2023.1

Multiple structure protein alignments are essential to protein function analysis. Most methods of multiple protein structure alignment are based on pairwise alignment methods, where a resulting alignment is built up by merging pairwise alignments into the resulting alignment according to a guide tree. In this paper we propose the genetic algorithm for guide tree optimisation and provide the theoretical proof of convergence and experimental study of the proposed algorithm.

Is proposed the description of the implementation stabilizer construction algorithm for a switched linear system operating under parametric uncertainty in the Matlab package of applied mathematics is proposed.

In this paper asymptotic theorems are proved for estimates of the characteristic index, the scale parameter, and the shape and scale parameters for the remaining fixed parameters of the digamma distribution with a random sample size. Particular cases of limit distributions are given in the case when the sample size has a mixed Poisson distribution.

We discuss how to get a normal matrix from a binormal one and, conversely, how to get a binormal matrix from a normal one via the right multiplication on a suitable unitary matrix. Let N be a normal matrix badly conditioned with respect to inversion, that is, having a large condition number cond2N. We show that, among the binormal matrices B that can be obtained from N, there is a matrix whose eigenvalues have individual condition numbers of order (cond2N)1/2.

The paper formulates and studies optimization problems of energy consumption and storage control for a small consumer, who does not make any impact on the market prices. The models take into account new technical and economic tools: renewable energy sources and energy storages.

A single server nonpreemptive priority queueing system with renewal type input stream and multiple vacations is studied. The distributions of intervals between arrivals, service time for each priority class and vacation periods are arbitrary and absolutely continuous. The extra component method, the Laplace transform and the special integral transform are used to obtain the non-stationary joint distribution of queue length for all priority classes.

Initial problems for the equations of motion of a viscous incompressible fluid and gas in Lagrangian variables are considered. It is shown that the motion of an incompressible fluid is not related to pressure. The pressure in the absence of external forces is constant, what allows the fluid to move freely. This motion is purely vortex in nature and is described by quasi-linear equations of the parabolic type. The existence and uniqueness of the classical periodic solution of the initial problem in Rn at n > 2 is proved. The equations of motion of liquid and gas in steady-state mode are obtained. The problem of turbulent flow of partially compressible liquid and gas is solved. It is established that there is no turbulent flow in an incompressible fluid. It is shown that as a result of frequency synchronization, spatially stable periodic structures arise.