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Find link is a tool written by Edward Betts.Longer titles found: Continuous function (set theory) (view), Continuous functional calculus (view), Nowhere continuous function (view), Cauchy-continuous function (view), Quasi-continuous function (view), Symmetrically continuous function (view), Continuous Function Chart (view), Approximately continuous function (view), Space of continuous functions on a compact space (view)
searching for Continuous function 207 found (800 total)
alternate case: continuous function
Discrete-time Fourier transform
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discrete values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operatesRoot mean square (2,786 words) [view diff] exact match in snippet view article find links to article
{\displaystyle M_{2}} ), a special case of the generalized mean. The RMS of a continuous function is denoted f R M S {\displaystyle f_{\mathrm {RMS} }} and can beInstantaneous phase and frequency (1,511 words) [view diff] exact match in snippet view article find links to article
is called unwrapped phase, which is a continuous function of argument t, assuming sa(t) is a continuous function of t. Unless otherwise indicated, theNyquist frequency (762 words) [view diff] exact match in snippet view article find links to article
Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. For a given sampling rate (samplesIsosurface (753 words) [view diff] exact match in snippet view article find links to article
within a volume of space; in other words, it is a level set of a continuous function whose domain is 3-space. The term isoline is also sometimes usedModulus of continuity (3,217 words) [view diff] exact match in snippet view article find links to article
continuous function is always ensured whenever the domain is either a compact, or a convex subset of a normed space. However, a uniformly continuous functionDisk algebra (245 words) [view diff] exact match in snippet view article find links to article
complex plane C {\displaystyle \mathbb {C} } ) that extend to a continuous function on the closure of D. That is, A ( D ) = H ∞ ( D ) ∩ C ( D ¯ ) , {\displaystyleDisk algebra (245 words) [view diff] exact match in snippet view article find links to article
complex plane C {\displaystyle \mathbb {C} } ) that extend to a continuous function on the closure of D. That is, A ( D ) = H ∞ ( D ) ∩ C ( D ¯ ) , {\displaystylePaul du Bois-Reymond (459 words) [view diff] exact match in snippet view article find links to article
series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficientLipschitz domain (647 words) [view diff] exact match in snippet view article find links to article
that it can be thought of as locally being the graph of a Lipschitz continuous function. The term is named after the German mathematician Rudolf LipschitzUpsampling (1,420 words) [view diff] exact match in snippet view article find links to article
upsampling is performed on a sequence of samples of a signal or other continuous function, it produces an approximation of the sequence that would have beenDownsampling (signal processing) (1,804 words) [view diff] exact match in snippet view article
the process is performed on a sequence of samples of a signal or a continuous function, it produces an approximation of the sequence that would have beenBaire set (1,204 words) [view diff] exact match in snippet view article find links to article
compact Hausdorff spaces. In particular, any compactly supported continuous function on such a space is integrable with respect to any finite Baire measureFuzzy set operations (928 words) [view diff] exact match in snippet view article find links to article
b ∈ [0, 1], if a < b, then c(a) > c(b) Axiom c3. Continuity c is continuous function. Axiom c4. Involutions c is an involution, which means that c(c(a))Ridders' method (637 words) [view diff] exact match in snippet view article find links to article
an exponential function to successively approximate a root of a continuous function f ( x ) {\displaystyle f(x)} . The method is due to C. Ridders. Ridders'Reaction coordinate (579 words) [view diff] exact match in snippet view article find links to article
Many collective variables than span the reaction coordinate with a continuous function ξ: ξ(t) = ξ{CVi(t)} with j ∈ N. An example is the complexation ofWhitney embedding theorem (2,038 words) [view diff] exact match in snippet view article find links to article
to Whitney). The weak Whitney embedding theorem states that any continuous function from an n-dimensional manifold to an m-dimensional manifold may beNyquist–Shannon sampling theorem (6,721 words) [view diff] exact match in snippet view article find links to article
expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result dependsTeiji Takagi (580 words) [view diff] exact match in snippet view article find links to article
Blancmange curve, the graph of a nowhere-differentiable but uniformly continuous function, is also called the Takagi curve after his work on it. He was bornKolmogorov–Arnold representation theorem (3,963 words) [view diff] exact match in snippet view article find links to article
theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n → R {\displaystyle f\colon [0,1]^{n}\to \mathbb {R}Riemann–Lebesgue lemma (961 words) [view diff] exact match in snippet view article find links to article
compactly supported continuous function. For ε > 0 {\displaystyle \varepsilon >0} , pick a compactly supported continuous function g {\displaystyle g}Null set (1,735 words) [view diff] exact match in snippet view article find links to article
nonmeasurable subset. Let f {\displaystyle f} be the Cantor function, a continuous function which is locally constant on K c , {\displaystyle K^{c},} and monotonicallyContraction mapping (1,120 words) [view diff] exact match in snippet view article find links to article
Lipschitz continuous and hence uniformly continuous (for a Lipschitz continuous function, the constant k is no longer necessarily less than 1). A contractionReduced ring (817 words) [view diff] no match in snippet view article find links to article
{p}})}(M\otimes k({\mathfrak {p}}))} is a locally constant (or equivalently continuous) function on Spec R. Then R is reduced if and only if every finitely generatedDigital geometry (980 words) [view diff] exact match in snippet view article find links to article
digitally continuous function (A. Rosenfeld, 1986) and the gradually varied function (L. Chen, 1989) were proposed, independently. A digitally continuous functionUniformly connected space (97 words) [view diff] exact match in snippet view article find links to article
Cantor connected space is a uniform space U such that every uniformly continuous function from U to a discrete uniform space is constant. A uniform space UStarred transform (839 words) [view diff] exact match in snippet view article find links to article
x^{*}(t)} , which is the output of an ideal sampler, whose input is a continuous function, x ( t ) {\displaystyle x(t)} . The starred transform is similarGeometric mean (4,390 words) [view diff] no match in snippet view article find links to article
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using theSub-Stonean space (274 words) [view diff] exact match in snippet view article find links to article
real-valued continuous function f {\displaystyle f} can be written as f = g | f | {\displaystyle f=g|f|} for some real-valued continuous function g {\displaystylePower domains (1,165 words) [view diff] exact match in snippet view article find links to article
nondeterminism. For most of this article we use the terms "domain" and "continuous function" quite loosely, meaning respectively some kind of ordered structureCarleson's theorem (1,792 words) [view diff] exact match in snippet view article find links to article
any continuous function would converge everywhere. This was disproved by Paul du Bois-Reymond, who showed in 1876 that there is a continuous function whoseKatětov–Tong insertion theorem (226 words) [view diff] exact match in snippet view article find links to article
semicontinuous, and g ≤ h {\displaystyle g\leq h} . Then there exists a continuous function f : X → R {\displaystyle f\colon X\to \mathbb {R} } with g ≤ f ≤Global optimization (2,097 words) [view diff] exact match in snippet view article find links to article
f(x):=(-1)\cdot g(x)} . Given a possibly nonlinear and non-convex continuous function f : Ω ⊂ R n → R {\displaystyle f:\Omega \subset \mathbb {R} ^{n}\toEdge-of-the-wedge theorem (1,930 words) [view diff] exact match in snippet view article find links to article
analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct theRiemann–Siegel theta function (1,521 words) [view diff] exact match in snippet view article find links to article
real values of t. Here the argument is chosen in such a way that a continuous function is obtained and θ ( 0 ) = 0 {\displaystyle \theta (0)=0} holds, iGeorg Landsberg (412 words) [view diff] exact match in snippet view article find links to article
fractal that is the graph of a nowhere-differentiable but uniformly continuous function, is named after Teiji Takagi and him. Landsberg was Jewish. He wasVariable structure system (601 words) [view diff] exact match in snippet view article find links to article
{T} }:\mathbb {R} ^{n+1}\mapsto \mathbb {R} ^{n}} is a piecewise continuous function. Due to the piecewise continuity of these systems, they behave likeMetric differential (512 words) [view diff] exact match in snippet view article find links to article
differential is a generalization of a derivative for a Lipschitz continuous function defined on a Euclidean space and taking values in an arbitrary metricBuchstab function (443 words) [view diff] exact match in snippet view article find links to article
The Buchstab function (or Buchstab's function) is the unique continuous function ω : R ≥ 1 → R > 0 {\displaystyle \omega :\mathbb {R} _{\geq 1}\rightarrowFuzzy differential inclusion (348 words) [view diff] exact match in snippet view article find links to article
Suppose f ( t , x ( t ) ) {\displaystyle f(t,x(t))} is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upperNyquist rate (990 words) [view diff] exact match in snippet view article find links to article
frequency band or a frequency division multiplex channel. When a continuous function, x ( t ) , {\displaystyle x(t),} is sampled at a constant rate, fRising sun lemma (573 words) [view diff] exact match in snippet view article find links to article
lemma. The lemma is stated as follows: Suppose g is a real-valued continuous function on the interval [a,b] and S is the set of x in [a,b] such that thereHausdorff space (2,156 words) [view diff] exact match in snippet view article find links to article
Hausdorff spaces. Let f : X → Y {\displaystyle f\colon X\to Y} be a continuous function and suppose Y {\displaystyle Y} is Hausdorff. Then the graph of fKinetic priority queue (622 words) [view diff] exact match in snippet view article find links to article
(key-value pair) when the priority of every element is changing as a continuous function of time. Kinetic priority queues have been used as components ofHausdorff space (2,156 words) [view diff] exact match in snippet view article find links to article
Hausdorff spaces. Let f : X → Y {\displaystyle f\colon X\to Y} be a continuous function and suppose Y {\displaystyle Y} is Hausdorff. Then the graph of fDendroid (topology) (530 words) [view diff] exact match in snippet view article
(1954) proved that dendroids have the fixed-point property: Every continuous function from a dendroid to itself has a fixed point. Cook (1970) proved thatPositive-definite function on a group (1,586 words) [view diff] exact match in snippet view article find links to article
\mu } . A positive-definite function on G {\displaystyle G} is a continuous function F : G → L ( H ) {\displaystyle F:G\to L(H)} that satisfies ∫ s ,Kinetic tournament (517 words) [view diff] exact match in snippet view article find links to article
functions as a priority queue for elements whose priorities change as a continuous function of time. It is implemented analogously to a "tournament" betweenSampling (signal processing) (3,131 words) [view diff] exact match in snippet view article
s(t)} be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every T {\displaystyleInfra-exponential (243 words) [view diff] exact match in snippet view article find links to article
all exponential growth rates, however great the doubling time. A continuous function with infra-exponential growth rate will have a Fourier transformContinuous-time Markov chain (4,240 words) [view diff] no match in snippet view article find links to article
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponentialP-variation (1,507 words) [view diff] exact match in snippet view article find links to article
decreases with p. If f has finite p-variation and g is an α-Hölder continuous function, then g ∘ f {\displaystyle g\circ f} has finite p α {\displaystyleClass kappa function (317 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathcal {K}}} functions belong to this family: Definition: a continuous function α : [ 0 , a ) → [ 0 , ∞ ) {\displaystyle \alpha :[0,a)\rightarrowKinetic heater (489 words) [view diff] exact match in snippet view article find links to article
associated with it in addition to its priority (which changes as a continuous function of time as in all kinetic data structures). The kinetic heater isGelfand–Raikov theorem (340 words) [view diff] exact match in snippet view article find links to article
defines for each pair of vectors h , k ∈ H {\displaystyle h,k\in H} a continuous function on G {\displaystyle G} , the matrix coefficient, by g ↦ ⟨ h , ρ (Poisson kernel (1,481 words) [view diff] exact match in snippet view article find links to article
the surface area of the unit (n − 1)-sphere. Then, if u(x) is a continuous function defined on S, the corresponding Poisson integral is the functionKinetic minimum spanning tree (331 words) [view diff] exact match in snippet view article find links to article
spanning tree (MST) of a graph whose edge weights are changing as a continuous function of time. The most efficient known data structure for the generalKinetic Euclidean minimum spanning tree (234 words) [view diff] exact match in snippet view article find links to article
tree (MST) of a planar graph whose edge weights are changing as a continuous function of time. Abam, Rahmati, and Zarei provide a significant improvementDini criterion (176 words) [view diff] exact match in snippet view article find links to article
continuous function such that g ( t ) / t {\displaystyle g(t)/t} is not locally integrable near 0 {\displaystyle 0} , there is a continuous function fPath (416 words) [view diff] exact match in snippet view article find links to article
problem, sometimes known as the "path problem" Path (topology), a continuous function Path (geometry), a curve Path, a name for the vectors in vector graphicsGershgorin circle theorem (2,973 words) [view diff] exact match in snippet view article find links to article
least d. Since the eigenvalues of B ( t ) {\displaystyle B(t)} are a continuous function of t, for any eigenvalue λ ( t ) {\displaystyle \lambda (t)} of BKinetic heap (1,097 words) [view diff] exact match in snippet view article find links to article
associated with priorities) where the priority is changing as a continuous function of time. As a type of kinetic priority queue, it maintains the maximumFundamental lemma of the calculus of variations (1,649 words) [view diff] exact match in snippet view article find links to article
formulate and prove. More powerful versions are used when needed. If a continuous function f {\displaystyle f} on an open interval ( a , b ) {\displaystylePerron method (658 words) [view diff] exact match in snippet view article find links to article
harmonic function in a domain, with boundary conditions given by a continuous function φ ( x ) {\displaystyle \varphi (x)} . The Perron solution is definedWhittaker–Shannon interpolation formula (785 words) [view diff] exact match in snippet view article find links to article
Cardinal series. Given a sequence of real numbers, x[n]=x(nT), the continuous function x ( t ) = ∑ n = − ∞ ∞ x [ n ] s i n c ( t − n T T ) {\displaystyleClass kappa-ell function (151 words) [view diff] exact match in snippet view article find links to article
{\mathcal {KL}}} functions belong to this family: Definition: A continuous function β : [ 0 , a ) × [ 0 , ∞ ) → [ 0 , ∞ ) {\displaystyle \beta :[0,a)\timesMoore plane (737 words) [view diff] exact match in snippet view article find links to article
coordinates is dense in Γ {\displaystyle \Gamma } ; hence every continuous function f : Γ → R {\displaystyle f:\Gamma \to \mathbb {R} } is determinedHenrik Petrini (135 words) [view diff] exact match in snippet view article find links to article
moved to Stockholm. He is best known for his counterexample of a continuous function for which the Newton potential is not twice differentiable. He wasSpatial verification (642 words) [view diff] exact match in snippet view article find links to article
dependent variable, and a family of functions, try to find the continuous function). Effective when one is able to find safe features without clutterQ-Weibull distribution (859 words) [view diff] exact match in snippet view article find links to article
\Gamma ()} is the Gamma function. The expression for the mean is a continuous function of q over the range of definition for which it is finite. The q-WeibullUniversal Taylor series (568 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \sum _{n=1}^{\infty }a_{n}x^{n}} , such that for every continuous function h {\displaystyle h} on [ − 1 , 1 ] {\displaystyle [-1,1]} , if hHarmonic morphism (883 words) [view diff] exact match in snippet view article find links to article
→ R 0 + {\displaystyle \lambda :M\to \mathbb {R} _{0}^{+}} is a continuous function called the dilation. Harmonic morphisms are therefore solutions toHomotopy colimit and limit (1,841 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\text{Top}}} and a natural transformation corresponds to a continuous function of topological spaces. Note this construction can be generalizedGradually varied surface (467 words) [view diff] exact match in snippet view article find links to article
f(x)=A_{i+1}} , or A i − 1 {\displaystyle A_{i-1}} . The concept of the continuous function in digital space (can be called digitally continuous functions) wasCFC (648 words) [view diff] exact match in snippet view article find links to article
applications Consideration of future consequences, a personality trait Continuous function chart, sort of Function block diagram enabling to program both BooleanHausdorff–Young inequality (2,376 words) [view diff] exact match in snippet view article find links to article
Riemann integration and infinite series as prerequisite. Given a continuous function f : ( 0 , 1 ) → R {\displaystyle f:(0,1)\to \mathbb {R} } , defineCharacteristic function (probability theory) (5,208 words) [view diff] exact match in snippet view article
random variable always exists, since it is an integral of a bounded continuous function over a space whose measure is finite. A characteristic function isDroplet-shaped wave (498 words) [view diff] exact match in snippet view article find links to article
delta and Heaviside step functions while J(τ, z) is an arbitrary continuous function representing the pulse shape. Notably, H (βτ − z) H (z) = 0 for τMaximum modulus principle (1,271 words) [view diff] exact match in snippet view article find links to article
→ C {\displaystyle f\colon {\overline {D}}\to \mathbb {C} } is a continuous function that is holomorphic on D {\displaystyle D} . Then | f ( z ) | {\displaystylePlurisubharmonic function (1,268 words) [view diff] exact match in snippet view article find links to article
complex analytic space X {\displaystyle X} as follows. An upper semi-continuous function f : X → R ∪ { − ∞ } {\displaystyle f\colon X\to {\mathbb {R} }\cupMassera's lemma (708 words) [view diff] exact match in snippet view article find links to article
all t ≥ 0 There exist positive constants k1, k2, such that for any continuous function u satisfying 0 ≤ u(t) ≤ g(t) for all t ≥ 0, ∫ 0 ∞ G ( u ( t ) ) dLimit point compact (985 words) [view diff] exact match in snippet view article find links to article
\}} of X . {\displaystyle X.} By the Tietze extension theorem the continuous function f {\displaystyle f} on A {\displaystyle A} defined by f ( x n ) =Fejér's theorem (2,963 words) [view diff] exact match in snippet view article find links to article
Theorem—Let f : R → C {\displaystyle f:\mathbb {R} \to \mathbb {C} } be a continuous function with period 2 π {\displaystyle 2\pi } , let s n ( f ) {\displaystyleDomain theory (2,689 words) [view diff] exact match in snippet view article find links to article
be monotonic. These properties give rise to the notion of a Scott-continuous function. Since this often is not ambiguous one also may speak of continuousStaircase paradox (559 words) [view diff] exact match in snippet view article find links to article
curves under uniform convergence, the length of a curve is not a continuous function of the curve. For any smooth curve, polygonal chains with segmentDistribution function (measure theory) (1,005 words) [view diff] exact match in snippet view article
{\displaystyle F:\mathbb {R} \to \mathbb {R} } is a nondecreasing right continuous function, then the function μ {\displaystyle \mu } defined on the collectionAlexandru Froda (696 words) [view diff] exact match in snippet view article find links to article
complex coefficients. In 1929 Dimitrie Pompeiu conjectured that any continuous function of two real variables defined on the entire plane is constant ifUnitary representation (1,003 words) [view diff] exact match in snippet view article find links to article
:G\rightarrow \operatorname {U} (H)} such that g → π(g) ξ is a norm continuous function for every ξ ∈ H. Note that if G is a Lie group, the Hilbert spaceModulus of smoothness (665 words) [view diff] exact match in snippet view article find links to article
\mathbb {N} } let W r {\displaystyle W^{r}} denote the space of continuous function on [ − 1 , 1 ] {\displaystyle [-1,1]} that have ( r − 1 ) {\displaystyleSimply connected space (1,330 words) [view diff] exact match in snippet view article find links to article
{\displaystyle Y.} The image of a simply connected set under a continuous function need not be simply connected. Take for example the complex planeWavelet transform modulus maxima method (817 words) [view diff] exact match in snippet view article find links to article
only a limited number of low-order terms are used to approximate a continuous function.) Generally, a continuous wavelet transform decomposes a signal asAmplitude (1,620 words) [view diff] exact match in snippet view article find links to article
where the amplitude is transient and must be represented as either a continuous function or a discrete vector. Percussive amplitude envelopes model many commonSinai–Ruelle–Bowen measure (891 words) [view diff] exact match in snippet view article find links to article
_{U}\varphi \,d\mu } for every x ∈ V {\displaystyle x\in V} and every continuous function φ : U → R {\displaystyle \varphi :U\rightarrow \mathbb {R} } . OneWeyl integration formula (1,148 words) [view diff] exact match in snippet view article find links to article
a maximal torus T. Precisely, it says there exists a real-valued continuous function u on T such that for every class function f on G (function invariantMercer's theorem (1,942 words) [view diff] exact match in snippet view article find links to article
more general formulation. A kernel, in this context, is a symmetric continuous function K : [ a , b ] × [ a , b ] → R {\displaystyle K:[a,b]\times [a,b]\rightarrowLeak noise correlator (451 words) [view diff] exact match in snippet view article find links to article
determine the location of the leak., The cross correlation signal of one continuous function, f, with another, g, is defined as: ( f ⋆ g ) ( t ) = d e f ∫ −Hopf link (892 words) [view diff] exact match in snippet view article find links to article
crossings will have two colors present. The Hopf fibration is a continuous function from the 3-sphere (a three-dimensional surface in four-dimensionalList of probabilistic proofs of non-probabilistic theorems (1,848 words) [view diff] exact match in snippet view article find links to article
Only in 1981 did Kaufman give a deterministic construction. Every continuous function on a compact interval can be uniformly approximated by polynomialsMathematical optimization (6,175 words) [view diff] exact match in snippet view article find links to article
More generally, a lower semi-continuous function on a compact set attains its minimum; an upper semi-continuous function on a compact set attains itsUniform boundedness principle (4,620 words) [view diff] exact match in snippet view article find links to article
sequence of equicontinuous functions on a compact set converges to a continuous function. By uniform boundedness principle, let M = max { sup n ‖ T n ‖ ,List of Fourier-related transforms (1,001 words) [view diff] no match in snippet view article find links to article
Fourier transform (DTFT): Equivalent to the Fourier transform of a "continuous" function that is constructed from the discrete input function by using theStratifold (1,387 words) [view diff] exact match in snippet view article find links to article
example to consider is the open cone over a manifold M. We define a continuous function from S to the reals to be in C if and only if it is smooth on M ×Simplicial approximation theorem (636 words) [view diff] exact match in snippet view article find links to article
{\displaystyle f:K\to L} is called a simplicial approximation of a continuous function F : | K | → | L | {\displaystyle F:|K|\to |L|} if for every pointMontel space (1,330 words) [view diff] exact match in snippet view article find links to article
{\displaystyle X} is a Montel space if and only if every bounded continuous function X → c 0 {\displaystyle X\to c_{0}} sends closed bounded absolutelyNamioka's theorem (432 words) [view diff] exact match in snippet view article find links to article
Mathematics, the theorem establishes conditions under which a separately continuous function must be jointly continuous on a topologically large subset of itsLocally connected space (3,186 words) [view diff] exact match in snippet view article find links to article
the subspace topology) are open. It follows, for instance, that a continuous function from a locally connected space to a totally disconnected space mustTopological geometry (4,297 words) [view diff] exact match in snippet view article find links to article
the pair of points and the intersection point of two lines is a continuous function of these lines. Linear geometries are incidence structures in whichKakutani's theorem (geometry) (133 words) [view diff] exact match in snippet view article
739–741, doi:10.2307/1968964 Yamabe, H.; Yujobô, Z. (1950), "On the continuous function defined on a sphere", Osaka Math. J., 2 (1): 19–22 Floyd, E. E. (1955)Hartogs–Rosenthal theorem (339 words) [view diff] exact match in snippet view article find links to article
rational functions. By the Stone–Weierstrass theorem any complex-valued continuous function on K can be uniformly approximated by a polynomial in z {\displaystyleErgodic flow (5,093 words) [view diff] exact match in snippet view article find links to article
f is a continuous function on G of compact support with ∫ f = 1, then ξ = ∫ f(g) gξ dg. The right hand side equals ξ ∗ f, a continuous function on G. SinceMinimax approximation algorithm (295 words) [view diff] exact match in snippet view article find links to article
b}|f(x)-p(x)|.} The Weierstrass approximation theorem states that every continuous function defined on a closed interval [a,b] can be uniformly approximatedBarycentric subdivision (2,533 words) [view diff] exact match in snippet view article find links to article
contractible. The simplicial approximation theorem guarantees for every continuous function f : V K → V L {\displaystyle f:V_{K}\rightarrow V_{L}} the existenceUniform property (325 words) [view diff] exact match in snippet view article find links to article
connected. A uniform space X is uniformly connected if every uniformly continuous function from X to a discrete uniform space is constant. Uniformly disconnectedCàdlàg (1,306 words) [view diff] exact match in snippet view article find links to article
Right continuous function with left limitsEquation of time (8,896 words) [view diff] exact match in snippet view article find links to article
mathematical discontinuities of its components, EOT is defined as a continuous function by adding (or subtracting) 24 hours in the small time interval betweenFuzzy differential equation (463 words) [view diff] exact match in snippet view article find links to article
real continuous function and f ( t ) : [ t 0 , ∞ ) → R F {\displaystyle f(t)\colon [t_{0},\infty )\rightarrow R_{F}} is a fuzzy continuous function y (Verona Cathedral (774 words) [view diff] exact match in snippet view article find links to article
Cattedrale di Verona) is claimed to be the world's oldest library in continuous function. Such is its importance that it has been dubbed the "Queen of ecclesiasticalFredholm operator (1,476 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \varphi =e_{1}} . More generally, let φ be a complex continuous function on T that does not vanish on T {\displaystyle \mathbf {T} } , andCompetitive equilibrium (3,841 words) [view diff] exact match in snippet view article find links to article
demand function is continuous. Hence, z {\displaystyle z} is also a continuous function of p {\displaystyle p} . C. Define the following function from theDiscrepancy function (243 words) [view diff] exact match in snippet view article find links to article
perfectly reproduce the observed data. The discrepancy function is a continuous function of the elements of S, the sample covariance matrix, and Σ(θ), thePeriodogram (1,251 words) [view diff] exact match in snippet view article find links to article
definition of interest here is that the power spectral density of a continuous function, x ( t ) , {\displaystyle x(t),} is the Fourier transform of itsGlossary of order theory (4,204 words) [view diff] exact match in snippet view article find links to article
is the supremum of a directed set contained in {y in B | y<<x}. Continuous function. See Scott-continuous. Converse. The converse <° of an order < isUndersampling (1,274 words) [view diff] exact match in snippet view article find links to article
exclusive (spectrally), the original transform and the original continuous function, or a frequency-shifted version of it (if desired), can be recoveredStone's representation theorem for Boolean algebras (727 words) [view diff] exact match in snippet view article find links to article
algebra A to a Boolean algebra B corresponds in a natural way to a continuous function from S(B) to S(A). In other words, there is a contravariant functorIntegral equation (5,605 words) [view diff] exact match in snippet view article find links to article
for an unknown function y ( t ) {\displaystyle y(t)} and a given continuous function g ( t ) {\displaystyle g(t)} on the interval I {\displaystyle I}Topological ring (1,100 words) [view diff] exact match in snippet view article find links to article
also a field, and such that inversion of non zero elements is a continuous function. The most common examples are the complex numbers and all its subfieldsGeorge Dantzig (2,362 words) [view diff] exact match in snippet view article find links to article
Corporation. pdf from RAND 1966. On the continuity of the minimum set of a continuous function. With Jon H. Folkman and Norman Shapiro. 1968. Mathematics of theConservation law (2,527 words) [view diff] exact match in snippet view article find links to article
and t is time. If we assume that the motion u of the charge is a continuous function of position and time, then j = ρ u ∂ ρ ∂ t = − ∇ ⋅ ( ρ u ) . {\displaystyleSpecialization (pre)order (1,414 words) [view diff] exact match in snippet view article
interest for T1 topologies, especially for all Hausdorff spaces. Any continuous function f {\displaystyle f} between two topological spaces is monotone withGaussian free field (1,511 words) [view diff] exact match in snippet view article find links to article
\varphi _{k}} are set up that way). So, in this case, it is a random continuous function (not belonging to H 1 [ 0 , 1 ] {\displaystyle H^{1}[0,1]} , however)Blaschke product (597 words) [view diff] exact match in snippet view article find links to article
open unit disc such that f {\displaystyle f} can be extended to a continuous function on the closed unit disc Δ ¯ = { z ∈ C ∣ | z | ≤ 1 } {\displaystyleHilbert's fifth problem (1,077 words) [view diff] exact match in snippet view article find links to article
Let V ⊆ U be open subsets of Euclidean space, such that there is a continuous function f : V × V → U satisfying the group axiom of associativity. Does itHilbert cube (928 words) [view diff] exact match in snippet view article find links to article
can also be proved without the axiom of choice by constructing a continuous function from the usual Cantor set onto the Hilbert cube. In ℓ 2 , {\displaystyleJackson's inequality (608 words) [view diff] exact match in snippet view article find links to article
, if f {\displaystyle f} is 2 π {\displaystyle 2\pi } -periodic continuous function, there exists a trigonometric polynomial T n {\displaystyle T_{n}}Fourier inversion theorem (2,737 words) [view diff] exact match in snippet view article find links to article
this section we assume that f {\displaystyle f} is an integrable continuous function. Use the convention for the Fourier transform that ( F f ) ( ξ )Itô's lemma (5,921 words) [view diff] exact match in snippet view article find links to article
, ∞ ] → R {\displaystyle x:[0,\infty ]\to \mathbb {R} } a right-continuous function with left limits and finite quadratic variation [ x ] {\displaystyleBinary classification (1,428 words) [view diff] exact match in snippet view article find links to article
Binary classification may be a form of dichotomization in which a continuous function is transformed into a binary variable. Tests whose results are ofFréchet mean (753 words) [view diff] exact match in snippet view article find links to article
{\displaystyle d_{m}(x,y)=\left|x^{m}-y^{m}\right|} Given an invertible and continuous function f {\displaystyle f} , the f-mean can be defined as the Fréchet meanCup product (1,333 words) [view diff] exact match in snippet view article find links to article
following sense: if f : X → Y {\displaystyle f\colon X\to Y} is a continuous function, and f ∗ : H ∗ ( Y ) → H ∗ ( X ) {\displaystyle f^{*}\colon H^{*}(Y)\toHadamard three-lines theorem (451 words) [view diff] exact match in snippet view article find links to article
be used to prove the Hadamard three-circle theorem for a bounded continuous function g ( z ) {\displaystyle g(z)} on an annulus { z : r ≤ | z | ≤ R }Fixed-point property (661 words) [view diff] exact match in snippet view article find links to article
A} is a retraction and f : A → A {\displaystyle f:A\to A} is any continuous function, then the composition i ∘ f ∘ r : X → X {\displaystyle i\circ f\circRange imaging (1,379 words) [view diff] exact match in snippet view article find links to article
Under the assumption that the true range image is a more or less continuous function of the image coordinates, the correct depth can be obtained usingNash equilibrium (8,777 words) [view diff] exact match in snippet view article find links to article
{\displaystyle f_{i}} is a continuous function of σ {\displaystyle \sigma } , and hence f {\displaystyle f} is a continuous function. As the cross productBernhard Riemann (2,926 words) [view diff] exact match in snippet view article find links to article
habilitation. Among other things, he showed that every piecewise continuous function is integrable. Similarly, the Stieltjes integral goes back to theContinuous wavelet transform (1,398 words) [view diff] exact match in snippet view article find links to article
{t-b}{a}}\right)\,\mathrm {d} t} where ψ ( t ) {\displaystyle \psi (t)} is a continuous function in both the time domain and the frequency domain called the motherÉtudes (Ligeti) (1,499 words) [view diff] exact match in snippet view article
2018-03-17. Steinitz, p. 299. Steinitz, p. 304. "The title refers to a continuous function in mathematics, known as the Devil's Staircase or Cantor functionPolynomial interpolation (9,027 words) [view diff] exact match in snippet view article find links to article
converge to any continuous function f(x)? The answer is unfortunately negative: Theorem—For any table of nodes there is a continuous function f(x) on an intervalCarl B. Allendoerfer Award (114 words) [view diff] case mismatch in snippet view article find links to article
Emerging Julia Sets Irl Bivens and Ben Klein 2016 The Median Value of a Continuous Function Daniel Heath 2015 Straightedge and Compass Constructions in SphericalThom–Mather stratified space (751 words) [view diff] exact match in snippet view article find links to article
[ 0 , + ∞ ) {\displaystyle \rho _{X}:T_{X}\to [0,+\infty )} is a continuous function. These data need to satisfy the following conditions. Each stratumComplete partial order (1,428 words) [view diff] exact match in snippet view article find links to article
every directed D ⊆ P {\displaystyle D\subseteq P} . Note that every continuous function between dcpos is a monotone function. This notion of continuity isAlexiewicz norm (517 words) [view diff] exact match in snippet view article find links to article
if f ∈ A(R), then f is a tempered distribution and there exists a continuous function F in the above collection such that ⟨ F ′ , φ ⟩ = − ⟨ F , φ ′ ⟩ =Convex preferences (1,195 words) [view diff] exact match in snippet view article find links to article
convexity. Convex function Level set Quasi-convex function Semi-continuous function Shapley–Folkman lemma Hal R. Varian; Intermediate MicroeconomicsHarmonic function (3,454 words) [view diff] exact match in snippet view article find links to article
harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider the sequenceMaximal torus (1,734 words) [view diff] exact match in snippet view article find links to article
permutation group on n {\displaystyle n} elements. Suppose f is a continuous function on G. Then the integral over G of f with respect to the normalizedComplete Heyting algebra (1,274 words) [view diff] exact match in snippet view article find links to article
O(Y) are subframes of P(X) and P(Y). If f {\displaystyle f} is a continuous function, then f − 1 : O ( Y ) → O ( X ) {\displaystyle f^{-1}:O(Y)\to O(X)}Complete Heyting algebra (1,274 words) [view diff] exact match in snippet view article find links to article
O(Y) are subframes of P(X) and P(Y). If f {\displaystyle f} is a continuous function, then f − 1 : O ( Y ) → O ( X ) {\displaystyle f^{-1}:O(Y)\to O(X)}Bar recursion (409 words) [view diff] exact match in snippet view article find links to article
Assuming L is a continuous sequence, there must be such r, because a continuous function can use only finitely much data. fn(p) = Bn(p, (λx:V)fn+1(cat(p,Sphere (5,342 words) [view diff] exact match in snippet view article find links to article
sphere). The sphere is the inverse image of a one-point set under the continuous function ‖x‖, so it is closed; Sn is also bounded, so it is compact by theClarke generalized derivative (392 words) [view diff] exact match in snippet view article find links to article
were introduced by Francis Clarke in 1975. For a locally Lipschitz continuous function f : R n → R , {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbbRing theory (3,093 words) [view diff] exact match in snippet view article find links to article
consisting of those with constant rank n. (The rank of a module M is the continuous function Spec R → Z , p ↦ dim M ⊗ R k ( p ) {\displaystyle \operatornameFourier series (11,149 words) [view diff] exact match in snippet view article find links to article
{\displaystyle s} is absolutely summable. The sum of this series is a continuous function, equal to s {\displaystyle s} , since the Fourier series convergesUtilitarian rule (1,384 words) [view diff] exact match in snippet view article find links to article
{\displaystyle X} is a compact space and u i {\displaystyle u_{i}} is a continuous function.) Then define w i ( x ) := u i ( x ) − m i M i − m i {\displaystyleNilsequence (1,265 words) [view diff] exact match in snippet view article find links to article
defined by an element g {\displaystyle g} of G {\displaystyle G} and continuous function f {\displaystyle f} on G / Γ {\displaystyle G/\Gamma } is to takeKernel smoother (1,484 words) [view diff] exact match in snippet view article find links to article
p → R {\displaystyle Y(X):\mathbb {R} ^{p}\to \mathbb {R} } be a continuous function of X. For each X 0 ∈ R p {\displaystyle X_{0}\in \mathbb {R} ^{p}}Loewner differential equation (2,606 words) [view diff] exact match in snippet view article find links to article
the boundary is independent of s {\displaystyle s} and defines a continuous function λ ( t ) {\displaystyle \lambda (t)} from [ 0 , ∞ ) {\displaystyleFourier transform (21,314 words) [view diff] exact match in snippet view article find links to article
frequency-domain function, and it converges at all frequencies to a continuous function tending to zero at infinity. If f ( x ) {\displaystyle f(x)} decaysGauss's law (3,806 words) [view diff] exact match in snippet view article find links to article
electric field, with ρ ( r ′ ) {\displaystyle \rho (\mathbf {r} ')} a continuous function (density of charge). It is true for all r ≠ r ′ {\displaystyle \mathbfEilenberg's inequality (473 words) [view diff] exact match in snippet view article find links to article
in the proof of the coarea formula. Let ƒ : X → Y be a Lipschitz-continuous function between metric spaces whose Lipschitz constant is denoted by Lip ƒTriangulation (topology) (5,150 words) [view diff] exact match in snippet view article
contractible. The simplicial approximation theorem guarantees for every continuous function f : V K → V L {\displaystyle f:V_{K}\rightarrow V_{L}} the existenceAlice Roth (742 words) [view diff] exact match in snippet view article find links to article
Roth's 1938 thesis was an example of a compact set on which not every continuous function can by approximated uniformly by rational functions. This set, nowEarle–Hamilton fixed-point theorem (799 words) [view diff] exact match in snippet view article find links to article
_{\gamma (0)=x,\gamma (1)=y}\ell (\gamma )}} for x and y in D. It is a continuous function on D x D for the norm topology. If the diameter of D is less thanFeedforward neural network (2,242 words) [view diff] exact match in snippet view article find links to article
) Multiple parallel non-linear units are able to approximate any continuous function from a compact interval of the real numbers into the interval [−1Completeness of the real numbers (1,511 words) [view diff] exact match in snippet view article find links to article
completeness given above. The intermediate value theorem states that every continuous function that attains both negative and positive values has a root. This isMinimax theorem (1,109 words) [view diff] exact match in snippet view article find links to article
× Y → R {\displaystyle f:X\times Y\rightarrow \mathbb {R} } is a continuous function that is concave-convex, i.e. f ( ⋅ , y ) : X → R {\displaystyle f(\cdotPlacement (electronic design automation) (1,994 words) [view diff] exact match in snippet view article
Analytical methods for global placement model interconnect length by a continuous function and minimize this function directly subject to component densityMultilinear form (4,605 words) [view diff] exact match in snippet view article find links to article
U ) {\displaystyle \omega \in \Omega ^{k}(U)} . By convention, a continuous function on U {\displaystyle U} is a differential 0-form: f ∈ C 0 ( U ) =Branch point (2,729 words) [view diff] exact match in snippet view article find links to article
will yield another possible angle. A branch of the logarithm is a continuous function L(z) giving a logarithm of z for all z in a connected open set inMumford–Shah functional (848 words) [view diff] exact match in snippet view article find links to article
energy functionals E[ J,z,ε ] where the boundary B is replaced by continuous function z whose magnitude indicates the presence of a boundary. Their analysisPendulum wave (266 words) [view diff] exact match in snippet view article find links to article
2001, two University of Minnesota Morris researchers have derived a continuous function explaining the patterns in the pendulums using an extension to the0 (8,231 words) [view diff] exact match in snippet view article find links to article
combination meant a zero angle. Minutes of immersion was also a continuous function 1/12 31′20″ √d(24−d) (a triangular pulse with convex sides), whereHomotopy theory (3,815 words) [view diff] exact match in snippet view article find links to article
Hausdorff or a CW complex. In the same vein as above, a "map" is a continuous function, possibly with some extra constraints. Often, one works with a pointedBochner's theorem (1,405 words) [view diff] exact match in snippet view article find links to article
f(k)=\int _{\mathbb {T} }e^{-2\pi ikx}\,d\mu (x).} Similarly, a continuous function f {\displaystyle f} on R {\displaystyle \mathbb {R} } with f ( 0Nowhere dense set (2,405 words) [view diff] exact match in snippet view article find links to article
nowhere dense sets with positive measure and a strictly monotonic continuous function with a dense set of points with zero derivative". Folland, G. B.Norton's dome (909 words) [view diff] exact match in snippet view article find links to article
(the force that appears in Newton's second law is not a Lipschitz continuous function of the particle's trajectory -- this allows evasion of the localQ-derivative (1,782 words) [view diff] exact match in snippet view article find links to article
is a given interval, and β ( t ) {\displaystyle \beta (t)} is any continuous function that strictly monotonically increases (i.e. t > s → β ( t ) > β (Time series (5,025 words) [view diff] exact match in snippet view article find links to article
entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set. ExtrapolationExpected value (7,614 words) [view diff] exact match in snippet view article find links to article
the general Lebesgue theory, due to the fact that every piecewise-continuous function is measurable. The expected value of any real-valued random variableDiscrete Laplace operator (5,716 words) [view diff] exact match in snippet view article find links to article
comprising images, can be viewed as a discrete representation of a continuous function f ( r ¯ ) {\displaystyle f({\bar {r}})} , where the coordinate vectorRademacher's theorem (1,317 words) [view diff] exact match in snippet view article find links to article
found by Charles Morrey. In the following, let u denote a Lipschitz-continuous function on Rn. The first step of the proof is to show that, for any fixedRec. 2020 (3,360 words) [view diff] exact match in snippet view article find links to article
09929682680944 and β ≈ 0.018053968510807 (values chosen to achieve a continuous function with a continuous first derivative) The standard says that for practicalLeast-squares function approximation (945 words) [view diff] exact match in snippet view article find links to article
another function by minimizing the area between two functions, a continuous function f {\displaystyle f} on [ a , b ] {\displaystyle [a,b]} and a functionCoulomb's law (6,652 words) [view diff] exact match in snippet view article find links to article
electric field, with ρ ( r ′ ) {\displaystyle \rho (\mathbf {r} ')} a continuous function (density of charge). It is true for all r ≠ r ′ {\displaystyle \mathbfTed Kaczynski (12,426 words) [view diff] case mismatch in snippet view article find links to article
2017. —— (November 1969). "The Set of Curvilinear Convergence of a Continuous Function Defined in the Interior of a Cube" (PDF). Proceedings of the AmericanDiscrete Fourier transform (12,333 words) [view diff] exact match in snippet view article find links to article
DTFT § Periodic data), and therefore so is its product with the continuous function DTFT { x } . {\displaystyle \scriptstyle {\text{DTFT}}\displaystyleCritical point (mathematics) (2,989 words) [view diff] exact match in snippet view article
in others. By Fermat's theorem, all local maxima and minima of a continuous function occur at critical points. Therefore, to find the local maxima andExtreme learning machine (3,643 words) [view diff] exact match in snippet view article find links to article
universal approximation capability. In theory, any nonconstant piecewise continuous function can be used as activation function in ELM hidden nodes, such an activationLambda-connectedness (1,101 words) [view diff] exact match in snippet view article find links to article
between them. In topology, two points are connected if there is a continuous function that could move from one point to another continuously. In managementHenry Helson (676 words) [view diff] exact match in snippet view article find links to article
Helson set is defined to be a compact set P in G such that every continuous function on P can be extended to a function in the Fourier algebra A(G) inEkeland's variational principle (2,299 words) [view diff] exact match in snippet view article find links to article
of the lower semicontinuous function f {\displaystyle f} and the continuous function ( x , y ) ↦ ε d ( x , y ) . {\displaystyle (x,y)\mapsto \varepsilonGaussian function (5,023 words) [view diff] exact match in snippet view article find links to article
function does not have the discrete analogs of the properties of the continuous function, and can lead to undesired effects, as described in the article scaleDenotational semantics (3,784 words) [view diff] exact match in snippet view article find links to article
Γ⊢P:σ. Then the meaning of this program-in-typing-context must be a continuous function 〚Γ⊢P:σ〛:〚Γ〛→〚σ〛. For instance, 〚⊢7:nat〛:1→ N {\displaystyle \mathbbCauchy's integral formula (4,364 words) [view diff] exact match in snippet view article find links to article
enclosed by the path and continuous on its closure. Note that not every continuous function on the boundary can be used to produce a function inside the boundaryDe Rham curve (2,813 words) [view diff] exact match in snippet view article find links to article
points. The resulting de Rham curve p x {\displaystyle p_{x}} is a continuous function of x, at all x. In general, the de Rham curves are not differentiableBusemann function (12,928 words) [view diff] exact match in snippet view article find links to article
It is non-zero on X and vanishes only at ∞. Hence it extends to a continuous function on X with zero set X \ X. It follows that X \ X is closed in X, asKhabibullin's conjecture on integral inequalities (773 words) [view diff] exact match in snippet view article find links to article
(version 3). Let q {\displaystyle \displaystyle q} be a non-negative continuous function on the half-line [ 0 , + ∞ ) {\displaystyle [0,+\infty )} and α >Spline interpolation (2,446 words) [view diff] exact match in snippet view article find links to article
take the form of a straight line with q′′ = 0. As q′′ should be a continuous function of x, "natural splines" in addition to the n − 1 linear equationsVariance (10,215 words) [view diff] exact match in snippet view article find links to article
\left(\left(X-m\right)^{2}\right)=\mathrm {E} (X)} . Conversely, if a continuous function φ {\displaystyle \varphi } satisfies a r g m i n m E ( φ ( X − m