Sentence examples for of wide classes from inspiring English sources

Our construction produces solutions, for all initial data in dense sets, of wide classes of first and second order Cauchy problems, including the Schrödinger equation, the backwards heat equation and the Laplace equation, on Lp(Rn) or Lp, I ≤ p ≤ ∞, where Ω is a region in Rn with smooth boundary.

This makes the proposed algorithms to be applicable for the online parameter calculation of wider classes of TS models compared to the recently published papers concerning the same issue.

But the images and phrases that we need to galvanize the sense of wider class solidarity still elude us.

The examples above describe general grammatical rules that hold for wide classes of word pairs.

Moreover, we introduce a new version of Schauder's theorem for not necessarily continuous operators which implies existence of solutions for wider classes of problems.

(However, as we will see, there does not seem to be any problem in extending the range of applicability of their definition to wider classes of languages).

This method has been used by many authors to show nonexistence of solutions of a wide class of equations.

In particular, the existence and uniqueness of solutions of a wide class of Cauchy-type problems have been intensively investigated; see for example [1] and the references therein.

The method may be applied to the solution of a wide class of the problems of mathematical physics that can be reduced to boundary pseudo-differential equations.

In Section 2, we prove the local solvability of a wide class of integro-differential equations of the parabolic type involving nonlinear memory terms, which include (1.1).

The application of quasi-polynomial system representation for the analysis and control of a wide class of smooth nonlinear systems is proposed in this paper.