In this article we propose a new mathematical model for calculating the system availability index that is at an arbitrary point of time in two possible states: an operable state and a failure state. In the construction of a mathematical model, the flows of failure and recovery were separated. New reliability characteristics of joint streams of events are introduced and defined. Some properties have been obtained, in particular, the connection of new reliability characteristics with the distributions of failure times and restores through the two-dimensional Volterra integral equations of the second kind is shown. A solution is obtained for the exponential distribution laws, which coincides with the classical one, obtained through the one-dimensional Volterra equation of the second kind. A new mathematical model allows to monotonely convert two independent recurrent flows of failure and recovery in an arbitrary way. Such opportunity allows, for example, to calculate the availability function of an aging system. In the final part of the article, an example of calculating the availability factor for a periodically non-uniform alternating process is considered. This situation takes place during work of supermarkets, seasonal sales, etc.

The building of the low-level simulation model of voluntary and involuntary hand movements with the help of the adaptive identification method is considered in the article. It is proposed to use the dynamic neural network as a mathematical apparatus for identifying the parameters of the regulation level of local movements. The presented solution allows carrying out parametric identification of complex objects, in real time as well. We propose the construction of the dynamic model of local voluntary and involuntary hand movements in three-dimensional space. The artificial neural network testing to solve the identification problem was carried out in the Matlab/Simulink simulation environment. The presented work illustrates the possibility of using the E-network apparatus as a mathematical apparatus for modeling heterogeneous interacting processes. The use of neural network identification is necessary for modeling the logical-dynamic level of a human-operator and elements of automated control systems for technological processes. For the construction of a top-level model, it is proposed to use modified Petri nets - E-networks, which allows solving the problem of analytical and simulation modeling of complex parallel processes efficiently. The specific feature of the proposed model is the hierarchy, that allows modeling the levels of object details and processes in the human machine system.

The paper considers the concept of open data and the results of the countries openness study. Today there is a steady trend towards greater transparency of counties and their government’s activities. The true potential of open data is the ability to create new services that can improve the quality of life. The spread of open data contributes to a range of existing technical solutions. The presented analysis of the open data status and trends was performed within the study framework of needs and relevance publication of the Surgut city administration open data. The results of the analysis led to an approval to the open data portal of the Surgut city administration.

The article deals with the problem of determining the shape and parameters of holes (shape, location (coordinates), size, etc.) with the method of image signature analysis. This subject is particularly relevant to the mechanical engineering, where it is necessary to control the quality of fabrication holes in real-time. The feedforward artificial neural network is used as the classifier. The application of the said approach allows of obtaining an acceptable quality of the image classification (holes) on the basis of the training samples and solving the problem of detecting holes under noise conditions. The design of artificial neural network, training and testing were carried out in Matlab. The filtering of images and obtained signatures was conducted to achieve the noise immunity of the classifier. As a result of computer experiment in the Matlab environment the given system showed the possibility of identification of fabricaion holes with acceptable accuracy.

The time dependence of the integral coefficient of back aerosol scattering of laser radiation in the stratosphere is presented throughout 30-year period of lidar sounding. The aerosol from volcanic eruptions is clearly distinguished in the time dependence of this parameter. Statistical methods were used to analyze the homogeneous time series from 2000 to 2016. It was revealed that the variations of the time series are determined by three processes: two are random and one is deterministic. Nevertheless, the distribution of variations in the aerosol filling of the stratosphere is close to the normal distribution.

The article is devoted to the description of a random midpoint displacement fractal and its types. The paper describes the algorithm that generates 3-dimensional random midpoint displacement fractals. The results of the generation program of 3-dimensional fractal clouds are presented with the use of the modified diamond- square algorithm.

The problem of the mathematical description of homeostatic systems occurs because of the statistical instability of consecutively received samples x_i - parameters of the state vector of biological systems x ( t ) = ( x₁, x₂, ..., x_m )^T . For the evaluation of homeostasis it has been proposed to make calculations of quasi-attractors and their volumes. The movement of quasi-attractors in phase space of states is measured as the evolution of biosystem. The criteria for this evolution have been developed that take into account a two-fold change in the volume of quasi-attractor or exceeding the original volume (at time t₁). The examples of this evolution are presented in cardiology.

The article describes the principles of fiber-optic system operation of vibroacoustic monitoring. The methodology of identification of impact on the perimetral fiber optical system is developed on the example of signals obtained when testing the system on the testing ground. The article describes fiber-optic system, the location of the cable sensor for test experiments. It shows the signals from the two types of impact on the secured perimeter: short-term (d-effect); extended in time (t-effect). The article presents the total Fourier-transform of these effects in three independent implementations that show the characteristic differences of these two effects in the frequency domain. The d-effect demonstrates itself across the frequency domain involved by the system, and the t-effect only in the low-frequency region. These differences in the frequency domain are the basis of the criterion for identifying these two types of effects. More clearly the difference between these types is shown in cross-spectra where coinciding harmonics intensify each other. The revealed features of fiber-optic system signals in the Fourier spectra and cross-spectra have allowed us to develop a method of identifying d or t-effects on perimetral security system.

The results of comparison of classification methods in medical diagnostics problems are presented on the example of outcomes of coronary artery bypass graft surgery in acute myocardial infarction. We consider the probability of an outcome for an operation with the use of various techniques of myocardium protection: blood cardioplegia or cardioplegia using the Custodiol. The article compares simulation results obtained using such classification methods as logistic regression, decision trees and support vector machine. As compared criteria were used: contingency table, Area Under Curve, accuracy, completeness, F-measure, the Matthews correlation coefficient. As a result, it was revealed that some models are more preferable for use as a mathematical core when creating decision support information systems for choosing the method of cardioplegia.

The methods of technology-related risk estimation of complex systems are considered in the article. New analytic dependencies for risk functions and densities are obtained for the case of a combination of independent random probabilities of initial events and damage to complex systems applied to the Pareto principle, Erlang, and Gamma distribution.

The relevance of mathematical modeling of blood circulation hydrodynamic processes in the human brain as one of the most important subsystems of the human body is substantiated. The genesis of a scientific problem related to the development of mathematical models for the study of the cerebral vascular system is described. The Dirichlet problem for the Laplace’s equation is formulated and numerically solved.

The article is devoted to the development of models and assessment algorithms of the employees' professional activity efficiency on the basis of the information system of the publishing house "Novosti Ugry". The process of setting and monitoring the tasks of the internal corporate website is developed. The "task" object is defined by the key fields: "Task type", "Difficulty level", "Deadline", "Responsible". An algorithm for calculating and analyzing the efficiency for the completed task is obtained. Based on the statistical material of the activities of the two departments of the organization, a model for calculating the employee's efficiency index is constructed. The dependent variable in the ordinal regression equation is the "Premium" - the value of the actual accrual of the premium to the employee in the organization. Covariates are variables "Complexity", "Outrunning", "Evaluation", "Labor activity index". In the package of statistical processing of information, threshold values for the calculated bonus figure and the size of the premium in percentage correlation are determined. The algorithm of decision support system based on the maximum frequency of the attribute values "Task type" and "Level of difficulty" of all tasks performed by the employee as successfully as possible in a month is presented. The developed model and algorithm were tested on the basis of the internal corporate site of the publishing house "Novosti Ugry".

Possible porosity and permeability changes of rocks are to be considered as a result of applying thermal gas treatment on the Bazhenov formation sedimentations. Brief review of published experimental works on sedimentations is presented in which core samples of different oil shale formations, similar to the Bazhenov formation, were investigated. It is underlined that within the temperature range 200-400 °С significant changes in permeability; total, effective and fracture porosity; pore structure should be expected. After heating up to 500 °С the occurrence of connected fracture system in the Bazhenov formation is very probable as a result of expansion of existing natural fractures.

The model of the particle diffuse reflection in the one-dimensional space is considered. This model is connected to the radiant energy transfer problem. The problem of finding the particle escape probability from the space is solved and the theorems are proved.

In the present paper the problem of non-interacting ideal gas kinetic model construction is considered. The direct simulation of Monte Carlo method was used to provide the problem solution. The results of statistical estimates of macroscopic parameters derived from numerical simulation were presented. These results were compared with the analytic solution. Numerical error depending on the number of particles and computing experiments were researched.

Within the model of magnetohydrodynamics (MHD) a new class of exact solutions is investigated, corresponding to the layered flow of a viscous incompressible fluid in a magnetic field parallel to the axis of the coaxial cylinder. A theorem is proved according to which the solution of the MHD system equations reduces to the solution of the heat equations for the components of the fluid velocity vector and of the magnetic field strength. The change in the flow geometry due to the motion of the coaxial cylinder walls and the influence exerted by the magnetic field is investigated. The effect of heat generation as a result of internal friction and Joule heating in viscous incompressible fluid flows is investigated. The results can be of interest in connection with the investigation of controlling dynamics of an incompressible fluid problem, and the creation of domestic technology “digital deposit”.

Nowadays 3D-periodic composite materials are widely used in the design of the bearing and enclosing structures. Such materials are multifunctional, one of the important functions of their application is to protect the bearing structures and vital components of machines and mechanisms from strong thermal action. To assess the strength of the structure under thermal action, it is necessary to be able to calculate the thermal stresses. To find the stresses occuring in the constructions made of 3D-periodic materials, the method of asymptotic splitting (also called the method of cellular functions), developed by the authors together with prof. Yu. V. Nemirovsky. Two scales of description are introduced: the scale of the periodic cell and the scale of the entire construction, and three levels of description: the real level, the macro level and the level of the periodic cell. The problem of minimization of the conditional functional for the macro environment, the corresponding boundary value problems for the macro continuum and the cell boundary value problems are obtained, the solution of which makes it possible to calculate deformations and stresses for the real level of the description from the effect of thermal loads. It is established that the components of the thermal expansion tensor for the macro environment depend both on the values of the thermal expansion coefficients for the matrix and the inclusions, and on the elastic properties of the matrix and inclusions. In addition, they depend on the shape of the inclusions, their location within the periodic cell, the volume content of inclusions and the temperature distribution inside the cell. An example of heating a multilayer periodic wall is considered.

We developed mathematical and computer modeling of sequence of triangles in the lines of inscribed circles. The theorem for sequence of triangles with inscribed circles is proved.