6,052 articles
Wick product
The Wick product is a specific multiplication of random variables or quantum field operators. It removes deterministic contractions from the ordinary product, resulting in zero expectation.
Widely applicable information criterion
The widely applicable information criterion (WAIC), also called the Watanabe–Akaike information criterion, is a fully Bayesian measure for comparing statistical models, introduced by Sumio Watanabe in 2010.
Wiener algebra
The Wiener algebra A(𝕋), or W(𝕋), is a commutative Banach algebra of continuous periodic functions with absolutely summable Fourier coefficients, introduced by Norbert Wiener and known for Wiener's lemma.
Wiener filter
The Wiener filter, also called the Kolmogorov-Wiener filter, is the linear filter minimizing mean-square error between a desired signal and its estimate, developed by Norbert Wiener in the 1940s.
Wiener index
The Wiener index, also called the Wiener number, is the sum of shortest-path distances between all pairs of vertices in a graph, introduced by Harry Wiener in 1947.
Wiener process
The Wiener process, also called standard Brownian motion, is a continuous-time stochastic process with independent, normally distributed increments, named after Norbert Wiener, who first constructed it rigorously around 1920.
Wiener–Hopf method
The Wiener–Hopf method is an analytical technique, created by Norbert Wiener and Eberhard Hopf in 1931, for solving integral equations on a half-line and mixed boundary-value problems in mathematical physics.
Wiener–Itô chaos expansion
The Wiener–Itô chaos expansion, also called the Itô–Wiener decomposition, is a theorem writing any square-integrable functional of Brownian motion as an orthogonal series of multiple integrals.
Wiener–Khinchin theorem
The Wiener–Khinchin theorem, also called the Wiener–Khintchine theorem, states that for a wide-sense stationary random process, the power spectral density and autocorrelation function form a Fourier transform pair.
Wigner D-matrix
The Wigner D-matrix, also known as the Wigner D-function, is the matrix of a rotation operator in angular momentum eigenstates, introduced by Eugene Wigner in 1927 and realizing irreducible representations of SU(2) and SO(3).
Wigner distribution function
The Wigner distribution function, known in signal processing as the Wigner–Ville distribution, is a bilinear transform representing a signal in time and frequency, introduced by Eugene Wigner in 1932.
Wigner matrix
A Wigner matrix is a Hermitian or real symmetric random matrix with independent, zero-mean, constant-variance entries, introduced by Eugene Wigner in the 1950s to model heavy nuclei.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a result of quantum mechanics stating that matrix elements of irreducible tensor operators factor into a Clebsch–Gordan coefficient and a single reduced matrix element.
Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a nonparametric test for paired data, proposed by Frank Wilcoxon in 1945 as the rank-based counterpart of the paired t-test.
Wiles's proof of Fermat's Last Theorem
Wiles's proof of Fermat's Last Theorem is Andrew Wiles's 1995 proof that every semistable elliptic curve over the rationals is modular, from which Fermat's 350-year-old conjecture follows.
Wilks' theorem
Wilks' theorem is a mathematical statistics result stating that, for nested models, the likelihood ratio test statistic follows an asymptotic chi-square distribution, established by Samuel S. Wilks in 1938.
William James Sidis
William James Sidis (1898–1944) was an American child prodigy known for mathematical and linguistic ability who entered Harvard at age 11 and later wrote on cosmology, psychology, and streetcar transfers.
William Lawvere
William Lawvere, also known as F. William Lawvere or F. W. Lawvere, was an American category theorist (1937 to 2023) known for ETCS, Lawvere theories, and elementary topos axioms.
Willmore conjecture
The Willmore conjecture, proposed by Thomas Willmore in 1965, states that any torus in space has bending energy at least 2π²; Marques and Neves proved it in 2012.
Wilson's theorem
Wilson's theorem, first stated by Edward Waring in 1770, states that n > 1 is prime if and only if (n−1)! + 1 is divisible by n.
Win ratio
The win ratio is a statistical method comparing two treatments on a hierarchy of outcomes by pairing patients, introduced by Pocock and colleagues in 2012.
WinBUGS
WinBUGS is a Windows software package for Bayesian inference using Gibbs Sampling, developed at the MRC Biostatistics Unit in Cambridge, whose final version 1.4.3 is no longer developed.
Winding number
The winding number, also called the index, counts the net number of times a closed curve travels around a point, positive for counterclockwise and negative for clockwise turns.
Wishart distribution
The Wishart distribution is a probability distribution on positive definite matrices describing the sample covariance matrix of multivariate normal data, derived by John Wishart in 1928.
Witt algebra
The Witt algebra, also called the centerless Virasoro algebra, is an infinite-dimensional Lie algebra of vector fields with basis l_n and bracket [l_n, l_m] = (n − m) l{n+m}.
Witt group
The Witt group of a field is the abelian group of nondegenerate quadratic forms over it modulo hyperbolic forms, under orthogonal sum; with tensor product it becomes the Witt ring.
Witt vector
A Witt vector is an infinite sequence from a ring A given unusual addition and multiplication, introduced by Ernst Witt as a tool in p-adic Hodge theory.
Witt vectors
Witt vectors are a construction turning a commutative ring R into a ring W(R) of sequences, built from universal integer polynomials; for finite fields they yield p-adic integers.
Wolf algorithm
The Wolf algorithm is a 1985 method by Wolf, Swift, Swinney, and Vastano for estimating the largest Lyapunov exponent of a dynamical system from a time series.
WolframAlpha
WolframAlpha is an answer engine by Wolfram Research, launched in May 2009, that computes factual answers from a curated knowledge base instead of listing web pages.