Abstract: The subject of the study is the problem of automation of genetic similarity and genetic distance calculation and building phylogenetic trees. The object of the research is the sequence of drives (alleles) in the arms of polytene chromosomes. The author considers in detail the chromosomal characteristics of species with seven chromosome arms by the example of chironomid mosquito (genus Chironomus). This article presents a Chironomus 1.0 software solution with a simple, intuitive user interface allowing to easily calculate the distance and genetic similarity between populations. The software is developed using C# and implements Nei method to calculate the genetic similarity and genetic distance. The special contribution made by the author in the study of the theme is in significant simplification of genetic studies relating to the calculation of genetic similarity and genetic distance using Nei method. The novelty of the research is in creation of a software product that allows to easily calculate the genetic similarity and distance for all types of populations with seven chromosome arms.

Keywords: genetic distance, genetic similarity, computing automation, programs, Nei method, genetics, phylogenetic trees, chironomids, polytene chromosomes, software

Abstract: The highest requirements on reliability and fire safety are applied to electrical equipment in the oil and gas industry, since its failure can lead to an emergency situation, followed by considerable economic and environmental damage. The paper raises a question of providing the reliability of the electric machine unit using spectral analysis of the higher harmonic components of current and voltage. The authors review main classification criteria for diagnostic systems, define its place in general software classification and analyze industrial software diagnostic equipment, represented on the Russian market. The study was conducted with the use of the description and comparison of methods, the theoretical foundations of electrical engineering, electrical engineering, electronics, design and programming. The authors formulated the basic requirements applicable to the software tool for motor diagnostics. The results are planned to be used in software development of a tool for the electric machine unit using spectral analysis of the higher harmonic components of current and voltage, which can be applicable to the oil and gas industry enterprises for the detection of defects and lowering repair costs.

Keywords: motor, defect, diagnostics, classification, method of diagnosis, spectral analysis, requirements, expert system, software tool, module

Abstract: The research focuses on the generating function, which is an effective tool for solving various mathematical problems in combinatorics, probability theory, mathematical physics, analysis of algorithms, etc. The subject of research is one class of generating functions – polynomials. Special attention is paid to the problem of polynomial decomposition, which has a number of solutions. The author proposes a new polynomial decomposition algorithm based on partitions. The article gives a brief description of the algorithm and gives an example of its usage. The study determines computational complexity of the algorithm, which consists of the time complexity of generating partitions, producing a monomial and solving the equation. The time complexity of the polynomial decomposition algorithm based on partitions is calculated on the basis of the results obtained by D. Knuth and given in the On-Line Encyclopedia of Integer Sequences. The original polynomial decomposition algorithm is also given. It is shown that the time complexity of the algorithm is O (n^2). The author compares the described algorithm with its analogs. The analysis shows that most of the decomposition algorithms have polynomial computational complexity of O (n^2). The experimental curves of the computational complexity of the polynomial decomposition algorithm based on partitions and known algorithms are shown.

Keywords: Decomposition of polynomials, Generation of partitions, algorithm, the computational complexity of the algorithm, generating functions, polynomial, computer algebra systems, composition, monomial, solution of equations

Abstract: The subject of the research in this paper is the probability density function (PDF) of the random variable, which is the sum of a finite number of beta values. This law is widespread in the theory of probability and mathematical statistics, because using it can be described by a sufficiently large number of random events, if the value of the corresponding continuous random variable concentrated in a certain range. Since the required sum of beta values can not be expressed by any of the known laws, there is the problem of estimating its density distribution. The aim is to find such approximation for the PDF of the sum of beta-values that would have the least error. To achieve this goal computational experiment was conducted, in which for a given number of beta values the numerical value of the PDF with the approximation of the desired density were compared. As the approximations it were used the normal and the beta distributions. As a conclusion of the experimental analysis the results, indicating the appropriateness the approximation of the desired law with the help of the beta distribution, were obtained. As one of the fields of application of the results the project management problem with the random durations of works is considered. Here, the key issue is the evaluation of project implementation time, which, because of the specific subject area, can be described by the sum of the beta values.

Keywords: random value, beta distribution, density function, normal distribution, the sum of random variables, computational experiment, recursive algorithm, approximation, error, PERT

Abstract: The research is devoted to architectural aspects of creation of fault-tolerant scalable computing systems of a special-purpose. In particular the study focuses on the principles of backup which can be used in a network subsystem of the computing system in the conditions of essential dependence of total cost of ownership of system on a level of degradation of performance metrics. Authors consider such approaches to backup as duplicating and a triple redundancy. For the principle of a triple redundancy in this research the new concept of the functional adaptation of elements of redundancy is offered. Special attention in the paper is paid to the dependence of a "Value at Risk" measure of risk, that characterizes by a random variable of total cost of ownership of the computing system and defines the greatest possible loss at the given level of probability, from such parameters of a system as number of the functional groups of hosts and a level of influence of single and group faults on degradation of performance metrics. For a risk process description in the computing system the notation of ordinary stochastic Petri nets is used. For computation of a measure of risk of "Value at Risk" on the given time-interval the methods of the algebraic theory of risk are used. The main result of the research is in proving the concept of productivity of a triple redundancy approach with the functional adaptation of elements of redundancy in the task of synthesis of topology of a network subsystem. The novelty of research consists in use of methods of the algebraic theory of risk in a task of synthesis of an optimum architecture of computing systems on the given discrete sets of possible decisions.

Keywords: willingness, availability, computer system, scaling, fault tolerance, reservation, feasibility study, triple redundancy, functional adaptation, Value at Risk

Abstract: The object of research is the process of scheduling the movie renting system of a cinema center. The subject of research is the development of a automated scheduling subsystem which allows to minimize the idle time of a cinema center. When making a schedule it is important to take into account a number of restrictions of movie rental companies, exclude the possibility of simultaneous display of one film in different cinema rooms (with the exception of films, which are very popular with the lack of availability in other cinema rooms), ensure that the best show time goes to the movies with the box office sales. When developing a subsystem of automated scheduling the authors used method of deduction, in which a conclusion about a common set studied attributes is made based on a variety of partial signs, method of analysis and method of mathematical modeling. The main result of the research is the developed software solution based on 1C:Enterprise for automated scheduling the movie renting system of a cinema center while taking into account existing criteria and restrictions. Novelty is that based on the list of movies specified by the user the subsystem forms a mathematical entity of an objective function and limitations of the system and transfers it to an optimizer. As the result while making a schedule the user uses only the information system of a cinema center. For the end-user it is not necessary to deal with the interface to other programs and modules, as well as the mathematical notation of the objective function and the constraints of the system. Currently the automated scheduling subsystem is integrated in the work process of the network of cinemas "Planeta Kino" and has been successfully used for a year.

Keywords: theory of scheduling, automated scheduling, optimization, MS Excel, 1C: Enterprise, scheduling algorithm, software implementation, signs of movies, schedule of films, the film industry