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Costas array Summary Costas_array In mathematics, a Costas array can be regarded geometrically as a set of n points, each at the center of a square in an n×n square tiling such that each row or column contains only one point, and all of the n(n − 1)/2 displacement vectors between each pair of dots are distinct. This re... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Costas array Summary Costas_array Costas arrays are named after John P. Costas, who first wrote about them in a 1965 technical report. Independently, Edgar Gilbert also wrote about them in the same year, publishing what is now known as the logarithmic Welch method of constructing Costas arrays. The general enumeration ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coulomb functions Summary Coulomb_functions In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric functions or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Countryman line Summary Countryman_line In mathematics, a Countryman line (named after Roger Simmons Countryman Jr.) is an uncountable linear ordering whose square is the union of countably many chains. The existence of Countryman lines was first proven by Shelah. Shelah also conjectured that, assuming PFA, every Arons... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coxeter system Summary Coxeter_group In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of reg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Coxeter system Summary Coxeter_group Coxeter groups find applications in many areas of mathematics. Examples of finite Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter groups include the triangle groups corresponding to regular tes... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cullen number Summary Cullen_prime In mathematics, a Cullen number is a member of the integer sequence C n = n ⋅ 2 n + 1 {\displaystyle C_{n}=n\cdot 2^{n}+1} (where n {\displaystyle n} is a natural number). Cullen numbers were first studied by James Cullen in 1905. The numbers are special cases of Proth numbers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cunningham chain Summary Cunningham_chain In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
D-module Summary D-module In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
D-module Summary D-module The methods of D-module theory have always been drawn from sheaf theory and other techniques with inspiration from the work of Alexander Grothendieck in algebraic geometry. The approach is global in character, and differs from the functional analysis techniques traditionally used to study diff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kleene algebra (with involution) Summary Kleene_algebra_(with_involution) In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kleene algebra (with involution) Summary Kleene_algebra_(with_involution) Thus ¬ is a dual automorphism of (A, ∨, ∧, 0, 1). If the lattice is defined in terms of the order instead, i.e. (A, ≤) is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, and the meet and join ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kleene algebra (with involution) Summary Kleene_algebra_(with_involution) (i-lattice being an abbreviation for lattice with involution.) They have been further studied in the Argentinian algebraic logic school of Antonio Monteiro.De Morgan algebras are important for the study of the mathematical aspects of fuzzy logic.... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Delannoy number Summary Delannoy_number In mathematics, a Delannoy number D {\displaystyle D} describes the number of paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m, n), using only single steps north, northeast, or east. The Delannoy numbers are named after French army officer a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Delzant's theorem Summary Delzant's_theorem In mathematics, a Delzant polytope is a convex polytope in R n {\displaystyle \mathbb {R} ^{n}} such for each vertex v {\displaystyle v} , exactly n {\displaystyle n} edges meet at v {\displaystyle v} , and these edges form a collection of vectors that form a Z {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Demazure module Summary Demazure_module In mathematics, a Demazure module, introduced by Demazure (1974a, 1974b), is a submodule of a finite-dimensional representation generated by an extremal weight space under the action of a Borel subalgebra. The Demazure character formula, introduced by Demazure (1974b, theorem 2),... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matiyasevich's theorem Summary MRDP_theorem In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk) = 0 (usually abbreviated P(x, y) = 0) where P(x, y) is a polynomial with integer coefficients, where x1, ..., xj indicate parameters and y1, ..., yk indicate unknowns. A Diophantine ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matiyasevich's theorem Summary MRDP_theorem The use of natural numbers both in S and the existential quantification merely reflects the usual applications in computability and model theory. It does not matter whether natural numbers refer to the set of nonnegative integers or positive integers since the two definitions... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matiyasevich's theorem Summary MRDP_theorem Also it is sufficient to assume P is a polynomial over Q {\displaystyle \mathbb {Q} } and multiply P by the appropriate denominators to yield integer coefficients. However, whether quantification over rationals can also be substituted for quantification over the integers is a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matiyasevich's theorem Summary MRDP_theorem This means that the concept of general Diophantine set, apparently belonging to number theory, can be taken rather in logical or recursion-theoretic terms. This is far from obvious, however, and represented the culmination of some decades of work. Matiyasevich's completion of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Diophantine equation Summary Linear_Diophantine_equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Diophantine equation Summary Linear_Diophantine_equation Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves, algebraic surfaces, or, more generally, algebraic sets, their study is a part of al... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac comb Summary Dirac_comb In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula for some given period T {\displaystyle T} . Here t is a real variable and the sum extends over all integers k. The Dirac delta function δ {\displaystyle \de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac comb Summary Dirac_comb This implies Because the Dirac comb function is periodic, it can be represented as a Fourier series based on the Dirichlet kernel: The Dirac comb function allows one to represent both continuous and discrete phenomena, such as sampling and aliasing, in a single framework of continuous Four... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac measure Summary Dirac_measure In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed element x or not. It is one way of formalizing the idea of the Dirac delta function, an important tool in physics and other technical fields. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirac spectrum Summary Dirac_spectrum In mathematics, a Dirac spectrum, named after Paul Dirac, is the spectrum of eigenvalues of a Dirac operator on a Riemannian manifold with a spin structure. The isospectral problem for the Dirac spectrum asks whether two Riemannian spin manifolds have identical spectra. The Dirac s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirichlet L-function Summary Dirichlet_L-series In mathematics, a Dirichlet L-series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s . {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty }{\frac {\chi (n)}{n^{s}}}.} where χ {\displaystyle \chi } is a Dirichlet character and s a complex variable with real part g... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirichlet L-function Summary Dirichlet_L-series It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane, and is then called a Dirichlet L-function and also denoted L(s, χ). These functions are named after Peter Gustav Lejeune Dirichle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirichlet L-function Summary Dirichlet_L-series In the course of the proof, Dirichlet shows that L(s, χ) is non-zero at s = 1. Moreover, if χ is principal, then the corresponding Dirichlet L-function has a simple pole at s = 1. Otherwise, the L-function is entire. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirichlet algebra Summary Dirichlet_algebra In mathematics, a Dirichlet algebra is a particular type of algebra associated to a compact Hausdorff space X. It is a closed subalgebra of C(X), the uniform algebra of bounded continuous functions on X, whose real parts are dense in the algebra of bounded continuous real fun... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dirichlet's problem Summary Dirichlet's_problem In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Formal Dirichlet series Summary Formal_Dirichlet_series In mathematics, a Dirichlet series is any series of the form where s is complex, and a n {\displaystyle a_{n}} is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory. Th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ditkin set Summary Ditkin_set In mathematics, a Ditkin set, introduced by (Ditkin 1939), is a closed subset of the circle such that a function f vanishing on the set can be approximated by functions φnf with φ vanishing in a neighborhood of the set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dold manifold Summary Dold_manifold In mathematics, a Dold manifold is one of the manifolds P ( m , n ) = ( S m × C P n ) / τ {\displaystyle P(m,n)=(S^{m}\times \mathbb {CP} ^{n})/\tau } , where τ {\displaystyle \tau } is the involution that acts as −1 on the m-sphere S m {\displaystyle S^{m}} and as complex conjugatio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Drinfeld module Summary Drinfeld_module In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Drinfeld module Summary Drinfeld_module He later invented shtukas and used shtukas of rank 2 to prove the remaining cases of the Langlands conjectures for GL2. Laurent Lafforgue proved the Langlands conjectures for GLn of a function field by studying the moduli stack of shtukas of rank n. "Shtuka" is a Russian word шту... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dupin cyclide Summary Dupin_cyclide In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter are themselves examples of Dupin cyclides. They were discovered c. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dupin cyclide Summary Dupin_cyclide 1802 by (and named after) Charles Dupin, while he was still a student at the École polytechnique following Gaspard Monge's lectures. The key property of a Dupin cyclide is that it is a channel surface (envelope of a one-parameter family of spheres) in two different ways. This propert... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dupin cyclide Summary Dupin_cyclide Dupin cyclides are often simply known as cyclides, but the latter term is also used to refer to a more general class of quartic surfaces which are important in the theory of separation of variables for the Laplace equation in three dimensions. Dupin cyclides were investigated not onl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean distance matrix Summary Euclidean_distance_matrix In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} in k-dimensional space ℝk, the elements of their Euclidean d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean distance matrix Summary Euclidean_distance_matrix However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. Euclidean distance matrices are closely related to Gram matrices (matrices of dot products, describing norms of vect... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean distance matrix Summary Euclidean_distance_matrix This allows to characterize Euclidean distance matrices and recover the points x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} that realize it. A realization, if it exists, is unique up to rigid transformations, i.e. distance-preserving transform... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean distance matrix Summary Euclidean_distance_matrix The goal may be to visualize such data by points in Euclidean space whose distance matrix approximates a given dissimilarity matrix as well as possible — this is known as multidimensional scaling. Alternatively, given two sets of data already represented by po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean field Summary Euclidean_closure In mathematics, a Euclidean field is an ordered field K for which every non-negative element is a square: that is, x ≥ 0 in K implies that x = y2 for some y in K. The constructible numbers form a Euclidean field. It is the smallest Euclidean field, as every Euclidean field cont... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Indirect isometry Summary Special_Euclidean_group In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\displaystyle \mathbb {E} ^{n}} ; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Indirect isometry Summary Special_Euclidean_group A Euclidean isometry can be direct or indirect, depending on whether it preserves the handedness of figures. The direct Euclidean isometries form a subgroup, the special Euclidean group, often denoted SE(n), whose elements are called rigid motions or Euclidean motions. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Euclidean plane Summary Plane_coordinates In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E2. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fatou–Bieberbach domain Summary Fatou–Bieberbach_domain In mathematics, a Fatou–Bieberbach domain is a proper subdomain of C n {\displaystyle \mathbb {C} ^{n}} , biholomorphically equivalent to C n {\displaystyle \mathbb {C} ^{n}} . That is, an open set Ω ⊊ C n {\displaystyle \Omega \subsetneq \mathbb {C} ^{n}} is call... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fedosov manifold Summary Fedosov_manifold In mathematics, a Fedosov manifold is a symplectic manifold with a compatible torsion-free connection, that is, a triple (M, ω, ∇), where (M, ω) is a symplectic manifold (that is, ω {\displaystyle \omega } is a symplectic form, a non-degenerate closed exterior 2-form, on a C ∞ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fedosov manifold Summary Fedosov_manifold In other words, the symplectic form is parallel with respect to the connection, i.e., its covariant derivative vanishes.) Note that every symplectic manifold admits a symplectic torsion-free connection. Cover the manifold with Darboux charts and on each chart define a connectio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fekete polynomial Summary Fekete_polynomial In mathematics, a Fekete polynomial is a polynomial f p ( t ) := ∑ a = 0 p − 1 ( a p ) t a {\displaystyle f_{p}(t):=\sum _{a=0}^{p-1}\left({\frac {a}{p}}\right)t^{a}\,} where ( ⋅ p ) {\displaystyle \left({\frac {\cdot }{p}}\right)\,} is the Legendre symbol modulo some integer... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Feller-continuous process Summary Feller-continuous_process In mathematics, a Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the future depend continuously on the initial condition of the process. The concept is nam... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fermat numbers Summary Fermat_number In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form F n = 2 2 n + 1 , {\displaystyle F_{n}=2^{2^{n}}+1,} where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fermat quintic threefold Summary Fermat_quintic_threefold In mathematics, a Fermat quintic threefold is a special quintic threefold, in other words a degree 5, dimension 3 hypersurface in 4-dimensional complex projective space, given by the equation V 5 + W 5 + X 5 + Y 5 + Z 5 = 0 {\displaystyle V^{5}+W^{5}+X^{5}+Y^{5}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ford circle Summary Ford_circle In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the x {\displaystyle x} -axis at rational points. For each rational number p / q {\displaystyle p/q} , expressed in lowest terms, there is a Ford circle whose center is at the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fredholm kernel Summary Fredholm_kernel In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredho... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frey curve Summary Frey_curve In mathematics, a Frey curve or Frey–Hellegouarch curve is the elliptic curve y 2 = x ( x − a ℓ ) ( x + b ℓ ) {\displaystyle y^{2}=x(x-a^{\ell })(x+b^{\ell })} associated with a (hypothetical) solution of Fermat's equation a ℓ + b ℓ = c ℓ . {\displaystyle a^{\ell }+b^{\ell }=c^{\ell }.} Th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fricke involution Summary Fricke_involution In mathematics, a Fricke involution is the involution of the modular curve X0(N) given by τ → –1/Nτ. It is named after Robert Fricke. The Fricke involution also acts on other objects associated with the modular curve, such as spaces of modular forms and the Jacobian J0(N) of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frink ideal Summary Frink_ideal In mathematics, a Frink ideal, introduced by Orrin Frink, is a certain kind of subset of a partially ordered set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frobenius kernel Summary Frobenius_group In mathematics, a Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. They are named after F. G. Frobenius. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Frobenius splitting Summary Frobenius_splitting In mathematics, a Frobenius splitting, introduced by Mehta and Ramanathan (1985), is a splitting of the injective morphism OX→F*OX from a structure sheaf OX of a characteristic p > 0 variety X to its image F*OX under the Frobenius endomorphism F*. Brion & Kumar (2005) giv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fréchet surface Summary Fréchet_surface In mathematics, a Fréchet surface is an equivalence class of parametrized surfaces in a metric space. In other words, a Fréchet surface is a way of thinking about surfaces independently of how they are "written down" (parametrized). The concept is named after the French mathemati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fuchsian group Summary Fuchsian_group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper hal... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fuchsian group Summary Fuchsian_group In this case, the group may be called the Fuchsian group of the surface. In some sense, Fuchsian groups do for non-Euclidean geometry what crystallographic groups do for Euclidean geometry. Some Escher graphics are based on them (for the disc model of hyperbolic geometry). General ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Fuchsian model Summary Fuchsian_model In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R as a quotient of the upper half-plane H by a Fuchsian group. Every hyperbolic Riemann surface admits such a representation. The concept is named after Lazarus Fuchs. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Følner sequence Summary Følner_sequence In mathematics, a Følner sequence for a group is a sequence of sets satisfying a particular condition. If a group has a Følner sequence with respect to its action on itself, the group is amenable. A more general notion of Følner nets can be defined analogously, and is suited for ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
G-measure Summary G-measure In mathematics, a G-measure is a measure μ {\displaystyle \mu } that can be represented as the weak-∗ limit of a sequence of measurable functions G = ( G n ) n = 1 ∞ {\displaystyle G=\left(G_{n}\right)_{n=1}^{\infty }} . A classic example is the Riesz product G n ( t ) = ∏ k = 1 n ( 1 + r co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
GCD domain Summary GCD_domain In mathematics, a GCD domain is an integral domain R with the property that any two elements have a greatest common divisor (GCD); i.e., there is a unique minimal principal ideal containing the ideal generated by two given elements. Equivalently, any two elements of R have a least common m... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Galois field extension Summary Galois_field_extension In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal integral basis Summary ℓ-adic_representation In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but can ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Garside element Summary Garside_element In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. Formally, if M is a monoid, then an element Δ of M is said to be a Garside element if the set of all right divisors of Δ, { r ∈ M ∣ for some x ∈ M , Δ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Error curve Summary Error_curve In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gaussian rational Summary Gaussian_rational In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the Gaussian rational field, denoted Q(i), obtained by adjoining the imaginary number i to the field of rational... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gelfand pair Summary Gelfand_pair In mathematics, a Gelfand pair is a pair (G,K) consisting of a group G and a subgroup K (called an Euler subgroup of G) that satisfies a certain property on restricted representations. The theory of Gelfand pairs is closely related to the topic of spherical functions in the classical t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gelfand ring Summary Gelfand_ring In mathematics, a Gelfand ring is an associative ring R with identity such that if I and J are distinct right ideals then there are elements i and j such that iRj=0, i is not in I, and j is not in J. Mulvey (1979) introduced them as rings for which one could prove a generalization of G... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Generalized Clifford algebra Summary Clock_and_shift_matrices In mathematics, a Generalized Clifford algebra (GCA) is a unital associative algebra that generalizes the Clifford algebra, and goes back to the work of Hermann Weyl, who utilized and formalized these clock-and-shift operators introduced by J. J. Sylvester (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Goldman domain Summary Goldman_domain In mathematics, a Goldman domain or G-domain is an integral domain A whose field of fractions is a finitely generated algebra over A. They are named after Oscar Goldman. An overring (i.e., an intermediate ring lying between the ring and its field of fractions) of a Goldman domain i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Goldman domain Summary Goldman_domain A Goldman ideal is thus prime, but not necessarily maximal. In fact, a commutative ring is a Jacobson ring if and only if every Goldman ideal in it is maximal. The notion of a Goldman ideal can be used to give a slightly sharpened characterization of a radical of an ideal: the radi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Golomb ruler Summary Golomb_ruler In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart. The number of marks on the ruler is its order, and the largest distance between two of its marks is its length. Translation and reflection of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Golomb ruler Summary Golomb_ruler The Golomb ruler was named for Solomon W. Golomb and discovered independently by Sidon (1932) and Babcock (1953). Sophie Piccard also published early research on these sets, in 1939, stating as a theorem the claim that two Golomb rulers with the same distance set must be congruent. Thi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Golomb ruler Summary Golomb_ruler It has been proved that no perfect Golomb ruler exists for five or more marks. A Golomb ruler is optimal if no shorter Golomb ruler of the same order exists. Creating Golomb rulers is easy, but proving the optimal Golomb ruler (or rulers) for a specified order is computationally very c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Golomb ruler Summary Golomb_ruler Distributed.net has completed distributed massively parallel searches for optimal order-24 through order-28 Golomb rulers, each time confirming the suspected candidate ruler.Currently, the complexity of finding optimal Golomb rulers (OGRs) of arbitrary order n (where n is given in unar... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grassmann–Cayley algebra Summary Grassmann–Cayley_algebra In mathematics, a Grassmann–Cayley algebra is the exterior algebra with an additional product, which may be called the shuffle product or the regressive product. It is the most general structure in which projective properties are expressed in a coordinate-free w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Green’s function Summary Green’s_function In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if L {\displaystyle \operatorname {L} } is the linear differential operator,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gregory number Summary Gregory_number In mathematics, a Gregory number, named after James Gregory, is a real number of the form: G x = ∑ i = 0 ∞ ( − 1 ) i 1 ( 2 i + 1 ) x 2 i + 1 {\displaystyle G_{x}=\sum _{i=0}^{\infty }(-1)^{i}{\frac {1}{(2i+1)x^{2i+1}}}} where x is any rational number greater or equal to 1. Consider... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck category Summary Grothendieck_category In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these cat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck space Summary Grothendieck_space In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space X {\displaystyle X} in which every sequence in its continuous dual space X ′ {\displaystyle X^{\prime }} that converges in the weak-* topology σ ( X ′ , X ) {\displaystyle \sigma \le... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck universe Summary Grothendieck_universe In mathematics, a Grothendieck universe is a set U with the following properties: If x is an element of U and if y is an element of x, then y is also an element of U. (U is a transitive set.) If x and y are both elements of U, then { x , y } {\displaystyle \{x,y\}} is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck universe Summary Grothendieck_universe (In fact, uncountable Grothendieck universes provide models of set theory with the natural ∈-relation, natural powerset operation etc.). Elements of a Grothendieck universe are sometimes called small sets. The idea of universes is due to Alexander Grothendieck, who us... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Grothendieck universe Summary Grothendieck_universe The existence of a nontrivial Grothendieck universe goes beyond the usual axioms of Zermelo–Fraenkel set theory; in particular it would imply the existence of strongly inaccessible cardinals. Tarski–Grothendieck set theory is an axiomatic treatment of set theory, used... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Data encoding Gödel code Information_encoding > Examples > Gödel code In mathematics, a Gödel code was the basis for the proof of Gödel's incompleteness theorem. Here, the idea was to map mathematical notation to a natural number (using a Gödel numbering). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gödel numbering for sequences Summary Gödel_numbering_for_sequences In mathematics, a Gödel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. While a set theoretical embedding is surely possible, the emphasis is on the effectiveness of the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadamard manifold Summary Hadamard_manifold In mathematics, a Hadamard manifold, named after Jacques Hadamard — more often called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold ( M , g ) {\displaystyle (M,g)} that is complete and simply connected and has everywhere non-positive sectional curva... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadamard matrix Summary Hadamard_conjecture In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric terms, this means that each pair of rows in a Hadamard matrix represents two per... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hadamard matrix Summary Hadamard_conjecture The n-dimensional parallelotope spanned by the rows of an n×n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant among ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haefliger structure Summary Haefliger_structure In mathematics, a Haefliger structure on a topological space is a generalization of a foliation of a manifold, introduced by André Haefliger in 1970. Any foliation on a manifold induces a special kind of Haefliger structure, which uniquely determines the foliation. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haken hierarchy Summary Haken_manifold In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Haken hierarchy Summary Haken_manifold This conjecture was proven by Ian Agol.Haken manifolds were introduced by Wolfgang Haken (1961). Haken (1962) proved that Haken manifolds have a hierarchy, where they can be split up into 3-balls along incompressible surfaces. Haken also showed that there was a finite procedure to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hall plane of order 9 Summary Hall_plane_of_order_9 In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order p2n for every prime p and every positive integer n provided p2n > 4. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hamiltonian matrix Summary Hamiltonian_matrix In mathematics, a Hamiltonian matrix is a 2n-by-2n matrix A such that JA is symmetric, where J is the skew-symmetric matrix J = {\displaystyle J={\begin{bmatrix}0_{n}&I_{n}\\-I_{n}&0_{n}\\\end{bmatrix}}} and In is the n-by-n identity matrix. In other words, A is Hamiltonia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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