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c_2hfrto9zkss3 | 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 can also be used to study the algebraic topology of suc... | Lie group decomposition |
c_k8488efqlk3f | 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 converse is not necessarily true. One obvi... | Left invariant |
c_ov9qj9d1a1st | 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 article, manifolds (in particular Lie group... | Left invariant |
c_3ozaxh4i17xj | 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 binary operation specified by a Cayley table, which compares th... | Light's associativity test |
c_im3ri3mlupzd | 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 straight line segments making right angle... | Lill's method |
c_vv04phlnzkfi | 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. | Lindelöf's lemma |
c_b9wmwdxbqp8n | 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 fast" in the unbounded direction of the strip mu... | Lindelöf's theorem |
c_xfjhvnm49702 | 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 coefficients of the system. The formula is named after... | Liouville's formula |
c_k4t3iw8zgbft | 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 elementary functions cannot themselves be expressed as elementary functions. These are called n... | Liouville's theorem (differential algebra) |
c_3pv12i3xpcvw | 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 field as the function, plus possibly a finite number of applications of the logarithm function. | Liouville's theorem (differential algebra) |
c_ru1q2gz0en55 | 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 expressed as a composition of translations, similarities, orthogonal transformations and inversio... | Liouville's theorem (conformal mappings) |
c_f4a59l4gkls7 | 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 transformations that are only weakly differentiable (Iwaniec & Martin 2001, Chapter 5). The focus of s... | Liouville's theorem (conformal mappings) |
c_i5bsi28ql81o | 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. Liouville's theorem is then that every weak solution (in this sense) is a Möbius transformation... | Liouville's theorem (conformal mappings) |
c_wkhf59ju47zc | 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–Riemann system in W1,p for any p < k that are not Möbius transformations. In odd dimensio... | Liouville's theorem (conformal mappings) |
c_9o9yi1beiv8r | 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 conformal manifold is isometric with the n-sphere or projective space. Local versions of the re... | Liouville's theorem (conformal mappings) |
c_2t5k2owzrhki | In mathematics, Littlewood's Tauberian theorem is a strengthening of Tauber's theorem introduced by John Edensor Littlewood (1911). | Littlewood's Tauberian theorem |
c_oqdnc6f1lmtv | 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. These functions arise naturally in mat... | Loewner order |
c_6eoo7y889lvm | 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 has a slice at each point x, in other words a subv... | Luna's slice theorem |
c_lm64sythwwlx | 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 constructed by mapping the regions of stabili... | Lyapunov fractal |
c_w634lqj9d0fx | 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. | Lüroth's theorem |
c_fcvs6tgonzlt | 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 ) {\displaystyle \mathrm {SL} _{2}(\... | Maass wave forms |
c_uhuqxjm2zdry | 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 Dixon's identity. | MacMahon master theorem |
c_12jc60v5lh9r | 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 associated his polynomials with weights λ of finite root systems and used just one var... | Macdonald's constant term conjecture |
c_yfik4xwbou95 | 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 and Askey–Wilson polynomials, which in turn include most of the named 1-variable ... | Macdonald's constant term conjecture |
c_dy6dstkk3cvm | 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–Wilson polynomials. They are the Macdonald polynomials atta... | Koornwinder polynomials |
c_jdly7zqco8re | 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 have also been studied with the aid of affine Hecke alge... | Koornwinder polynomials |
c_efh0gfs4o118 | 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 {\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5... | Machin-like formulas |
c_l1uk7rfdt3qy | 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 < ⋯ < i k ≤ n a i 1 a i 2 ⋯ a i k ( n k ) . {\displaystyle S... | Maclaurin's inequality |
c_ivfw3d9m68fa | 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 the unit interval on the reals), and "purely... | Maharam's theorem |
c_hasesds05w08 | 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 product of discrete abelian von Neumann alge... | Maharam's theorem |
c_vt5gvia2106p | 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 conjectured in 1968 that there are no Z-numbers. More genera... | Mahler's 3/2 problem |
c_6cos2imzvre7 | 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 ways in which a lattice could degenerate (go off to infinity) in a s... | Mahler's compactness theorem |
c_gv81d4xnl6qj | 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 ( R ) / G L n ( Z ) {\displaystyle \mathrm {GL} _{n}(\mathbb {R} )... | Mahler's compactness theorem |
c_engv51lpoyc3 | 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 itself. The assertion of Mahler's theorem is equivalent to the comp... | Mahler's compactness theorem |
c_y9vqd61r7ly2 | 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 = 1 n x k 1 / n + ∏ k = 1 n y k 1 / n {\displays... | Mahler's inequality |
c_k646lyiftvnn | 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 interval. | Mahler's theorem |
c_v7xjhtkh7zax | 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). Malo (1914) calculated the determinant Dp for p = ... | Maillet's determinant |
c_sql2cvope9oy | 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). | Maillet's determinant |
c_p7xljby32tsu | 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 solutions. | Malmquist's theorem |
c_vp0g81hjvmax | 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 the determinant for them and most lin... | Manin matrices |
c_t5rmcqr8w0t1 | 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 (q)-(super)-analogs of Manin matrices,... | Manin matrices |
c_uqwmmego813g | 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 properties of polynomial roots. | Marden's theorem |
c_k6a47pb2hsbl | 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 representations of a finite group G without actually c... | Maschke's theorem |
c_z5sg49cb744d | 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 real-valued parameters. Since we may add π/2 to x to change the sign ... | Mathieu differential equation |
c_l9sotnedhti3 | 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 polynomial. | Matsumoto zeta function |
c_nqzvmkr3774l | 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 giving dimensions of spaces of automorphic forms, ... | Matsushima's formula |
c_1miute2jwel4 | 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 theorem. | Mazur's lemma |
c_55vlk8inntbi | 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 ) = ∑ k = 0 n ( − 1 ) k ( n k ) ( x k ) k ! ( x + β )... | Meixner polynomials |
c_vrk2fi1eqv0x | 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 representation of a/p is 2n, so that a p = 0... | Midy's Theorem |
c_fjszag8g4oon | {\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. | Midy's Theorem |
c_vnfduxl1jj7q | {\displaystyle {\frac {1}{13}}=0. {\overline {076923}}{\text{ and }}076+923=999.} 1 17 = 0. | Midy's Theorem |
c_mu3dco5tzrev | 0588235294117647 ¯ and 05882352 + 94117647 = 99999999. {\displaystyle {\frac {1}{17}}=0. {\overline {0588235294117647}}{\text{ and }}05882352+94117647=99999999.} | Midy's Theorem |
c_uagcfexwq0b3 | 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 {\displaystyle \mathbb {S} _{T}^{n}} the collection of all strong... | Milliken's tree theorem |
c_ai2l4jnnv3pj | 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 illuminate the structure for algebraic K-theo... | Milnor ring |
c_gcq5bpg6u8t2 | 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 the phrase Milnor fibration is mor... | Milnor fiber |
c_fd9ztgt9s91c | 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 isoperimetric inequality. | Minkowski's first inequality for convex bodies |
c_ir7e85pp8pew | 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 expression relating the continued fraction expansions of the quadratics to the bin... | Minkowski's question-mark function |
c_2d0mk4e2c6kg | 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. | Minkowski's second theorem |
c_m5z49bvq6pwl | 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 in Z n {\displaystyle \mathbb {Z} ^{n}} that is ... | Minkowski's theorem |
c_1eo9xpl881oc | 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 polynomial algebra with generators of degrees 6, 12... | Mitchell's group |
c_mnlwur852l2g | 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) | Mittag-Leffler summation |
c_dpoz1ijdl9tp | 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. Precisely, it says: given a finite-dimension... | Molien's formula |
c_6we0ks9679s9 | 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 flag manifold. Write tij for the tran... | Monk's formula |
c_32s7q44git2e | 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 randomly chooses points at which the integrand ... | MISER algorithm |
c_j8zag5rs1hh3 | 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 + δ ( u ) , {\displaystyle 1-\left({\frac {\sin(\pi u)}{\pi u}}\r... | Pair correlation conjecture |
c_ouhlwti3imqf | 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 approximation, which is defined in terms o... | Moreau's theorem |
c_gjxlr78dzygi | 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. | Sweedler's Hopf algebra |
c_mgugbju3fx0s | 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 and hence unique. The theorem was proven for closed manifol... | Mostow's rigidity theorem |
c_qcror3vr32oj | 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, for a hyperbolic surface of genus g > 1 {\displaystyle g>1} ... | Mostow's rigidity theorem |
c_gk4zfk4x5kom | 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 equations by relaxation methods". | Motz's problem |
c_zuaaujsnzuad | 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 theorem, proved independently by Tits and Weis... | Moufang polygon |
c_p34nuvjp6gpi | In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means. | Muirhead's Inequality |
c_72tj6jlohk1z | 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) as a consequence of a theorem about the compactness of sets of discr... | Mumford's compactness theorem |
c_zezdb2d25m4y | 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 of the generalized Nakayama conjecture. Nakayama's c... | Nakayama's conjecture |
c_pif88i19t9t5 | 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, some authors refer to it as Hartwig–Nambooripad ord... | Natural partial order |
c_eb9p53760bog | 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 Liouville's theorem. This was soon general... | Nambu dynamics |
c_bh3z4kjbndzb | 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 and much studied Shapiro inequality, and was publish... | Nesbitt's inequality |
c_bqly0famr2ii | 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 for starlike univalent functions. | Carathéodory's lemma |
c_c70x225xlgck | 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 evaluates this polynomial. Neville's algorithm ... | Neville's schema |
c_9smi5i4te42t | 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 Meacham, F. James Rohlf, and David Swof... | Newick format |
c_4epian04mqgk | 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 allow expressing the sums of the k-th powers of a... | Newton's identities |
c_9extiahbah32 | 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 show that the position of a planet moving in an orbit is not an algeb... | Newton's theorem about ovals |
c_0dd0d143kau4 | 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 states that a compact topological space is the co... | Nikiel's conjecture |
c_8ygkgsm2i3j8 | 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. | Nirenberg's conjecture |
c_whh85ux9v0h0 | 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^{\circ }&=0,\\\sin 30^{\circ }&={\frac {... | Niven's theorem |
c_gjljsku65ri6 | 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–Lagrange operator obeys Noether identities whic... | Noether identities |
c_zkqwdnss5y08 | 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 called reducible if there exist non-trivial hig... | Noether identities |
c_9mo1vpw2n2ux | 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 symmetries. Formulated in a very general setti... | Noether identities |
c_46985iofie5r | 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-singular and projective. Suppose there is a morphism φ from S to the projective line, with general fibre ... | Noether's theorem on rationality for surfaces |
c_x227rbdzr0pj | 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. | Novikov's compact leaf theorem |
c_2sbl6i3qdvx6 | 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 that the domain is pseudoconvex.... | Oka's lemma |
c_iqo2oacn2ku8 | 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 1916. | Ono's inequality |
c_3bj9tfvy1yoo | 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 continuous can be dropped, but that form o... | Osgood's lemma |
c_uk70bcu9ygtb | 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 counterexample in two dimensions is g... | Osgood's lemma |
c_q8nl65ys04ut | 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 irrational number α with continued fraction expansion . ... | Ostrowski numeration |
c_dmq37gn8sdax | 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^{2})}}{1+x^{2}}}dx\quad \left(-\infty | Owen's T function |
c_axc92h7p7fko | 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=1\\0,&{\mbox{if }}n=2\\x,&{\mbox{if }}n=3\\xP_{n... | Padovan polynomials |
c_o6jce0f6364r | {\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 sequence is ∑ n = 1 ∞ P n ( x ) t n = t 1 − x t 2 − t... | Padovan polynomials |
c_bktr35hw6cld | 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 functions. They were discovered by Émile Picard (... | Painleve equations |
c_ngq2juh4rdm0 | 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 symmetric conference matrices. Paley graph... | Paley digraph |
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