Sentence examples for regularity method from inspiring English sources

These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods.

To this purpose, we will use the regularity method developed in [7], which we will state as follows.

The existence of solutions for quasilinear parabolic equation with boundary conditions and initial conditions can be discussed by maximal regularity, and more and more works on this field show that the maximal regularity method is efficient.

In this paper we present a new approach, the so-called p-regularity method, and show that this approximate method works well and is effective.

Three groups of outliers are found using samples from 1989 to 2008 and the Partial Least Square (PLS) regularity test method.

Combining simple, high-yield, and good orientation regularity, the method is used to tunable control the gap size of nanoparticle.

Secondly, by the regularity lifting method, we show the boundedness of each component of the solution triple.

Then, using the regularity lifting method, we prove ( u, v, w ) ∈ L ∞ ( R n ) × L ∞ ( R n ) × L ∞ ( R n ) in Section 3.

Moreover, by the regularity lifting method, we prove that ( u, v, w ) belongs to L ∞ ( R n ) × L ∞ ( R n ) × L ∞ ( R n ) and which is then locally Hölder continuous.

In the proof of Theorem 1.2, we first lift the integrability of a suitable cut-off function of the solution by the regularity lifting method to some L q ˜, and then we show that they are actually in L ∞. Finally, we assert that the solution triple is locally Hölder continuous.

Besides, without any regularity assumptions, our method can deal with asymmetric and several other failure cases of existing approaches.