Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya

This paper explores a competitive opinion dynamic system representing a social network evolving over time. The agents compare their own opinions with the average ones and form new opinions. There are players who control agents’ opinions in a social network, and their aims are to make opinions in the society closer to the desired levels over a finite time horizon by minimizing their costs. The feature of this model is that players can influence agents in a limited number of time moments. We show how players can choose the moments of influence from Pareto optimal set on numerical examples. The results of numerical simulations are provided in the work.

Jingjing Gao

Vestnik of Saint Petersburg University Applied Mathematics Computer Science Control Processes

Competition for agents’ opinions in small dynamic systems with limited control

小动态系统中有限控制下的代理人意见竞争

Based on a class of semicontinuous functions, we prove a common fixed point theorem for a pair of commuting mappings. As a consequence, we give another common fixed point for the so-called weakly contractive mappings of type ET. The proven results are established in the setting of bounded metric spaces without using neither the compactness nor the uniform convexity. Some examples are built to demonstrate the superiority of the obtained results compared to the existing ones in the literature. Furthermore, an application to a system of functional equations arising in dynamic programming is given.

Youssef Touail

Common fixed point results: New developments on commuting mappings and application in dynamic programming

公共不动点结果：交换映射的新进展及其在动态规划中的应用

Zipf’s law have been shown to hold true in many places. From it’s first idea of a statistical phenomenon related to natural language to it’s later adaptations for economical, social and many other fields, it has been shown to work almost universally. In all of these cases authors discuss the applicability of the Zipf’s law in terms of semantically complex structures. We take this notion a step further and show how this law can work for data analysis, in particular for the sequences of byte data, obtained from various sources. We show that, using the basic chunking methodology, the Zipf’s law can be shown to hold true for many different types of raw sequences of byte data. In particular, the law holds true in all cases for the “middle point” of data, where it is present with a degree of certainty of more than 90 %. We conclude by discussing the implications and potential use cases of these findings.

Sergey L. Sergeev

Ivan S. Blekanov

Fedor V. Ezhov

Nikita A. Tarasov

Extending the applicability of the Zipf’s laws to the sequences of byte data

扩展Zipf定律在字节数据序列中的适用性

The article provides an analysis of research into the mathematical foundations of model-based systems engineering (MBSE, Model-Based Systems Engineering). Both the classical mathematical theory of Wymore’s system design and modern research are considered, in particular, the formalization of the semantics of the SysML language using automata theory, the use of category theory as a formal mathematical basis for model-based system design, the study of the possibilities of combining the theoretical basis of Wymore’s systems and the universal Discrete Event System Specification (DEVS) modeling formalism.

Vladimir A. Sukhomlin

Analysis of research into the mathematical foundations of model-based systems engineering

基于模型的系统工程数学基础研究分析

Within the framework of Kirchhoff’s theory, a new approach to constructing a solution to the problem of modeling the bending of a thin rectangular orthotropic plate clamped along the contour, which is under the influence of a load normally distributed over its surface, is proposed. the solution to the inhomogeneous biharmonic equation for an orthotropic plate is obtained in the form of a partial sum of a double series in Chebyshev polynomials of the first kind. To find the coefficients in this expansion, the boundary value problem is reduced by the collocation method to a system of linear algebraic equations in matrix form using the properties of these polynomials. Based on matrix and differential transformations, expressions for bending moments and shearing forces are obtained. the results of calculations of the bending of the middle surface of the plate under different loads on the plate are presented, which demonstrate the effectiveness of the proposed approach.

Oksana V. Germider

Vasilii N. Popov

Mathematical modeling of bending of a thin orthotropic plate clamped along the contour

薄正交各向异性板沿轮廓夹紧弯曲的数学建模

Abbreviation
Journal Impact	0.12
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q4)

ISSN	1811-9905, 2542-2251
h-index	10

Publication Information	Publisher: Saint Petersburg State University，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2017，Proportion of original research papers: 100.00%，Self Citation Rate:66.70%， Gold OA Rate: 82.50%

Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya

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Competition for agents’ opinions in small dynamic systems with limited control

Common fixed point results: New developments on commuting mappings and application in dynamic programming

Extending the applicability of the Zipf’s laws to the sequences of byte data

Analysis of research into the mathematical foundations of model-based systems engineering

Mathematical modeling of bending of a thin orthotropic plate clamped along the contour

Competition for agents’ opinions in small dynamic systems with limited control

Common fixed point results: New developments on commuting mappings and application in dynamic programming

Extending the applicability of the Zipf’s laws to the sequences of byte data

Analysis of research into the mathematical foundations of model-based systems engineering

Mathematical modeling of bending of a thin orthotropic plate clamped along the contour