Sentence examples for functional of the from inspiring English sources

(P[x t) | y,t_{0}]) is a functional of the function (x t)) conditioned on two scalars y and (t_{0}).

This yields a distinctive problem structure where long term average variables are determined by the expectation of a not necessarily concave functional of the resource allocation functions.

In this paper estimation of a linear functional of the indirectly observed regression function is considered, when a deterministic design is used.

The free energy is a function of the parameters and a functional of the approximating distribution q (x).

The characteristic function f can be considered as a functional of the path defined on Γ ⊗ Γ ˙.

In summary, the energy functional of the shells is expressed as a function of five displacement components firstly.

The FPM is based on considering the target function (here, the buckling load P) as a functional of the stochastic morphology.

Although the lemma seems somewhat inaccessible due to the integrals, we note that it provides an exact expression as a functional of the first- and second-hop fading density functions, regardless of the underlying distributions.

An equivalent energy functional of the original Mumford-Shah model was proposed in [11] via elliptic function approximation based on Gamma-convergence theory.

Mutual information is thus a functional of the joint distribution of X and Y.

So we have two possible formulations for the energy functional of the ε ∞ -minimizing problem.