6,052 articles
Distributive property
The distributive property, also called the distributive law, is the arithmetic rule that a factor times a sum equals the sum of the factor times each addend, written a(b + c) = ab + ac.
Divergence
Divergence, or divergence operator, is a vector calculus operator measuring a vector field's net outflow per unit volume, positive at sources and negative at sinks.
Divergence theorem
The divergence theorem, also called Gauss's theorem or Ostrogradsky's theorem, states that a vector field's outward flux through a closed surface equals the volume integral of its divergence.
Divergent series
A divergent series, also known as a nonconvergent series, is an infinite series whose sequence of partial sums does not approach a finite limit, diverging either to infinity or by oscillating.
Divisia index
The Divisia index is an index number whose growth rate is the expenditure-share-weighted average of its components' growth rates, introduced by François Divisia in 1926.
Divisibility (ring theory)
Divisibility in ring theory studies when one element of a ring divides another, generalizing integer divisibility; properties like unique factorization into primes can fail in general rings.
Divisibility rule
A divisibility rule, also called a divisibility test, is a shortcut that checks whether an integer is divisible by another by examining its digits instead of dividing.
Division (mathematics)
Division is the arithmetic operation of taking the ratio of two numbers, the inverse of multiplication, where x is the dividend, y the divisor, and the result the quotient.
Division algorithm
The division algorithm is a theorem of elementary number theory: any integer divided by a nonzero divisor yields a unique quotient and remainder, with 0 ≤ r < divisor.
Division by zero
Division by zero, also called dividing by zero or a zero denominator, is dividing a number by zero, undefined for real numbers, with 0/0 an indeterminate form.
Division ring
A division ring, also called a skew field, is a nonzero ring in which every nonzero element has a multiplicative inverse, while multiplication need not commute.
Division sign
The division sign (÷), also called the obelus, is a mathematical symbol used to indicate division. Johann Rahn first used it for division in his 1659 book Teutsche Algebra.
Divisor
A divisor (also called a factor) of an integer n is an integer that divides n with no remainder; its study is the starting point of number theory.
Divisor (algebraic geometry)
In algebraic geometry, a divisor is a formal object on an algebraic variety or scheme recording codimension-1 subvarieties with integer multiplicities, tied to line bundles through the Picard group.
Divisor function
The divisor function, also called the sum-of-divisors function, is the number-theoretic function σk(n) summing the k-th powers of n's divisors; σ0 counts them and σ1 adds them up.
Dixon's Q test
Dixon's Q test is a statistical test for detecting a single outlier in a small univariate sample, introduced by W. J. Dixon in 1950 and standard in analytical chemistry.
DMAIC
DMAIC, or Define, Measure, Analyze, Improve, and Control, is a five-phase, data-driven Six Sigma methodology for improving existing processes, standardized in ISO 13053-1:2011 and used in manufacturing, service, and healthcare.
Do-calculus
Do-calculus is a system of three inference rules, introduced by Judea Pearl in 1995, that determines whether causal effects can be computed from non-experimental, observational data alone.
Dodecagon
A dodecagon is a polygon with 12 sides and 12 vertices; in the regular case each interior angle measures 150° and the shape has 12 lines of symmetry.
Dodecahedron
A dodecahedron is any polyhedron with twelve faces, and in everyday use usually means the regular dodecahedron, a Platonic solid of twelve pentagonal faces, 30 edges, and 20 vertices.
Domain decomposition methods
Domain decomposition methods (DDMs) are numerical methods that solve large systems from discretized partial differential equations by splitting them into smaller subdomain problems, coupled at interfaces and solved in parallel.
Domain of a function
The domain of a function, also called the function domain, is the set of inputs for which it is defined, the X in f: X → Y.
Domains of attraction of probability laws
A domain of attraction of probability laws is the set of distributions whose normalized sums of independent copies converge to a stable law, typically the normal or an α-stable limit.
Dominance analysis
Dominance analysis is a statistical method for ranking the relative importance of predictor variables in a regression model, introduced by David V. Budescu in 1993.
Dominated convergence theorem
Dominated convergence theorem, also called Lebesgue's dominated convergence theorem, is a measure theory result giving a condition under which a limit and an integral can be exchanged.
Dominating number
The dominating number, written 𝔡, is a cardinal characteristic of set theory: the smallest size of a family of natural-number functions that eventually dominates every such function.
Dominating set
The dominating set problem, in graph theory, asks for a smallest set of vertices covering a graph, so every vertex is in the set or adjacent to it.
Dominator (graph theory)
In graph theory, a dominator of a vertex v in a flowgraph is a vertex every path from the root to v must pass through; dominators form a dominator tree.
Donaldson–Thomas invariants
Donaldson–Thomas invariants are enumerative invariants of a Calabi–Yau threefold that count stable sheaves or curves, introduced by Richard Thomas in 2000 as a holomorphic analog of the Casson invariant.
Donsker's theorem
Donsker's theorem, also called the functional central limit theorem, states that rescaled partial-sum processes of random walks converge in distribution to Brownian motion, proved by Monroe Donsker in 1951.