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Longer titles found: Differentiable vector-valued functions from Euclidean space (view)

searching for Vector-valued function 41 found (83 total)

Invex function (1,119 words) [view diff] no match in snippet view article find links to article

^{n}} to R {\displaystyle \mathbb {R} } for which there exists a vector valued function η {\displaystyle \eta } such that f ( x ) − f ( u ) ≥ η ( x , u

Korn's inequality (543 words) [view diff] exact match in snippet view article find links to article

that an elastic body experiences when it is deformed by a given vector-valued function. The inequality is therefore an important tool as an a priori estimate

Optimal instruments (997 words) [view diff] exact match in snippet view article find links to article

{\displaystyle E[ux]=E[ux^{2}]=E[ux^{3}]=\dots =0} More generally, for any vector-valued function z of x, it will be the case that E [ z ( x ) ( y − f ( x , θ ) )

Geometric calculus (3,338 words) [view diff] exact match in snippet view article find links to article

\partial _{i}F.} In particular, if F {\displaystyle F} is grade 1 (vector-valued function), then we can write ∇ F = ∇ ⋅ F + ∇ ∧ F {\displaystyle \nabla F=\nabla

Bilinear map (1,570 words) [view diff] exact match in snippet view article find links to article

displaying short descriptions of redirect targets Multilinear map – Vector-valued function of multiple vectors, linear in each argument Trèves 2006, pp. 424–426

Helix (1,852 words) [view diff] exact match in snippet view article find links to article

helix has constant non-zero curvature and torsion. A helix is the vector-valued function r = a cos ⁡ t i + a sin ⁡ t j + b t k v = − a sin ⁡ t i + a cos

Myra Wilson (319 words) [view diff] exact match in snippet view article find links to article

Berlin, Heidelberg, 2010. Burbidge, Robert, and Myra S. Wilson. "Vector-valued function estimation by grammatical evolution for autonomous robot control

Cauchy–Kovalevskaya theorem (986 words) [view diff] exact match in snippet view article find links to article

derivatives of h appearing on the right hand side as components of a vector-valued function. The heat equation ∂ t h = ∂ x 2 h {\displaystyle \partial _{t}h=\partial

Pseudoconvex function (1,457 words) [view diff] exact match in snippet view article find links to article

variant of the simplex algorithm (of George B. Dantzig). Given a vector-valued function η {\displaystyle \eta } , there is a more general notion of η {\displaystyle

Fuglede's theorem (1,205 words) [view diff] exact match in snippet view article find links to article

\|F(\lambda )\|\leq \|T\|\ \forall \lambda .} So F is a bounded analytic vector-valued function, and is thus constant, and equal to F(0) = T. Considering the first-order

Multiplet (1,702 words) [view diff] no match in snippet view article find links to article

{\displaystyle {\text{SU}}(2)} . Then ϕ ( x ) {\displaystyle \phi (x)} is a vector valued function of spacetime, but is still referred to as a scalar field, as it

Quasi-Newton method (2,264 words) [view diff] exact match in snippet view article find links to article

gradient of f {\displaystyle f} , then searching for the zeroes of the vector-valued function g {\displaystyle g} corresponds to the search for the extrema of

Broyden's method (1,998 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbf {f} (\mathbf {x} )=\mathbf {0} ,} where f is a vector-valued function of vector x x = ( x 1 , x 2 , x 3 , … , x k ) , {\displaystyle \mathbf

Nonlinear eigenproblem (1,767 words) [view diff] no match in snippet view article find links to article

1 , … , r − 1 {\displaystyle \ell =0,1,\dots ,r-1} , where the vector valued function χ ℓ ( λ ) {\displaystyle \chi _{\ell }(\lambda )} is defined as

Multilinear map (2,235 words) [view diff] exact match in snippet view article find links to article

Vector-valued function of multiple vectors, linear in each argument

LOOP (programming language) (2,096 words) [view diff] exact match in snippet view article

doi:10.1016/S0022-0000(72)80032-1. PlanetMath. "primitive recursive vector-valued function". Retrieved 21 August 2021. Matos, Armando B. (3 November 2014)

Analytic signal (2,675 words) [view diff] exact match in snippet view article find links to article

variables in a straightforward manner, producing an (n + 1)-dimensional vector-valued function for the case of n-variable signals. Practical considerations for

Partial derivative (4,182 words) [view diff] exact match in snippet view article find links to article

differentiable at every point in some domain, then the gradient is a vector-valued function ∇f which takes the point a to the vector ∇f(a). Consequently, the

Green's theorem (4,074 words) [view diff] exact match in snippet view article find links to article

three-dimensional field with a z component that is always 0. Write F for the vector-valued function F = ( L , M , 0 ) {\displaystyle \mathbf {F} =(L,M,0)} . Start with

Umbilical point (1,596 words) [view diff] no match in snippet view article find links to article

the Jacobian is formed by taking the Jacobian determinant of the vector valued function F : R 2 → R 2 {\displaystyle F:\mathbb {R} ^{2}\rightarrow \mathbb

Exact differential (2,838 words) [view diff] no match in snippet view article find links to article

equivalent to the following sentence: If G is the graph of this vector valued function then for all tangent vectors X,Y of the surface G then s(X, Y) = 0

Directional derivative (4,812 words) [view diff] no match in snippet view article find links to article

f_{2}}{\partial \mathbf {v} }}\cdot \mathbf {u} } Let f(v) be a vector valued function of the vector v. Then the derivative of f(v) with respect to v (or

Spherical coordinate system (6,355 words) [view diff] exact match in snippet view article find links to article

Jacobian matrix and determinant – Matrix of partial derivatives of a vector-valued function List of canonical coordinate transformations Sphere – Set of points

Gradient discretisation method (2,302 words) [view diff] exact match in snippet view article find links to article

from an element of X D , 0 {\displaystyle X_{D,0}} , a "gradient" (vector-valued function) over Ω {\displaystyle \Omega } . This gradient reconstruction must

Gaussian process (5,929 words) [view diff] exact match in snippet view article find links to article

multi-output prediction problem, Gaussian process regression for vector-valued function was developed. In this method, a 'big' covariance is constructed

Mean value theorem (5,401 words) [view diff] exact match in snippet view article find links to article

applicable in the one dimensional case: Theorem—For a continuous vector-valued function f : [ a , b ] → R k {\displaystyle \mathbf {f} :[a,b]\to \mathbb

Jensen's inequality (5,129 words) [view diff] case mismatch in snippet view article find links to article

in Perlman, Michael D. (1974). "Jensen's Inequality for a Convex Vector-Valued Function on an Infinite-Dimensional Space". Journal of Multivariate Analysis

Integration by parts (6,879 words) [view diff] exact match in snippet view article find links to article

multivariate calculus, involving a scalar-valued function u and vector-valued function (vector field) V. The product rule for divergence states: ∇ ⋅ (

Logistic function (8,069 words) [view diff] exact match in snippet view article find links to article

generalizes to more alternatives as the softmax function, which is a vector-valued function whose i-th coordinate is e x i / ∑ i = 0 n e x i {\textstyle e^{x_{i}}/\sum

Newton's method (8,960 words) [view diff] exact match in snippet view article find links to article

\mathbb {R} .} This is equivalent to finding the zeroes of a single vector-valued function F : R k → R k . {\displaystyle F:\mathbb {R} ^{k}\to \mathbb {R}

Verlet integration (5,506 words) [view diff] exact match in snippet view article find links to article

}}(t)=\mathbf {A} {\bigl (}\mathbf {x} (t){\bigr )}} with some suitable vector-valued function A ( x ) {\displaystyle \mathbf {A} (\mathbf {x} )} representing

Algebra (14,098 words) [view diff] exact match in snippet view article find links to article

decomposition – Representation of a matrix as a product Multilinear map – Vector-valued function of multiple vectors, linear in each argument Non-associative algebra –

Connection (vector bundle) (8,674 words) [view diff] exact match in snippet view article

Let M be a differentiable manifold, such as Euclidean space. A vector-valued function M → R n {\displaystyle M\to \mathbb {R} ^{n}} can be viewed as a

Elliptic boundary value problem (3,615 words) [view diff] exact match in snippet view article find links to article

{\displaystyle b(x)} be a n {\displaystyle n} -dimensional column vector-valued function of x {\displaystyle x} , and then we may write (the divergence form

Peridynamics (5,936 words) [view diff] no match in snippet view article find links to article

{u}}({\bf {x}})\right)dV_{{\bf {x}}'}+{\bf {b}}({\bf {x}},t)}\,.} The vector valued function f {\displaystyle {\bf {f}}} is the force density that x ′ {\displaystyle

Deep backward stochastic differential equation method (4,113 words) [view diff] exact match in snippet view article find links to article

space variable, respectively. σ {\displaystyle \sigma } is a known vector-valued function, σ T {\displaystyle \sigma ^{T}} denotes the transpose associated

Banach space (17,048 words) [view diff] exact match in snippet view article find links to article

map sending the tensor f ⊗ y {\displaystyle f\otimes y} to the vector-valued function s ∈ K → f ( s ) y ∈ Y . {\displaystyle s\in K\to f(s)y\in Y.} Let

Kernel methods for vector output (4,220 words) [view diff] exact match in snippet view article find links to article

scalar-valued case Bayesian interpretation of regularization. The vector-valued function f {\displaystyle {\textbf {f}}} , consisting of D {\displaystyle

Calculus on Euclidean space (11,442 words) [view diff] exact match in snippet view article find links to article

F)\cdot dS} where F = ( f , g , h ) {\displaystyle F=(f,g,h)} is the vector-valued function and ∇ = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) {\displaystyle \nabla =\left({\frac

Tensor derivative (continuum mechanics) (9,085 words) [view diff] no match in snippet view article

f_{2}}{\partial \mathbf {v} }}\cdot \mathbf {u} } Let f(v) be a vector valued function of the vector v. Then the derivative of f(v) with respect to v (or

Fokas method (5,052 words) [view diff] no match in snippet view article find links to article

x , y ) ∈ C 2 {\displaystyle \beta (x,y)\in \mathbb {C} ^{2}} a vector valued function and γ {\displaystyle \gamma } a function (all sufficiently smooth)