We analyse properties of the mass outflow from Roche-lobe filling component a semi-detached binary system. follow approaches published by Paczy\'nski \& Sienkiewicz and Lubow Shu, which we compare with other simplified approaches. find that density flow at $L_1$ is orders magnitude lower than on same equipotential but away $L_1$. Furthermore, effective cross section flow, after averaging over i...

Numerical study of various processes leads to the need for clarification (extensions) limits applicability computational constructs and modeling tools. In this article, we differentiability in space Lebesgue integrable functions consistency concept with fundamental constructions such as Taylor expansion finite differences is considered. The function $f$ from $L_1 [a; b]$ called $(k,L)$-differen...

Biconservative submanifolds, with important role in mathematical physics and differential geometry, arise as the conservative stress-energy tensor associated to variational problem of biharmonic submanifolds. Many examples biconservative hypersurfaces have constant mean curvature. A famous conjecture Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null Inspired by co...

In the past decades, exactly recovering the intrinsic data structure from corrupted observations, which is known as robust principal component analysis (RPCA), has attracted tremendous interests and found many applications in computer vision. Recently, this problem has been formulated as recovering a low-rank component and a sparse component from the observed data matrix. It is proved that unde...