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c_xv202b4qjn7l | In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő. | Grace–Walsh–Szegő theorem |
c_mlv9d4iksvud | 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, Rothschild, and Klaus Leeb in 1972, it became part of the founda... | Graham–Rothschild theorem |
c_trrpqg1jp8ni | 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 space of one dimension lower than V.When V is a real... | Grassmannian variety |
c_q50nf36vs10l | 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 concept in general. Notations for the Grassmannian va... | Grassmannian variety |
c_ylgz3597dmil | 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 Riemenschneider (1970). | Grauert-Riemenschneider conjecture |
c_2tnx6prcpigd | 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 to construct M. The Monster fixes (vect... | Griess algebra |
c_a2wddyu6h7kc | 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}}}\right)} The following paragraphs display the s... | Griewank function |
c_5qewvy1ynsbw | 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 the real line is two points, corresponding... | Gromov boundary |
c_xjaug2tdbck1 | 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 covers of 2-tori with self-intersection 0 are also counted.) T... | Taubes's Gromov invariant |
c_labstcg28jp5 | 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 pseudoholomorphic curves which controls embeddedness and bounds th... | Taubes's Gromov invariant |
c_i2pkbh0nwzlz | 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 pseudoholomorphic cylinders with "ECH index" 1 in Y × R {\d... | Taubes's Gromov invariant |
c_gbtmvyg59lze | 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 relation and generalizes the Stickelberger theorem. B... | Gross–Koblitz formula |
c_g65qqabpbr9h | 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 over a subscheme of a scheme S to schemes over S. The theorem can be vi... | Grothendieck existence theorem |
c_yq43p20kr53s | 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 contain a homomorphic image of the Grothendieck gro... | Grothendieck group |
c_uwvfqgee2uv0 | 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_{j}{\Big |}\leq 1} for all (real or complex) numbers ... | Grothendieck constant |
c_ixu7yxbdxhi5 | 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 the polynomial case. It is a conjecture of Alexander Gro... | Grothendieck conjecture |
c_ijyihpp3rr5z | 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 Teichmüller, based on Grothendieck's suggestion in his 1984 essay... | Galois–Teichmüller theory |
c_og4gxti78lpt | In mathematics, the Grünwald–Letnikov derivative is a basic extension of the derivative in fractional calculus that allows one to take the derivative a non-integer number of times. It was introduced by Anton Karl Grünwald (1838–1920) from Prague, in 1867, and by Aleksey Vasilievich Letnikov (1837–1888) in Moscow in 186... | Grünwald–Letnikov derivative |
c_vd22kc14tp8l | 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 function reveals a close relationship between the... | Gudermannian function |
c_z0i6fuycn0ng | {\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 \equiv \int _{0}^{\psi }\operatorname {sech} t\,\ma... | Gudermannian function |
c_plqm5zgvjovx | 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} ^{-1}\phi =\int _{0}^{\phi }\operatorname {sec} t\,\... | Gudermannian function |
c_1z2lw7g1fahx | {\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 meridional part of ϕ {\displaystyle \phi } (French: latit... | Gudermannian function |
c_w7qw96syzb0n | In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus. | H-derivative |
c_0tgu4baqhg8o | 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 {\displaystyle x_{1},x_{2},\ldots ,x_{n}} are positive real numb... | HM-GM-AM-QM inequalities |
c_7swkybeqik6x | 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 given isomorphic subgroups of G are conju... | Britton's Lemma |
c_k3whwkbj9e3d | 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 basis. The Haar sequence is now recognised... | Haar transform |
c_h6wl5t73j2w8 | 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 wavelet is also known as Db1. | Haar transform |
c_2w6x94hbqgnv | 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. | Haar transform |
c_wdlgmxm5pvql | 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 ≤ t < 1 2 , − 1 1 2 ≤ t < 1 , 0 otherwise. {\... | Haar transform |
c_tk15rq1cl7iw | 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. | Hadamard derivative |
c_ua41ed3f7vi8 | 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 can be thought as a "naive matrix multiplication"... | Elementwise division |
c_5rk7q64g7v90 | 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 | Hadwiger–Finsler inequality |
c_cz4j4favsq4p | 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 \sigma } -algebra Σ {\displaystyle \Sigma } , there exist two Σ {\dis... | Jordan decomposition theorem |
c_vc411zmzjw8g | 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 cases of Hahn polynomials, including Hahn... | Hahn polynomials |
c_wpnlyj78xt1s | {\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 identical to the discrete Chebyshev polynom... | Hahn polynomials |
c_sm3wvxjjr05u | 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 case and by Exton (1983) in general. The Hahn–Exton q-Bessel funct... | Hahn–Exton q-Bessel function |
c_dfxzwvsekd6g | 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 impossible for such objects to be "completely random".An ... | Hales–Jewett theorem |
c_p6xtdb2r1ai5 | 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 summaries of their work. The Hall po... | Hall algebra |
c_azhb2dar7t1w | 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 were first defined indirectly by Philip Hall using the Hall algebra... | Hall-Littlewood polynomials |
c_xueucwnv4yq2 | 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 the Halpern–Läuchli theorem, but the proper attribution... | Halpern–Läuchli theorem |
c_mmezddkwgq9p | 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 function of a random variable) on the real line such that m n = ... | Hamburger moment problem |
c_nhs2a6u9qgv0 | 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)}} where H n {\displaystyle H_{n}} is the set of n-permutations havin... | Hamiltonian cycle polynomial |
c_dfwju4ernioh | 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 the Hamiltonian cycle problem is computable on such graphs in polyno... | Hamiltonian cycle polynomial |
c_tcqnuxh6ojnz | 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 ) {\displaystyle H(U)} whose i,j-th entry is the Hamiltonian cycle polynomial of ... | Hamiltonian cycle polynomial |
c_n0dlu13gf74n | . + 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 polynomial-time computability of the Hamiltonian cycle polynomial of an... | Hamiltonian cycle polynomial |
c_c0ne1h9dujqb | 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 multiplied by the Hamiltonian cycle polynomial of the matrix recei... | Hamiltonian cycle polynomial |
c_oom92e6to2o0 | 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 matrix compression operators performed in polynomial time and pre... | Hamiltonian cycle polynomial |
c_x11j8o5ke672 | 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 r axis. The necessary coefficient Fν of each Bessel funct... | Fourier–Bessel transform |
c_14lo9lafze2t | 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 interval, so the Hankel transform over an infinite interval i... | Fourier–Bessel transform |
c_a5dmm358au05 | In mathematics, the Haran diamond theorem gives a general sufficient condition for a separable extension of a Hilbertian field to be Hilbertian. | Haran's diamond theorem |
c_vwnpoj4rae7r | In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. | Hardy–Littlewood maximal operator |
c_xaw3z0k5cfg1 | 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 zeta function. | Hardy–Littlewood zeta-function conjectures |
c_pxxfkmono22e | 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 distinct prime factors. | Hardy–Ramanujan theorem |
c_zk1qyssshddf | 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. | Hardy–Littlewood circle method |
c_p8m8no4al8ne | 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 group. | Distributional character |
c_pe8mgbser4yz | 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}}))} of the universal enveloping algebra U ( g ) {\displaysty... | Harish-Chandra isomorphism |
c_57vliwlow2no | 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 is one of many known Fourier-related tran... | Cas (mathematics) |
c_ztdcy51y89b8 | 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 mathematicians Friedrich Hartogs and Arthur Rosenthal and has been wide... | Hartogs–Rosenthal theorem |
c_bmtqsnh1rvtz | 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 | − n ∗ | u | 2 {\displaystyle V(u)=\pm |x|^{-n}*|u|^{2}} and 0 < n < d {\displaystyle 0 | Hartree equation |
c_kdtc5crp325m | 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. | Hasse derivative |
c_zfheil8h0hz8 | 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 diagonal form Σ aixi2.Its invariant is then defined as the product of the classe... | Hasse invariant of a quadratic form |
c_drh6ze5ueqxt | 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. | Hasse invariant of an algebra |
c_6zrfiyjdyuxr | 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. It is a global L-function defined as an Euler product... | Hasse–Weil zeta function |
c_uif3u4alk3tq | 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 kind. It is a g × g matrix where C has genus g.... | Hasse-Witt matrix |
c_e5yiwz0qvng7 | 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 is named after Felix Hausdorff and Dimitrie Po... | Hausdorff convergence |
c_cojq1anuemn6 | 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 closest point in the other set. This distance wa... | Hausdorff convergence |
c_k8qcu1adm2nl | 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 totally ordered subset. The Hausdorff maximal principle is one o... | Hausdorff maximal principle |
c_ode4j35ygoow | 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)} of some Borel measure μ supported on the closed unit int... | Hausdorff moment problem |
c_xskbyi9lusdy | 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 indeterminate, and it depends on whether measure is extremal or no... | Hausdorff moment problem |
c_2cr7l9yx0vvr | 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 {\displaystyle {\tfrac {1}{n}}} for n = 1 , 2 , 3... | Hawaiian earring |
c_vsq7o3a244jd | 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 rose with infinitely many petals, but thes... | Hawaiian earring |
c_nj25wabjlc4c | 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 is partitioned.The inertia of a Hermitian matrix H is defined as the ordered triple I... | Haynsworth inertia additivity formula |
c_gzsm6e5aln2g | 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 ) 2 ⌋ {\displaystyle H(S)=\left\lfloor ... | Heawood number |
c_ugx38o6yzb1m | 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 with H ( S ) {\displaystyle H(S)} vertice... | Heawood number |
c_n81kukict4uw | In mathematics, the Hecke algebra is the algebra generated by Hecke operators. | Hecke algebra |
c_yq4ekgzdt5t8 | 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 compact, then f {\displaystyle f} is uniformly continuou... | Heine-Cantor theorem |
c_spmyclm1k87l | 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 equation has the form d 2 S d z 2 + ( ∑ j = 1 N γ j z − a j ) d S d z... | Heine–Stieltjes polynomials |
c_f93y1wsog6vb | 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 values of x, this Heinz mean inter... | Heinz mean |
c_4ol51ctbokrb | 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 multiplication. Elements a, b and c can be taken fro... | Heisenberg group |
c_g959kzm0chx3 | 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. | Hellinger integral |
c_v1s3j9k5r6lv | 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 applied to waves, k is known as the wave number. The Helmholtz ... | Paraxial Helmholtz equation |
c_uwpy7hzaf2iz | 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 number of inequivalent definitions of the integr... | Henstock integral |
c_i76bh7qf3ngz | 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. | Henstock integral |
c_aqu3lvra4y7r | 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 were given by Nikolai Luzin (using variations... | Henstock integral |
c_u43oqsp5hwn5 | 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 gauge integral. Ralph Henstock independently i... | Henstock integral |
c_hizty30uf2cb | 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. | Herbrand quotient |
c_h4emo86j94js | 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 p divides the numerator of the n-th Bernoulli number B... | Herbrand–Ribet theorem |
c_2da687z85oow | 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 (nx)}}-\log(nx)\right\}{\frac {1}{n}}.} introduced by Zagier... | Herglotz–Zagier function |
c_i9k868of9tq1 | 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) = 1, let λ1(L) denote the least length of a... | Hermite constant |
c_ojzb7rx1ngxp | 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; combinatorics, as an example of an Appell seq... | Hermite polynomials |
c_e9gm756uz52z | 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 b − a ∫ a b f ( x ) d x ≤ f ( a ) + f ( b ) 2 . {\displaystyle ... | Hermite–Hadamard inequality |
c_vmw35adqd4qr | 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. | Heronian mean |
c_xh1h5rimqhiw | 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}G_{1},\ \ldots ,\ a_{k}G_{k}\}} be a finite system of left coset... | Herzog–Schönheim conjecture |
c_uadq0qd6goh0 | 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 is an elementary abelian group of ord... | Hessian group |
c_62jpdl57ofbu | 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 developed in the 19th century by the German mathematic... | Hessian determinant |
c_87hbkiy2i86c | 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) later found some finitely presented in... | Higman group |
c_a35s15bbf35e | 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 cube (see below). | Hilbert cube |
c_6i9fre53im01 | 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 distance in the Cayley–Klein model of ... | Hilbert metric |
c_p268gxesh9q5 | 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 exists a unique vector m ∈ C {\displaystyle m\in C} for which ‖ c −... | Hilbert projection theorem |
c_ff0dzyd66hrx | 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 symbol of local class field theory. The Hilbert sym... | Hilbert's reciprocity law |
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