Sentence examples for regular theory from inspiring English sources

Remark 1 The existence of local nonnegative solutions in time to problem (1.1 - 1.3) can be obtained by using a fixed point theorem or a parabolic regular theory to get a suitable estimate in a standard limiting process, see [6, 15, 16].

Remark 5 The local existence, in time, of nonnegative solutions of problem (1.1 - 1.3) can be obtained by using the fixed point theorem or the parabolic regular theory to get a suitable estimate in the standard limiting process (see [18, 19]).

A function u is called a locally weak solution of problem (1 - 3) if it is both a subsolution and a supersolution for some T > 0. Remark 1 The existence and uniqueness of locally nonnegative solutions in time to problem (1 - 3) can be obtained by the standard parabolic regular theory that can be applied to get suitable estimates in the standard limiting process (cf. [2, 21, 22]).

Because of difficulty of the problem to be modeled, the model involves several different concepts – linear solvation energy relationships, density-dependent solvent power of scCO2, regular solution theory, and the Flory–Huggins theory of athermal solutions.

Our approach relies on Karamata regular variation theory established by Karamata in 1930, which is a basic tool in the theory of stochastic processes (see [39 43] and the references therein).

(Example 3.1 (revisited)) One might have the impression that regular perturbation theory is associated with norm continuity of resolvents and spectral projections and asymptotic perturbation theory always only strong convergence.

Theoretical treatments were carried out to explain molecular interaction in the mixed micelles based on regular solution theory of Rubingh, micellization thermodynamics of Molyneux et al. and Maeda, and molecular thermodynamic theory of Pavvada and Blankschtein.

One blouse in particular was part of my regular wardrobe: Theory, ivory silk, sailor tie to be worn in a bow or a knot.

Our approach uses rigorous Regular Perturbation Theory.

We recover regular HMM theory in the uninformed situation.

In Section 2, we present some notation and results in regular variation theory.