The study on the exon combinatoric rules of human genes during the process of splicing is of great interest for the diagnosis and treatment of cancer. A certain part of the research is aimed at developing reliable prediction models for global exon combinatorics during the formation of mature RNA. The primary task is to develop standards or uniform systematic statistical approaches to the analysis and interpretation of possible exon sequences of genes.

A computational approach is proposed to group alternative splicing events in primary messenger RNA of human genes with the aim of determining the gene correspondence or molecule class. The method consists of reducing the dimension of the exon feature space and combining closely located exons into a limited number of classes, replacing the exon pathways of RNA generation with sequences of corresponding exon class labels, calculating the distances between RNA transcripts by some measure of similarity, and associating closely spaced RNA objects into clusters. The performance evaluation of developed algorithms has been done using the examples of RNA molecules of selected nonhomologous human genes and human hybrid oncogene RUNX1/RUNX1T1. The mean accuracy of the assignment of the transcript to given gene is about 99,5 % for the considered nonhomologous pairs of genes.

A software package and web application RNAexploreR, integrating the implemented algorithms for the analysis of alternative splicing of human gene RNA products, have been developed. The proposed algorithms and software can be used to study the organization and functioning of both aberrant and normal human genes.

A description of the software complex for modeling the thermal conditions of non-hermetic spacecrafts in circular and elliptical orbits is given. The software complex structure, mathematical models of thermal processes in the presence of thermal control system are presented. For thermal processes calculation the method of lumped parameters is used. The results of thermal stabilization for model of orbital optical device are given. The software complex can be used in the design and development of thermal control systems of nonhermetic spacecraft, and in the determination of the causes of emergency situations in these systems in orbit as well.

This paper considers the alternative theory of measurement - theory of ratings. The axiomatic definition of ranking is based on definitions from category theory. The scope of the rating definition is the set of objects and the set of ordered pairs of objects. The rating is the transformation that maps the set of objects to the set of numeric values and the set of ordered pairs of objects to the difference of the corresponding numeric values. Finding the rating by subjective measurement requires special control of the information received. The method of alternatives can be used to verify the adequacy of experimental data to the axiomatic definition of the rating.

In the paper the definition of the independence of two variables in magnitude is formulated. It is assumed that for independent variables there is an additive or multiplicative representation of the rating. An example of subjective measurement using multi-criteria utility theory (MAUT), hierarchy analysis (AHP) and rating theory is considered. The AHP heuristic method can lead to classification errors. The mathematical model of the utility function in the axiomatic method MAUT is multiplicative or additive and generally corresponds to the rating model with independent variables.

The paper deals with the dynamic systems with perturbed parameters described by the families of the third order characteristic polynomials having coefficients within the given intervals of values. The system dynamics is represented in the form of the root locus portrait. The notion of the root locus field of the family is introduced that is the basis for the system stability condition formulation. Root locus portrait configuration peculiarities of the systems of the kind and graphic-analytical approach to their analysis and synthesis serve as the basis for the system characteristic equation parameters calculation algorithm ensuring its robust stability in case of the given system proven unstable. Algorithm is implemented in the graphic-analytical form. System stability investigation and synthesis, in case of necessity, of the new parameters values are performed on the basis of estimation of the family root locus dominating field location character in the roots plane.

A homogeneous three-domain boundary-value problem for a one-layer plane screen from a bi-isotropic material is formulated. Monochromatic electromagnetic fields with axial symmetry propagating behind the screen, in front of the screen and into the screen layer are calculated. Classical boundary conditions of the continuity of the tangential field components on the planes of media separation are used. To simplify the procedure of constructing analytical solutions, the original problem is transformed into a boundary problem with two-sided boundary conditions connecting electromagnetic fields on both sides of the screen. As a result, the field in the screen layer is excluded from consideration. A method for calculating surface electromagnetic waves with axial symmetry, propagating from two sides of the screen in the radial directions of the layers, is developed. A screen from a chiral material is considered as a bi-isotropic screen. For chiral screen a second-order dispersion equation was obtained, which made it possible to calculate the frequencies of the two sequences of surface electromagnetic fields. The parameters of the chiral material for which non-attenuating surface waves exist are calculated. Surface waves are presented as a combination of basis cylindrical TE- and ТЯ-polarized electromagnetic fields. Other variants of surface waves are possible.

The problem of bi-decomposition of a Boolean function is to represent a given Boolean function in the form of a given logic algebra operation over two Boolean functions and so is reduced to specification of these functions. Any of the required functions must have fewer arguments than the given function. A method of bi-decomposition for an incompletely specified (partial) Boolean function is suggested, this method uses the approach applied in solving the general problem of parallel decomposition of partial Boolean functions. The specification of the given function must be in the form of a pair of matrices. One of them, argument matrix, can be ternary or binary and represents the definitional domain of the given function. The other one, value matrix, is a binary column-vector and represents the function values on the intervals or elements of the Boolean space of the arguments. The graph of orthogonality of the argument matrix rows and the graph of orthogonality of one-element rows of the value matrix are considered. The problem of bi-decomposition is reduced to the problem of a weighted two-block covering the edge set of the orthogonality graph of the value matrix rows by complete bipartite subgraphs (bicliques) of the orthogonality graph of the argument matrix rows. Every biclique is assigned with a disjunctive normal form (DNF) in definite way. The weight of a biclique is the minimum rank of a term of the assigned DNF. According to each biclique of the obtained cover, a Boolean function is constructed whose arguments are the variables from the term of minimal rank on the DNF.

A few small suggestions of language design reflect the author's views are presented. These suggestions are mainly related to the reliability and safety of simple, typical structures and statements in programming: typification, compile-time elaborations of variables, status of variables, high-level statements, etc. The programmers often spend working time with similar constructions. From mathematical point of view these suggestions do not effect seriously on the complexity and efficiency of calculations; they are designed exclusively to help a programmer to write reliable, secure and clear programs. These suggestions are illustrated on Ada language, which is very suitable for this purpose, but they can be applied in other languages also.

The development of a complex mechanical device with microcontroller control using of model-based design and Mathworks software products is described. The object was a robotic arm based on a parallel structure mechanism with six degrees of freedom. To create a microcontroller control system for this manipulator, a solution to the inverse kinematics problem was proposed. The operability of the model was proved using a moving computer model of geometric primitives in MATLAB. Analysis of the physical properties of developing object was carried out on the basis of its three-dimensional model, implemented by Simscape Multibody package and composed of solid-state models. The operability of the control system hardware was proved by Embedded Systems Toolbox, which also allowed to generate an executive code for selected Arduino Mega 2560 microcontroller board. The manipulator is a complete electromechanical device with cyclic microcontroller control, which allows to move the moving platform according to the predefined trajectories.