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Lie group decomposition Summary Lie_group_decomposition In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and Lie algebras; they... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Left invariant Summary Left_invariant In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the conv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Left invariant Summary Left_invariant However, by restricting our attention to the simply connected Lie groups, the Lie group-Lie algebra correspondence will be one-to-one.In this article, a Lie group refers to a real Lie group. For the complex and p-adic cases, see complex Lie group and p-adic Lie group. In this artic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Light's associativity test Summary Light's_associativity_test In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The naive procedure for verification of the associativity of a b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lill's method Summary Lill's_method In mathematics, Lill's method is a visual method of finding the real roots of a univariate polynomial of any degree. It was developed by Austrian engineer Eduard Lill in 1867. A later paper by Lill dealt with the problem of complex roots.Lill's method involves drawing a path of strai... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lindelöf's lemma Summary Lindelöf's_lemma In mathematics, Lindelöf's lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lindelöf's theorem Summary Lindelöf's_theorem In mathematics, Lindelöf's theorem is a result in complex analysis named after the Finnish mathematician Ernst Leonard Lindelöf. It states that a holomorphic function on a half-strip in the complex plane that is bounded on the boundary of the strip and does not grow "too fa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's formula Summary Liouville's_formula In mathematics, Liouville's formula, also known as the Abel-Jacobi-Liouville Identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coeffi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (differential algebra) Summary Liouville's_theorem_(differential_algebra) In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in 1833 to 1841, places an important restriction on antiderivatives that can be expressed as elementary functions. The antiderivatives of certain e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (differential algebra) Summary Liouville's_theorem_(differential_algebra) Other examples include the functions sin ( x ) x {\displaystyle {\frac {\sin(x)}{x}}} and x x . {\displaystyle x^{x}.} Liouville's theorem states that elementary antiderivatives, if they exist, are in the same differential f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (conformal mappings) Summary Liouville's_theorem_(conformal_mappings) In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space. It states that any smooth conformal mapping on a domain of Rn, where n > 2, can be express... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (conformal mappings) Summary Liouville's_theorem_(conformal_mappings) By contrast, conformal mappings in R2 can be much more complicated – for example, all simply connected planar domains are conformally equivalent, by the Riemann mapping theorem. Generalizations of the theorem hold for transformati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (conformal mappings) Summary Liouville's_theorem_(conformal_mappings) A weak solution of this system is defined to be an element f of the Sobolev space W1,nloc(Ω, Rn) with non-negative Jacobian determinant almost everywhere, such that the Cauchy–Riemann system holds at almost every point of Ω. Liouv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (conformal mappings) Summary Liouville's_theorem_(conformal_mappings) The result is not optimal however: in even dimensions n = 2k, the theorem also holds for solutions that are only assumed to be in the space W1,kloc, and this result is sharp in the sense that there are weak solutions of the Cauchy... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Liouville's theorem (conformal mappings) Summary Liouville's_theorem_(conformal_mappings) The group of conformal isometries of an n-dimensional conformal Riemannian manifold always has dimension that cannot exceed that of the full conformal group SO(n + 1, 1). Equality of the two dimensions holds exactly when the confo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Littlewood's Tauberian theorem Summary Littlewood's_Tauberian_theorem In mathematics, Littlewood's Tauberian theorem is a strengthening of Tauber's theorem introduced by John Edensor Littlewood (1911). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loewner order Summary Loewner_order In mathematics, Loewner order is the partial order defined by the convex cone of positive semi-definite matrices. This order is usually employed to generalize the definitions of monotone and concave/convex scalar functions to monotone and concave/convex Hermitian valued functions. Th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Luna's slice theorem Summary Luna's_slice_theorem In mathematics, Luna's slice theorem, introduced by Luna (1973), describes the local behavior of an action of a reductive algebraic group on an affine variety. It is an analogue in algebraic geometry of the theorem that a compact Lie group acting on a smooth manifold X ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lyapunov fractal Summary Lyapunov_fractal In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B.A Lyapunov fractal is con... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lüroth's theorem Summary Lüroth's_theorem In mathematics, Lüroth's theorem asserts that every field that lies between two other fields K and K(X) must be generated as an extension of K by a single element of K(X). This result is named after Jacob Lüroth, who proved it in 1876. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maass wave forms Summary Maass_form In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup Γ {\displaystyle \Gamma } of S L 2 ( R ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
MacMahon master theorem Summary MacMahon's_master_theorem In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916). It is often used to derive binomial identities, most notably... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Macdonald's constant term conjecture Summary Macdonald's_constant_term_conjecture In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally asso... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Macdonald's constant term conjecture Summary Macdonald's_constant_term_conjecture The Macdonald polynomials are polynomials in n variables x=(x1,...,xn), where n is the rank of the affine root system. They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Koornwinder polynomials Summary Koornwinder_polynomials In mathematics, Macdonald-Koornwinder polynomials (also called Koornwinder polynomials) are a family of orthogonal polynomials in several variables, introduced by Koornwinder (1992) and I. G. Macdonald (1987, important special cases), that generalize the Askey–Wil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Koornwinder polynomials Summary Koornwinder_polynomials Furthermore, there is a large class of interesting families of multivariable orthogonal polynomials associated with classical root systems which are degenerate cases of the Macdonald-Koornwinder polynomials (van Diejen 1999). The Macdonald-Koornwinder polynomials ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Machin-like formulas Summary Machin-like_formula In mathematics, Machin-like formulae are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits. They are generalizations of John Machin's formula from 1706: π 4 = 4 arctan 1 5 − arctan 1 239 {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maclaurin's inequality Summary Maclaurin's_inequality In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a1, a2, ..., an be positive real numbers, and for k = 1, 2, ..., n define the averages Sk as follows: S k = ∑ 1 ≤ i 1 < ⋯ < ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maharam's theorem Summary Maharam's_theorem In mathematics, Maharam's theorem is a deep result about the decomposability of measure spaces, which plays an important role in the theory of Banach spaces. In brief, it states that every complete measure space is decomposable into "non-atomic parts" (copies of products of t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maharam's theorem Summary Maharam's_theorem Maharam's theorem can also be translated into the language of abelian von Neumann algebras. Every abelian von Neumann algebra is isomorphic to a product of σ-finite abelian von Neumann algebras, and every σ-finite abelian von Neumann algebra is isomorphic to a spatial tensor ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's 3/2 problem Summary Mahler's_3/2_problem In mathematics, Mahler's 3/2 problem concerns the existence of "Z-numbers". A Z-number is a real number x such that the fractional parts of x ( 3 2 ) n {\displaystyle x\left({\frac {3}{2}}\right)^{n}} are less than 1/2 for all positive integers n. Kurt Mahler conjecture... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's compactness theorem Summary Mahler's_compactness_theorem In mathematics, Mahler's compactness theorem, proved by Kurt Mahler (1946), is a foundational result on lattices in Euclidean space, characterising sets of lattices that are 'bounded' in a certain definite sense. Looked at another way, it explains the wa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's compactness theorem Summary Mahler's_compactness_theorem It is also called his selection theorem, following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the possibility of selecting a convergent subsequence). Let X be the space G L n ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's compactness theorem Summary Mahler's_compactness_theorem Mahler's compactness theorem states that a subset Y of X is relatively compact if and only if Δ is bounded on Y, and there is a neighbourhood N of 0 in R n {\displaystyle \mathbb {R} ^{n}} such that for all Λ in Y, the only lattice point of Λ in N is 0 i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's inequality Summary Mahler's_inequality In mathematics, Mahler's inequality, named after Kurt Mahler, states that the geometric mean of the term-by-term sum of two finite sequences of positive numbers is greater than or equal to the sum of their two separate geometric means: ∏ k = 1 n ( x k + y k ) 1 / n ≥ ∏ k ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mahler's theorem Summary Mahler's_theorem In mathematics, Mahler's theorem, introduced by Kurt Mahler (1958), expresses any continuous p-adic function as an infinite series of certain special polynomials. It is the p-adic counterpart to the Stone-Weierstrass theorem for continuous real-valued functions on a closed inte... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maillet's determinant Summary Maillet's_determinant In mathematics, Maillet's determinant Dp is the determinant of the matrix introduced by Maillet (1913) whose entries are R(s/r) for s,r = 1, 2, ..., (p – 1)/2 ∈ Z/pZ for an odd prime p, where and R(a) is the least positive residue of a mod p (Muir 1930, pages 340–342)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maillet's determinant Summary Maillet's_determinant In particular this verifies Maillet's conjecture that the determinant is always non-zero. Chowla and Weil had previously found the same formula but did not publish it. Their results have been extended to all non-prime odd numbers by K. Wang(1982). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Malmquist's theorem Summary Malmquist's_theorem In mathematics, Malmquist's theorem, is the name of any of the three theorems proved by Axel Johannes Malmquist (1913, 1920, 1941). These theorems restrict the forms of first order algebraic differential equations which have transcendental meromorphic or algebroid solutio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manin matrices Summary Manin_matrices In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute. In particular there is natural definition of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manin matrices Summary Manin_matrices Manin matrices are particular examples of Manin's general construction of "non-commutative symmetries" which can be applied to any algebra. From this point of view they are "non-commutative endomorphisms" of polynomial algebra C. Taking (q)-(super)-commuting variables one will get ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Marden's theorem Summary Marden's_theorem In mathematics, Marden's theorem, named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative. See also geometrical proper... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maschke's theorem Summary Maschke's_theorem In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. Maschke's theorem allows one to make general conclusions about representa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathieu differential equation Summary Mathieu_differential_equation In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation d 2 y d x 2 + ( a − 2 q cos ( 2 x ) ) y = 0 , {\displaystyle {\frac {d^{2}y}{dx^{2}}}+(a-2q\cos(2x))y=0,} where a, q are r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matsumoto zeta function Summary Matsumoto_zeta_function In mathematics, Matsumoto zeta functions are a type of zeta function introduced by Kohji Matsumoto in 1990. They are functions of the form ϕ ( s ) = ∏ p 1 A p ( p − s ) {\displaystyle \phi (s)=\prod _{p}{\frac {1}{A_{p}(p^{-s})}}} where p is a prime and Ap is a po... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matsushima's formula Summary Matsushima's_formula In mathematics, Matsushima's formula, introduced by Matsushima (1967), is a formula for the Betti numbers of a quotient of a symmetric space G/H by a discrete group, in terms of unitary representations of the group G. The Matsushima–Murakami formula is a generalization ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mazur's lemma Summary Mazur's_lemma In mathematics, Mazur's lemma is a result in the theory of normed vector spaces. It shows that any weakly convergent sequence in a normed space has a sequence of convex combinations of its members that converges strongly to the same limit, and is used in the proof of Tonelli's theore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Meixner polynomials Summary Meixner_polynomials In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner (1934). They are given in terms of binomial coefficients and the (rising) Pochhammer symbol by M n ( x , β , γ ) = ∑... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Midy's Theorem Summary Midy's_Theorem In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period (sequence A028416 in the OEIS). If the period of the decimal repres... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Midy's Theorem Summary Midy's_Theorem {\displaystyle a_{1}\dots a_{n}+a_{n+1}\dots a_{2n}=10^{n}-1.} For example, 1 13 = 0. 076923 ¯ and 076 + 923 = 999. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Midy's Theorem Summary Midy's_Theorem {\displaystyle {\frac {1}{13}}=0. {\overline {076923}}{\text{ and }}076+923=999.} 1 17 = 0. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Midy's Theorem Summary Midy's_Theorem 0588235294117647 ¯ and 05882352 + 94117647 = 99999999. {\displaystyle {\frac {1}{17}}=0. {\overline {0588235294117647}}{\text{ and }}05882352+94117647=99999999.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Milliken's tree theorem Summary Milliken's_tree_theorem In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting rooted tree of height ω, n a positive integer, and S T n {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Milnor ring Summary Milnor_K-theory In mathematics, Milnor K-theory is an algebraic invariant (denoted K ∗ ( F ) {\displaystyle K_{*}(F)} for a field F {\displaystyle F} ) defined by John Milnor (1970) as an attempt to study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Milnor fiber Summary Milnor_fiber In mathematics, Milnor maps are named in honor of John Milnor, who introduced them to topology and algebraic geometry in his book Singular Points of Complex Hypersurfaces (Princeton University Press, 1968) and earlier lectures. The most studied Milnor maps are actually fibrations, and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minkowski's first inequality for convex bodies Summary Minkowski's_first_inequality_for_convex_bodies In mathematics, Minkowski's first inequality for convex bodies is a geometrical result due to the German mathematician Hermann Minkowski. The inequality is closely related to the Brunn–Minkowski inequality and the isop... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minkowski's question-mark function Summary Minkowski_question-mark_function In mathematics, Minkowski's question-mark function, denoted ? (x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers to rational numbers on the unit interval, via an expres... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minkowski's second theorem Summary Minkowski's_second_theorem In mathematics, Minkowski's second theorem is a result in the geometry of numbers about the values taken by a norm on a lattice and the volume of its fundamental cell. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minkowski's theorem Summary Minkowski's_theorem In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to the origin and which has volume greater than 2 n {\displaystyle 2^{n}} contains a non-zero integer point (meaning a point ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mitchell's group Summary Mitchell's_group In mathematics, Mitchell's group is a complex reflection group in 6 complex dimensions of order 108 × 9!, introduced by Mitchell (1914). It has the structure 6.PSU4(F3).2. As a complex reflection group it has 126 reflections of order 2, and its ring of invariants is a polynomia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mittag-Leffler summation Summary Mittag-Leffler_summation In mathematics, Mittag-Leffler summation is any of several variations of the Borel summation method for summing possibly divergent formal power series, introduced by Mittag-Leffler (1908) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Molien's formula Summary Molien's_formula In mathematics, Molien's formula computes the generating function attached to a linear representation of a group G on a finite-dimensional vector space, that counts the homogeneous polynomials of a given total degree that are invariants for G. It is named for Theodor Molien. Pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monk's formula Summary Monk's_formula In mathematics, Monk's formula, found by Monk (1959), is an analogue of Pieri's formula that describes the product of a linear Schubert polynomial by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology of a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
MISER algorithm Summary MISER_algorithm In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randoml... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pair correlation conjecture Summary Pair_correlation_conjecture In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is 1 − ( sin ( π u ) π u ) 2 +... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moreau's theorem Summary Moreau's_theorem In mathematics, Moreau's theorem is a result in convex analysis named after French mathematician Jean-Jacques Moreau. It shows that sufficiently well-behaved convex functionals on Hilbert spaces are differentiable and the derivative is well-approximated by the so-called Yosida ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Sweedler's Hopf algebra Summary Sweedler's_Hopf_algebra In mathematics, Moss E. Sweedler (1969, p. 89–90) introduced an example of an infinite-dimensional Hopf algebra, and Sweedler's Hopf algebra H4 is a certain 4-dimensional quotient of it that is neither commutative nor cocommutative. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mostow's rigidity theorem Summary Mostow's_rigidity_theorem In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mostow's rigidity theorem Summary Mostow's_rigidity_theorem Besson, Courtois & Gallot (1996) gave the simplest available proof. While the theorem shows that the deformation space of (complete) hyperbolic structures on a finite volume hyperbolic n {\displaystyle n} -manifold (for n > 2 {\displaystyle n>2} ) is a point, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Motz's problem Summary Motz's_problem In mathematics, Motz's problem is a problem which is widely employed as a benchmark for singularity problems to compare the effectiveness of numerical methods. The problem was first presented in 1947 by H. Motz in the paper "The treatment of singularities of partial differential eq... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moufang polygon Summary Moufang_polygon In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of rank two that admit the action of root groups. In a book on the topic, Tits and Richard Weiss classify them all. An earlier theore... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Muirhead's Inequality Summary Muirhead's_Inequality In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mumford's compactness theorem Summary Mumford's_compactness_theorem In mathematics, Mumford's compactness theorem states that the space of compact Riemann surfaces of fixed genus g > 1 with no closed geodesics of length less than some fixed ε > 0 in the Poincaré metric is compact. It was proved by David Mumford (1971) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nakayama's conjecture Summary Nakayama's_conjecture In mathematics, Nakayama's conjecture is a conjecture about Artinian rings, introduced by Nakayama (1958). The generalized Nakayama conjecture is an extension to more general rings, introduced by Auslander and Reiten (1975). Leuschke & Huneke (2004) proved some cases ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Natural partial order Summary Natural_partial_order In mathematics, Nambooripad order (also called Nambooripad's partial order) is a certain natural partial order on a regular semigroup discovered by K S S Nambooripad in late seventies. Since the same partial order was also independently discovered by Robert E Hartwig,... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nambu dynamics Summary Nambu_dynamics In mathematics, Nambu mechanics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liou... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nesbitt's inequality Summary Nesbitt's_inequality In mathematics, Nesbitt's inequality states that for positive real numbers a, b and c, a b + c + b a + c + c a + b ≥ 3 2 . {\displaystyle {\frac {a}{b+c}}+{\frac {b}{a+c}}+{\frac {c}{a+b}}\geq {\frac {3}{2}}.} It is an elementary special case (N = 3) of the difficult an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Carathéodory's lemma Summary Carathéodory's_lemma In mathematics, Nevanlinna's criterion in complex analysis, proved in 1920 by the Finnish mathematician Rolf Nevanlinna, characterizes holomorphic univalent functions on the unit disk which are starlike. Nevanlinna used this criterion to prove the Bieberbach conjecture ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neville's schema Summary Neville's_algorithm In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville in 1934. Given n + 1 points, there is a unique polynomial of degree ≤ n which goes through the given points. Neville's algorithm ev... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newick format Summary Newick_format In mathematics, Newick tree format (or Newick notation or New Hampshire tree format) is a way of representing graph-theoretical trees with edge lengths using parentheses and commas. It was adopted by James Archie, William H. E. Day, Joseph Felsenstein, Wayne Maddison, Christopher Mea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton's identities Summary Newton_identities In mathematics, Newton's identities, also known as the Girard–Newton formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable, they all... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Newton's theorem about ovals Summary Newton's_theorem_about_ovals In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant. Isaac Newton stated it as lemma 28 of section VI of book 1 of Newton's Principia, and used it to sho... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nikiel's conjecture Summary Nikiel's_conjecture In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by Jacek Nikiel in 1986. The conjecture was proven by Mary Ellen Rudin in 1999.The conjecture s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nirenberg's conjecture Summary Osserman's_theorem In mathematics, Nirenberg's conjecture, now Osserman's theorem, states that if a neighborhood of the sphere is omitted by the Gauss map of a complete minimal surface, then the surface in question is a plane. It was proved by Robert Osserman in 1959. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Niven's theorem Summary Niven's_theorem In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: sin 0 ∘ = 0 , sin 30 ∘ = 1 2 , sin 90 ∘ = 1. {\displaystyle {\begin{aligned}\sin 0^... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether identities Summary Noether_identities In mathematics, Noether identities characterize the degeneracy of a Lagrangian system. Given a Lagrangian system and its Lagrangian L, Noether identities can be defined as a differential operator whose kernel contains a range of the Euler–Lagrange operator of L. Any Euler–L... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether identities Summary Noether_identities Noether identities need not be independent, but satisfy first-stage Noether identities, which are subject to the second-stage Noether identities and so on. Higher-stage Noether identities also are separated into the trivial and non-trivial once. A degenerate Lagrangian is c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether identities Summary Noether_identities Yang–Mills gauge theory and gauge gravitation theory exemplify irreducible Lagrangian field theories. Different variants of second Noether’s theorem state the one-to-one correspondence between the non-trivial reducible Noether identities and the non-trivial reducible gauge ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Noether's theorem on rationality for surfaces Summary Noether's_theorem_on_rationality_for_surfaces In mathematics, Noether's theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let S be an algebraic surface that is non-singu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Novikov's compact leaf theorem Summary Novikov's_compact_leaf_theorem In mathematics, Novikov's compact leaf theorem, named after Sergei Novikov, states that A codimension-one foliation of a compact 3-manifold whose universal covering space is not contractible must have a compact leaf. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Oka's lemma Summary Oka's_lemma In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in C n {\displaystyle \mathbb {C} ^{n}} , the function − log d ( z ) {\displaystyle -\log d(z)} is plurisubharmonic, where d {\displaystyle d} is the distance to the boundary. This property shows ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ono's inequality Summary Ono's_inequality In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement is true for acute triangles and right triangles, as shown by F. Balitrand in 19... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Osgood's lemma Summary Osgood's_lemma In mathematics, Osgood's lemma, introduced by William Fogg Osgood (1899), is a proposition in complex analysis. It states that a continuous function of several complex variables that is holomorphic in each variable separately is holomorphic. The assumption that the function is cont... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Osgood's lemma Summary Osgood's_lemma If we assume that a function f: R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } is globally continuous and separately differentiable on each variable (all partial derivatives exist everywhere), it is not true that f {\displaystyle f} will necessarily be differentiable. A... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ostrowski numeration Summary Ostrowski_numeration In mathematics, Ostrowski numeration, named after Alexander Ostrowski, is either of two related numeration systems based on continued fractions: a non-standard positional numeral system for integers and a non-integer representation of real numbers. Fix a positive irrati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Owen's T function Summary Owen's_T_function In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by T ( h , a ) = 1 2 π ∫ 0 a e − 1 2 h 2 ( 1 + x 2 ) 1 + x 2 d x ( − ∞ < h , a < + ∞ ) . {\displaystyle T(h,a)={\frac {1}{2\pi }}\int _{0}^{a}{\frac {e^{-{\frac {1}{2}}h^{2}(1+x^... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Padovan polynomials Summary Padovan_polynomials In mathematics, Padovan polynomials are a generalization of Padovan sequence numbers. These polynomials are defined by: P n ( x ) = { 1 , if n = 1 0 , if n = 2 x , if n = 3 x P n − 2 ( x ) + P n − 3 ( x ) , if n ≥ 4. {\displaystyle P_{n}(x)={\begin{cases}1,&{\mbox{if }}n=... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Padovan polynomials Summary Padovan_polynomials {\displaystyle P_{11}(x)=x^{5}+6x^{2}.\,} The Padovan numbers are recovered by evaluating the polynomials Pn−3(x) at x = 1. Evaluating Pn−3(x) at x = 2 gives the nth Fibonacci number plus (−1)n. (sequence A008346 in the OEIS) The ordinary generating function for the seque... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Painleve equations Summary Painlevé_function In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvable in terms of elementary func... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Paley digraph Summary Paley_digraph In mathematics, Paley graphs are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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