Sentence examples for by using the regularity from inspiring English sources

In addition, the continuity, such as ((eta, u,q in C^{0}([0,T],H^{7}times H^{6}timathcal{})), (mathcal{G}(t)) and so on, can be verified by using the regularity of ((eta,u,q)), the transformed MHD equations and a standard regularized method.

Finally, our conclusion will follow by using the regularity result for the elliptic transmission problem (see [11]).

Accordingly, retinal adaptation should improve coding efficiency by using the regularity and scale invariance of contrasts and other visual features in the natural scenes [4], [8], [10], [14].

As a third estimate we computed the functional evenness, FEve, as the regularity with which the functional space is filled by species, using the regularity of branch lengths in a minimum spanning tree and evenness in species abundances [10].

Although a shorter proof has been given later by Cicalese and Leonardi [45] using the regularity theory for area minimizing sets of finite perimeter, the proof by symmetrization uses no deep results from geometric and functional analysis, is geometrically intuitive and can be adapted to other situations where a complete regularity theory is not available.

We can also avoid approximating A and B in the proof of Theorems 4.1 and 4.2 by using the linear (L^p) regularity theory, ([7], Chapter 9), which implies, under our smoothness hypotheses on A and B, that a (C^{2,alpha }) solution of (1.1)–(1.2) lies in the Sobolev space (W^{4,p}_{mathrm{{loc}}}(Omega )), for any (p

We note that by doing this we are using the regularities of PDEs indirectly, because the comparison principle in PDE literature relies on the regularities through a regularization procedure.

In the perspective of Stumpf's Erfahrungsphilosophie, physics takes as its starting point the phenomena of external perception, and its task is to explain the regularity of phenomena by using the laws of physics.

We discuss the existence and uniqueness of weak solution by using the acute angle principle, then study the regularity of solution by using inverse Hölder inequalities in the anisotropic Sobolev Space.

Then by using the inverse Hölder inequalities, we obtain the regularity of the weak solution in the anisotropic Sobolev space.

In [7], Luo and Pu obtained the existence and regularity of solutions to 3He-4He system by using the Galerkin method.