Mathematical Structures and Modeling. - Omsk : OmSU, 2018. N3(47), 135 p.
ISSN  (print): 2222-8772 
ISSN (online): 2222-8799

For researchers, post-graduate students and senior students.

Journal issue in one file

Fundamental Mathematics and Physics

A.K. Guts.
Quantum Time Machine and Loop Quantum Gravity.

The description of a quantum time machine, implementing intertemporal transitions, within the framework of loop quantum gravity is given. In contrast to quantum geometrodynamics, in this case it becomes clear how to produce influences that change the modern geometry to the past one.
Keywords: quantum time machine, loop quantum gravity, spin net, spin foam.

A.K. Guts
Alternative New Cosmogony

In the article the mathematical apparatus is indicated, by means of which we can realize the ideas of Hegel about being, about the alienation of ideas in Nature, as well as the theory of the creation of the Universe by active consciousness, which is alternative to the theory of the Big Bang.
Keywords: Cosmogony, the creation of the universe, being, nothing, fractal compression, materialization (localization) of ideas.

A.N. Kabanov
Central Series of the Group of Unitriangular Automorphisms of a Free Nilponent Leibniz Algebra with Index 2.

The central series of the group of unitriangular automorphisms of a free nilpotent Leibniz algebra with index 2 over an arbitrary field is described.
Keywords: Leibniz algebra, nilpotent algebra, unitriangular automorphism, central series.

Applied Mathematics and Modeling

P.I. Vaynmaster.
Solution for Data Processing in Systems of Microseismic Monitoring of Hydraulic Fracturing.

Performing operations on Hydraulic fracturing (HF) requires control of the fracture growth. A common technology providing such control is microseismic monitoring. It's based on solving problems of location of sources of seismic emission and their visualization on a three-dimensional coordinate grid. The existing methods of HF monitoring have a number of drawbacks, among which is the low accuracy of measuring the geometrical parameters of fractures and the dynamics of their growth. In this article, the original approach to the processing of microseismic monitoring data is described, which allows us to represent the fracturing zone in the form of three-dimensional continuous objects --- one or several fracture layers filled with proppant. The proposed algorithms are based on the application of a number of digital signal processing procedures: detection of a pulse on the background of noise and location of its source, spatial filtering of sources, construction of fracture trajectories, interpolation of a set of sources and visualization of a three-dimensional graphic model.
Keywords: hydraulic fracturing, fracture, seismic pulse, detection, filtering, trajectory construction, Delaunay triangulation.

O.V. Opryshko.
Calculation of the Parameters of Special Three-Dimensional Stationary Flows.

Tornadoes and tropical cyclones are a natural phenomenon that is characterized by what arises from the ordinary, rising upward flow of air warmed by the sun. Under certain conditions, such a flow acquires high speeds, as a result of which, multiple disruptions occur. The original scheme of initiation of the natural ascending swirling flows in the form of tornadoes or tropical cyclones was put forward and substantiated by S. P. Bautin. The mathematic simulation of gas flow in a bottom part of a tornado is effectuated due to Fujita scale and enhanced Fujita scale which comprises systematized data of in situ observations of tornadoes of various intensity, namely, values of the width of damage path and maximum wind speed. For the system of equations of gas dynamics, one Cauchy problem is posed with the initial conditions given on an impenetrable horizontal plane \(z = 0\). In the numerically-analytical method for solving this problem, the gas dynamic parameters are determined, including the kinetic energy of ascending swirling flows. Calculations were carried out for various classes of tornadoes and tropical cyclones from the enhanced Fujita scale for different heights of the considered flows.
Keywords: system of equations of gas dynamics, gas dynamic parameters, Fujita scale, kinetic energy of the flow.

V.A. Shovin.
Autocorrelation Neural Network of Factor Analysis.

An algorithm for performing factor analysis based on an autocorrelation neural network is developed. The neural network of this type has the ability to autocorrelation the input and output signals. In this neural network, an additional layer of neurons with weight coefficients equal to the values of the input signal is added to carry out the back propagation of the error from the maximum of the correlation of the input and output signals. Maximizing the correlation of the input and output signals leads to the realization of factor analysis and calculation of the principal components in the case of a smaller number of neurons on the output layer than on the input layer of the neural network. Test calculations of the principal components of this algorithm on the data of arterial hypertension showed the identity of significant factor loads and factor structures with other methods of searching for the principal components.
Keywords: factor analysis, neural network, back propagation method

T.Yu. Nazarova, D.N. Lavrov.
Computer Modeling of Identification by the Iris of The Eye Based on OpenCV.

The results of recognition algorithm construction based on the use of the OpenCV library are given. The results of primary experiments on image recognition on a small base are presented.
Keywords: iris, identification, recognition.

Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich.
Fuzzy Ideas Explain a Complex Heuristic Algorithm for Gauging Pavement Conditions.

To gauge pavement conditions, researchers have come up with a complex heuristic algorithm that combines several expert estimates of pavement characteristics into a single index --- which is well correlated with the pavement's durability and other physical characteristics. While empirically, this algorithm works well, it lacks physical or mathematical justification beyond being a good fit for the available data. This lack of justification decreases our confidence in the algorithm's results --- since it is known that often, empirically successful heuristic algorithms need change when the conditions change. To increase the practitioners' confidence in the resulting pavement condition estimates, it is therefore desirable to come up with a theoretical justification for this algorithm. In this paper, we show that by using fuzzy techniques, it is possible to come up with the desired justification.
Keywords: gauging pavement conditions, fuzzy logic.

Solymar Ayala, Aaron Velasco, Vladik Kreinovich.
Soft Computing Ideas Can Help Earthquake Geophysics.

Earthquakes can be devastating, thus it is important to gain a good understanding of the corresponding geophysical processes. One of the challenges in geophysics is that we cannot directly measure the corresponding deep-earth quantities, we have to rely on expert knowledge, knowledge which often comes in terms of imprecise (``fuzzy'') words from natural language. To formalize this knowledge, it is reasonable to use techniques that were specifically designed for such a formalization --- namely, fuzzy techniques. In this paper, we formulate the problem of optimally representing such knowledge. By solving the corresponding optimization problem, we conclude that the optimal representation involves using piecewise-constant functions. For geophysics applications, this means that we need to go beyond tectonic plates to explicitly consider parts of the plates that move during the earthquake. We argue that such an analysis will lead to a better understanding of earthquake-related geophysics.
Keywords: earthquake geophysics, soft computing, Haar wavelets.

Francisco Zapata, Olga Kosheleva, Vladik Kreinovich.
How to Select the Best Paper: Towards Justification (and Possible Enhancement) of Current Semi-Heuristic Procedures.

To select the best paper at a conference or in a journal, people use reasonably standard semi-heuristic procedures like averaging scores. These procedures usually work well, but sometimes, new situations appear for which the existing procedures are not automatically applicable. Since the existing procedures are heuristic, it is often not clear how to extend them to new situations. In this paper, we provide a possible explanation for the existing procedures. This explanations enables us to naturally generalize these procedures to possible new situations.
Keywords: selecting the best paper, probabilistic approach

Computer Science

L.A. Volodchenkova, S.I. Korolev.
Software for Teaching Children of Lower Grades Fast Reading.

The article the software application for automatization of the process of children teaching to fast reading.
Keywords: fast reading, software application, techniques of rapid reading.

A.D. Gorodetsky, D.N. Lavrov.
Semi-Automatic Application Memory Management

The article presents an approach to memory management of an application based on semi-automatic control that combines the convenience of an automatic "garbage collector" and completely manual control, as is customary in the C language. This is a fairly flexible approach that can change the types of memory managers during program execution and / or even depending on the platform.
Keywords: garbage collector, application memory, memory management algorithms.

Information Security

S.V. Belim, S.Yu. Belim.
Problems of Security Policy Creation at Information Systems Association

In article the problem of security policy creation at two information systems association as an optimizing task is considered. In this task two parameters --- confidentiality and availability of information are allocated. Criterion function is make up. Options of systems association with identical security models are considered. The optimality of the proposed solutions is investigated.
Keywords: security policy, discretionary access control, mandatory access control.