Every idea

Ideas 8101–8250 of 14183.

Name	Kind	Subject
Universal property	Concept	Category theory; homological algebra
Hamiltonian of an optimal control problem	Definition	Calculus of variations and optimal control; optimization
Strictly singular operator	Definition	Operator theory
Bornological space	Definition	Functional analysis
Arithmetic genus	Definition	Algebraic geometry
Bochner integral	Definition	Measure and integration
Siegel's theorem on meromorphic function fields	Theorem	Several complex variables and analytic spaces
Ruelle zeta function	Concept	Dynamical systems and ergodic theory
Discrete Painlevé equations	Definition	Difference and functional equations
Bézier curve	Definition	Numerical analysis
Jacobi amplitude	Definition	Special functions
Exponential family	Concept	Statistics
Homotopy type theory	Concept	Mathematical logic and foundations
Simplicial set	Definition	Category theory; homological algebra
Total variation of a measure	Concept	Measure and integration
Unilateral Z-transform	Concept	Integral transforms, operational calculus
Complete intersection ring	Concept	Commutative algebra
Symplectic capacity	Definition	Differential geometry
Noncommutative Gröbner basis	Concept	Associative rings and algebras
Restriction of a measure	Concept	Measure and integration
Unit distance problem	Problem	Convex and discrete geometry
Mountain pass theorem	Theorem	Global analysis, analysis on manifolds
Schrödinger equation	Concept	Partial differential equations
Submartingale	Definition	Probability theory and stochastic processes
Superharmonic potential	Definition	Potential theory
Dawson function	Concept	Special functions
Helicoid	Example	Differential geometry
Gauss sum	Concept	Number theory
Congruence subgroup	Definition	Number theory
Slice-ribbon conjecture	Conjecture	Manifolds and cell complexes
Heisenberg inequality for the Fourier transform	Theorem	Harmonic analysis on Euclidean spaces
Manifold with corners	Definition	Global analysis, analysis on manifolds
Abelian extension	Concept	Field theory and polynomials
Choi's theorem on completely positive maps	Theorem	Functional analysis
Cartan's uniqueness theorem	Theorem	Several complex variables and analytic spaces
Integral functional with a Lagrangian density	Definition	Calculus of variations and optimal control; optimization
Quasi-projective variety	Concept	Algebraic geometry
Mapping cylinder	Concept	Algebraic topology
Morphism of schemes	Definition	Algebraic geometry
Associated prime	Concept	Commutative algebra
Total variation	Definition	Real functions
Convolution on the line	Concept	Integral transforms, operational calculus
Morse lemma	Lemma	Manifolds and cell complexes
Normal function	Concept	Mathematical logic and foundations
Lattice homomorphism	Definition	Order, lattices, ordered algebraic structures
Model complete theory	Definition	Mathematical logic and foundations
Hodges–Lehmann estimator	Definition	Statistics
Irreducible analytic germ	Definition	Several complex variables and analytic spaces
Order theory	Concept	Order, lattices, ordered algebraic structures
Missing data mechanisms	Concept	Statistics
Trivial variety	Example	General algebraic systems
Relatively complemented lattice	Concept	Order, lattices, ordered algebraic structures
Algebra over an operad	Concept	Category theory; homological algebra
Nakano positivity	Definition	Several complex variables and analytic spaces
Gauss–Bonnet theorem	Theorem	Differential geometry
Young's lattice	Example	Order, lattices, ordered algebraic structures
Regular scheme	Concept	Algebraic geometry
Kruskal–Wallis test	Definition	Statistics
Smash product	Definition	Associative rings and algebras
Intuitionistic type theory	Concept	Mathematical logic and foundations
Hypergeometric function	Definition	Special functions
Verlet integration	Proposition	Numerical analysis
Geometric invariant theory	Definition	Algebraic geometry
Stone algebra	Concept	Order, lattices, ordered algebraic structures
Hilbert system	Definition	Mathematical logic and foundations
Polytope	Definition	Convex and discrete geometry
Amenable Banach algebra	Definition	Functional analysis
Loop-erased random walk	Concept	Probability theory and stochastic processes
Pontryagin dual	Definition	Abstract harmonic analysis
Upper set	Concept	Order, lattices, ordered algebraic structures
Paraconsistent logic	Definition	Mathematical logic and foundations
Lindelöf space	Definition	General topology
Resolutivity of boundary functions	Definition	Potential theory
Brauer character	Definition	Group theory and generalizations
Szemerédi regularity lemma	Lemma	Combinatorics
Schur orthogonality for compact groups	Theorem	Topological groups, Lie groups
Jacobi sum	Definition	Number theory
Gromov–Hausdorff space	Object	Differential geometry
Canonical module	Definition	Commutative algebra
Hankel transform	Definition	Integral transforms, operational calculus
Exponential integral	Concept	Special functions
Mixed model	Definition	Statistics
Local coefficient system	Definition	Algebraic topology
C0-semigroup	Concept	Operator theory
Compact group	Concept	Topological groups, Lie groups
Separably closed field	Definition	Field theory and polynomials
Ring of convergent power series	Concept	Several complex variables and analytic spaces
Fourier integral operator	Concept	Partial differential equations
Crystalline cohomology	Concept	Algebraic geometry
Weak operator topology	Definition	Operator theory
Eilenberg swindle	Definition	Associative rings and algebras
Entropy solution	Definition	Partial differential equations
Symbolic dynamics	Concept	Dynamical systems and ergodic theory
Duistermaat–Heckman formula	Theorem	Differential geometry
Plane curve	Concept	Algebraic geometry
Macdonald polynomial	Definition	Combinatorics
Transversality	Definition	Manifolds and cell complexes
Renewal equation	Example	Integral equations
Brown–McCoy radical	Concept	Associative rings and algebras
Kodaira–Spencer map	Concept	Several complex variables and analytic spaces
Brauer group	Definition	Associative rings and algebras
Enumerative combinatorics	Concept	Combinatorics
Lefschetz hyperplane theorem	Theorem	Algebraic geometry
Krull dimension of a poset	Concept	Order, lattices, ordered algebraic structures
Lattice of clones	Concept	General algebraic systems
Radiative transfer equation	Example	Astronomy and astrophysics
Geometric morphism	Definition	Category theory; homological algebra
Quillen equivalence	Definition	Category theory; homological algebra
Zariski topology	Definition	Algebraic geometry
Smooth morphism	Concept	Algebraic geometry
De Rham cohomology of varieties	Definition	Algebraic geometry
Lyusternik–Fet theorem	Theorem	Global analysis, analysis on manifolds
Non-uniform discrete Fourier transform	Definition	Numerical analysis
Tensor product of Hilbert spaces	Concept	Functional analysis
Charlier polynomials	Definition	Special functions
Non-wandering set	Concept	Dynamical systems and ergodic theory
Differential-algebraic system of equations	Concept	Ordinary differential equations
Convolution integral equation	Concept	Integral equations
Born series	Definition	Quantum theory
Euler–Boole summation	Definition	Numerical analysis
Comparison principle	Theorem	Partial differential equations
Steinhaus theorem	Theorem	Measure and integration
Dehn invariant	Definition	Convex and discrete geometry
Positive harmonic function	Concept	Potential theory
Eisenstein series	Concept	Number theory
Cauchy formula for repeated integration	Theorem	Real functions
Lidskii's trace formula for integral operators	Corollary	Integral equations
Varieties as categories of algebras over a monad	Theorem	Category theory; homological algebra
Attractor	Definition	Dynamical systems and ergodic theory
Multidimensional scaling	Concept	Statistics
Optimal control	Definition	Calculus of variations and optimal control; optimization
Skolem normal form	Definition	Mathematical logic and foundations
Weyl group of a compact Lie group	Concept	Topological groups, Lie groups
Koebe function	Example	Functions of a complex variable
Noncommutative Gröbner basis	Definition	Associative rings and algebras
Field homomorphism	Concept	Field theory and polynomials
Abel summation	Concept	Sequences, series, summability
Steenrod reduced power	Concept	Algebraic topology
Viscosity solution	Definition	Partial differential equations
Simple homotopy equivalence	Definition	Manifolds and cell complexes
Sperner property	Concept	Order, lattices, ordered algebraic structures
Steiner formula	Theorem	Convex and discrete geometry
Voronoi's conjecture on parallelohedra	Conjecture	Convex and discrete geometry
Heteroclinic orbit	Definition	Ordinary differential equations
Projection operation	Definition	General algebraic systems
Whitehead problem	Problem	Group theory and generalizations
Fenchel's theorem	Theorem	Differential geometry
Straszewicz's theorem	Theorem	Convex and discrete geometry
Stability condition	Concept	Category theory; homological algebra
Midpoint convex function	Definition	Real functions