Sentence examples for a new regularity from inspiring English sources

Very recently, Jiu, Niu, and Wu et al. [17] gave a new regularity criterion by the Besov space technique.

The first aim of this paper is to prove a new regularity criterion for problem (1.1 - 1.5).

In this paper, we obtained a new regularity criterion that improves and extends some known regularity criteria of the 3D generalized Hall-MHD system.

A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field in Morrey-Campanato spaces was established (see [21]).

then ( u, w, b ) can be extended beyond T. Remark 1.2 When b = 0, we also obtain a new regularity criterion for the micropolar equations determined by one direction derivative of the pressure π alone.

Applications include a new route to a regularity result by Kusuoka for stochastic differential equations, integration against Besov-paths, a regularity criterion for rough paths and a new regularity result for Cameron Martin paths associated to fractional Brownian motion.

Descartes's statement of the sine law of refraction, relating the angles of incidence and emergence at interfaces of the media through which light passes, had added a new mathematical regularity to the science of light, supporting the conviction that the universe is constructed according to mathematical regularities.

We establish a new magnetic regularity criterion in terms of the magnetic field.

For example, Changizi and his team propose a new empirical regularity for systematization of illusions [9], motivated by the theory of 'perceiving-the-present'.

Two new regularity criteria for the 3D incompressible MHD equations involving partial components of the velocity and magnetic fields were obtained by Jia and Zhou [17].

In Section 3, we give some new regularity conditions which completely characterize the strong dualities and the stable strong dualities between (P) and (D) and between ((tilde{P})) and (D).