Mathematical Structures and Modeling ¹3(51)

 Mathematical Structures and Modeling. - Omsk : OmSU, 2019. ¹3(51), 148 p. ISSN (print): 2222-8772 ISSN (online): 2222-8799 For researchers, post-graduate students and senior students. Journal issue in one file

The Fundamental Mathematics and Physics

10-periodic extension of Mendeleev table is studied within group theoretical approach. A multiplet structure is considered in detail for periods of the extended table. It is shown that period lengths are defined by a structure of basic representation of the Rumer-Fet group. Theoretical masses of elements are calculated for 10-th and 11-th periods. A notion of hypertwistor is introduced.
Keywords: periodic law, Mendeleev table, Bohr model, Rumer-Fet group

We study the problem of signal transmission using discharges flows of primary particles and calculate the probability of such signals registration, as well as probability of highlighting them against the background of the Pousson noise. The computer simulations of such useful signals and noises are discussed
Keywords: Discharge of primary particles, signal transmission, Poisson signals and noises, registration of useful signals

V.N. Borodikhin, M.M. Mikhailovskiy
Computer Simulation of the Nonequilibrium Critical Behavior of the Weakly Disordered Potts Model with the Number of Spin States $$q = 3$$.

In this paper, by the method of short-time dynamics the behavior of weakly disordered three-dimensional Potts model with the number of spin components equal to three was studied. The critical temperature value has been clarified. For spin concentrations 0.95 critical indexes $$z$$ and $$\nu$$ were calculated.
Keywords: phase transitions, Potts model, effect of impurities, critical dynamics

Applied Mathematics and Modeling

D.N. Gorelov
Reflections on Turbulence

The characteristic properties of the turbulent fluid flow behind the plate are analyzed based on the hypothesis of L. Landau on the possibility of using the ideal fluid model for the study of turbulent flows.
Keywords: turbulent flow, separated flow, self-oscillations

For the system of gas dynamics equations, taking into account the action of the Coriolis force, the linearization is carried out in two cases: when the effect of gravity is and when it is not taken into account. For linearized systems, their characteristics are defined. In the case of a rectangular coordinate system, a partial splitting of the linear system of equations iss carried out. Particular solutions in the form of standing and running waves are found. The flow in the vicinity of the impenetrable horizontal plane is constructed.
Keywords: system of equations of gas dynamics, Coriolis force, linearization, exact solutions

L.A. Volodchenkova, A.K. Guts
Interspecific Cmpetition in Forest Phytocenoses as a Strategic Bimatrix Game

The article examines the equilibrium in interspecific competition in forest phytocenoses from the point of view of the mathematical theory of games. Game strategies are described. Various types of payoff matrices that can be used to describe the competition are analyzed.
Keywords: interspecific competition, forest phytocenosis, game theory, Nash equilibrium

V.A. Shovin
Factor Analysis of Quality Indicators

The paper proposes new approaches for conducting factor analysis for qualitative indicators: the approach of calculating quantitative indicators on the basis of multidimensional scaling and matrix of mutual distances of objects; and a new approach to calculating the correlation matrix. Both methods can be preliminarily used for quantitative factor analysis. Also we propose a new approach to reconstructing the distances of objects and their location in a multidimensional space. The basis of the method is the principle of choosing the nearest object from two other objects. As a result, the distances between all pairs of objects are determined. Such a distance matrix is further used in the method of multidimensional scaling based on the Verlet method. All objects are placed in a multidimensional space of the selected dimension. This method of restoring distances between objects and placing them in a multidimensional space can also be used previously for classical classification methods.
Keywords: qualitative indicators, factor analysis, Verlet method, multidimensional scaling, distance reconstruction

Michael Beer, Afshin Gholamy, Vladik Kreinovich
A Theoretical Explanation for the Efficiency of Generalized Harmonic Wavelets in Engineering and Seismic Spectral Analysis

Wavelets of different shapes are known to be very efficient in many data processing problems. In many engineering applications, the most efficient shapes are shapes of a generalized harmonic wavelet, i.e., a wavelet of the shape $$w(t)=t^a\exp(b\cdot t)$$ for complex $$b$$. Similar functions are empirically the most successful in the seismic analysis - namely, in simulating the earthquake-related high-frequency ground motion. In this paper, we provide a theoretical explanation for the empirical success of these models.
Keywords: Generalized harmonic wavelets, seismic spectral analysis, symmetries

Griselda Acosta, Eric D. Smith, Vladik Kreinovich
Why Patients Do Not Always Follow Doctor's Advice: Systems Approach Explains Empirical Observation

Empirical studies show that when a medical doctor prescribes a medicine, only two third of the patients fill the prescription, and of this filling-prescription group, only half follow the doctor's instructions when taking the medicine. In this paper, we show that a general systems approach - namely, abstracting from the specifics of this situation - helps explain these empirical observations. We also mention that systems approach can not only explains this problem, it can also help solve it - i.e., it can help increase the patients' adherence to the doctors' recommendations.
Keywords: doctor's recommendations, systems approach, Laplace Indeterminacy Principle

Why Experts Sometimes Do Not Perform Well in Unusual Situations

We expect that the quality of experts' decisions increases with their experience. This is indeed true for reasonably routine situations. However, surprisingly, empirical data shows that in unusual situations, novice experts make much better decisions than more experienced ones. This phenomenon is especially unexpected for medical emergency situations: it turns out that the mortality rate of patients treated by novice doctors is a third lower than for patients treated by experience doctors. In this paper, we provide a possible explanation for this seemingly counterintuitive phenomenon.
Keywords: experts, statistics, unusual vs. routine situations

Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
How We Can Explain Simple Empirical Memory Rules

Researchers have found out that normally, we remember about 30\% of the information; however, if immediately after reading, we get a test, the rate increases to 45\%. In this paper, we show that Zipf law can explain this empirical dependence.
Keywords: human memory; Zipf's law; empirical memory rules

Computer Science

S.V. Lejhter, S.N. Chukanov
The Use of Affine Normalization for Enhancement of the Accuracy of Images Comparison

The problem of comparing the forms of the source and terminal images is considered. For the analysis of images deformations, diffeomorphic transformations are used. For enhancement of an accuracy of comparing source image and terminal image, it is proposed to normalize these images. The original image is exposed to affine transformation and the cost functional between the transformed original and terminal images is minimized. The solution for a problem of the image form evolution is based on the using of simulated annealing algorithm.
Keywords: pattern recognition, image normalization, affine transformations, simulated annealing algorithm

The article describes the main approaches to the implementation of educational programs. It presents features of the modeling of the learning process at various stages of the curricula organization. The possibility of reducing the duration of training due to the simulation of the curriculum as a directed graph is analyzed.
Keywords: curriculum, oriented graph, modeling, educational process

D.N. Lavrov, A.P. Lapin, M.A. Kharlamova, I.A. Cherkashchenko
Text Processing with Phonetic and Thematic Markup for Displaying Texts of Dialect Corpus

The paper describes the developed finite state machine schemes that underlie the development of a web application for the dialect corpus of the Middle Irtysh. The paper proposes refinement of the structure of an XML document representing a text recording of an interview with one or more informants with phonetic and thematic markings. The study was carried out with the financial support of the Russian Federal Property Fund in the framework of the scientific project No. 18-012-00519.
Keywords: web development, thematic markup, state machines, dialect corpus