Sentence examples for be a vector function from inspiring English sources

be a vector function such that for a.e. the function.

Let now X be a vector function with values in (mathbf {R}^{n}).

Let D ⊆ X be a nonempty open set, x 0 ∈ D, and let f : D → Y be a vector function.

Theorem 3.9 (Generalized Fenchel-Moreau theorem) Let f be a vector function from a nonempty convex set D ⊆ R n to R m.

Let f i : K i × K i ˆ × K i → Y i be a vector function and C i ⊂ Y i be a nonempty, closed, and convex cone.

Next, we state the following Sobolev embedding (see [23, 24]), which will be used to deal with the estimate of H. Let (v in H^{1}(Omega)) be a vector function satisfying (v|_{partialOmega}=0) or (vcdot n|_{partial Omega}=0), then begin{aligned} |v|_{L^{2}}leq C|nabla v|_{L^{2}}.

A particle moving in three-dimensional space can be located at each instant of time t by a position vector r drawn from some fixed reference point O. Since the position of the terminal point of r depends on time, r is a vector function of t.

Suppose f : A → Z is a vector function.

Suppose f : X × Y × X → Z is a vector function.

Definition 4.2 Assume that f is a vector function of class C 1, 1.

where v(r) = V1 r, ·) is a vector function with the values from L2 0, 1).