Sentence examples for be continuously differentiable and from inspiring English sources

By exploring the inherent nature of the CNDP, the marginal function for the lower-level user equilibrium problem is proved to be continuously differentiable and its functional value and derivative in link capacity enhancement can be obtained efficiently by implementing a user equilibrium assignment subroutine.

Let f : R → R be continuously differentiable and suppose that g : T → R is delta differentiable.

We require instead that g be continuously differentiable and apply Lemma 2 to. to obtain.

Let (f:mathbb{Rrightarrow R}) be continuously differentiable and suppose (g:mathbb{Trightarrow R}) is delta differentiable.

Let e be continuously differentiable, and (nabla e(x)) be nonsingular at (x^) which satisfies (e(x^)=0).

Let F be continuously differentiable and suppose that the second derivative exists throughout an open convex set (Usubseteq V).

By the assumption (2.1 - 2.4 2.1 - 2.4asy to check that the functitn Q ( Y ) : H ˙ 1 × L 2 → H ˙ 1 × L 2 is continuously diffeasytoable and globally Lipscheck conthatous witherespect to Y.

It follows from assumption (A) and the continuity of g k, by a standard argument as in [29], that ϕ is continuously differentiable and weakly lower semi-continuous on  H 1.

Suppose that,, are continuously differentiable and their derivatives are Lipschitz continuous.

In some neighborhood N of Ω, f is continuously differentiable and its gradient is Lipschitz continuous, namely there exists a constant L > 0 such that ∥ g ( x ) − g ( y ) ∥ ≤ L ∥ x − y ∥, ∀ x, y ∈ N. (14)   3.

(4.5) where φ is continuously differentiable and that φ and (varphi') are bounded and f, g are continuous functions.