Every idea

Ideas 6001–6150 of 14183.

Name	Kind	Subject
Neumann series	Theorem	Operator theory
Locally finite variety	Concept	General algebraic systems
Solving linear difference equations by the Z-transform	Definition	Difference and functional equations
Cauchy interlacing theorem	Theorem	Linear and multilinear algebra; matrix theory
Bernstein–Gelfand–Ponomarev reflection functors	Definition	Associative rings and algebras
Hartogs–Bochner extension theorem	Theorem	Several complex variables and analytic spaces
Paracompact space	Concept	General topology
B-spline	Definition	Approximations and expansions
Ricker model	Example	Biology and other natural sciences
Conservation law	Concept	Partial differential equations
Alternating-direction implicit method	Theorem	Numerical analysis
Catenary problem	Problem	Calculus of variations and optimal control; optimization
Shape operator	Definition	Differential geometry
Bergman kernel	Concept	Functions of a complex variable
Remez inequality	Theorem	Approximations and expansions
Kurosh–Amitsur radical theory	Definition	Associative rings and algebras
Apollonian gasket	Example	Convex and discrete geometry
Kolmogorov automorphism	Definition	Dynamical systems and ergodic theory
Singular cardinals hypothesis	Axiom	Mathematical logic and foundations
Tauber's theorem	Theorem	Sequences, series, summability
Zariski topology	Concept	Algebraic geometry
Residue field	Definition	Commutative algebra
Elementary abelian group	Definition	Group theory and generalizations
MV-algebra	Concept	Order, lattices, ordered algebraic structures
Contractible space	Definition	Algebraic topology
Fence	Example	Order, lattices, ordered algebraic structures
Birkhoff sum and average	Concept	Dynamical systems and ergodic theory
Standard map	Example	Dynamical systems and ergodic theory
Tempered distribution	Definition	Functional analysis
2-category	Definition	Category theory; homological algebra
Cap product	Definition	Algebraic topology
Toeplitz–Hausdorff theorem	Theorem	Operator theory
Markov chain mixing time	Concept	Probability theory and stochastic processes
Orthogonal polynomials	Concept	Harmonic analysis on Euclidean spaces
Freyd–Mitchell embedding theorem	Theorem	Category theory; homological algebra
Rational singularity	Definition	Algebraic geometry
Abstract Volterra equation	Definition	Integral equations
Carleson embedding theorem	Theorem	Functions of a complex variable
Singular integral operator	Definition	Harmonic analysis on Euclidean spaces
Efficiency of an estimator	Concept	Statistics
Polygon	Concept	Geometry
Liouville's theorem (differential algebra)	Theorem	Field theory and polynomials
Polyconvexity	Concept	Calculus of variations and optimal control; optimization
Simple ring	Definition	Associative rings and algebras
Weil divisor	Definition	Algebraic geometry
Inversive geometry	Definition	Geometry
Descriptive geometry	Definition	Geometry
The even integers form a subgroup of the integers	Example	Group theory and generalizations
Computed tomography as an inverse problem	Example	Integral transforms, operational calculus
Cartan's theorem on fine continuity of superharmonic functions	Theorem	Potential theory
Excluded point topology	Example	General topology
Elementary substructure	Concept	Mathematical logic and foundations
Property (T)	Definition	Topological groups, Lie groups
Summability method	Concept	Sequences, series, summability
Score	Definition	Statistics
Khinchin integral	Definition	Real functions
Tikhonov's theorem on slow-fast systems	Theorem	Ordinary differential equations
Cohomology of Lie groups	Definition	Manifolds and cell complexes
Non-Archimedean absolute value	Definition	Field theory and polynomials
Statistical convergence	Definition	Sequences, series, summability
Galois ring	Definition	Commutative algebra
Homogeneous and inhomogeneous linear recurrences	Concept	Difference and functional equations
Arbitrary-precision arithmetic	Definition	Numerical analysis
Nash embedding theorems	Theorem	Differential geometry
Dual object	Definition	Category theory; homological algebra
Loop theorem	Theorem	Manifolds and cell complexes
Cayley–Menger determinant	Definition	Geometry
Bolza problem	Problem	Calculus of variations and optimal control; optimization
Cantor–Lebesgue theorem	Theorem	Harmonic analysis on Euclidean spaces
Hall's theorem on solvable groups	Theorem	Group theory and generalizations
Derived set	Concept	General topology
Poincaré group	Example	Topological groups, Lie groups
Frölicher space	Definition	Global analysis, analysis on manifolds
Moishezon manifold	Concept	Several complex variables and analytic spaces
Exterior differential system	Concept	Global analysis, analysis on manifolds
Hopf degree theorem	Theorem	Algebraic topology
Reduced function	Concept	Potential theory
Series acceleration	Definition	Numerical analysis
Fractional ideal	Definition	Commutative algebra
Geometric optics	Concept	Optics, electromagnetic theory
Logarithm of a matrix	Definition	Linear and multilinear algebra; matrix theory
Clopen set	Definition	General topology
11/8 conjecture	Conjecture	Manifolds and cell complexes
Daubechies wavelet	Example	Harmonic analysis on Euclidean spaces
Orientation of a manifold	Concept	Manifolds and cell complexes
Henselization	Concept	Commutative algebra
Stanley–Reisner ring	Concept	Commutative algebra
Maximum modulus principle in several variables	Theorem	Several complex variables and analytic spaces
Supercompact cardinal	Concept	Mathematical logic and foundations
Maslov index	Concept	Differential geometry
Formal group law in topology	Definition	Algebraic topology
F-distribution	Definition	Statistics
Shift operator	Definition	Difference and functional equations
Singular control	Concept	Calculus of variations and optimal control; optimization
Hörmander's condition	Concept	Partial differential equations
Open segment	Definition	Convex and discrete geometry
Conway base 13 function	Counterexample	Real functions
Quotient of a normed space	Concept	Functional analysis
Borel functional calculus	Concept	Operator theory
Topological group	Concept	Topological groups, Lie groups
Lax pair	Definition	Dynamical systems and ergodic theory
Hyperbolic partial differential equation	Concept	Partial differential equations
Lyapunov equation	Concept	Linear and multilinear algebra; matrix theory
Finite field arithmetic	Definition	Field theory and polynomials
Multidimensional Mellin transform	Concept	Integral transforms, operational calculus
Dynkin quiver	Concept	Associative rings and algebras
Pseudo algebraically closed field	Concept	Field theory and polynomials
Theory	Concept	Mathematical logic and foundations
Quasi-category	Concept	Category theory; homological algebra
Feuerbach's theorem	Theorem	Geometry
Dual Radon transform	Concept	Integral transforms, operational calculus
Fixed-point property	Definition	General topology
Nelson–Aalen estimator	Concept	Statistics
Global analysis	Definition	Global analysis, analysis on manifolds
Serre's theorem on regular local rings	Theorem	Commutative algebra
Initial and terminal objects	Definition	Category theory; homological algebra
Period three implies chaos	Theorem	Dynamical systems and ergodic theory
Aoki–Rassias theorem	Theorem	Difference and functional equations
Suslin's theorem	Theorem	Mathematical logic and foundations
P-adic analysis	Definition	Functions of a complex variable
Finitely generated projective modules over local rings are free	Theorem	Commutative algebra
Adaptive quadrature	Proposition	Numerical analysis
Pascal's theorem	Theorem	Geometry
Ionescu-Tulcea theorem	Theorem	Probability theory and stochastic processes
Morse homology	Concept	Manifolds and cell complexes
Gauss variational problem	Problem	Potential theory
Quasi-identity	Concept	General algebraic systems
Krull–Schmidt theorem	Theorem	Associative rings and algebras
Cartan matrix of an algebra	Definition	Associative rings and algebras
Weakly singular kernel	Concept	Integral equations
Weak-type estimate	Concept	Harmonic analysis on Euclidean spaces
Proper morphism	Concept	Algebraic geometry
j-invariant of an elliptic curve	Concept	Algebraic geometry
Subnormal number	Definition	Numerical analysis
Equalizer	Definition	Category theory; homological algebra
Schur's inequality	Theorem	Real functions
Semi-continuity	Concept	Real functions
Cauchy matrix	Concept	Linear and multilinear algebra; matrix theory
Rational equivalence	Definition	Algebraic geometry
Unitary dual	Concept	Topological groups, Lie groups
Besov space	Concept	Functional analysis
System of parameters	Concept	Commutative algebra
Fiber of a morphism	Concept	Algebraic geometry
Purely inseparable extension	Concept	Field theory and polynomials
Magma	Concept	Group theory and generalizations
Statistical decision theory	Definition	Statistics
Quasiregular map	Definition	Functions of a complex variable
Lie group action	Concept	Manifolds and cell complexes
Polylogarithm	Concept	Special functions
Δ-complex	Definition	Algebraic topology