Sentence examples for a functional of from inspiring English sources

The control function is a functional of a previous phase state.

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

According to this definition, we know that γ-variance Var γ ( f, p ) is a functional of the function f : Ω → ( 0, ∞ ) and p : Ω → ( 0, ∞ ), and such a definition is compatible with the generalized integral means studied elsewhere (see, e.g., [1 6]).

Let ϕ(F) be a functional of the distribution function F and let ϕ(F n ) be its sample version, where F n is the empirical distribution function defined by the data { x i } i = i,… n.

For a given differentiable relative convex function F and a nondifferentiable relative convex function f, we consider a functional of the type I [ v ] = f ( g ( v ) ) − F ( g ( v ) ), ∀ v ∈ K. (2.5).

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

Indeed, for instance, if the function ℱ is actually a functional of the past trajectory of variable v ϵ which can be expressed as the solution of an additional SDE, then it may be possible to include a certain form of history-dependence.

To derive the EIFs for the functionals (i)–(iii) of M n, we first express M n as a functional of the empirical distribution function F n. Let L γ, θ; F)= ∫ ℓ γ, θ; y) dF y).

If the internal porous structure of the material is modeled as myriad nonintersecting cylindrical pores, an equation may be derived for the flux as a function of pressure, in which the flux is a functional of the pore-size distribution.

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

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