Every idea

Ideas 21301–21450 of 21839.

Name	Kind	Subject
Whittaker–Shannon interpolation formula	Theorem	Information and communication theory, circuits
Abstract Wiener space	Definition	Measure and integration
Primitive ideal	Definition	Associative rings and algebras
Proof of the first Borel–Cantelli lemma	Proof	Probability theory and stochastic processes
Doob martingale	Example	Probability theory and stochastic processes
Band matrix	Concept	Linear and multilinear algebra; matrix theory
Oracle machine	Concept	Mathematical logic and foundations
Anderson–Kadec theorem	Theorem	Manifolds and cell complexes
Relatively complemented lattice	Definition	Order, lattices, ordered algebraic structures
Duality in category theory	Concept	Category theory; homological algebra
Projective morphism	Concept	Algebraic geometry
Chudnovsky algorithm	Definition	Number theory
Change detection	Problem	Statistics
Metabolic control analysis	Concept	Biology and other natural sciences
3-manifold	Definition	Manifolds and cell complexes
Bullen parameter	Definition	Geophysics
Limiting proportion of derangements	Theorem	Combinatorics
Zonotope	Concept	Convex and discrete geometry
Proper cone	Concept	Convex and discrete geometry
Bernstein–Bézier form	Concept	Approximations and expansions
Dévissage	Theorem	K-theory
Asymptotic expansion from poles of a Mellin transform	Definition	Integral transforms, operational calculus
Proof of Liouville's theorem by Cauchy's estimates	Proof	Functions of a complex variable
Absolute stability problem of Lur'e	Problem	Systems theory; control
Thermal efficiency	Concept	Classical thermodynamics, heat transfer
Lomb–Scargle periodogram	Definition	Statistics
Lebesgue measure as Haar measure	Example	Abstract harmonic analysis
Proof of the law of excluded middle extended to the infinite	Proof
Heisenberg picture	Definition	Quantum theory
Complete elliptic integral of the first kind	Definition	Special functions
No-retraction theorem	Theorem	Algebraic topology
Tarskian hierarchy	Concept
Fisher–Neyman factorization theorem	Theorem	Statistics
Komar mass	Definition	Relativity and gravitational theory
Goldreich–Tremaine theory of disk–satellite interaction	Definition	Astronomy and astrophysics
Current	Definition	Calculus of variations and optimal control; optimization
Four-vertex theorem	Theorem	Differential geometry
Normal Moore space problem	Problem	General topology
Locally compact abelian group	Definition	Topological groups, Lie groups
Inherently nonfinitely based algebra	Concept	General algebraic systems
Scaling relations among critical exponents	Proposition	Statistical mechanics, structure of matter
Triebel–Lizorkin space	Definition	Functional analysis
Atiyah–Hirzebruch spectral sequence	Theorem	Algebraic topology
Aristotelian comprehension schema	Concept
Massey product	Concept	Algebraic topology
Girsanov theorem	Theorem	Probability theory and stochastic processes
Zolotarev polynomials	Definition	Approximations and expansions
World line	Concept	Relativity and gravitational theory
Wheeler–DeWitt equation	Definition	Relativity and gravitational theory
Thomson scattering	Concept	Optics, electromagnetic theory
Spectral theory of dynamical systems	Concept	Dynamical systems and ergodic theory
Real analytic manifold	Concept	Several complex variables and analytic spaces
Epsilon-induction	Concept
Monomial ideal	Definition	Commutative algebra
Interior operator	Concept	Order, lattices, ordered algebraic structures
Solvable by radicals	Definition	Field theory and polynomials
Golden–Thompson inequality	Theorem	Linear and multilinear algebra; matrix theory
Sard's theorem	Theorem	Global analysis, analysis on manifolds
Successor order	Definition	Order, lattices, ordered algebraic structures
Strongly pseudoconvex domain	Concept	Several complex variables and analytic spaces
Optical transfer function	Concept	Optics, electromagnetic theory
Nyquist plot	Concept	Systems theory; control
Data envelopment analysis	Concept	Operations research, mathematical programming
Polar space	Concept	Geometry
Hunt process	Concept	Probability theory and stochastic processes
Undecidability of the halting problem	Theorem	Mathematical logic and foundations
Morris–Lecar model	Concept	Biology and other natural sciences
Symmetric and self-reciprocal kernels	Definition	Integral transforms, operational calculus
Curve-shortening flow	Definition	Differential geometry
Variable-mass system	Concept	Mechanics of particles and systems
Almost periodic sequence	Concept	Difference and functional equations
Expressive completeness	Concept
Tensor decomposition	Definition	Linear and multilinear algebra; matrix theory
Word problem for free lattices	Theorem	Order, lattices, ordered algebraic structures
Stone–von Neumann theorem	Theorem	Topological groups, Lie groups
Essentially self-adjoint operator	Definition	Operator theory
Euler integral for the gamma function	Theorem	Special functions
Gravitational memory effect	Fact	Relativity and gravitational theory
Derivable rule	Concept
Vibration of plates	Concept	Mechanics of deformable solids
Finite-rank operator	Concept	Operator theory
Synge's theorem	Theorem	Differential geometry
Monogenic function	Definition	Functions of a complex variable
Hopf manifold	Example	Several complex variables and analytic spaces
Fourier series of Bernoulli polynomials	Example	Harmonic analysis on Euclidean spaces
Martin's axiom	Definition	Mathematical logic and foundations
Christoffel symbols	Definition	Differential geometry
Metamaterial cloaking	Definition	Optics, electromagnetic theory
First uncountable ordinal	Concept
Congruence lattice	Definition	General algebraic systems
Reeb stability theorem	Theorem	Manifolds and cell complexes
Riemann problem for gas dynamics	Problem	Fluid mechanics
Bellman equation	Concept	Operations research, mathematical programming
Kervaire invariant problem	Problem	Algebraic topology
Parametrix	Concept	Global analysis, analysis on manifolds
Kasparov product	Definition	K-theory
McEliece cryptosystem	Definition	Information and communication theory, circuits
Weil divisor	Concept	Algebraic geometry
Topological manifold	Definition	Manifolds and cell complexes
Aizenman–Higuchi theorem	Theorem	Statistical mechanics, structure of matter
Flag variety	Definition	Algebraic geometry
Proof that orbits partition the set	Proof	Group theory and generalizations
Zinbiel algebra	Definition	Nonassociative rings and algebras
Steinberg group	Definition	K-theory
Young–Laplace equation	Theorem	Fluid mechanics
Prime ring	Concept	Associative rings and algebras
Short-rate model	Definition	Game theory, economics, finance, and other social and behavioral sciences
Symbol class	Definition	Partial differential equations
Hurewicz theorem	Theorem	Algebraic topology
Transform pair	Concept	Integral transforms, operational calculus
Axioms used in the book	Proposition
Dehn surgery	Concept	Manifolds and cell complexes
CSP dichotomy theorem	Theorem	General algebraic systems
S-wave	Definition	Mechanics of deformable solids
Singular perturbation	Definition	Ordinary differential equations
Boutet de Monvel's embedding theorem	Theorem	Several complex variables and analytic spaces
Curvature form	Concept	Differential geometry
Prim's algorithm	Concept	Combinatorics
Well-founded order	Definition	Order, lattices, ordered algebraic structures
Diversity index	Definition	Biology and other natural sciences
Allen–Cahn equation	Definition	Partial differential equations
Moment map	Concept	Differential geometry
Heat potential	Concept	Partial differential equations
Linear discriminant analysis	Concept	Statistics
Subadditive function	Definition	Difference and functional equations
Ramsey problem of optimal taxation	Problem	Game theory, economics, finance, and other social and behavioral sciences
Steiner conic	Definition	Geometry
Skin effect	Definition	Optics, electromagnetic theory
First and second variation of arc length	Theorem	Differential geometry
Relativistic mechanics	Concept	Relativity and gravitational theory
Modern portfolio theory	Concept	Game theory, economics, finance, and other social and behavioral sciences
Costas array	Definition	Combinatorics
Gowers norm	Concept	Number theory
Theta correspondence	Concept	Number theory
Fundamental groupoid	Concept	Algebraic topology
Lattice gauge theory	Concept	Quantum theory
Category of posets	Concept	Category theory; homological algebra
Cauchy's functional equation	Problem	Difference and functional equations
Numerical quantifier	Concept
Power series in several variables	Definition	Several complex variables and analytic spaces
Cartan matrix of an algebra	Concept	Associative rings and algebras
Kohn Laplacian	Concept	Several complex variables and analytic spaces
Bernstein's theorem on monotone functions	Theorem	Real functions
Radial basis function	Concept	Approximations and expansions
Fuchsian equation	Concept	Ordinary differential equations
Hirsch conjecture	Counterexample	Convex and discrete geometry
K2 of the integers	Example	K-theory
Littlewood–Paley square function	Definition	Harmonic analysis on Euclidean spaces
Quadratic variation	Definition	Probability theory and stochastic processes
Normal form	Definition	Ordinary differential equations