Sentence examples for functional defined by from inspiring English sources

Soft constraint formulation The problem ((mathcal {P}_{A})) is recast as an unconstrained optimal control problem by adding a penalty function to the cost functional defined by (34).

Specifically given such a "complete quadratic" functional, defined by polynomials, we give an algorithm for constructing the inverse of the linear operator which defines that functional.

Consider the functional defined by.

Consider the functional defined by (1.1).

and is the Chebyshev functional defined by (1.4).

Let be nonnegative continuous concave functional defined by (3.1).

Further, we give the concept of n-exponential convexity and log-convexity of the functions associated with the linear functionals defined by these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals.

Let (vartheta _{q}colon W^{1,q}(Omega longrightarrow mathbb{R}) be the (C^{1} -functional defined by vartheta _{q}(u)= Vert Du Vert _{q}^{q}+ int_{partialOmega }beta (z) vert u vert ^{q},dsigma quadforall uin W^{1} -functional

Corollary 2.12 Let L i, i = 1, …, 4 be linear functionals defined by (M1 - M4).

In the paper, consider the vector of path-independent curvilinear functionals defined by F ( x = ∫ γ t 0, t 1 f α ( π x ( t ) ) d t α = ( F 1 ( x , …, F r ( x.

For each, consider the functional defined on by.