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Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Topics referred to by the same term
mathematics contraction theorem may refer to: The Banach contraction mapping theorem in functional analysis Castelnuovo's contraction theorem in algebraic
Contraction_theorem
Constructs the minimal model of a given smooth algebraic surface
In mathematics, Castelnuovo's contraction theorem is used in the classification theory of algebraic surfaces to construct the minimal model of a given
Castelnuovo's contraction theorem
Castelnuovo's_contraction_theorem
Theorem for reducing high-order derivatives
after all single contractions among operator pairs, plus all double contractions, etc., plus all full contractions. Applying the theorem to the above examples
Wick's_theorem
Mathematical theorem regarding operators
mathematics, Blackwell's contraction mapping theorem provides a set of sufficient conditions for an operator to be a contraction mapping. It is widely used
Blackwell's contraction mapping theorem
Blackwell's_contraction_mapping_theorem
Existence and uniqueness of solutions to initial value problems
{\displaystyle y} , this integral operator is a contraction (See detailed proof below) and so the Banach fixed-point theorem proves that a solution can be obtained
Picard–Lindelöf_theorem
Theorem in mathematics
theorem was first established by Picard and Goursat using an iterative scheme: the basic idea is to prove a fixed point theorem using the contraction
Inverse_function_theorem
Theorem
stated for the special case of contraction semigroups, with the general case being called the Feller–Miyadera–Phillips theorem (after William Feller, Isao
Hille–Yosida_theorem
Bounded operators with sub-unit norm
explicit description of contractions leads to (operator-)parametrizations of positive and unitary matrices. Sz.-Nagy's dilation theorem, proved in 1953, states
Contraction_(operator_theory)
Function reducing distance between all points
less than 1). A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty
Contraction_mapping
{\displaystyle F} gives rise to such a contraction morphism (cf. cone theorem). Castelnuovo's contraction theorem Flip (mathematics) Kollár & Mori 1998
Contraction_morphism
Lumer–Phillips theorem A generates a contraction semigroup. There are many more examples where a direct application of the Lumer–Phillips theorem gives the
Lumer–Phillips_theorem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
partial differential equations to an elliptic system, to which the contraction mapping theorem could be applied. Given an m-dimensional Riemannian manifold
Nash_embedding_theorems
Topics referred to by the same term
In mathematics, contraction principle may refer to: Contraction principle (large deviations theory), a theorem that states how a large deviation principle
Contraction_principle
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Mathematical theory about infinitely iterated function composition
Many results can be considered extensions of the following result: Contraction Theorem for Analytic Functions—Let f be analytic in a simply-connected region
Infinite compositions of analytic functions
Infinite_compositions_of_analytic_functions
Concept in algebraic geometry
0, we have the following assertion, sometimes referred to as the Contraction Theorem: 3. Let F ⊂ N E ( X ) ¯ {\displaystyle F\subset {\overline {NE(X)}}}
Cone_of_curves
Theorem in formal logic
The cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus. It was originally proved
Cut-elimination_theorem
proved a general theorem relating the location of the roots of a contracted polynomial to that of the original. Asano contractions have also been used
Asano_contraction
On forbidden minors in planar graphs
(minors formed by at least one deletion or contraction) are planar. Another way of stating Wagner's theorem is that there are only two minor-minimal non-planar
Wagner's_theorem
Formula in graph theory
denotes contraction. Tutte refers to such a function as a W-function. The formula is sometimes referred to as the fundamental reduction theorem. In this
Deletion–contraction_formula
Branch of algebraic geometry
any curves with negative self-intersection. In fact, Castelnuovo’s contraction theorem states the converse: every (−1)-curve is the exceptional curve of
Intersection_theory
Effort to birationally classify algebraic varieties
investigated by the geometers of the Italian school around 1900; the contraction theorem of Guido Castelnuovo essentially describes the process of constructing
Minimal_model_program
Physics theorem
pressure to support its own weight. This contraction decreases its potential energy and, the virial theorem states, increases its thermal energy. The
Virial_theorem
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
American mathematician and statistician (1919–2010)
Rao–Blackwell theorem, and is also known for the Blackwell channel, Blackwell's contraction mapping theorem, Blackwell's approachability theorem, and the Blackwell
David_Blackwell
Process of energy release of a contracting star or planet
the main candidate for the source of solar energy was gravitational contraction. However, it soon was recognized by Sir Arthur Eddington and others that
Kelvin–Helmholtz_mechanism
Topological space that is homeomorphic to a metric space
different set of contraction maps than a metric space to which it is homeomorphic. One of the first widely recognized metrization theorems was Urysohn's
Metrizable_space
Fundamental result of mathematical logic
logic. Herbrand's theorem is the logical foundation for most automatic theorem provers. Although Herbrand originally proved his theorem for arbitrary formulas
Herbrand's_theorem
Finiteness of sets of forbidden graph minors
each contraction or deletion reduces the number of edges and vertices of the graph (a non-negative integer). The nontrivial part of the theorem is that
Robertson–Seymour_theorem
Topics referred to by the same term
theorem may refer to: Dilation theorem for contraction semigroups Sz.-Nagy's dilation theorem Stinespring dilation theorem Naimark's dilation theorem
Dilation_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
Theorems generalizing the Brouwer fixed-point theorem
(a previous result in a different vein, the Banach fixed-point theorem for contraction mappings in complete metric spaces was proved in 1922). Quite a
Fixed-point theorems in infinite-dimensional spaces
Fixed-point_theorems_in_infinite-dimensional_spaces
Every square matrix with positive entries can be written in a certain standard form
Sinkhorn's theorem states that every square matrix with positive entries can be written in a certain standard form. If A is an n × n matrix with strictly
Sinkhorn's_theorem
Gives condition for a set of functions to be relatively compact in an Lp space
In functional analysis, the Fréchet–Kolmogorov theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition
Fréchet–Kolmogorov_theorem
Mathematical classification of surfaces
another non-singular surface by blowing up a point. By Castelnuovo's contraction theorem, this is equivalent to saying that X has no (−1)-curves (smooth rational
Enriques–Kodaira classification
Enriques–Kodaira_classification
Strong form of uniform continuity
A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. We have the following chain of strict inclusions
Lipschitz_continuity
Rule of mathematical logic
on the right. Known as monotonicity of entailment in classical logic. Contraction, where two equal (or unifiable) members on the same side of a sequent
Structural_rule
contraction mapping. Every bounded sequence in R n {\displaystyle \mathbb {R} ^{n}} has a convergent subsequence, by the Bolzano–Weierstrass theorem.
Convergence_proof_techniques
Technique in parallel algorithms
claim a theorem that Theorem: After O(log n) expected rake and compress steps, a tree is reduced to a single node. Now rephrase the tree contraction algorithm
Tree_contraction
Dilation theorem
The Sz.-Nagy dilation theorem (proved by Béla Szőkefalvi-Nagy) states that every contraction T {\displaystyle T} on a Hilbert space H {\displaystyle H}
Sz.-Nagy's_dilation_theorem
Theorem
In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring,[when?] is a result
Stinespring_dilation_theorem
Northern Irish physicist (1928–1990)
physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022
John_Stewart_Bell
French mathematician, physicist and engineer (1854–1912)
theory. He famously introduced the concept of the Poincaré recurrence theorem, which states that a state will eventually return arbitrarily close to
Henri_Poincaré
the domain, the holomorphic mapping becomes a contraction mapping to which the Banach fixed-point theorem can be applied. Let D be a connected open subset
Earle–Hamilton fixed-point theorem
Earle–Hamilton_fixed-point_theorem
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
Links the homology groups of a product space with those of the individual spaces
mathematics, specifically in algebraic topology, the Eilenberg–Zilber theorem is an important result in establishing the link between the homology groups
Eilenberg–Zilber_theorem
Theorem in statistical mechanics
Lee–Yang theorem to the Heisenberg model and provided a simpler proof using Asano contractions. Simon & Griffiths (1973) extended the Lee–Yang theorem to certain
Lee–Yang_theorem
Japanese mathematician
Kawamata proved the basepoint-free theorem. The cone theorem and contraction theorem, central results in the theory, are the result of a joint effort
Yujiro_Kawamata
Theorem that every subgroup of a free group is itself free
In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob
Nielsen–Schreier_theorem
subadditive ergodic theorem is one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem. Intuitively, the subadditive
Kingman's subadditive ergodic theorem
Kingman's_subadditive_ergodic_theorem
Subgraph with contracted edges
and contractions may be recognized in polynomial time. Other results and conjectures involving graph minors include the graph structure theorem, according
Graph_minor
Concepts in commutative algebra
Cohen–Seidenberg theorems, which were proved by Irvin S. Cohen and Abraham Seidenberg. These are known as the going-up and going-down theorems. Let A ⊆ B be
Going_up_and_going_down
appearance in the Lumer–Phillips theorem which characterizes maximally dissipative operators as the generators of contraction semigroups. A dissipative operator
Dissipative_operator
Operation on differential forms
natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k {\displaystyle
Exterior_derivative
Theorem in dynamical system mathematics
the study of dynamical systems, the Hartman–Grobman theorem or linearization theorem is a theorem about the local behaviour of dynamical systems in the
Hartman–Grobman_theorem
Concept in algebraic geometry
which faces correspond to contractions. The cone theorem describes a significant class of faces that do correspond to contractions, and the abundance conjecture
Nef_line_bundle
Characterises an iterated function system whose attractor is close to a given set
In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set
Collage_theorem
Invariant measure of fractal dimension
^{n}\rightarrow \mathbf {R} ^{n},\quad i=1,\ldots ,m} are each a contraction mapping on Rn with contraction constant ri < 1. Then there is a unique non-empty compact
Hausdorff_dimension
Generalization of the exponential function
is strongly stable. Hille–Yosida theorem Lumer–Phillips theorem Trotter–Kato theorem Analytic semigroup Contraction (operator theory) Matrix exponential
C0-semigroup
Philosophical argument for the existence of God
theorem: Past eternal static state followed by cosmic expansion (Havg = 0) e.g. emergent models. Perpetual cycle of cosmic expansion then contraction
Kalam_cosmological_argument
Randomized algorithm for minimum cuts
of contraction of an edge ( u , v ) {\displaystyle (u,v)} in an undirected graph G = ( V , E ) {\displaystyle G=(V,E)} . Informally, the contraction of
Karger's_algorithm
In algebraic topology, the cellular approximation theorem states that a map between CW-complexes can always be taken to be of a specific type. Concretely
Cellular approximation theorem
Cellular_approximation_theorem
Theorem relating unitary operators to one-parameter Lie groups
Hille–Yosida theorem generalizes Stone's theorem to strongly continuous one-parameter semigroups of contractions on Banach spaces. Hall 2013 Theorem 10.15 Hall
Stone's theorem on one-parameter unitary groups
Stone's_theorem_on_one-parameter_unitary_groups
Automated theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover
List of mathematical logic topics
List_of_mathematical_logic_topics
Methodic assignment of colors to elements of a graph
algorithms were developed based on backtracking and on the deletion-contraction recurrence of Zykov (1949). One of the major applications of graph coloring
Graph_coloring
Formula of matrix exponentials
exponential of A. The Lie–Trotter product formula and the Trotter–Kato theorem extend this to certain unbounded linear operators A and B. This formula
Lie_product_formula
Two-dimensional Turing machine with emergent behavior
itself has a color that can change. These ants are called turmites, a contraction of "Turing machine termites". Common behaviours include the production
Langton's_ant
Concept in special relativity, governing a body's dynamics at high speeds
the proper length) is constant and is therefore subjected to Lorentz contraction in relatively moving frames. Born rigidity is a constraint on the motion
Born_rigidity
Operation on self-adjoint operators
{\displaystyle A} , its Cayley transform is a contraction satisfying the stated "partial" self-adjoint property. Theorem—The positive symmetric extensions of A
Extensions of symmetric operators
Extensions_of_symmetric_operators
Matroid obtained by restrictions and contractions
of restriction and contraction operations. Matroid minors are closely related to graph minors, and the restriction and contraction operations by which
Matroid_minor
Submodule of a mathematical ring
ideals of a ring are analogous to prime numbers, and the Chinese remainder theorem can be generalized to ideals. There is a version of unique prime factorization
Ideal_(ring_theory)
[citation needed] Dyckhoff & Negri (2015) list eight consequences of the above theorem that explain its significance (omitting footnotes and most references):
Geometric_logic
Mathematical transform that expresses a function of time as a function of frequency
sufficient regularity and decay properties is given by the Fourier inversion theorem, i.e., Inverse transform The functions f {\displaystyle f} and f ^ {\displaystyle
Fourier_transform
Root-finding algorithm
set. The Banach fixed-point theorem gives a sufficient condition for the existence of attracting fixed points. A contraction mapping function f {\displaystyle
Fixed-point_iteration
Mathematical notation
n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } ). Multinomial theorem ( ∑ i = 1 n x i ) k = ∑ | α | = k ( k α ) x α {\displaystyle \left(\sum
Multi-index_notation
Moment of inertia of diff geometric shapes
additive function and exploit the parallel axis and the perpendicular axis theorems. This article considers mainly symmetric mass distributions, with constant
List_of_moments_of_inertia
Area of discrete mathematics
vertices and edges, and by edge-contraction. The earliest result of the graph minor theory is from Wagner's theorem, stating that a finite graph is planar
Graph_theory
Tree which includes all vertices of a graph
the deletion-contraction recurrence t(G) = t(G − e) + t(G/e), where G − e is the multigraph obtained by deleting e and G/e is the contraction of G by e.
Spanning_tree
Italian theoretical physicist (1909–1992)
contributions to quantum field theory. The Wick rotation, Wick contraction, Wick's theorem, and the Wick product are named after him. Gian Carlo Wick, first
Gian_Carlo_Wick
Tendency of matter to change volume in response to a change in temperature
usually contract with decreasing temperature which is called thermal contraction. The SI unit of thermal expansion is the inverse kelvin (K−1). Temperature
Thermal_expansion
Style of formal logical argumentation
line is an unconditional tautology (or theorem). Gentzen style. Every line is a conditional tautology (or theorem) with zero or more conditions on the left
Sequent_calculus
Pictorial representation of the behavior of subatomic particles
operators to bring them together for a contraction (a propagator) and A represents all possible contractions. The diagrams are drawn according to the
Feynman_diagram
Topics referred to by the same term
dual of a generator of a category. An operator in the dilation theorem for contraction semigroups This disambiguation page lists articles associated with
Cogenerator
Size of largest complete graph made by contracting edges of a given graph
graph obtained from G by edge contractions and vertex and edge deletions. The Hadwiger number is also known as the contraction clique number of G or the homomorphism
Hadwiger_number
Mutual information Kullback–Leibler divergence Le Cam's theorem Large deviations theory Contraction principle (large deviations theory) Varadhan's lemma
List_of_probability_topics
properties. See, for example, the commutant lifting theorem. We can show that every contraction on Hilbert spaces has a unitary dilation. A possible
Dilation_(operator_theory)
theorem Wigner 3-j symbols Wigner's 6-j symbols Wigner's 9-j symbols Wigner–Araki–Yanase theorem Wigner–Yanase–Dyson conjecture Wigner–Eckart theorem
List of things named after Eugene Wigner
List_of_things_named_after_Eugene_Wigner
Theorem
mathematics — specifically, in large deviations theory — the contraction principle is a theorem that states how a large deviation principle on one space "pushes
Contraction principle (large deviations theory)
Contraction_principle_(large_deviations_theory)
Operator generalizing the Laplacian in differential geometry
X\operatorname {vol} _{n}} where the last equality is an application of Stokes' theorem. Dualizing gives for all compactly supported functions f {\displaystyle
Laplace–Beltrami_operator
Operator theorem
lifting theorem, due to Sz.-Nagy and Foias, is a powerful theorem used to prove several interpolation results. The commutant lifting theorem states that
Commutant_lifting_theorem
Mathematics of real numbers and real functions
complete in this sense. One key theorem for complete metric spaces is the contraction mapping theorem. This theorem says that if a transformation T {\displaystyle
Real_analysis
Unproven generalization of the four-color theorem
1\leq t\leq 6} . The conjecture is a generalization of the four color theorem and is considered to be one of the most important and challenging open
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
Kähler manifold relating the Dolbeault operators and their adjoints, contraction and wedge operators of the Kähler form, and the Laplacians of the Kähler
Kähler_identities
English mathematician, mathematical physicist (born 1931)
Prize in Physics with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole
Roger_Penrose
Mathematical study of linear operators
category. The spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions
Operator_theory
Hungarian-American physicist and mathematician (1902–1995)
classification Wigner's disease Wigner's friend Wigner's theorem Wigner–Eckart theorem Wigner–Inonu contraction Wigner–Seitz cell Wigner–Seitz radius Wigner–Weyl
Eugene_Wigner
Experiments probing the accuracy of special relativity's predictions
of motion with respect to the aether (length contraction). That is, the older hypothesis of a contraction of electrostatic fields was extended to intermolecular
Tests_of_special_relativity
Metric geometry
Banach fixed-point theorem states that a contraction mapping on a complete metric space admits a fixed point. The fixed-point theorem is often used to prove
Complete_metric_space
CONTRACTION THEOREM
CONTRACTION THEOREM
Biblical
bitter contrition, without judgment
Girl/Female
Biblical
Bitter contrition.
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Construction; Arrangement; Creative Art; All Creation
Girl/Female
Hindu
Creation, Construction, Arrangement
Girl/Female
Indian
Built; Construction; Creative Art; All Creation
Girl/Female
Tamil
Creation, Construction, Arrangement
Girl/Female
Hindu
Light, Beauty, Prosperity, Rank, Power, Steel construction company
Boy/Male
Biblical Hebrew
Contrition, bitter, bruising'.
Boy/Male
American, Australian, British, English, French
Record Keeper; Chancellor; Secretary; Contraction of Chancellor
Girl/Female
Tamil
Creation, Construction, Arrangement
Girl/Female
Biblical American English Hebrew Latin
Who possesses contrition.
Biblical
bitter contrition
Boy/Male
Biblical
Bitter contrition, without judgment.
Girl/Female
Tamil
Light, Beauty, Prosperity, Rank, Power, Steel construction company
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Creation; Evolution; Construction
Girl/Female
Hindu, Indian, Marathi
Produce; New Construction
Boy/Male
American, Anglo, British, Chinese, Christian, English, French, Latin
Church Official; Chancellor; A Gamble; Good Fortune; Contraction of Chancellor
Biblical
who possesses contrition
Girl/Female
Hindu
Creation, Construction, Arrangement
Boy/Male
American, Australian, Christian, Danish, Dutch, French, German, Swedish, Teutonic
Contraction of Frederick; Peace; Peaceful Ruler
CONTRACTION THEOREM
CONTRACTION THEOREM
Girl/Female
Muslim
A noble hearted, Generous lady, Had this name, She built a religious school (Daughter of al-muzaffar)
Girl/Female
Hindu, Indian
Bird
Boy/Male
Indian, Telugu
Moon
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu, Traditional
Parvati; One who Lives in the Mountain
Boy/Male
Indian
Well-established, Well-found
Girl/Female
English
White wave.
Boy/Male
Sikh
God, Rams Love which is Sita, Protected by God
Girl/Female
English Hebrew
Girl/Female
Hindu, Indian
Beautiful
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Well- Heard
CONTRACTION THEOREM
CONTRACTION THEOREM
CONTRACTION THEOREM
CONTRACTION THEOREM
CONTRACTION THEOREM
n.
The shortening of a word, or of two words, by the omission of a letter or letters, or by reducing two or more vowels or syllables to one; as, ne'er for never; can't for can not; don't for do not; it's for it is.
n.
A contraction of cousin.
n.
A contraction of Sophomore.
a.
Of or pertaining to systole, or contraction; contracting; esp., relating to the systole of the heart; as, systolic murmur.
n.
Peristaltic contraction or action.
a.
Capable of contraction.
n.
A contraction of Photograph.
n.
The process of shortening an operation.
n.
Contradiction.
n.
The act of incurring or becoming subject to, as liabilities, obligation, debts, etc.; the process of becoming subject to; as, the contraction of a disease.
a.
tending to contract; having the power or property of contracting, or of shrinking into shorter or smaller dimensions; as, the contractile tissues.
prep.
A contraction of Against.
n.
The act or process of contracting, shortening, or shrinking; the state of being contracted; as, contraction of the heart, of the pupil of the eye, or of a tendion; the contraction produced by cold.
adv.
a contraction of Never.
n.
Something contracted or abbreviated, as a word or phrase; -- as, plenipo for plenipotentiary; crim. con. for criminal conversation, etc.
a.
Tending to contract; having the property or power or power of contracting.
n.
Constriction or contraction of some natural passage, as in constipation from inflammation.
n.
A contraction for Violoncello.
n.
A marriage contract.