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c_ih0dnnoekqwm | In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodular lattices of rank 24, which were classified by Hans-Volker Niemeier (1973). Venkov (1978) gave a simplified proof of the classification. In the 1970s, Witt (1941) has a sentence mentioning that he found more than 10 such lattices in th... | Niemeier lattice |
c_s1f43bjk46eu | In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively. That is, every increasing sequence I 1 ⊆ I 2 ⊆ I 3 ⊆ ⋯ ... | Noetherian rings |
c_9zp4oygr7nmg | Equivalently, a ring is left-Noetherian (resp. right-Noetherian) if every left ideal (resp. right-ideal) is finitely generated. | Noetherian rings |
c_3o0ejwz43lf7 | A ring is Noetherian if it is both left- and right-Noetherian. Noetherian rings are fundamental in both commutative and noncommutative ring theory since many rings that are encountered in mathematics are Noetherian (in particular the ring of integers, polynomial rings, and rings of algebraic integers in number fields),... | Noetherian rings |
c_3l5dpgbk6cfj | In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the complements of the closed subsets. The Noetherian prop... | Noetherian space |
c_t2jeega0pta6 | In mathematics, a Nori semistable vector bundle is a particular type of vector bundle whose first definition has been first implicitly suggested by Madhav V. Nori, as one of the main ingredients for the construction of the fundamental group scheme. The original definition given by Nori was obviously not called Nori sem... | Nori-semistable vector bundle |
c_43c0z5t4yqu3 | In mathematics, a Novikov–Shubin invariant, introduced by Sergei Novikov and Mikhail Shubin (1986), is an invariant of a compact Riemannian manifold related to the spectrum of the Laplace operator acting on square-integrable differential forms on its universal cover. The Novikov–Shubin invariant gives a measure of the ... | Novikov–Shubin invariant |
c_zdsau3a3azh7 | In mathematics, a Néron differential, named after André Néron, is an almost canonical choice of 1-form on an elliptic curve or abelian variety defined over a local field or global field. The Néron differential behaves well on the Néron minimal models. For an elliptic curve of the form y 2 + a 1 x y + a 3 y = x 3 + a 2 ... | Néron differential |
c_wovxyrvm2wd1 | In mathematics, a P-matrix is a complex square matrix with every principal minor is positive. A closely related class is that of P 0 {\displaystyle P_{0}} -matrices, which are the closure of the class of P-matrices, with every principal minor ≥ {\displaystyle \geq } 0. | P-matrix |
c_yh129fmxeve8 | In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k th powers for 1 ≤ k ≤ P. 2-multimagic cubes are called bimagic, 3-multimagic cubes are called trimagic, and 4-multimagic cubes tetramagic. A P-multimagic cube is said to be semi-perfect if the k th pow... | Tetramagic cube |
c_e4evmuwodc00 | The first known example of a bimagic cube was given by John Hendricks in 2000; it is a semiperfect cube of order 25 and magic constant 195325. In 2003, C. Bower discovered two semi-perfect bimagic cubes of order 16, and a perfect bimagic cube of order 32.MathWorld reports that only two trimagic cubes are known, discove... | Tetramagic cube |
c_ohn921n3r3e3 | In mathematics, a P-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. 2-multimagic squares are called bimagic, 3-multimagic squares are called trimagic, 4-multimagic squares tetramagic, and 5-multimagic squares... | Tetramagic square |
c_l0rkj7z5wjbq | In mathematics, a P2-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided R P 2 {\displaystyle \mathbb {R} P^{2}} (real projective plane). An orientable manifold is P2-irreducible if and only if it is irreducible. Every non-orientable P2-irreducible manifold is a Haken manifold. == Reference... | P2-irreducible manifold |
c_kj4xluvnzjsr | In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed around 1890 by Henri Padé, but goes... | Padé approximant |
c_qdsbdiqzpbuw | For these reasons Padé approximants are used extensively in computer calculations. They have also been used as auxiliary functions in Diophantine approximation and transcendental number theory, though for sharp results ad hoc methods—in some sense inspired by the Padé theory—typically replace them. Since Padé approxima... | Padé approximant |
c_qkbmvp8zuz5r | In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley (1907–1933) and Norbert Wiener (1894–1964). The original theorems did not use the language of distributions, and... | Paley–Wiener theorem |
c_sy7ai489phut | In mathematics, a Perron number is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than α in absolute value. For example, the larger of the two roots of the irreducible polynomial x 2 − 3 x + 1 {\displaystyle x^{2}-3x+1} is a Perron number. Perron numbers are named ... | Perron number |
c_52fvdr9jile6 | In mathematics, a Petersson algebra is a composition algebra over a field constructed from an order-3 automorphism of a Hurwitz algebra. They were first constructed by Petersson (1969). | Petersson algebra |
c_4dl1o8t3l1gx | In mathematics, a Petrovsky lacuna, named for the Russian mathematician I. G. Petrovsky, is a region where the fundamental solution of a linear hyperbolic partial differential equation vanishes. They were studied by Petrovsky (1945) who found topological conditions for their existence. Petrovsky's work was generalized ... | Petrovsky lacuna |
c_udprf30si1v3 | In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965. In what follows, quadratic forms are considered over a field F of characteristic not 2. For a natural number n, an n-fold Pfister form over F is a quadratic form of dimension 2n that can be written as a tensor... | Pfister form |
c_3gxi8nzzeo67 | An n-fold Pfister form can also be constructed inductively from an (n−1)-fold Pfister form q and a nonzero element a of F, as q ⊕ ( − a ) q {\displaystyle q\oplus (-a)q} . So the 1-fold and 2-fold Pfister forms look like: ⟨ ⟨ a ⟩ ⟩ ≅ ⟨ 1 , − a ⟩ = x 2 − a y 2 {\displaystyle \langle \!\langle a\rangle \!\rangle \cong \l... | Pfister form |
c_anv6985dixjs | {\displaystyle \langle \!\langle a,b\rangle \!\rangle \cong \langle 1,-a,-b,ab\rangle =x^{2}-ay^{2}-bz^{2}+abw^{2}.} For n ≤ 3, the n-fold Pfister forms are norm forms of composition algebras. In that case, two n-fold Pfister forms are isomorphic if and only if the corresponding composition algebras are isomorphic. In ... | Pfister form |
c_i4r7ugmh0m4w | In mathematics, a Picard modular group, studied by Picard (1881), is a group of the form SU(J,L), where L is a 3-dimensional lattice over the ring of integers of an imaginary quadratic field and J is a hermitian form on L of signature (2, 1). Picard modular groups act on the unit sphere in C2 and the quotient is called... | Picard modular group |
c_slgnkk5opwe7 | In mathematics, a Picard modular surface, studied by Picard (1881), is a complex surface constructed as a quotient of the unit ball in C2 by a Picard modular group. Picard modular surfaces are some of the simplest examples of Shimura varieties and are sometimes used as a test case for the general theory of Shimura vari... | Picard modular surface |
c_az3ley7kbn51 | In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute value. These numbers were discovered by Axel Thue in 1912 and rediscovered by G. H. Hardy in 1919 within the context of ... | PV number |
c_1h7mnmidskne | Tirukkannapuram Vijayaraghavan and Raphael Salem continued their study in the 1940s. Salem numbers are a closely related set of numbers. A characteristic property of PV numbers is that their powers approach integers at an exponential rate. | PV number |
c_quff66altkbb | Pisot proved a remarkable converse: if α > 1 is a real number such that the sequence ‖ α n ‖ {\displaystyle \|\alpha ^{n}\|} measuring the distance from its consecutive powers to the nearest integer is square-summable, or ℓ 2, then α is a Pisot number (and, in particular, algebraic). Building on this characterization o... | PV number |
c_kknkfjkfbixe | In mathematics, a Plücker formula, named after Julius Plücker, is one of a family of formulae, of a type first developed by Plücker in the 1830s, that relate certain numeric invariants of algebraic curves to corresponding invariants of their dual curves. The invariant called the genus, common to both the curve and its ... | Plücker formula |
c_8oxadjvi4zcm | In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition. Usually, either of the boundary conditions determines the solution. Thus... | Dirichlet-to-Neumann operator |
c_hp4ux1b3ou0x | In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structur... | Poisson algebra |
c_3k4iukgk5hkq | In mathematics, a Poisson ring is a commutative ring on which an anticommutative and distributive binary operation {\displaystyle } satisfying the Jacobi identity and the product rule is defined. Such an operation is then known as the Poisson bracket of the Poisson ring. Many important operations and results of symple... | Poisson ring |
c_q0egezna7frq | In mathematics, a Poisson superalgebra is a Z2-graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra A with a Lie superbracket : A ⊗ A → A {\displaystyle :A\otimes A\to A} such that (A, ) is a Lie superalgebra and the operator : A → A {\displaystyle :A\to A} i... | Poisson superbracket |
c_iag74131em95 | This gives the classical dynamics of fermion fields and classical spin-1/2 particles. The other is to define an antibracket algebra instead. This is used in the BRST and Batalin-Vilkovisky formalism. | Poisson superbracket |
c_rhpw22e7kxal | In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The infinitesimal counterpart of a Poisson–Lie group is a Lie bialgebra, in analogy to Lie algebras as the infinitesimal counterparts of ... | Poisson–Lie group |
c_lhwm8d3p8cfy | In mathematics, a Pontryagin cohomology operation is a cohomology operation taking cohomology classes in H2n(X,Z/prZ) to H2pn(X,Z/pr+1Z) for some prime number p. When p=2 these operations were introduced by Pontryagin (1942) and were named Pontrjagin squares by Whitehead (1949) (with the term "Pontryagin square" also b... | Pontryagin cohomology operation |
c_3yf6kap601z4 | In mathematics, a Priestley space is an ordered topological space with special properties. Priestley spaces are named after Hilary Priestley who introduced and investigated them. Priestley spaces play a fundamental role in the study of distributive lattices. In particular, there is a duality ("Priestley duality") betwe... | Priestley duality |
c_maek8t18l6hc | In mathematics, a Prym differential of a Riemann surface is a differential form on the universal covering space that transforms according to some complex character of the fundamental group. Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle. Prym d... | Prym differential |
c_v4ucrpnmk986 | In mathematics, a Prüfer domain is a type of commutative ring that generalizes Dedekind domains in a non-Noetherian context. These rings possess the nice ideal and module theoretic properties of Dedekind domains, but usually only for finitely generated modules. Prüfer domains are named after the German mathematician He... | Prüfer domain |
c_d0t10s8xyfrc | In mathematics, a Q-category or almost quotient category is a category that is a "milder version of a Grothendieck site." A Q-category is a coreflective subcategory. The Q stands for a quotient. The concept of Q-categories was introduced by Alexander Rosenberg in 1988. The motivation for the notion was its use in nonco... | Q-category |
c_0rasnfemvmbk | In mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q. | Q-matrix |
c_r7mki609f3dq | In mathematics, a Rajchman measure, studied by Rajchman (1928), is a regular Borel measure on a locally compact group such as the circle, whose Fourier transform vanishes at infinity. | Rajchman measure |
c_ssvknh0tz1d2 | In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function. | Ramanujan prime |
c_qkenbphhoho5 | In mathematics, a Ramanujan–Sato series generalizes Ramanujan’s pi formulas such as, 1 π = 2 2 99 2 ∑ k = 0 ∞ ( 4 k ) ! k ! 4 26390 k + 1103 396 4 k {\displaystyle {\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{99^{2}}}\sum _{k=0}^{\infty }{\frac {(4k)! | Ramanujan–Sato series |
c_yfl64smqujfy | }{k!^{4}}}{\frac {26390k+1103}{396^{4k}}}} to the form 1 π = ∑ k = 0 ∞ s ( k ) A k + B C k {\displaystyle {\frac {1}{\pi }}=\sum _{k=0}^{\infty }s(k){\frac {Ak+B}{C^{k}}}} by using other well-defined sequences of integers s ( k ) {\displaystyle s(k)} obeying a certain recurrence relation, sequences which may be express... | Ramanujan–Sato series |
c_pkd3fchyqxry | In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by Erdős & Hajnal (1962) and named after Frank P. Ramsey, whose theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable case. Let <ω denote the set of all finite subsets of κ. A cardi... | Ramsey cardinal |
c_kfsq6ypj2nuo | In mathematics, a Raynaud surface is a particular kind of algebraic surface that was introduced in William E. Lang (1979) and named for Michel Raynaud (1978). To be precise, a Raynaud surface is a quasi-elliptic surface over an algebraic curve of genus g greater than 1, such that all fibers are irreducible and the fibr... | Raynaud surface |
c_9sq0yuzeczmu | In mathematics, a Redheffer matrix, often denoted A n {\displaystyle A_{n}} as studied by Redheffer (1977), is a square (0,1) matrix whose entries aij are 1 if i divides j or if j = 1; otherwise, aij = 0. It is useful in some contexts to express Dirichlet convolution, or convolved divisors sums, in terms of matrix prod... | Redheffer matrix |
c_3uragaujdqjw | In mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree (1960, 1961) from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki groups found by Suzuki using a different method. They were the last of the infinite famil... | Ree group |
c_5ycl6gw9elvv | However, there are some exotic pseudo-reductive algebraic groups over non-perfect fields whose construction is related to the construction of Ree groups, as they use the same exotic automorphisms of Dynkin diagrams that change root lengths. Tits (1960) defined Ree groups over infinite fields of characteristics 2 and 3.... | Ree group |
c_fo1h906bq5st | In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification. It is actuall... | Relevance vector machine |
c_kvzj8v16pfov | In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form y ′ ( x ) = q 0 ( x ) + q 1 ( x ) y ( x ) + q 2 ( x ) y 2 ( x ) {\displaystyle y'(x)=q_{0}(x)+q_{1}(x)\,y(x)+q_{2}(x)\,y^{2... | Riccati differential equation |
c_ve81jh52fpeq | In mathematics, a Rickart space (after Charles Earl Rickart), also called a basically disconnected space, is a topological space in which open σ-compact subsets have compact open closures. Grove & Pedersen (1984) named them after C. E. Rickart (1946), who showed that Rickart spaces are related to monotone σ-complete C*... | Rickart space |
c_psi9t866jw6w | In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: A lattice Λ in a complex vector space Cg. An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations:the real linear extension αR:Cg × Cg→R of α satisfies αR(iv, iw)... | Riemann relations |
c_4201906hh1jr | In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations. The... | Rectangle method |
c_cx8zl47flarn | This approach can be used to find a numerical approximation for a definite integral even if the fundamental theorem of calculus does not make it easy to find a closed-form solution. Because the region by the small shapes is usually not exactly the same shape as the region being measured, the Riemann sum will differ fro... | Rectangle method |
c_3jvnjwo74r8j | In mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°. The universal cover of a complete flat manif... | Flat metric |
c_2o8s59p7dqrq | In mathematics, a Riemann–Roch theorem for smooth manifolds is a version of results such as the Hirzebruch–Riemann–Roch theorem or Grothendieck–Riemann–Roch theorem (GRR) without a hypothesis making the smooth manifolds involved carry a complex structure. Results of this kind were obtained by Michael Atiyah and Friedri... | Riemann–Roch theorem for smooth manifolds |
c_zuw7pb4pee8k | In mathematics, a Riesel number is an odd natural number k for which k × 2 n − 1 {\displaystyle k\times 2^{n}-1} is composite for all natural numbers n (sequence A101036 in the OEIS). In other words, when k is a Riesel number, all members of the following set are composite: { k × 2 n − 1: n ∈ N } . {\displaystyle \left... | Riesel problem |
c_edbg8tmae07b | In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper Sur la décomposition des opérations fonctionelles linéaires. Riesz spaces have wid... | Vector lattice |
c_yqfntgnsmy8h | In mathematics, a Ringel–Hall algebra is a generalization of the Hall algebra, studied by Claus Michael Ringel (1990). It has a basis of equivalence classes of objects of an abelian category, and the structure constants for this basis are related to the numbers of extensions of objects in the category. | Ringel–Hall algebra |
c_k3a83ou7nc99 | In mathematics, a Rosati involution, named after Carlo Rosati, is an involution of the rational endomorphism ring of an abelian variety induced by a polarization. Let A {\displaystyle A} be an abelian variety, let A ^ = P i c 0 ( A ) {\displaystyle {\hat {A}}=\mathrm {Pic} ^{0}(A)} be the dual abelian variety, and for ... | Rosati involution |
c_x3pahda4yxmo | In mathematics, a Rota–Baxter algebra is an associative algebra, together with a particular linear map R which satisfies the Rota–Baxter identity. It appeared first in the work of the American mathematician Glen E. Baxter in the realm of probability theory. Baxter's work was further explored from different angles by Gi... | Rota–Baxter algebra |
c_55gf4qzqos02 | In mathematics, a Rothberger space is a topological space that satisfies a certain a basic selection principle. A Rothberger 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 sets U 1 ∈ U 1 , U 2 ∈ U 2 , … {\dis... | Rothberger space |
c_10a3myhj1udl | In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: 714 = 2 × 3 × 7 × 17, 715 = 5 × 11 × 13,and 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29.There are different variations in the definition, depending on how many times to cou... | Ruth–Aaron pair |
c_ny8dyq1qkocc | In mathematics, a Salem number is a real algebraic integer α > 1 whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem. | Salem number |
c_gw3ufx0xcgq3 | In mathematics, a Sastry automorphism, is an automorphism of a field of characteristic 2 satisfying some rather complicated conditions related to the problem of embedding Ree groups of type 2F4 into Chevalley groups of type F4. They were introduced by Sastry (1995), and named and classified by Bombieri (2002) who showe... | Sastry automorphism |
c_rbosasvqnj7m | In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This makes Schauder bases more suitable for the analysis of infinite-dimension... | Schauder dimension |
c_3tzzzju9vrkq | In mathematics, a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834; his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces (the fir... | Scherk surface |
c_wxklwsnwd7s8 | In mathematics, a Schottky group is a special sort of Kleinian group, first studied by Friedrich Schottky (1877). | Schottky group |
c_7otyz116mywm | In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function f: R d → R {\displaystyle f:\mathbb {R} ^{d}\rightarrow \mathbb {R} } that for all x , y ∈ R d {\displaystyle x,y\in \mathbb {R} ^{d}} such that x {\displaystyle x} is majorized by y {\displays... | Schur-concave function |
c_5r3yb5zqi4bd | In mathematics, a Schwartz–Bruhat function, named after Laurent Schwartz and François Bruhat, is a complex valued function on a locally compact abelian group, such as the adeles, that generalizes a Schwartz function on a real vector space. A tempered distribution is defined as a continuous linear functional on the spac... | Schwartz–Bruhat function |
c_aetzxalfg1pf | In mathematics, a Segal category is a model of an infinity category introduced by Hirschowitz & Simpson (1998), based on work of Graeme Segal in 1974. | Segal category |
c_phadr5q120km | In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions iff it is the nerve of a category. The condition for Segal spaces ... | Segal space |
c_ky5vdsuwmxel | In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert surface. Se... | Seifert matrix |
c_wiket5ga81ol | Specifically, let L be a tame oriented knot or link in Euclidean 3-space (or in the 3-sphere). A Seifert surface is a compact, connected, oriented surface S embedded in 3-space whose boundary is L such that the orientation on L is just the induced orientation from S. Note that any compact, connected, oriented surface w... | Seifert matrix |
c_npkjf8k7m40i | In mathematics, a Severi variety is an algebraic variety in a Hilbert scheme that parametrizes curves in projective space with given degree and geometric genus and at most node singularities. Its dimension is 3d + g − 1. It is a theorem that Severi varieties are algebraic varieties, i.e. it is irreducible. | Severi variety (Hilbert scheme) |
c_djp1wurgthvj | In mathematics, a Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras in such a way that the algebra splits over K if and only if the variety has a rational point over K. Fra... | Severi–Brauer variety |
c_c4y6ac3iktet | They represent (at least if K is a perfect field) Galois cohomology classes in H1(PGLn), where PGLn is the projective linear group, and n is the dimension of the variety V. There is a short exact sequence 1 → GL1 → GLn → PGLn → 1of algebraic groups. This implies a connecting homomorphism H1(PGLn) → H2(GL1)at the level ... | Severi–Brauer variety |
c_8x7nfjk3q5ms | Therefore, Severi–Brauer varieties can be faithfully represented by Brauer group elements, i.e. classes of central simple algebras. Lichtenbaum showed that if X is a Severi–Brauer variety over K then there is an exact sequence 0 → P i c ( X ) → Z → δ B r ( K ) → B r ( K ) / ( X ) → 0 . {\displaystyle 0\rightarrow \math... | Severi–Brauer variety |
c_a154whjzspor | In mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence (pn(x): n = 0, 1, 2, 3, ...) of polynomials in which the index of each polynomial equals its degree, satisfying conditions related to the umbral calculus in combinatorics. They are named for Isador M. Sheffer. | Sheffer sequence |
c_grd70uyks5o1 | In mathematics, a Shintani zeta function or Shintani L-function is a generalization of the Riemann zeta function. They were first studied by Takuro Shintani (1976). They include Hurwitz zeta functions and Barnes zeta functions. | Shintani zeta function |
c_vwc9rancrzp7 | In mathematics, a Shioda modular surface is one of the elliptic surfaces studied by Shioda (1972). | Shioda modular surface |
c_ckk1fctaoajd | In mathematics, a Siegel domain or Piatetski-Shapiro domain is a special open subset of complex affine space generalizing the Siegel upper half plane studied by Siegel (1939). They were introduced by Piatetski-Shapiro (1959, 1969) in his study of bounded homogeneous domains. | Siegel domain |
c_uue9ebat34h8 | In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension. They are named after Carl Lud... | Moduli space of abelian varieties |
c_i7lzuwp6fp5y | In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin. The first decimal Smarandache–Wellin numbers are: 2, 23, 235, 2357, 235711, 23571113... | Smarandache–Wellin number |
c_efh6wub7bomq | In mathematics, a Sobolev mapping is a mapping between manifolds which has smoothness in some sense. Sobolev mappings appear naturally in manifold-constrained problems in the calculus of variations and partial differential equations, including the theory of harmonic maps. | Sobolev mapping |
c_0t00puc3qd4u | In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space i... | Sobolev space |
c_t22o3e7jaxq4 | In mathematics, a Solinas prime, or generalized Mersenne prime, is a prime number that has the form f ( 2 m ) {\displaystyle f(2^{m})} , where f ( x ) {\displaystyle f(x)} is a low-degree polynomial with small integer coefficients. These primes allow fast modular reduction algorithms and are widely used in cryptography... | Generalized Mersenne prime |
c_4m8zjjypyw45 | In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. They were discovered by mathematician Michael Somos. From the form of their defining recurrence (which involves division), one would expect the terms of the sequence to be fractions, but nevertheless man... | Somos sequence |
c_meaqemo5dufb | In mathematics, a Specht module is one of the representations of symmetric groups studied by Wilhelm Specht (1935). They are indexed by partitions, and in characteristic 0 the Specht modules of partitions of n form a complete set of irreducible representations of the symmetric group on n points. | Specht modules |
c_hpyj2ed5n9w5 | In mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold whose holonomy group is contained in Spin(7). Spin(7)-manifolds are Ricci-flat and admit a parallel spinor. They also admit a parallel 4-form, known as the Cayley form, which is a calibrating form for a special class of submanifolds called C... | Spin(7) manifold |
c_s8eru2j38nt3 | In mathematics, a Stanley sequence is an integer sequence generated by a greedy algorithm that chooses the sequence members to avoid arithmetic progressions. If S {\displaystyle S} is a finite set of non-negative integers on which no three elements form an arithmetic progression (that is, a Salem–Spencer set), then the... | Stanley sequence |
c_08xs9mixmlln | In mathematics, a Stanley–Reisner ring, or face ring, is a quotient of a polynomial algebra over a field by a square-free monomial ideal. Such ideals are described more geometrically in terms of finite simplicial complexes. The Stanley–Reisner ring construction is a basic tool within algebraic combinatorics and combina... | Stanley–Reisner ring |
c_w0bdiakt0kon | In mathematics, a Stone algebra, or Stone lattice, is a pseudo-complemented distributive lattice such that a* ∨ a** = 1. They were introduced by Grätzer & Schmidt (1957) and named after Marshall Harvey Stone. Boolean algebras are Stone algebras, and Stone algebras are Ockham algebras. Examples: The open-set lattice of ... | Stone algebra |
c_ksbgieh0nkpv | In mathematics, a Sturmian word (Sturmian sequence or billiard sequence), named after Jacques Charles François Sturm, is a certain kind of infinitely long sequence of characters. Such a sequence can be generated by considering a game of English billiards on a square table. The struck ball will successively hit the vert... | Sturmian word |
c_30j6tz0sygvh | In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n {\displaystyle n} for which the greatest prime factor of n 2 + 1 {\displaystyle n^{2}+1} is greater than or equal to 2 n {\displaystyle 2n} . They are named after Carl Størmer. | Størmer number |
c_1wgtvcpl3aib | In mathematics, a Suslin algebra is a Boolean algebra that is complete, atomless, countably distributive, and satisfies the countable chain condition. They are named after Mikhail Yakovlevich Suslin.The existence of Suslin algebras is independent of the axioms of ZFC, and is equivalent to the existence of Suslin trees ... | Suslin algebra |
c_d5gwcw1097hc | In mathematics, a Suslin representation of a set of reals (more precisely, elements of Baire space) is a tree whose projection is that set of reals. More generally, a subset A of κω is λ-Suslin if there is a tree T on κ × λ such that A = p. By a tree on κ × λ we mean here a subset T of the union of κi × λi for all i ∈ ... | Suslin set |
c_a8d2ya279m2o | In mathematics, a Suslin tree is a tree of height ω1 such that every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown ... | Suslin tree |
c_bcj5i6bo9nh0 | The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees. More generally, for any infinite cardinal κ, a κ-Suslin tree is a tree of height κ such that every branch and antichain has cardinality less than κ. In particular a Suslin ... | Suslin tree |
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