Every idea

Ideas 4501–4650 of 14183.

Name	Kind	Subject
Sumset	Definition	Number theory
Lopatinskii–Shapiro condition	Concept	Partial differential equations
Young's inequality for integral operators	Theorem	Integral equations
Hermitian form	Concept	Linear and multilinear algebra; matrix theory
Homotopy category	Concept	Category theory; homological algebra
Representable functor	Definition	Category theory; homological algebra
Jensen's formula	Theorem	Functions of a complex variable
Rational difference equation	Definition	Difference and functional equations
Functional inequality	Definition	Difference and functional equations
Weierstrass preparation theorem	Theorem	Commutative algebra
Catastrophic cancellation	Definition	Numerical analysis
Sectional curvature	Definition	Differential geometry
Hopf algebra	Definition	Associative rings and algebras
Perfect ring	Concept	Associative rings and algebras
Fefferman's ball multiplier theorem	Theorem	Harmonic analysis on Euclidean spaces
Homotopic maps	Definition	Algebraic topology
Pluriharmonic function	Concept	Several complex variables and analytic spaces
Continuous dual space	Concept	Functional analysis
Soundness	Concept	Mathematical logic and foundations
Knot sum	Definition	Manifolds and cell complexes
Conjugacy problem	Problem	Group theory and generalizations
Ringed space	Definition	Algebraic geometry
Hamiltonian Monte Carlo	Proposition	Numerical analysis
Truncation error	Concept	Numerical analysis
Graph enumeration	Concept	Combinatorics
Superharmonic function	Definition	Potential theory
Proper holomorphic map	Definition	Several complex variables and analytic spaces
Goldie ring	Definition	Associative rings and algebras
Schoenberg's embedding criterion	Theorem	Geometry
Essential extension	Definition	General algebraic systems
Partial difference equation	Concept	Difference and functional equations
Jacobi polynomials	Definition	Special functions
Mostow rigidity theorem	Theorem	Differential geometry
Schrödinger equation	Definition	Partial differential equations
Relative homology	Concept	Algebraic topology
Horn	Definition	Algebraic topology
Solution of equations with degenerate kernels	Proposition	Integral equations
Localization	Concept	Commutative algebra
Second variation	Concept	Calculus of variations and optimal control; optimization
Regular semigroup	Definition	Group theory and generalizations
Pointless topology	Definition	Order, lattices, ordered algebraic structures
Quartic formula	Theorem	Field theory and polynomials
Ramanujan–Petersson conjecture	Theorem	Number theory
Teichmüller space	Definition	Functions of a complex variable
Reproducing kernel Hilbert space	Concept	Functional analysis
Galois group of a prime degree polynomial with two nonreal roots	Theorem	Field theory and polynomials
Growth rate of a group	Concept	Group theory and generalizations
Near-unanimity term	Concept	General algebraic systems
Tate module	Concept	Algebraic geometry
g-theorem	Theorem	Convex and discrete geometry
Rational map	Concept	Algebraic geometry
Carathéodory's existence theorem	Theorem	Ordinary differential equations
Bilateral Laplace transform of a probability law	Example	Integral transforms, operational calculus
Partial isometry	Definition	Operator theory
Minkowski question-mark function	Example	Real functions
Local cohomology	Definition	Commutative algebra
Center manifold theorem	Theorem	Dynamical systems and ergodic theory
Normed algebra	Concept	Functional analysis
Yoneda embedding	Concept	Category theory; homological algebra
General recursive function	Definition	Mathematical logic and foundations
Net of a polyhedron	Definition	Convex and discrete geometry
Operator system	Concept	Functional analysis
Jordan algebra	Definition	Nonassociative rings and algebras
Net	Concept	General topology
Lagrange's theorem in S3	Example	Group theory and generalizations
van Dantzig's theorem	Theorem	Topological groups, Lie groups
Quillen's theorem on complex cobordism	Theorem	Algebraic topology
Topological index	Definition	Global analysis, analysis on manifolds
Chain homotopy	Concept	Category theory; homological algebra
Dirac equation	Definition	Partial differential equations
Dini–Lipschitz criterion	Theorem	Harmonic analysis on Euclidean spaces
Semimartingale	Concept	Probability theory and stochastic processes
C-infinity ring	Concept	Global analysis, analysis on manifolds
Wald–Wolfowitz optimality of the sequential probability ratio test	Theorem	Statistics
Weakly compact cardinal	Definition	Mathematical logic and foundations
Homotopy fiber	Concept	Algebraic topology
Resonance	Concept	Ordinary differential equations
Sparse grid	Definition	Numerical analysis
Coproduct	Concept	Category theory; homological algebra
Pringsheim convergence	Definition	Sequences, series, summability
Monomial ideal	Concept	Commutative algebra
Doob's martingale inequality	Theorem	Probability theory and stochastic processes
Brun sieve	Definition	Number theory
Homotopy fiber	Definition	Algebraic topology
Smale's degree for proper Fredholm maps	Definition	Global analysis, analysis on manifolds
XYZ inequality	Theorem	Order, lattices, ordered algebraic structures
Chern class	Definition	Algebraic geometry
Maass wave form	Definition	Number theory
Lamplighter group	Example	Group theory and generalizations
Radon transform	Definition	Integral transforms, operational calculus
Semisimple module	Definition	Associative rings and algebras
Ricci curvature	Concept	Differential geometry
Hamilton–Jacobi equation	Definition	Partial differential equations
Erdős distinct distances problem	Problem	Convex and discrete geometry
Realizability	Concept	Mathematical logic and foundations
Poisson manifold	Definition	Differential geometry
Determinacy	Definition	Mathematical logic and foundations
Linear recurrence with polynomial coefficients	Definition	Difference and functional equations
Fredholm alternative	Theorem	Linear and multilinear algebra; matrix theory
Covering relation	Concept	Order, lattices, ordered algebraic structures
Function having a given Mellin transform	Definition	Integral transforms, operational calculus
Max-flow min-cut theorem	Theorem	Combinatorics
WZ theory	Definition	Combinatorics
Bifurcation from a characteristic value	Concept	Operator theory
Feller process	Concept	Probability theory and stochastic processes
Fukaya category	Concept	Differential geometry
Intersection theory	Concept	Algebraic geometry
Legendre condition	Theorem	Calculus of variations and optimal control; optimization
Random group	Concept	Group theory and generalizations
Mazur–Ulam theorem	Theorem	Functional analysis
Hilbert symbol	Definition	Number theory
Kahan summation algorithm	Theorem	Numerical analysis
Block design	Concept	Combinatorics
Determinantal variety	Definition	Algebraic geometry
Siggers term	Definition	General algebraic systems
Discrete valuation ring	Definition	Commutative algebra
Eilenberg–Steenrod axioms	Definition	Algebraic topology
Legendre polynomials	Definition	Special functions
Character sum	Definition	Number theory
Markov random field	Definition	Statistics
Kolmogorov quotient	Definition	General topology
Spherical Bessel functions	Concept	Special functions
Turán's inequalities	Theorem	Special functions
Beltrami equation	Definition	Functions of a complex variable
Integral extension	Definition	Commutative algebra
Fresnel integrals	Definition	Special functions
Open subgroup	Definition	Topological groups, Lie groups
Isolated hypersurface singularity	Definition	Several complex variables and analytic spaces
Daniell integral	Concept	Measure and integration
Hom-set characterization of adjunctions	Theorem	Category theory; homological algebra
1 + 2 + 3 + 4 + ⋯	Example	Sequences, series, summability
Spectrum of an element	Definition	Functional analysis
Barbalat's lemma	Lemma	Ordinary differential equations
Siegel's theorem on integral points	Theorem	Number theory
Seminorm	Definition	Functional analysis
Weierstrass's counterexample to the Dirichlet principle	Counterexample	Calculus of variations and optimal control; optimization
Variational integrator	Concept	Numerical analysis
Rational map	Definition	Algebraic geometry
Compactly generated space	Concept	General topology
Regular function	Concept	Algebraic geometry
Artin–Tate lemma	Lemma	Commutative algebra
Commuting probability	Concept	Group theory and generalizations
Closed geodesic	Concept	Differential geometry
Exchangeable random variables	Concept	Probability theory and stochastic processes
Wavelet	Definition	Harmonic analysis on Euclidean spaces
Proof that subgroups of index two are normal	Proof	Group theory and generalizations
Sober space	Concept	General topology
Mehta integral	Theorem	Special functions
Whitney C-infinity topology	Definition	Global analysis, analysis on manifolds
Lewy's example	Counterexample	Partial differential equations