6,052 articles
Uniform continuity
Uniform continuity is a strengthened form of continuity for functions: for every error tolerance ε > 0, a single δ works at every point of the domain at once.
Uniform convergence
Uniform convergence is a mode of convergence of functions in which one index works for every point of the domain at once, making it stronger than pointwise convergence.
Uniform integrability
Uniform integrability, also called equi-integrability, is a property of a family of random variables requiring their tail integrals to be small uniformly, and it upgrades convergence in probability to L1 convergence.
Uniform interpolation
Uniform interpolation is a technique in modal and description logic that rewrites a formula or ontology over a reduced signature while preserving all its entailments in that signature.
Uniform matroid
A uniform matroid is a matroid in which every subset of size at most the rank is independent; the rank-t matroid on n elements, U_t,n, has rank function min(t, |A|).
Uniform sampling (statistics)
Uniform sampling is a sampling method in which every unit in a population or every value in a range has the same probability of being chosen.
Uniform space
A uniform space, also known as a uniform structure, is a set equipped with a uniformity formalizing uniform nearness, introduced by André Weil in 1936 to cover metric spaces and topological groups.
Uniformization (continuous-time Markov chains)
Uniformization, also called randomization or Jensen's method, is a numerically stable technique for computing the transient behavior of a continuous-time Markov chain, introduced by Arne Jensen in 1953.
Uniformization (set theory)
Uniformization in set theory is the operation of choosing one point from each nonempty section of a relation, posed as a problem by Luzin in 1930.
Union (set theory)
The union, or set union, of two sets is the set of all objects belonging to at least one of them, written A ∪ B.
Union-closed sets conjecture
The union-closed sets conjecture, also known as Frankl's conjecture, is an open problem stating that every finite union-closed family of sets has an element in at least half its members.
Unique factorization domain
A unique factorization domain, also called a factorial ring or factorial domain, is an integral domain in which every nonzero nonunit factors uniquely into irreducible elements.
Unit (ring theory)
In ring theory, a unit is an element of a ring that has a multiplicative inverse, and the units together form a group under multiplication.
Unit circle
The unit circle is the circle of radius 1 centered at the origin of the Cartesian plane, the standard device for defining the trigonometric functions for every real number.
Unit disk graph
A unit disk graph is an intersection graph of unit-diameter disks in the plane, where two vertices are adjacent when their disks intersect; it models cellular and broadcast networks.
Unit group
The unit group of a number field is the group of elements of its ring of integers with a multiplicative inverse there, structured by Dirichlet's unit theorem (1846).
Unit root test
A unit root test is a statistical hypothesis test used in time series analysis to decide whether a series contains a stochastic trend rather than being stationary.
Unit vector
A unit vector, also called a normalized or unit-norm vector, is a vector whose length equals 1, written with a hat as the standard way to express direction.
Unitary dual
The unitary dual of a group G, written Ĝ, is the set of its irreducible unitary representations, identified with the spectrum of the group C-algebra.
Unitary group
The unitary group U(n) is the group of n × n complex matrices that preserve the Hermitian inner product, with dimension n² as a compact Lie group.
Unitary matrix
A unitary matrix is a complex square matrix whose conjugate transpose equals its inverse, the complex analog of a real orthogonal matrix that preserves lengths.
Unitary representation
A unitary representation is a continuous homomorphism from a topological group into the unitary operators on a Hilbert space, central to harmonic analysis and quantum mechanics.
United Nations Statistics Division
The United Nations Statistics Division, the statistical office of the United Nations, is a DESA division in New York that compiles global statistics and services the UN Statistical Commission.
United States Census Bureau
The United States Census Bureau is the federal statistical agency that counts the U.S. population every ten years and produces the nation's demographic and economic statistics.
Univalence axiom
The univalence axiom, introduced by Vladimir Voevodsky, states that identity of types is equivalent to equivalence of types, forming the basis of homotopy type theory.
Universal algebra
Universal algebra is the branch of mathematics that studies algebraic structures themselves, treating groups, rings, and lattices uniformly; Garrett Birkhoff founded the modern subject in 1935.
Universal cover
A universal cover of a connected space X is a simply connected space with a covering map to X, existing when X is semilocally simply connected.
Universal enveloping algebra
The universal enveloping algebra U(g) of a Lie algebra g is the associative algebra in which the Lie bracket becomes a commutator, so Lie algebra representations and modules of U(g) coincide.
Universal kriging
Universal kriging, also called kriging with a trend or drift, is a geostatistical interpolation method that models a spatial trend plus a correlated residual, generalized by Matheron in 1969.
Universal property
A universal property, also called a universal mapping property, defines a mathematical object by unique morphisms from every object of its category rather than by internal construction.