Sentence examples for improving the regularity from inspiring English sources

As an example of application, we apply our theorem to a control and a Cauchy problem for quasi-linear perturbations of KdV equations, improving the regularity of a previous result.

"The baby's head pushing down on the cervix improves the regularity and intensity of contractions," she said.

To further improve the regularity of u, we recall some technical lemmas in [1, 16, 17].

To improve the regularity of the magnetic fields, we need the following result on the elliptic system.

Precisely, the lower bound of (mu(rho)) and (nu(rho)) will be used to improve the regularity of the velocity u and the magnetic fields b, respectively.

In the following, in order to improve the regularity of the velocity, we need to use the estimates of the Stokes equations.

To improve the regularity of pore arrangement of porous alumina, two-step anodization [27] or nanoindentation process [28] are found to be a useful technique.

Using a standard bootstrap procedure, we can improve the regularity of the solution, and we conclude that the problem (1.1 - 1.3 1.1 - 1.3 nontriviadmitsssical periodic solutionontrivial2+alpha,1+fraclassical2}} _{omega}( Q_{omega} )) for some (alperiodic1)).

Comparison of the results in Figures 5 and 6 makes it very clear that the multi-step AAO method can improve the regularity more easily than the high applied voltage.

Using a standard bootstrap procedure, we can improve the regularity of the solution and conclude that the problem (1.1 - 1.3 1.1 - 1.3 cladmitsl radial periodiclassicaln (uin C^{2+alpha,1+fradiallperiodic _{omega}(Q_{omega})) for solutionphain(0,1)).

To improve the regularity of the cell configuration, a low electrolyte temperature and a relatively high electrolyte concentration were effective for maintaining a high-current-density to prevent burning.