language:
Find link is a tool written by Edward Betts.Longer titles found: Constant function market maker (view), Locally constant function (view)
searching for constant function 182 found (240 total)
alternate case: Constant function
Up to
(814 words)
[view diff]
exact match in snippet
view article
find links to article
relation R between functions, defined by fRg if the difference f−g is a constant function, and means that the solution and the function sin(x) are equal upDifferentiation rules (2,763 words) [view diff] exact match in snippet view article find links to article
{\displaystyle c\in \mathbb {R} } , if f ( x ) {\displaystyle f(x)} is the constant function given by f ( x ) = c {\displaystyle f(x)=c} , then d f d x = 0 {\displaystyleConstant (computer programming) (2,699 words) [view diff] no match in snippet view article
In computer programming, a constant is a value that is not altered by the program during normal execution. When associated with an identifier, a constantPtychography (5,000 words) [view diff] exact match in snippet view article find links to article
one constant function (e.g. a field of illumination or an aperture stop) moving laterally by a known amount with respect to another constant function (theLinear-fractional programming (1,292 words) [view diff] exact match in snippet view article find links to article
case of a linear-fractional program in which the denominator is the constant function 1. Formally, a linear-fractional program is defined as the problemMarkov's principle (1,333 words) [view diff] exact match in snippet view article find links to article
arithmetic), then Markov's principle is justified: a realizer is the constant function that takes a realization that P {\displaystyle P} is not everywhereStone–Weierstrass theorem (3,021 words) [view diff] exact match in snippet view article find links to article
space and A is a subalgebra of C(X, R) which contains a non-zero constant function. Then A is dense in C(X, R) if and only if it separates points. ThisList of periodic functions (224 words) [view diff] exact match in snippet view article find links to article
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacksDavid Kaplan (philosopher) (1,933 words) [view diff] exact match in snippet view article
expression is context-sensitive if and only if its character defines a non-constant function (i.e., if, and only if it yields different content-values given differentDirichlet convolution (2,527 words) [view diff] exact match in snippet view article find links to article
(n)=\lfloor {\tfrac {1}{n}}\rfloor } ). 1 {\displaystyle 1} is the constant function with value 1: 1 ( n ) = 1 {\displaystyle 1(n)=1} for all n {\displaystyleFraction of variance unexplained (605 words) [view diff] exact match in snippet view article find links to article
Y, the most naive regression function that we can think of is the constant function predicting the mean of Y, i.e., f ( x i ) = y ¯ {\displaystyle f(x_{i})={\barStalk (sheaf) (1,582 words) [view diff] exact match in snippet view article
is identically one, so at the origin it has the same germ as the constant function with value 1. Suppose that we want to reconstruct f {\displaystylePrimitive recursive set function (564 words) [view diff] exact match in snippet view article find links to article
because the constant function with value ω (or any other infinite set) is not primitive recursive, so one might want to add this constant function to the initialEndomorphism (583 words) [view diff] exact match in snippet view article find links to article
and is bijective and invertible. If S has more than one element, a constant function on S has an image that is a proper subset of its codomain, and thusIndex group (376 words) [view diff] exact match in snippet view article find links to article
G0 consists of elements homotopic, in G, to the identity in G, the constant function 1. One can choose the functions fn(z) = zn as representatives in GPerturbation problem beyond all orders (280 words) [view diff] exact match in snippet view article find links to article
expansion vanish and the difference between the function and the constant function 0 cannot be detected by a power series. A simple example is understoodHaar wavelet (4,518 words) [view diff] exact match in snippet view article find links to article
be approximated uniformly on [0, 1] by linear combinations of the constant function 1, ψ ( t ) , ψ ( 2 t ) , ψ ( 4 t ) , … , ψ ( 2 n t ) , … {\displaystyleMaximum principle (3,699 words) [view diff] exact match in snippet view article find links to article
boundary of M. The strong maximum principle says that, unless u is a constant function, the maximum cannot also be achieved anywhere on M itself. Such statementsSalting in (470 words) [view diff] no match in snippet view article find links to article
solubility of the protein, B is a constant (function of protein, pH and temperature), K is the salting out constant (function of pH, mixing and salt), andHadjicostas's formula (464 words) [view diff] exact match in snippet view article find links to article
T. (2008). "Vacca-type series for values of the generalized-Euler-constant function and its derivative". arXiv:0808.0410. Sondow, J (2005). "Double integralsPicard theorem (995 words) [view diff] exact match in snippet view article find links to article
Liouville's theorem which states that the image of an entire non-constant function must be unbounded. Many different proofs of Picard's theorem wereAntiderivative (complex analysis) (1,154 words) [view diff] exact match in snippet view article
real-valued function. The derivative of a constant function is the zero function. Therefore, any constant function is an antiderivative of the zero functionLambert series (3,613 words) [view diff] exact match in snippet view article find links to article
new series are given by the Dirichlet convolution of an with the constant function 1(n) = 1: bm=(a∗1)(m)=∑n∣man.{\displaystyle b_{m}=(a*1)(m)=\sum _{n\midPrimitive recursive functional (521 words) [view diff] exact match in snippet view article find links to article
of type 0 is simply a natural number; it can also be viewed as a constant function that takes no input and returns an output in the set N of naturalValuation (logic) (355 words) [view diff] no match in snippet view article
determines the range of the quantifiers, along with interpretations of the constant, function, and relation symbols in the language. Corresponding to each structureMeasurable function (1,329 words) [view diff] exact match in snippet view article find links to article
non-measurable A . {\displaystyle A.} As another example, any non-constant function f : X → R {\displaystyle f:X\to \mathbb {R} } is non-measurable withIterated integral (743 words) [view diff] no match in snippet view article find links to article
integration with respect to x, we would rigorously need to introduce a "constant" function of y. That is, If we were to differentiate this function with respectMeromorphic function (1,114 words) [view diff] exact match in snippet view article find links to article
holomorphic function that maps to the Riemann sphere and which is not the constant function equal to ∞. The poles correspond to those complex numbers which areConvergence in measure (1,023 words) [view diff] exact match in snippet view article find links to article
R {\displaystyle X=\mathbb {R} } μ be Lebesgue measure, and f the constant function with value zero. The sequence f n = χ [ n , ∞ ) {\displaystyle f_{n}=\chiDependent type (2,442 words) [view diff] exact match in snippet view article find links to article
{(x:A)}B(x)} . If B : A → U {\displaystyle B:A\to {\mathcal {U}}} is a constant function, the corresponding dependent product type is equivalent to an ordinaryPeriodic sequence (911 words) [view diff] exact match in snippet view article find links to article
sequence is p-periodic is called its least period or exact period. Every constant function is 1-periodic. The sequence 1 , 2 , 1 , 2 , 1 , 2 … {\displaystyleDifferential coefficient (149 words) [view diff] exact match in snippet view article find links to article
usually a constant quantity, but the differential coefficient of f is a constant function only if f is a linear function. When f is not linear, its differentialSign function (1,738 words) [view diff] exact match in snippet view article find links to article
function Sigmoid function (Hard sigmoid) Step function (Piecewise constant function) Three-way comparison Zero crossing Polar decomposition "Signum functionMan or boy test (713 words) [view diff] no match in snippet view article find links to article
beforehand (in this program it is only B), this can be worked around. Constant/function dualism: The x1 through x5 parameters of A may be numeric constantsAsymptotic equipartition property (3,946 words) [view diff] exact match in snippet view article find links to article
{\displaystyle x\mapsto {\frac {1}{n}}I_{P^{(n)}}(x)} converges in L1 to the constant function x ↦ h T ( P ) {\textstyle x\mapsto h_{T}(P)} . In other words, E xVolume (2,951 words) [view diff] exact match in snippet view article find links to article
three-dimensional space is given by the triple or volume integral of the constant function f ( x , y , z ) = 1 {\displaystyle f(x,y,z)=1} over the region. ItPost's lattice (1,887 words) [view diff] exact match in snippet view article find links to article
allow to generate a nullary function from the corresponding unary constant function, this is the technical reason why nullary functions are excluded fromBarsotti–Tate group (516 words) [view diff] exact match in snippet view article find links to article
locally free scheme. The group G(1) has rank ph for some locally constant function h on S, called the rank or height of the group G. The subgroup G(n)Piecewise linear function (1,171 words) [view diff] exact match in snippet view article find links to article
for the second segment method of least squares is used. Piecewise constant function Linear interpolation Spline interpolation Tropical geometry PolygonalComplex analysis (2,517 words) [view diff] exact match in snippet view article find links to article
entire function f {\displaystyle f} , then f {\displaystyle f} is a constant function. Moreover, a holomorphic function on a connected open set is determinedMultivalued function (1,299 words) [view diff] exact match in snippet view article find links to article
constant of integration follows from the fact that the derivative of a constant function is 0. Inverse hyperbolic functions over the complex domain are multiple-valuedDominated convergence theorem (1,947 words) [view diff] exact match in snippet view article find links to article
sequence is dominated by g. Furthermore, g is integrable since it is a constant function on a set of finite measure. Therefore, the result follows from theZero-order hold (972 words) [view diff] exact match in snippet view article find links to article
instead output a sequence of rectangular pulses, xZOH(t) (a piecewise constant function), means that there is an inherent effect of the ZOH on the effectiveLambda calculus (11,500 words) [view diff] exact match in snippet view article find links to article
x} . Further, λ x . y {\displaystyle \lambda x.y} represents the constant function x ↦ y {\displaystyle x\mapsto y} , the function that always returnsGlossary of game theory (1,963 words) [view diff] exact match in snippet view article find links to article
there is some tuple of complement strategies s.t. π (σ_i) is not a constant function. Antonym: Dummy. Shannon number A conservative lower bound of theLinear combination (2,666 words) [view diff] exact match in snippet view article find links to article
{\displaystyle 2\sin t=(-i)e^{it}+(i)e^{-it}.} On the other hand, the constant function 3 is not a linear combination of f and g. To see this, suppose thatCompact convergence (466 words) [view diff] exact match in snippet view article find links to article
f_{n}(x):=x^{n}} , then f n {\displaystyle f_{n}} converges compactly to the constant function with value 0, but not uniformly. If X = ( 0 , 1 ] {\displaystyle X=(0Biryukov equation (802 words) [view diff] exact match in snippet view article find links to article
{dy}{dt}}+y=0,\qquad \qquad (1)} where ƒ(y) is a piecewise constant function which is positive, except for small y as f ( y ) = { − F , | y | ≤Completely multiplicative function (870 words) [view diff] exact match in snippet view article find links to article
{\displaystyle g=h=1} , where 1 ( n ) = 1 {\displaystyle 1(n)=1} is the constant function. Here τ {\displaystyle \tau } is the divisor function. f ⋅ ( g ∗ hTheta divisor (492 words) [view diff] exact match in snippet view article find links to article
in the sense that they do not dominate the polar divisor of a non constant function. Riemann further proved the Riemann singularity theorem, identifyingDelta-v (2,148 words) [view diff] exact match in snippet view article find links to article
{\text{m/s}}=460\,{\text{m/s}}.} If v exh {\displaystyle v_{\text{exh}}} is a non-constant function of the amount of fuel left v exh = v exh ( m ) {\displaystyleTangent space (3,167 words) [view diff] exact match in snippet view article find links to article
is modeled on the product rule of calculus. (For every identically constant function f = const , {\displaystyle f={\text{const}},} it follows that D (Area of a circle (5,877 words) [view diff] exact match in snippet view article find links to article
coordinates. Namely, the area is given by a double integral of the constant function 1 over the disk itself. If D denotes the disk, then the double integralUniform absolute-convergence (441 words) [view diff] exact match in snippet view article find links to article
excluding these terms results in a series with total sum less than the constant function ε, and this property does not refer to the ordering. Modes of convergenceEuler's formula (3,834 words) [view diff] exact match in snippet view article find links to article
quotient of the trigonometric and exponential expressions is the constant function one, so they must be equal (the exponential function is never zeroIgusa zeta function (558 words) [view diff] exact match in snippet view article find links to article
:K^{n}\to \mathbb {C} } be a Schwartz–Bruhat function, i.e. a locally constant function with compact support and let χ {\displaystyle \chi } be a characterNumerical integration (3,246 words) [view diff] exact match in snippet view article find links to article
method approximates the function by a step function (a piecewise constant function, or a segmented polynomial of degree zero) that passes through theBoolean algebra (9,405 words) [view diff] exact match in snippet view article find links to article
argument, x, which returns the same value independently of x, called a constant function. As far as their outputs are concerned, constants and constant functionsHermite class (1,093 words) [view diff] exact match in snippet view article find links to article
root in the upper half-plane, that is, of Hermite class. Since a non-constant function of Hermite class is the limit of a sequence of such polynomials, itsHardy field (924 words) [view diff] exact match in snippet view article find links to article
constant functions, that is by considering the number α in F as the constant function fα that maps every x in R to α. This is a field since F is, and sinceLanczos resampling (1,469 words) [view diff] exact match in snippet view article find links to article
interpolation of a discrete signal with constant samples does not yield a constant function. This defect is most evident when a = 1. Also, for a = 1 the interpolatedBernoulli differential equation (993 words) [view diff] exact match in snippet view article find links to article
{2y}{x}}=-x^{2}y^{2}} (in this case, more specifically a Riccati equation). The constant function y = 0 {\displaystyle y=0} is a solution. Division by y 2 {\displaystyleConditional probability distribution (2,144 words) [view diff] exact match in snippet view article find links to article
{G}}=\{\emptyset ,\Omega \}} , the conditional probability is the constant function P ( A ∣ { ∅ , Ω } ) = P ( A ) . {\displaystyle \operatorname {P}Alexiewicz norm (517 words) [view diff] exact match in snippet view article find links to article
equivalence relation of equality almost everywhere. (Note that the only constant function f: R → R that is integrable is the one with constant value zero.)Principle of indifference (2,374 words) [view diff] exact match in snippet view article find links to article
of the uniform prior for two reasons. The first reason is that the constant function is not normalizable, and thus is not a proper probability distributionAlexiewicz norm (517 words) [view diff] exact match in snippet view article find links to article
equivalence relation of equality almost everywhere. (Note that the only constant function f: R → R that is integrable is the one with constant value zero.)Principle of indifference (2,374 words) [view diff] exact match in snippet view article find links to article
of the uniform prior for two reasons. The first reason is that the constant function is not normalizable, and thus is not a proper probability distributionTerm (logic) (2,807 words) [view diff] exact match in snippet view article
abstraction λx.x denotes the identity function, while λx.y denotes the constant function always returning y. The lambda term λx.(x x) takes a function x andProduct rule (4,117 words) [view diff] exact match in snippet view article find links to article
nxn − 1 = 0. The rule holds in that case because the derivative of a constant function is 0. If the rule holds for any particular exponent n, then for theTrace (linear algebra) (5,364 words) [view diff] exact match in snippet view article
linear functions (given by the rows of A). Its divergence div F is a constant function, whose value is equal to tr(A). By the divergence theorem, one canChain rule (7,051 words) [view diff] exact match in snippet view article find links to article
equal, their derivatives must be equal. The derivative of x is the constant function with value 1, and the derivative of f ( g ( x ) ) {\displaystyle f(g(x))}Arithmetic function (7,508 words) [view diff] exact match in snippet view article find links to article
function of a(n). The simplest such series, corresponding to the constant function a(n) = 1 for all n, is ζ(s) the Riemann zeta function. The generatingIsogeometric analysis (2,344 words) [view diff] exact match in snippet view article find links to article
T-splines. B-splines can be derived recursively from a piecewise constant function with p = 0 {\displaystyle p=0} : N i , 0 ( ξ ) = I [ ξ i , ξ i + 1Satisfaction equilibrium (3,856 words) [view diff] exact match in snippet view article find links to article
k\in {\mathcal {K}}} the function c k {\displaystyle c_{k}} is a constant function, the set of ESE and the set of SE are identical. This highlights thePicard–Lindelöf theorem (2,932 words) [view diff] exact match in snippet view article find links to article
the space of continuous (and bounded) functions "centered" at the constant function y 0 {\displaystyle y_{0}} . Hence we need to show that ‖ φ − y 0 ‖Logistic function (6,102 words) [view diff] exact match in snippet view article find links to article
{\displaystyle T} ) or (in case of continuous infusion therapy) as a constant function, and one has that 1 T ∫ 0 T c ( t ) d t > r → lim t → + ∞ x ( t )Softmax function (4,929 words) [view diff] exact match in snippet view article find links to article
0 = 1 {\displaystyle b=e^{\beta }=e^{0}=1} , and this becomes the constant function ( 1 / n , … , 1 / n ) {\displaystyle (1/n,\dots ,1/n)} , correspondingIntegral (9,153 words) [view diff] exact match in snippet view article find links to article
generalization of the above inequalities, as M(b − a) is the integral of the constant function with value M over [a, b]. In addition, if the inequality between functionsNon-malleable code (2,173 words) [view diff] no match in snippet view article find links to article
which, for every constant c ∗ {\displaystyle c^{*}} , includes a "constant" function f c ∗ {\displaystyle f_{c^{*}}} that maps all inputs to c ∗ {\displaystylePiecewise-constant valuation (446 words) [view diff] exact match in snippet view article find links to article
piecewise-constant, if the corresponding value-density function v is a piecewise-constant function. In other words: there is a partition of the resource C into finitelyProjective module (3,076 words) [view diff] exact match in snippet view article find links to article
{p}}} -module P p {\displaystyle P_{\mathfrak {p}}} . It is a locally constant function on X. In particular, if X is connected (that is if R has no otherGödel metric (3,800 words) [view diff] exact match in snippet view article find links to article
this way evidently would have this coefficient be some nonzero but constant function of the radial coordinate. Specifically, with a bit of foresight, letIntermediate value theorem (4,317 words) [view diff] exact match in snippet view article find links to article
be shown by setting φ {\displaystyle \varphi } to the appropriate constant function. Augustin-Louis Cauchy provided the modern formulation and a proofVolume element (2,003 words) [view diff] exact match in snippet view article find links to article
volume element is a volume form equal to the Hodge dual of the unit constant function, f ( x ) = 1 {\displaystyle f(x)=1} : ω = ⋆ 1. {\displaystyle \omegaLagrange polynomial (3,990 words) [view diff] exact match in snippet view article find links to article
( x ) = 1 {\textstyle \sum _{j=0}^{k}\ell _{j}(x)=1} because the constant function g ( x ) = 1 {\textstyle g(x)=1} is the unique polynomial of degreeMultiplicative function (2,979 words) [view diff] exact match in snippet view article find links to article
functions are defined to make formulas easier to write: 1(n): the constant function, defined by 1(n) = 1 (completely multiplicative) Id(n): identity functionGeneral recursive function (2,748 words) [view diff] exact match in snippet view article find links to article
following the string of parameters x1, ..., xn is abbreviated as x: Constant function: Kleene uses " Cn q(x) = q " and Boolos-Burgess-Jeffrey (2002) (B-B-J)Laplace–Beltrami operator (3,336 words) [view diff] exact match in snippet view article find links to article
the eigenspaces are all finite-dimensional. Notice by taking the constant function as an eigenfunction, we get λ = 0 {\displaystyle \lambda =0} is anAxiom schema of replacement (3,440 words) [view diff] exact match in snippet view article find links to article
F_{a}(x)=x} wherever θ ( x ) {\displaystyle \theta (x)} is true and as the constant function F a ( x ) = a {\displaystyle F_{a}(x)=a} wherever θ ( x ) {\displaystylePoisson bracket (3,771 words) [view diff] exact match in snippet view article find links to article
Lie bracket of vector fields, but this is true only up to a locally constant function. However, to prove the Jacobi identity for the Poisson bracket, itMercer's theorem (1,783 words) [view diff] exact match in snippet view article find links to article
_{i=1}^{N}\sum _{j=1}^{N}\,g_{i}\,K_{ij}\,g_{j}\geq 0} . A positive constant function K ( x , y ) = c {\displaystyle K(x,y)=c\,} satisfies Mercer's conditionTrigonometric functions (8,994 words) [view diff] exact match in snippet view article find links to article
Therefore, f 1 ( x ) / f 2 ( x ) {\displaystyle f_{1}(x)/f_{2}(x)} is a constant function, which equals 1, as f 1 ( 0 ) = f 2 ( 0 ) = 1. {\displaystyle f_{1}(0)=f_{2}(0)=1Colombeau algebra (869 words) [view diff] exact match in snippet view article find links to article
embedded into A ( R ) {\displaystyle A(\mathbb {R} )} such that the constant function 1 {\displaystyle 1} becomes the unity in A ( R ) {\displaystyle A(\mathbbHaar measure (5,360 words) [view diff] exact match in snippet view article find links to article
{\textstyle \sum a_{i}=1} ) of its left translates that differs from a constant function by at most some small number ϵ {\displaystyle \epsilon } . Then onePositive and negative parts (516 words) [view diff] exact match in snippet view article find links to article
clear that f is not measurable, but its absolute value is, being a constant function. The positive part and negative part of a function are used to defineProlog (7,988 words) [view diff] no match in snippet view article find links to article
atomic formula; an atom of Prolog (depending on the context) is a constant, function symbol or predicate symbol of logic. Clocksin, William F.; MellishHardy–Littlewood Tauberian theorem (1,407 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \rho =1} and F ( t ) {\displaystyle F(t)} to be a piecewise constant function with value ∑ k = 0 n a k {\displaystyle \textstyle {\sum _{k=0}^{n}a_{k}}}Examples of vector spaces (2,119 words) [view diff] exact match in snippet view article find links to article
the right hand side are those in V. The zero vector is given by the constant function sending everything to the zero vector in V. The space of all functionsLinear programming (6,567 words) [view diff] exact match in snippet view article find links to article
problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere). For this feasibility problem withHarish-Chandra's c-function (1,225 words) [view diff] exact match in snippet view article find links to article
\displaystyle A(s,\lambda )\xi _{0}=c_{s}(\lambda )\xi _{0},} where ξ0 is the constant function 1 in L2(K/M). The cocycle property of the intertwining operators impliesGauge theory (6,757 words) [view diff] exact match in snippet view article find links to article
truly local quantity. A gauge transformation whose parameter is not a constant function is referred to as a local symmetry; its effect on expressions thatIntroduction to the mathematics of general relativity (3,173 words) [view diff] exact match in snippet view article find links to article
derivative of v(x) along γ is 0. This is similar to the fact that a constant function is one whose derivative is constantly 0. The equation for the covariantKőnig's lemma (2,298 words) [view diff] exact match in snippet view article find links to article
is 0 or 1, which is to say the tree is computably bounded via the constant function 2. The full form of Kőnig's lemma is not provable in WKL0, but isPower law (7,906 words) [view diff] exact match in snippet view article find links to article
lower tail. For instance, if L ( x ) {\displaystyle L(x)} is the constant function, then we have a power law that holds for all values of x {\displaystyleLists of integrals (5,617 words) [view diff] exact match in snippet view article find links to article
larger intervals, the constant C must be replaced by a piecewise constant function): ∫ | ( a x + b ) n | d x = sgn ( a x + b ) ( a x + b ) n + 1 aSimplex algorithm (6,145 words) [view diff] exact match in snippet view article find links to article
program is a fractional–linear program in which the denominator is the constant function having the value one everywhere. A linear–fractional program can beQuantum harmonic oscillator (6,839 words) [view diff] exact match in snippet view article find links to article
by z = x + i p {\displaystyle z=x+ip} and the ground state is the constant function 1, the normalized harmonic oscillator states in this representationSKI combinator calculus (2,338 words) [view diff] exact match in snippet view article find links to article
argument: Ix = x K, when applied to any argument x, yields a one-argument constant function Kx, which, when applied to any argument y, returns x: Kxy = x S isWave packet (5,351 words) [view diff] exact match in snippet view article find links to article
state of zero energy, which is a wave with infinite wavelength, a constant function of space. For any energy eigenstate η(x), the inner product, ⟨ η |Group scheme (2,860 words) [view diff] exact match in snippet view article find links to article
is a locally free OS-module of finite rank. The rank is a locally constant function on S, and is called the order of G. The order of a constant groupMonstrous moonshine (4,482 words) [view diff] exact match in snippet view article find links to article
representation of the centralizer of g in M. Each f(g, h, τ) is either a constant function, or a Hauptmodul. Each f(g, h, τ) is invariant under simultaneousPrimitive recursive function (6,723 words) [view diff] exact match in snippet view article find links to article
functions Ck n: For each natural number n and every k, the k-ary constant function, defined by C n k ( x 1 , … , x k ) = d e f n {\displaystyle C_{n}^{k}(x_{1}Fourier series (10,850 words) [view diff] exact match in snippet view article find links to article
dx=0;} furthermore, the sines and cosines are orthogonal to the constant function 1 {\displaystyle 1} . An orthonormal basis for L 2 ( [ − π , π ] )Klein–Gordon equation (6,536 words) [view diff] exact match in snippet view article find links to article
the function θ ( x ) {\displaystyle \theta (x)} is taken to be a constant function. A well-formulated theory should be invariant under such transformationsConstant scalar curvature Kähler metric (1,035 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \omega } is cscK, then the associated holomorphy potential is a constant function, and the induced holomorphic vector field is the zero vector fieldGradient boosting (4,188 words) [view diff] exact match in snippet view article find links to article
empirical risk. It does so by starting with a model, consisting of a constant function F 0 ( x ) {\displaystyle F_{0}(x)} , and incrementally expands itSeries (mathematics) (9,676 words) [view diff] exact match in snippet view article
\omega _{1}} viewed as a topological space in the order topology, the constant function f : [ 0 , ω 1 ) → [ 0 , ω 1 ] {\displaystyle f:\left[0,\omega _{1}\right)\toIncidence algebra (3,019 words) [view diff] exact match in snippet view article find links to article
b.\end{cases}}} The zeta function of an incidence algebra is the constant function ζ(a, b) = 1 for every nonempty interval [a, b]. Multiplying by ζ isBerkovich space (1,544 words) [view diff] exact match in snippet view article find links to article
topological space. A seminorm on a ring A{\displaystyle A} is a non-constant function |−|:A→R≥0{\displaystyle |\!-\!|:A\to \mathbb {R} _{\geq 0}} such thatKappa calculus (1,694 words) [view diff] exact match in snippet view article find links to article
the unit type, and so a function from this type is necessarily a constant function. Note that the kappa rule allows abstractions only when the variableDifferentiable manifold (9,509 words) [view diff] exact match in snippet view article find links to article
scalar fields or simply the algebra of scalars. This algebra has the constant function 1 as the multiplicative identity, and is a differentiable analog ofCounter machine (4,601 words) [view diff] exact match in snippet view article find links to article
creating the total- and partial- recursive functions: Zero function (or constant function) Successor function Identity function Composition function PrimitiveSturm–Liouville theory (4,692 words) [view diff] exact match in snippet view article find links to article
and λ are replaced in (1) by 0, −q, and μ respectively. Then the constant function 1 is a nonvanishing solution corresponding to the eigenvalue μ0 =Fourier transform (20,919 words) [view diff] exact match in snippet view article find links to article
a function, is a finite Borel measure. Its Fourier transform is a constant function (whose specific value depends upon the form of the Fourier transformPhragmén–Lindelöf principle (1,991 words) [view diff] exact match in snippet view article find links to article
its modulus on the boundary of the region. More precisely, if a non-constant function f : C → C {\displaystyle f:\mathbb {C} \to \mathbb {C} } is holomorphicBorel–Carathéodory theorem (1,867 words) [view diff] exact match in snippet view article find links to article
by Liouville's theorem, f ( n + 1 ) {\displaystyle f^{(n+1)}} is a constant function, and it converges to zero, so it is zero. So f {\displaystyle f} isMabuchi functional (937 words) [view diff] exact match in snippet view article find links to article
}}\varphi >0\}.} Since any two Kähler potentials which differ by a constant function define the same Kähler metric, the space of Kähler metrics in theAbsolute convergence (5,146 words) [view diff] exact match in snippet view article find links to article
integrable, but | f | ≡ 1 / 2 {\displaystyle |f|\equiv 1/2} is a constant function and clearly integrable. On the other hand, a function f {\displaystyleRing (mathematics) (13,682 words) [view diff] exact match in snippet view article
functions. Let x be the identity function. Each r in R defines a constant function, giving rise to the homomorphism R → S. The universal property saysDistribution (mathematics) (21,601 words) [view diff] exact match in snippet view article
sequence of test functions on U {\displaystyle U} that converges to the constant function 1 ∈ C ∞ ( U ) . {\displaystyle 1\in C^{\infty }(U).} For any distributionCalculus on Euclidean space (11,443 words) [view diff] exact match in snippet view article find links to article
^{n}} is called simply connected if every loop is homotopic to a constant function. A typical example of a simply connected set is a disk D = { ( xGradient discretisation method (2,302 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \psi _{i}} , in the sense that it is the piecewise constant function equal in each simplex to the gradient of the affine function in theCanonical quantization (4,741 words) [view diff] exact match in snippet view article find links to article
Q {\displaystyle Q} . First, Q {\displaystyle Q} should send the constant function 1 to the identity operator. Second, Q {\displaystyle Q} should takeGeneralized Ozaki cost function (1,517 words) [view diff] exact match in snippet view article find links to article
highly general manner. The concavity condition which ensures that a constant function aligns with cost minimization for a specific set of p {\displaystyleElliptic integral (7,418 words) [view diff] exact match in snippet view article find links to article
constantly takes the value zero, then the concerned function is a constant function. This means that this function results in the same function valueLocally integrable function (3,846 words) [view diff] exact match in snippet view article find links to article
Radon–Nikodym theorem given by Stanisław Saks in his treatise. The constant function 1 defined on the real line is locally integrable but not globallyQuantized state systems method (1,198 words) [view diff] exact match in snippet view article find links to article
This formulation therefore approximates the state by a piecewise constant function, q ( t ) {\displaystyle q(t)} , that updates its value as soon asAmbisonics (5,764 words) [view diff] exact match in snippet view article find links to article
(the mono signal) is the zero-order information, corresponding to a constant function on the sphere, while X Y Z {\displaystyle XYZ} are the first-orderWeierstrass transform (2,331 words) [view diff] exact match in snippet view article find links to article
implemented on R2) as a Gaussian blur. As mentioned above, every constant function is its own Weierstrass transform. The Weierstrass transform of anyCéa's lemma (2,242 words) [view diff] exact match in snippet view article find links to article
example, that force may be the gravity, when f {\displaystyle f} is a constant function (since the gravitational force is the same at all points). Let theCompressed-air energy storage (7,130 words) [view diff] exact match in snippet view article find links to article
built on this concept is that charge and discharge pressures are a constant function of depth. Carnot inefficiencies can thereby be reduced in the powerLangevin equation (5,221 words) [view diff] exact match in snippet view article find links to article
multiplicative noise, which refers to noise terms that are multiplied by a non-constant function of the dependent variables, e.g., | v ( t ) | η ( t ) {\displaystyleRelative effective Cartier divisor (1,093 words) [view diff] exact match in snippet view article find links to article
D and is denoted by degD{\displaystyle \deg D}. It is a locally constant function on SpecR{\displaystyle \operatorname {Spec} R}. If D and D' are properMöbius transformation (10,549 words) [view diff] exact match in snippet view article find links to article
{b}{d}},} where a fraction with a zero denominator is ignored. A constant function is not bijective and is thus not considered a Möbius transformationAlgebraic torus (3,878 words) [view diff] exact match in snippet view article find links to article
the scheme) is called the rank of the torus, and it is a locally constant function on S. Most notions defined for tori over fields carry to this moreCommutation theorem for traces (2,664 words) [view diff] exact match in snippet view article find links to article
L∞(X, μ) acts by multiplication operators on H = L2(X, μ) and the constant function 1 is a cyclic-separating trace vector. It follows that A ′ = A , {\displaystyleLegendre's relation (2,248 words) [view diff] exact match in snippet view article find links to article
constantly takes the value zero, then the concerned function is a constant function. This means that this function results in the same function valuePoisson manifold (9,159 words) [view diff] exact match in snippet view article find links to article
three terms in the Jacobiator are zero, being the bracket with a constant function. Any bivector field on a 2-dimensional manifold is automatically aBrouwer fixed-point theorem (8,372 words) [view diff] exact match in snippet view article find links to article
it is not difficult to check that φ′(t) = 0 for all t, so φ is a constant function, which is a contradiction because φ(0) is the n-dimensional volumeGlossary of engineering: M–Z (31,104 words) [view diff] exact match in snippet view article find links to article
model observed experimental behaviour, in particular that p is a constant function of V at given temperatures. As such, the Van der Waals model is notQuillen metric (1,992 words) [view diff] exact match in snippet view article find links to article
{\text{ind}}(D_{t}):=\dim \ker D_{t}-\dim {\text{coker}}D_{t}} is a constant function on X{\displaystyle X}. Since it is not possible to take a differencePoisson boundary (2,290 words) [view diff] exact match in snippet view article find links to article
The measure ν o , 1 {\displaystyle \nu _{o,1}} corresponding to the constant function is called the harmonic measure on the Martin boundary. With this measureInfinite compositions of analytic functions (4,487 words) [view diff] exact match in snippet view article find links to article
Compositions Theorem — {Fn} converges uniformly on compact subsets of S to a constant function F(z) = λ. Backward (outer or left) Compositions Theorem — {Gn} convergesKähler–Einstein metric (4,231 words) [view diff] exact match in snippet view article find links to article
-lemma up to changing φ {\displaystyle \varphi } by the addition of a constant function. In particular, after removing ∂ ∂ ¯ {\displaystyle \partial {\barClock (model checking) (1,621 words) [view diff] exact match in snippet view article
0}^{n}} . The initial assignment ν 0 {\displaystyle \nu _{0}} is the constant function sending each clock to 0. Intuitively, it represents the initial timeNeumann–Poincaré operator (11,016 words) [view diff] exact match in snippet view article find links to article
The third computation above is equivalent to the statement that the constant function 1 is an eigenfunction of TK with eigenvalue 1/2. To establish jumpModular lambda function (3,138 words) [view diff] exact match in snippet view article find links to article
the original proof of the Little Picard theorem, that an entire non-constant function on the complex plane cannot omit more than one value. This theoremFréchet algebra (3,459 words) [view diff] exact match in snippet view article find links to article
the product rule for differentiation.) It is commutative, and the constant function 1 {\displaystyle 1} acts as an identity. Define a countable set ofOriginal proof of Gödel's completeness theorem (4,798 words) [view diff] no match in snippet view article find links to article
We work with first-order predicate calculus. Our languages allow constant, function and relation symbols. Structures consist of (non-empty) domains andSymmetric product (topology) (3,279 words) [view diff] exact match in snippet view article
the subset of B(G, X) consisting of all maps that differ from the constant function 1 at no more than n points. Bn(G, X) gets equipped with the finalFunctional correlation (1,521 words) [view diff] exact match in snippet view article find links to article
the integrals of the functions, which are the projections on the constant function 1, are subtracted. This part corresponds to a "static part" and theQuantum tomography (5,507 words) [view diff] exact match in snippet view article find links to article
function describing the experimenter's prior knowledge (which might be a constant function), then integrate over all density matrices using the product of theFunctional data analysis (6,666 words) [view diff] exact match in snippet view article find links to article
In particular, taking X j ( ⋅ ) {\displaystyle X_{j}(\cdot )} as a constant function yields a special case of model (6) Y ( s ) = α 0 ( s ) + ∑ j = 1 pPlancherel theorem for spherical functions (11,769 words) [view diff] exact match in snippet view article find links to article
namely the value at 1 of the intertwining operator applied to ξ0, the constant function 1, in L2(K/M). Equivalently, since ξ0 is up to scalar multiplicationZonal spherical function (6,693 words) [view diff] exact match in snippet view article find links to article
S. The representation σ is irreducible, so that if v denotes the constant function 1 on K, fixed by K, φ α ( g ) = ( σ ( g ) v , v ) {\displaystyle \varphiHong Kong mahjong scoring rules (2,170 words) [view diff] exact match in snippet view article find links to article
Jockey Club on horse racing and football, is forbidden, and thus the constant function is used as "prize money". In the most extreme of styles, there isHindley–Milner type system (8,445 words) [view diff] exact match in snippet view article find links to article
variables originate from the use of free variables in an expression. The constant function K = λ x . λ y . x {\displaystyle \lambda x.\lambda y.x} provides anFunctional regression (2,733 words) [view diff] exact match in snippet view article find links to article
In particular, taking X j ( ⋅ ) {\displaystyle X_{j}(\cdot )} as a constant function yields a special case of model (5) Y ( t ) = ∑ j = 1 p X j β j ( tGeneralized functional linear model (2,688 words) [view diff] exact match in snippet view article find links to article
assumed to have a Normal distribution. The variance function is a constant function and the link function is identity. Under these assumptions the GFLMAlgorithm characterizations (8,851 words) [view diff] exact match in snippet view article find links to article
recursive functions: Computable by Turing machine: Addition (also is the Constant function if one operand is 0) Increment (Successor function) Common subtractionMarkov operator (1,078 words) [view diff] exact match in snippet view article find links to article
measurable functions. Let 1 {\displaystyle \mathbf {1} } be the constant function x ↦ 1 {\displaystyle x\mapsto 1} , then P ( 1 ) = 1 {\displaystyleComplexity of constraint satisfaction (4,485 words) [view diff] exact match in snippet view article find links to article
when viewed as a function in the way specified above, is either a constant function, a majority function, an idempotent binary function, an affine functionErgodic flow (5,093 words) [view diff] exact match in snippet view article find links to article
The induced flow corresponds to the ceiling function h ≡ 1, the constant function. Again W1, and hence (T ⊗ I) W1, commutes with I ⊗ λ(t). The specialK-stability (8,333 words) [view diff] exact match in snippet view article find links to article
we may always take one of the h i {\displaystyle h_{i}} to be the constant function 0 {\displaystyle 0} . We say a convex function is simple piecewise-linearExterior calculus identities (5,470 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\star }\mathbf {1} =\mathbf {det} } ( Hodge dual of constant function 1 is the volume form ) δ ∘ δ = 0 {\displaystyle \delta \circ \deltaStochastic portfolio theory (4,696 words) [view diff] exact match in snippet view article find links to article
X j ) {\displaystyle \log(X_{j})} with respect to the market. The constant function G := w > 0 {\displaystyle \mathbb {G} :=w>0} generates the marketImaginary hyperelliptic curve (7,168 words) [view diff] exact match in snippet view article find links to article
∑ P ∈ C 0 [ P ] {\textstyle 0=\sum _{P\in C}{0[P]}} comes from a constant function which is non-zero. Suppose D 1 = ∑ P ∈ C o r d P ( f ) [ P ] , D 2Oscillator representation (21,529 words) [view diff] exact match in snippet view article find links to article
} The only holomorphic function satisfying this condition is the constant function. So P E 0 = λ E 0 , {\displaystyle PE_{0}=\lambda E_{0},} with λ =Singular integral operators of convolution type (11,821 words) [view diff] exact match in snippet view article find links to article
calculated by the principle of the argument. It tends in L2 to the constant function 1, so that limε→0Hεhf(ζ)=f(ζ)+1πi∫f(z)−f(ζ)z−ζdz,{\displaystyle \limSobolev spaces for planar domains (8,493 words) [view diff] exact match in snippet view article find links to article
eigenvalue 0 occurs with multiplicity one and corresponds to the constant function. For if u ∈ H1(Ω) satisfies Lu = 0, then (ux,ux)+(uy,uy)=(Lu,u)=0Busemann function (12,928 words) [view diff] exact match in snippet view article find links to article
that h(δ(t)) = h(y) – t; then h is a Busemann function. h − hδ is a constant function. Let Cr be the closed convex set of points z with h(z) ≤ −r. SinceSpaces of test functions and distributions (18,993 words) [view diff] exact match in snippet view article find links to article
{\displaystyle F\psi } . In particular, the Fourier transform of the constant function equal to 1 is the δ {\displaystyle \delta } distribution. Expressing