6,052 articles
Jon Kosloski
Jon Kosloski is an American NSA research scientist in quantum optics and crypto-mathematics, named in August 2024 as director of the Pentagon's UAP office, AARO.
Jones polynomial
The Jones polynomial is a polynomial invariant of knots and links in three-dimensional space, introduced by Vaughan Jones in 1984. It distinguishes all knots of 10 crossings or fewer, though computing it is #P-hard.
Jordan algebra
A Jordan algebra is a commutative non-associative algebra satisfying the Jordan identity, introduced by Pascual Jordan in 1933 as an algebraic foundation for quantum mechanics.
Jordan block
A Jordan block is a square matrix with a single number λ on its main diagonal, 1s on the diagonal above, and 0s everywhere else.
Jordan normal form
The Jordan normal form, also called the Jordan canonical form, is a block-diagonal matrix representing a linear operator when a matrix cannot be diagonalized, with eigenvalues on the diagonal and 1s on the superdiagonal.
Joseph Fourier
Jean-Baptiste Joseph Fourier (1768–1830) was a French mathematician and prefect of Isère who founded heat conduction theory and systematized Fourier series in his 1822 book Théorie analytique de la chaleur.
Josephus problem
The Josephus problem, named for the historian Flavius Josephus, asks where the sole survivor stands when n people in a circle are removed every q-th in turn.
Journal of Algebraic Combinatorics
The Journal of Algebraic Combinatorics is a peer-reviewed mathematics journal published by Springer. It was founded in 1992 and publishes research where combinatorics and algebra interact.
Journal of Combinatorial Theory
The Journal of Combinatorial Theory (JCT) is a mathematics research journal founded in 1966 as the first devoted exclusively to combinatorics, splitting in 1971 into Elsevier's Series A and Series B.
Journal of Logic and Computation
The Journal of Logic and Computation is a peer-reviewed journal published by Oxford University Press under license from owner Dov Gabbay, founded in 1990.
Journal of Symbolic Logic
The Journal of Symbolic Logic (JSL) is a quarterly peer-reviewed journal of mathematical logic, founded in 1936 and published by Cambridge University Press for the Association for Symbolic Logic.
Journal of the American Statistical Association
The Journal of the American Statistical Association (JASA) is a quarterly peer-reviewed journal of statistical science published for the American Statistical Association by Taylor & Francis since 1922.
Journal of the Royal Statistical Society
The Journal of the Royal Statistical Society is a family of peer-reviewed statistics journals published by Oxford University Press for the Royal Statistical Society, publishing continuously since 1838.
Judgment sampling
Judgment sampling is a nonprobability sampling method in which the researcher deliberately selects units judged to be representative of the population, used in pilot, exploratory, and emergency studies.
Julia set
The Julia set, or Julia fractal, is the boundary of complex points whose orbits stay bounded under iteration of a function, a fractal studied by Fatou and Julia around 1918.
Jump diffusion
Jump diffusion is a class of stochastic process, also called jump-diffusion models, that combines smooth diffusion with sudden jumps, best known through Merton's 1976 option pricing model.
Jump operator
The jump operator (Turing jump) maps a set of natural numbers to its jump, the halting problem for machines with an oracle for that set, always strictly harder.
Junction tree algorithm
The junction tree algorithm is an exact inference method for probabilistic graphical models that computes marginals by message passing on a tree of variable clusters, introduced by Lauritzen and Spiegelhalter in 1988.
Just another Gibbs sampler
Just another Gibbs Sampler (JAGS) is a free, open-source program for analyzing Bayesian hierarchical models using Markov Chain Monte Carlo simulation, created by statistician Martyn Plummer.
Just-world fallacy
The just-world fallacy, also called the just-world hypothesis, is the belief that people get what they deserve, introduced by social psychologist Melvin J. Lerner in 1965.
k-induction
k-induction is a proof technique that verifies safety properties of transition systems by checking that the property holds in the first k states of every execution.
K-stability
K-stability is an algebro-geometric stability condition for Fano varieties, introduced by Gang Tian and reformulated algebraically by Simon Donaldson, that characterizes which Fano manifolds admit Kähler–Einstein metrics.
K-theory
K-theory is a branch of mathematics assigning algebraic invariants, the K-groups, to spaces, rings, and operator algebras; introduced by Grothendieck in 1957, it splits into algebraic and topological branches.
K3 surface
A K3 surface, also called a K3 manifold, is a compact complex surface with trivial canonical bundle and vanishing irregularity, making it a two-dimensional Calabi-Yau manifold central to string theory.
Kac–Moody algebra
A Kac–Moody algebra is a usually infinite-dimensional Lie algebra defined by generators and relations from a generalized Cartan matrix, studied independently by Victor Kac and Robert Moody.
Kac–Moody flag variety
A Kac–Moody flag variety is the homogeneous space of flags attached to a Kac–Moody group, built from a generalized Cartan matrix; in finite type it is the familiar projective variety G/P.
Kaczmarz method
The Kaczmarz method, also called the Kaczmarz algorithm, is an iterative method for solving systems of linear equations by projecting onto one equation's hyperplane at a time, widely used in computed tomography as ART.
Kadison–Singer problem
A 1959 problem posed by Richard Kadison and Isadore Singer asking whether every pure state on the diagonal operators extends uniquely to all bounded operators, solved by Marcus, Spielman, and Srivastava in 2013.
Kadomtsev–Petviashvili equation
The Kadomtsev–Petviashvili (KP) equation is an integrable nonlinear partial differential equation, derived by Soviet physicists Kadomtsev and Petviashvili in 1970, describing weakly dispersive long waves such as water and plasma waves.
Kahan summation algorithm
The Kahan summation algorithm, also called compensated summation, is a method for adding floating-point numbers that captures each addition's rounding error in a compensation variable, cutting accumulated error; William Kahan published it in 1965.