Sentence examples for regularity space from inspiring English sources

A characterization of the total variation TV u,Ω) of the Jacobian determinant det Du is obtained for some classes of functions u:Ω⊂R2→R2 outside the traditional regularity space W1,2(Ω;R2).

end{aligned} (1.3) Based on the above observation, the condition (1.3) demands higher time integrability and lower regularity of space than the regularity condition imposed by Zhou and Fan [16].

For the low regularity of space in which we study the weak solutions and weakly compact priori estimates of the approximate solutions, we use the method in [17] to improve the weak convergence to strong convergence.

These images, in the form of lines, appear to have a regularity in spacing, coming closer together toward the shortest wavelength, called the series limit.

Atomic force microscopy analysis allowed to optimize the procedure of nanoparticle cluster array fabrication in terms of electron beam dose and chemical protocol, enabling to achieve a good regularity in spacing and size (i.e. area and layer number) of the clusters.

The aim of this work was to verify if the quality, regularity and spacing of nanoconcaves formed on the Al surface during the first step of anodization (pre-texturing) have a significant effect on the morphology of AAO layers grown during the second anodization continued at the same potential but in different electrolytes.

The bamboo microfibrils were also loosely aggregated into bundles with a limited degree of regularity in spacing.

Indeed, the solution is not of regularity H1 (in space) in general.

In the following theorem, we replace the continuity condition on Suzuki α-ψ-proximal contraction T by regularity of the space ( X, d ).

Unfortunately, if (0<alphaleq1), for the scaling property of the decompositions(see Section 2 for details), we will lose the regularity of the space by our method.

Exploiting the advantages gained by takingXto be the column Hilbert spaceHc, an equivalence is established between the matrix regularity of a space and that of its operator dual.