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c_qg8h7pdelk62 | In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to (+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values o... | Hankel contour |
c_b8dj5za3cs2o | The contour is traversed in the positively-oriented sense, meaning that the circle around the origin is traversed counter-clockwise. Use of Hankel contours is one of the methods of contour integration. This type of path for contour integrals was first used by Hermann Hankel in his investigations of the Gamma function. ... | Hankel contour |
c_6dcativrru4a | In mathematics, a Hardy field is a field consisting of germs of real-valued functions at infinity that are closed under differentiation. They are named after the English mathematician G. H. Hardy. | Hardy field |
c_ol2e0qhtksyt | In mathematics, a Hartshorne ellipse is an ellipse in the unit ball bounded by the 4-sphere S4 such that the ellipse and the circle given by intersection of its plane with S4 satisfy the Poncelet condition that there is a triangle with vertices on the circle and edges tangent to the ellipse. They were introduced by Har... | Hartshorne ellipse |
c_5i1sbd3ttk5p | In mathematics, a Hasse–Schmidt derivation is an extension of the notion of a derivation. The concept was introduced by Schmidt & Hasse (1937). | Hasse–Schmidt derivation |
c_q52n3ahd5xrv | In mathematics, a Hausdorff gap consists roughly of two collections of sequences of integers, such that there is no sequence lying between the two collections. The first example was found by Hausdorff (1909). The existence of Hausdorff gaps shows that the partially ordered set of possible growth rates of sequences is n... | Hausdorff gap |
c_jiwvjmm1o6te | In mathematics, a Hausdorff space X is called a fixed-point space if every continuous function f: X → X {\displaystyle f:X\rightarrow X} has a fixed point. For example, any closed interval in R {\displaystyle \mathbb {R} } is a fixed point space, and it can be proved from the intermediate value property of real contin... | Fixed-point space |
c_nfxffn8u21mw | To see it, consider the function f ( x ) = a + 1 b − a ⋅ ( x − a ) 2 {\displaystyle f(x)=a+{\frac {1}{b-a}}\cdot (x-a)^{2}} , for example. Any linearly ordered space that is connected and has a top and a bottom element is a fixed point space. Note that, in the definition, we could easily have disposed of the condition ... | Fixed-point space |
c_ekipx7qh3ua4 | In mathematics, a Hausdorff space is said to be H-closed, or Hausdorff closed, or absolutely closed if it is closed in every Hausdorff space containing it as a subspace. This property is a generalization of compactness, since a compact subset of a Hausdorff space is closed. Thus, every compact Hausdorff space is H-clos... | H-closed space |
c_yvc938hfzrr7 | In mathematics, a Hecke algebra is classically the algebra of Hecke operators studied by Erich Hecke. It may also refer to one of several algebras (some of which are related to the classical Hecke algebra): Iwahori–Hecke algebra of a Coxeter group. Hecke algebra of a pair (g,K) where g is the Lie algebra of a Lie group... | Hecke algebra (disambiguation) |
c_96ci69s852vq | In mathematics, a Hecke algebra of a locally compact group is an algebra of bi-invariant measures under convolution. | Hecke algebra of a locally compact group |
c_3rlvhid8dnle | In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one. | Heegner point |
c_zmf9z6kfrpjh | In mathematics, a Heilbronn set is an infinite set S of natural numbers for which every real number can be arbitrarily closely approximated by a fraction whose denominator is in S. For any given real number θ {\displaystyle \theta } and natural number h {\displaystyle h} , it is easy to find the integer g {\displaystyl... | Heilbronn set |
c_i8b1qlh6bj6o | In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel's lemma holds. They were introduced by Azumaya (1951), who named them after Kurt Hensel. Azumaya originally allowed Henselian rings to be non-commutative, but most authors now restrict them to be commutative. Some standard references for ... | Henselian field |
c_xiupykjbn5rg | In mathematics, a Hermitian connection ∇ {\displaystyle \nabla } is a connection on a Hermitian vector bundle E {\displaystyle E} over a smooth manifold M {\displaystyle M} which is compatible with the Hermitian metric ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } on E {\displaystyle E} , meaning that v ⟨ s ,... | Hermitian connection |
c_i072q034f688 | In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian... | Hermitian matrices |
c_7i1csqb7g189 | In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian sy... | Hermitian symmetric domain |
c_e47f38vv245e | The irreducible spaces arise in pairs as a non-compact space that, as Borel showed, can be embedded as an open subspace of its compact dual space. Harish Chandra showed that each non-compact space can be realized as a bounded symmetric domain in a complex vector space. The simplest case involves the groups SU(2), SU(1,... | Hermitian symmetric domain |
c_j2yfe2ghitml | In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex plane C. The one-point compactification of C, the Riemann sphere, is the dual space, a homogeneous space for SU(2) and SL(2,C). Irreducible compact Hermitian symmetric spaces are exactly the homog... | Hermitian symmetric domain |
c_pnupzljmm2qi | In mathematics, a Hessian pair or Hessian duad, named for Otto Hesse, is a pair of points of the projective line canonically associated with a set of 3 points of the projective line. More generally, one can define the Hessian pair of any triple of elements from a set that can be identified with a projective line, such ... | Hessian pair |
c_mt404515664a | In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that (c ∧ a) ≤ b is equivalent to c ≤ (a → b). From a logical standpoin... | Heyting algebra |
c_rqvnqau1kger | As lattices, Heyting algebras are distributive. Every Boolean algebra is a Heyting algebra when a → b is defined as ¬a ∨ b, as is every complete distributive lattice satisfying a one-sided infinite distributive law when a → b is taken to be the supremum of the set of all c for which c ∧ a ≤ b. In the finite case, every... | Heyting algebra |
c_983n0404dj6z | Although the negation operation ¬a is not part of the definition, it is definable as a → 0. The intuitive content of ¬a is the proposition that to assume a would lead to a contradiction. The definition implies that a ∧ ¬a = 0. | Heyting algebra |
c_dh6pdrc839e3 | It can further be shown that a ≤ ¬¬a, although the converse, ¬¬a ≤ a, is not true in general, that is, double negation elimination does not hold in general in a Heyting algebra. Heyting algebras generalize Boolean algebras in the sense that Boolean algebras are precisely the Heyting algebras satisfying a ∨ ¬a = 1 (excl... | Heyting algebra |
c_neh50r32iu7c | The internal logic of an elementary topos is based on the Heyting algebra of subobjects of the terminal object 1 ordered by inclusion, equivalently the morphisms from 1 to the subobject classifier Ω. The open sets of any topological space form a complete Heyting algebra. Complete Heyting algebras thus become a central ... | Heyting algebra |
c_qqg4yd6vp8z4 | It follows that even among the finite Heyting algebras there exist infinitely many that are subdirectly irreducible, no two of which have the same equational theory. Hence no finite set of finite Heyting algebras can supply all the counterexamples to non-laws of Heyting algebra. This is in sharp contrast to Boolean alg... | Heyting algebra |
c_pbtks4ff302k | In mathematics, a Higgs bundle is a pair ( E , φ ) {\displaystyle (E,\varphi )} consisting of a holomorphic vector bundle E and a Higgs field φ {\displaystyle \varphi } , a holomorphic 1-form taking values in the bundle of endomorphisms of E such that φ ∧ φ = 0 {\displaystyle \varphi \wedge \varphi =0} . Such pairs wer... | Higgs bundle |
c_dqspelnn48xz | In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dime... | Hilbert bundle |
c_d6oz442le8b2 | In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function on the m-fold product of upper half-planes H {\displaystyle {\mathcal {H}}} satisfying a certain kind of functional equation. | Hilbert modular form |
c_h9qrq88fay8a | In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular variety is an algebraic variety obtained by taking a quotient of a product of mul... | Hilbert modular surface |
c_onsvfm54zfpf | In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain (an open and connected set) Ω in n-dimensional Euclidean space Rn, a Hilbert–Schmidt kernel is a function k: Ω × Ω → C with ∫ Ω ∫ Ω | k ( x , y ) | 2 d x d y < ∞ {\displaystyle \int _{\Omega }\int _{\Omega ... | Hilbert–Schmidt integral operator |
c_sdv8b2lk7dl3 | {\displaystyle \Vert K\Vert _{\mathrm {HS} }=\Vert k\Vert _{L^{2}}.} Hilbert–Schmidt integral operators are both continuous (and hence bounded) and compact (as with all Hilbert–Schmidt operators). The concept of a Hilbert–Schmidt operator may be extended to any locally compact Hausdorff spaces. | Hilbert–Schmidt integral operator |
c_o6kblt8whg3t | Specifically, let X be a locally compact Hausdorff space equipped with a positive Borel measure. Suppose further that L2(X) is a separable Hilbert space. The above condition on the kernel k on Rn can be interpreted as demanding k belong to L2(X × X). | Hilbert–Schmidt integral operator |
c_9bwl486lr7u2 | Then the operator ( K f ) ( x ) = ∫ X k ( x , y ) f ( y ) d y {\displaystyle (Kf)(x)=\int _{X}k(x,y)f(y)\,dy} is compact. If k ( x , y ) = k ( y , x ) ¯ {\displaystyle k(x,y)={\overline {k(y,x)}}} then K is also self-adjoint and so the spectral theorem applies. This is one of the fundamental constructions of such opera... | Hilbert–Schmidt integral operator |
c_32hserpe3br8 | In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A: H → H {\displaystyle A\colon H\to H} that acts on a Hilbert space H {\displaystyle H} and has finite Hilbert–Schmidt norm where { e i: i ∈ I } {\displaystyle \{e_{i}:i\in I\}} is an orthonormal basis. The ... | Hilbert–Schmidt operator |
c_lptqu4lf0nz0 | In mathematics, a Hironaka decomposition is a representation of an algebra over a field as a finitely generated free module over a polynomial subalgebra or a regular local ring. Such decompositions are named after Heisuke Hironaka, who used this in his unpublished master's thesis at Kyoto University (Nagata 1962, p.217... | Miracle flatness |
c_r3crxegxmpb5 | In mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by Friedrich Hirzebruch (1951). | Hirzebruch surface |
c_0z66j2vb9mtk | In mathematics, a Hodge algebra or algebra with straightening law is a commutative algebra that is a free module over some ring R, together with a given basis similar to the basis of standard monomials of the coordinate ring of a Grassmannian. Hodge algebras were introduced by Corrado De Concini, David Eisenbud, and Cl... | Hodge algebra |
c_3au07u6uipfi | In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. Hodge structures have been generalized for all complex varieties (even if they are singula... | Hodge filtration |
c_t442shjk89ba | In mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre (1967) introduced and named Hodge–Tate structures using the results of Tate (1967) on p-divisible groups. | Hodge-Tate theory |
c_zgx1i69dxhb3 | In mathematics, a Hofstadter sequence is a member of a family of related integer sequences defined by non-linear recurrence relations. | Hofstadter sequence |
c_mmmdpu3jmoqa | Also as a consequence of the properties of quasitriangularity, ( ϵ ⊗ 1 ) R = ( 1 ⊗ ϵ ) R = 1 ∈ H {\displaystyle (\epsilon \otimes 1)R=(1\otimes \epsilon )R=1\in H} ; moreover R − 1 = ( S ⊗ 1 ) ( R ) {\displaystyle R^{-1}=(S\otimes 1)(R)} , R = ( 1 ⊗ S ) ( R − 1 ) {\displaystyle R=(1\otimes S)(R^{-1})} , and ( S ⊗ S ) (... | Quasitriangular Hopf algebra |
c_zkmpx1ckrl3m | In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property. The re... | Hopf algebra |
c_o6ivlt25zwip | In mathematics, a Hopfian group is a group G for which every epimorphism G → Gis an isomorphism. Equivalently, a group is Hopfian if and only if it is not isomorphic to any of its proper quotients. A group G is co-Hopfian if every monomorphism G → Gis an isomorphism. Equivalently, G is not isomorphic to any of its prop... | Hopfian group |
c_pymp1y049ddj | In mathematics, a Hughes plane is one of the non-Desarguesian projective planes found by Hughes (1957). There are examples of order p2n for every odd prime p and every positive integer n. | Hughes plane |
c_zj3x4hvzp0xz | In mathematics, a Hurewicz space is a topological space that satisfies a certain basic selection principle that generalizes σ-compactness. A Hurewicz space is a space in which for every sequence of open covers U 1 , U 2 , … {\displaystyle {\mathcal {U}}_{1},{\mathcal {U}}_{2},\ldots } of the space there are finite sets... | Hurewicz space |
c_li4pdzd4ifh2 | In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients of a real polynomial. | Hurwitz matrix |
c_sowsjix4t6lw | In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative. Such a polynomial must have coefficients that are positive real numbers. The te... | Hurwitz polynomial |
c_p9y1gmitsvrv | P(s) is real when s is real.2. The roots of P(s) have real parts which are zero or negative.Hurwitz polynomials are important in control systems theory, because they represent the characteristic equations of stable linear systems. Whether a polynomial is Hurwitz can be determined by solving the equation to find the roo... | Hurwitz polynomial |
c_ryodh9lxxyeb | In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd integers; a mixture of integers and half-integers is excluded). The set of all Hurwitz quaternions is H = { a + b i + c j + d k ∈ H ∣ a , b , c , d ∈ Z or a , b , c , d ... | Integral quaternion |
c_bfw4ajrtyrug | That is, either a, b, c, d are all integers, or they are all half-integers. H is closed under quaternion multiplication and addition, which makes it a subring of the ring of all quaternions H. Hurwitz quaternions were introduced by Adolf Hurwitz (1919). A Lipschitz quaternion (or Lipschitz integer) is a quaternion whos... | Integral quaternion |
c_cyy8yme4rfo7 | In mathematics, a Inoue–Hirzebruch surface is a complex surface with no meromorphic functions introduced by Inoue (1977). They have Kodaira dimension κ = −∞, and are non-algebraic surfaces of class VII with positive second Betti number. Sankaran (1987) studied some higher-dimensional analogues. | Inoue-Hirzebruch surface |
c_galf5k0wxi92 | In mathematics, a J-structure is an algebraic structure over a field related to a Jordan algebra. The concept was introduced by Springer (1973) to develop a theory of Jordan algebras using linear algebraic groups and axioms taking the Jordan inversion as basic operation and Hua's identity as a basic relation. There is ... | J-structure |
c_l5v8tr4byq9m | In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a, 1906b, 1905a, 1905b). The third Jackson q-Bessel function is the same as the Hahn–Exton q-Bessel function. | Jackson q-Bessel function |
c_6l41pjkg50uo | In mathematics, a Jacobi form is an automorphic form on the Jacobi group, which is the semidirect product of the symplectic group Sp(n;R) and the Heisenberg group H R ( n , h ) {\displaystyle H_{R}^{(n,h)}} . The theory was first systematically studied by Eichler & Zagier (1985). | Jacobi form |
c_tcr58vk1gfje | In mathematics, a Jacobi sum is a type of character sum formed with Dirichlet characters. Simple examples would be Jacobi sums J(χ, ψ) for Dirichlet characters χ, ψ modulo a prime number p, defined by J ( χ , ψ ) = ∑ χ ( a ) ψ ( 1 − a ) , {\displaystyle J(\chi ,\psi )=\sum \chi (a)\psi (1-a)\,,} where the summation run... | Jacobi sum |
c_nh52que747vo | Jacobi sums J can be factored generically into products of powers of Gauss sums g. For example, when the character χψ is nontrivial, J ( χ , ψ ) = g ( χ ) g ( ψ ) g ( χ ψ ) , {\displaystyle J(\chi ,\psi )={\frac {g(\chi )g(\psi )}{g(\chi \psi )}}\,,} analogous to the formula for the beta function in terms of gamma func... | Jacobi sum |
c_pc0l1g7xfsgk | Like Gauss sums, Jacobi sums have known prime ideal factorisations in their cyclotomic fields; see Stickelberger's theorem. When χ is the Legendre symbol, J ( χ , χ ) = − χ ( − 1 ) = ( − 1 ) p + 1 2 . | Jacobi sum |
c_y0f3edlav72s | {\displaystyle J(\chi ,\chi )=-\chi (-1)=(-1)^{\frac {p+1}{2}}\,.} In general the values of Jacobi sums occur in relation with the local zeta-functions of diagonal forms. The result on the Legendre symbol amounts to the formula p + 1 for the number of points on a conic section that is a projective line over the field o... | Jacobi sum |
c_yhbp2wxrcjvg | A paper of André Weil from 1949 very much revived the subject. Indeed, through the Hasse–Davenport relation of the late 20th century, the formal properties of powers of Gauss sums had become current once more. As well as pointing out the possibility of writing down local zeta-functions for diagonal hypersurfaces by mea... | Jacobi sum |
c_u0x2v9vw6fcz | This was to become important once the complex multiplication of abelian varieties became established. The Hecke characters in question were exactly those one needs to express the Hasse–Weil L-functions of the Fermat curves, for example. The exact conductors of these characters, a question Weil had left open, were deter... | Jacobi sum |
c_xgdevhzbjxw3 | In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to: Jacobian matrix and determinant Jacobian elliptic functions Jacobian variety Intermediate Jacobian | Jacobian |
c_6fl1awpb3u7l | In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring, for which Krull dimension behaves as expected in polynomial extensions. They are named for Paul Jaffard who first studied them in 1960. Formally, a Jaffard ring is a ring R such that the polynomial ring dim R = n + dim R , {\dis... | Jaffard ring |
c_il8qbg5cdi73 | A Jaffard ring that is also an integral domain is called a Jaffard domain. The Jaffard property is satisfied by any Noetherian ring R, and examples of non-Noetherian rings might appear to be quite difficult to find, however they do arise naturally. For example, the ring of (all) algebraic integers, or more generally, a... | Jaffard ring |
c_x8nnokh2coz8 | In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness of any such system. It was introduced in 1920 by Maurice Janet. It was first called the Janet basis by Fritz Schwarz in 1998.The left hand sides of such systems ... | Janet basis |
c_qx0l8hl8fwth | By abuse of language, this terminology will be applied both to the original system and the ideal of differential polynomials generated by the left hand sides. A Janet basis is the predecessor of a Gröbner basis introduced by Bruno Buchberger for polynomial ideals. In order to generate a Janet basis for any given system... | Janet basis |
c_x1f3gku2q6qd | In mathematics, a Jónsson–Tarski algebra or Cantor algebra is an algebraic structure encoding a bijection from an infinite set X onto the product X×X. They were introduced by Bjarni Jónsson and Alfred Tarski (1961, Theorem 5). Smirnov (1971), named them after Georg Cantor because of Cantor's pairing function and Cantor... | Jónsson–Tarski algebra |
c_mlysd1ycypt0 | In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-di... | Kac algebra |
c_fbp9o1lvt8tn | In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 in three-dimensional space, forms a Kakeya set. Much of the research in this area has studied ... | Kakeya conjecture |
c_wm836z3c4lgn | Besicovitch showed that there are Besicovitch sets of measure zero. A Kakeya needle set (sometimes also known as a Kakeya set) is a (Besicovitch) set in the plane with a stronger property, that a unit line segment can be rotated continuously through 180 degrees within it, returning to its original position with reverse... | Kakeya conjecture |
c_zqfxq2lo3k66 | In mathematics, a Kato surface is a compact complex surface with positive first Betti number that has a global spherical shell. Kato (1978) showed that Kato surfaces have small analytic deformations that are the blowups of primary Hopf surfaces at a finite number of points. In particular they have an infinite cyclic fu... | Kato surface |
c_t40c9karhg4s | In mathematics, a Kempe chain is a device used mainly in the study of the four colour theorem. Intuitively, it is a connected chain of points on a graph with alternating colors. | Kempe chain |
c_51tvjipwqkqz | In mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields. It is a concept in pseudo-Riemannian geometry, and is mainly used in the theory of general relativity. Killing tensors satisfy an equation similar to Killing's equ... | Killing tensor |
c_djtcl407pntu | Like Killing vectors, every Killing tensor corresponds to a quantity which is conserved along geodesics. However, unlike Killing vectors, which are associated with symmetries (isometries) of a manifold, Killing tensors generally lack such a direct geometric interpretation. Killing tensors are named after Wilhelm Killin... | Killing tensor |
c_9e7itjw13jur | In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuo... | Killing vectors |
c_43n46ck59mib | In mathematics, a Kleene algebra ( KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions. | Regular algebra |
c_g3a7uzmrm0br | In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts as the symmetry group of the geometry. For background and motivation see the article on ... | Klein geometry |
c_db8dfbjjfua3 | In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize Riemann surfaces. While the latter are used to study algebraic curves over the complex numbers analytically, the former are used to study algebraic cu... | Klein surface |
c_d94uruu38bk5 | Klein surfaces were introduced by Felix Klein in 1882.A Klein surface is a surface (i.e., a differentiable manifold of real dimension 2) on which the notion of angle between two tangent vectors at a given point is well-defined, and so is the angle between two intersecting curves on the surface. These angles are in the ... | Klein surface |
c_ipzbn0hczfut | In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable with PSL(2, C), is the quotient group of the 2 by 2 complex matrices of determinant 1 by their center, which consists of the identity matrix and its product by −1.... | Kleinian group |
c_f2by1m5arb7n | In mathematics, a Kleinian model is a model of a three-dimensional hyperbolic manifold N by the quotient space H 3 / Γ {\displaystyle \mathbb {H} ^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a discrete subgroup of PSL(2,C). Here, the subgroup Γ {\displaystyle \Gamma } , a Kleinian group, is defined so that it is is... | Kleinian model |
c_328gvmnpv3i0 | In mathematics, a Kline sphere characterization, named after John Robert Kline, is a topological characterization of a two-dimensional sphere in terms of what sort of subset separates it. Its proof was one of the first notable accomplishments of R. H. Bing; Bing gave an alternate proof using brick partitioning in his p... | Kline sphere characterization |
c_manvmex0y6j9 | In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents. Given n + 1 knots, p0, ..., pn,to be interpolated with n cubic Hermite curve segments, for each curve we have a starting point pi an... | Kochanek–Bartels spline |
c_16qfnhm1bi5a | In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. The concept is named after Kunihiko Kodaira. These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira surfaces with trivial... | Kodaira surface |
c_fmzuwqonsrv6 | The secondary Kodaira surfaces have the same relation to primary ones that Enriques surfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants: If the surface is the quotient of a primary Kodaira surface by a group of order k = 1,2,3,4,6, then the plurigenera Pn are 1 if n is divisible by... | Kodaira surface |
c_za9iqhowwbo2 | In mathematics, a Koecher–Maass series is a type of Dirichlet series that can be expressed as a Mellin transform of a Siegel modular form, generalizing Hecke's method of associating a Dirichlet series to a modular form using Mellin transforms. They were introduced by Koecher (1953) and Maass (1950). | Koecher–Maass series |
c_4ylbdbphbn0q | In mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability space that obeys Kolmogorov's zero–one law. All Bernoulli automorphisms are K-automorphisms (one says they have the K-property), but not vice versa. Many erg... | Kolmogorov system |
c_qqkm1ftbwtct | In mathematics, a Koszul–Tate resolution or Koszul–Tate complex of the quotient ring R/M is a projective resolution of it as an R-module which also has a structure of a dg-algebra over R, where R is a commutative ring and M ⊂ R is an ideal. They were introduced by Tate (1957) as a generalization of the Koszul resolutio... | Koszul–Tate resolution |
c_i9ozemzt230i | In mathematics, a Lagrangian foliation or polarization is a foliation of a symplectic manifold, whose leaves are Lagrangian submanifolds. It is one of the steps involved in the geometric quantization of a square-integrable functions on a symplectic manifold. | Lagrangian foliation |
c_m7bf1qlsiaft | In mathematics, a Lagrangian system is a pair (Y, L), consisting of a smooth fiber bundle Y → X and a Lagrangian density L, which yields the Euler–Lagrange differential operator acting on sections of Y → X. In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangi... | Lagrangian system |
c_qtbmgu349x73 | In mathematics, a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Laguerre planes are named after the French mathematician Edmond Nicolas Laguerre. The classical Laguerre plane is an incidence structure that describes the incidence behaviour of the... | Laguerre plane |
c_4sb9mmdj4s00 | In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form S ( q ) = ∑ n = 1 ∞ a n q n 1 − q n . {\displaystyle S(q)=\sum _{n=1}^{\infty }a_{n}{\frac {q^{n}}{1-q^{n}}}.} It can be resumed formally by expanding the denominator: S ( q ) = ∑ n = 1 ∞ a n ∑ k = 1 ∞ q n k = ∑ m = 1 ∞ b m... | Lambert series |
c_yelwaqr8vpkp | In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation. It was introduced in the paper (Gabriel Lamé 1837). Lamé's equation appears in the method of separation of variables applied to the Laplace equation in elliptic coordinates... | Lamé function |
c_fxgtz9eko21y | In mathematics, a Lattès map is a rational map f = ΘLΘ−1 from the complex sphere to itself such that Θ is a holomorphic map from a complex torus to the complex sphere and L is an affine map z → az + b from the complex torus to itself. Lattès maps are named after French mathematician Samuel Lattès, who wrote about them ... | Lattès map |
c_ae3ls0u6iwf9 | In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field F {\displaystyle \mathbb {F} } is a linear combination of positive and negative powers of the variable with coefficients in F {\displaystyle \mathbb {F} } . Laurent polynomials in X form a ring denoted F {\displayst... | Laurent polynomials |
c_qplwfcyqsoog | In mathematics, a Lawvere–Tierney topology is an analog of a Grothendieck topology for an arbitrary topos, used to construct a topos of sheaves. A Lawvere–Tierney topology is also sometimes also called a local operator or coverage or topology or geometric modality. They were introduced by William Lawvere (1971) and Myl... | Lawvere–Tierney topology |
c_vmxlzfuek0hb | In mathematics, a LeBrun manifold is a connected sum of copies of the complex projective plane, equipped with an explicit self-dual metric. Here, self-dual means that the Weyl tensor is its own Hodge star. The metric is determined by the choice of a finite collection of points in hyperbolic 3-space. These metrics were ... | Lebrun manifold |
c_mhz7x4ea847a | In mathematics, a Leavitt path algebra is a universal algebra constructed from a directed graph. Leavitt path algebras generalize Leavitt algebras and may be considered as algebraic analogues of graph C*-algebras. | Leavitt path algebra |
c_xzowm534ycar | In mathematics, a Lefschetz manifold is a particular kind of symplectic manifold ( M 2 n , ω ) {\displaystyle (M^{2n},\omega )} , sharing a certain cohomological property with Kähler manifolds, that of satisfying the conclusion of the Hard Lefschetz theorem. More precisely, the strong Lefschetz property asks that for k... | Lefschetz manifold |
c_5fc28fqxths6 | In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an algebraic variety V. | Lefschetz pencil |
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