Kalmetev, R. Sh. Orlov, Yu. N. Sakbaev, V. Zh.
Published in
Lobachevskii Journal of Mathematics

AbstractThe properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generaliz...

Klyushnev, N. V. Rykov, Yu. G.
Published in
Lobachevskii Journal of Mathematics

AbstractThe paper deals with various generalized solutions to one-dimensional pressureless gas dynamics. Along with the entropy solutions other solutions are considered that include the combination of concentration and decay processes. This research is motivated by multidimensional case where the concentration mechanism seems to be not enough for t...

Kiselev, E. A. Telegin, P. N. Shabanov, B. M.
Published in
Lobachevskii Journal of Mathematics

AbstractThe evolution of high-performance computing is associated with the growth of energy consumption. Performance of cluster computes (CC) is increased via rise in performance and the number of used processors, GPUs and coprocessors. Increment in the number of computing elements results significant growth of energy consumption. Power grids limit...

Yashunsky, A. D.
Published in
Lobachevskii Journal of Mathematics

AbstractWe consider read-once functions over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{Z}_{3}$$\end{document}, i.e., functions expressed by a formula with...

Popkov, K. A.
Published in
Lobachevskii Journal of Mathematics

AbstractWe consider a problem of implementation of Boolean functions by self-correcting logic circuits of unreliable gates in different bases. A set of permitted faults for each gate is predefined, with no restrictions imposed, except that it should be non-void. The following statements are proved:1) For any integer \documentclass[12pt]{minimal} \u...

Shabanov, B. M. Rybakov, A. A. Shumilin, S. S. Vorobyov, M. Yu.
Published in
Lobachevskii Journal of Mathematics

AbstractWhen solving complex problems of numerical modeling, computational meshes, containing hundreds millions of cells are quite often. Modern tasks even cross the line of billion cells. Workstations are unable to cope with such volume of data and computation. To perform computations of this volume we need to use supercomputer clusters consisting...

Rykov, Yu. G.
Published in
Lobachevskii Journal of Mathematics

AbstractThe paper is devoted to the new approach to systems of quasilinear conservation laws which leads to the alternative view of weak solution and to the possibility of developing a new type calculation algorithms for such systems on the basis of neural networks technology. The approach under consideration is the further development of variation...

Bagrov, A. D. Rybakov, A. A.
Published in
Lobachevskii Journal of Mathematics

AbstractIce accretion simulation on aircraft profiles during their flight in an air stream containing supercooled water droplets is an extremely important task for flight safety, since the form of accreted ice significantly affects flight characteristics. In one of the models for solving the problem, the shallow-water icing model (SWIM), the proble...

Sorokin, V. N.
Published in
Lobachevskii Journal of Mathematics

AbstractAsymptotics of Hermite–Padé approximants of the first type for Weil functions of discrete Meixner measure and its derivative is studied. We describe a piecewise-analytic curve in the complex plane which attracts part of the zeros of the Meixner multiple orthogonal polynomials. This curve possesses a symmetry property in the equilibrium prob...

Aptekarev, A. I. Dudnikova, T. V. Tulyakov, D. N.
Published in
Lobachevskii Journal of Mathematics

AbstractWe consider \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-difference equations for colored Jones polynomials. These sequences of polynomials...