in a local field K such as the fields of reals or p-adic numbers. It is related to reciprocity laws, and can be defined in terms of the Artin sy... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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