The paper presents the software package CellDataMiner for data analysis of lumencent images of cancer cells. The comparative analysis of classification and clustering methods is carried out. The most sufficient of them are implemented in the software. The software package is tested on the dataset of the experimental images of breast cancer.

The article contains a number of solutions for the key element of paraunitary filter banks based on quaternionic algebra (Q-PUBF) – the multiplier of quaternions with usage of CORDIC (Coordinate Rotation Digital Computer) techniques for the fixed angle of rotation where, unlike known solutions, 4D rotation control parameters are represented by nonlinear function of shifts number of input operands of the microrotation operation. Suggested approach of the multiplier designing on a quaternion-constant allows reaching the maximum performance of the multiplier scheme with low use of resources, for example, of FPGA.

For vector autoregressive models RS-VARX with cyclic regime switching of states the method of excluding of short-term system state fluctuations is proposed. The method is based on a sequential application of two algorithms, realizing the Bayesian “plug-in” decision rule of point wise classification and a statistical test for expected probability of misclassification. Accuracy of the approach is examined by means of computer simulation experiments.

A method for calculation of the effective material parameters of matrix composites, consisting of magnetodielectric conducting matrix with a set of bi-isotropic spherical fractions, is developed. Under the calculations of parameters, taking into account a multiple scattering of the field between particles, a new type of addition theorems, connecting basic spherical electromagnetic fields relating to different particles, is used. The developed method allows to calculate the effective parameters for the composites with sufficiently dense ensemble of the fractions.

The paper describes a method of generating vertices of the polytopes of integer partitions that was used by the authors to calculate all vertices and support vertices of the partition polytopes for all n ≤ 105 and all knapsack partitions of n ≤ 165. The method avoids generating all partitions of n. The vertices are determined with the help of sufficient and necessary conditions; in the hard cases, the well-known program Polymake is used. Some computational aspects are exposed in more detail. These are the algorithm for checking the criterion that characterizes partitions that are convex combinations of two other partitions; the way of using two combinatorial operations that transform the known vertices to the new ones; and employing the Polymake to recognize a limited number (for small n) of partitions that need three or more other partitions for being convexly expressed. We discuss the computational results on the numbers of vertices and support vertices of the partition polytopes and some appealing problems these results give rise to.

A problem of planning production of a vessel body section is considered. The problem is reduced to the classic Johnson’s tree-machine flow-shop scheduling problem. A genetic algorithm and computer experiment to compare efficiency of this algorithm and the algorithm of full enumeration are described.

The problem of minimizing the weight of transfer machine with a multi-position rotary table by placing of a work-piece at the table for processing of homogeneous batch of work-pieces is considered. To solve this problem the mathematical model and heuristic particle swarm optimization algorithm are proposed. The results of numerical experiments for two real problems of this type are given. The experiments revealed that the particle swarm optimization algorithm is more effective for the solution of the problem compared to the methods of random search and LP-search.

The technique of an assessment of current state of reliability of the onboard equipment of small spacecrafts during their flight is given. А mathematical representation of the reliability indicator of onboard equipment and the model of structure of a small spacecraft, as well as formulas for calculating the fail-safe functioning indicators of realibility diagram blocks of onboard equipment are adduced.