Sentence examples for a given function and from inspiring English sources

Let (1leqlambda<frac{T-omega_{0}}{eta-omega_{0}}), (hin C ([omega_{0},T]_{q,omega}, {mathbb{R}} )) be a given function, and (varphi: C ([omega_{0},T]_{q,omega }, {mathbb{R}} )rightarrow{mathbb{R}}) be a given functional.

Let (alpha,betain 0,1)), (omega>0), (qin 0,1)), (h in C (I_{q,omega}^{T},mathbb{R} )) be a given function, and (phi,psi: C (I_{q,omega}^{T},mathbb{R} )rightarrow mathbb{R}) be given functionals.

In this section we define three possible functionals that measure similarity of a given function and its shifted counterpart.

where is a given function and is an integrable function.

For convenience, we use the following abbreviation for a given function and.

All perfect models for a given function and all perfect functions in a given model are characterized.

Also, 0 ≤ C ( x, t ) ∈ L p ( 0, T ; W 1, p , f ( x, t ) ∈ V ∗ is a given function, T and a are positive constants, and ε is a nonnegative constant.

where is a given function in and is an elliptic operator of the form with the coefficients and satisfying the classical Leray-Lions conditions.

A basic problem in approximation theory is to represent a given function approximately, and solving this problem is to choose a representation system.

As for the premise variable we consider three cases where the premise variable is a given function, the output and the state of the underlying system.

The magnetic reconnection process is initiated by variation of a local resistivity assumed to be a given function of time and spatial coordinates.