Contemporary Mathematics. Fundamental Directions最新文献

Research of the problem of fair distribution of fishing quotas by the methods of game theory 用博弈论方法研究捕捞配额公平分配问题

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-224-236

E. Bogatov, N. E. Bogatova

{"title":"Research of the problem of fair distribution of fishing quotas by the methods of game theory","authors":"E. Bogatov, N. E. Bogatova","doi":"10.22363/2413-3639-2023-69-2-224-236","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-2-224-236","url":null,"abstract":"Game theory emerged as a science in the second half of the 20th century. It managed to prove itself well in the analysis of economic situations involving several subjects of economic activity (players), whose interests are completely or partially opposite. At the same time, in a number of cases, the solution of the game satisfied all players, but was not the most profitable (there was a Nash equilibrium), and in a number of other cases, it was possible to take into account the interests of all parties to the maximum (there was a Pareto optimal solution). The transfer of the principles of game theory to other areas turned out to have a number of difficulties associated, among other things, with the correct interpretation of strategies and gains of the parties in a conflict situation. For this reason, despite the obvious benefit from the possible application of game theory methods to problems of a fair distribution of quotas for catching fish and other seafood, this step has not been taken until recently. In this paper, we consider a scheme for applying the algorithms of the theory of bimatrix and cooperative games on the example of solving the problem of finding the percentage of the allowable catch of the black halibut in the Barents Sea for two countries participating in the catch and give a meaningful interpretation of the results. The basis for the calculations was real data collected by the Russian-Norwegian Fisheries Commission in recent decades to determine the proportions of the catch of the indicated fish species in the respective sea zones. Since not all components of the payoff matrices of the players are uniquely determined, it became possible to perform a parametric analysis of the mathematical model of the conflict situation both in the search for an equilibrium solution and in the implementation of the arbitration scheme. The work is an extended and supplemented version of the report [2].","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134547038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized initial-boundary problem for the wave equation with mixed derivative 混合导数波动方程的广义初边问题

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-342-363

V. Rykhlov

{"title":"Generalized initial-boundary problem for the wave equation with mixed derivative","authors":"V. Rykhlov","doi":"10.22363/2413-3639-2023-69-2-342-363","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-2-342-363","url":null,"abstract":"We study an initial-boundary problem for a second-order inhomogeneous hyperbolic equation in a half-strip of the plane containing a mixed derivative with constant coefficients and zero or nonzero potential. This equation is the equation of transverse oscillations of a moving finite string. The case of zero initial velocity and fixed ends (Dirichlet conditions) is considered. It is assumed that the roots of the characteristic equation are simple and lie on the real axis on opposite sides of the origin. The classical solution of the initial-boundary problem is determined. In the case of zero potential, a uniqueness theorem for the classical solution is formulated and a formula for the solution is given in the form of a series consisting of contour integrals containing the initial data of the problem. Based on this formula, the concepts of a generalized initial-boundary value problem and a generalized solution are introduced. The main theorems on finite formulas for the generalized solution in the case of homogeneous and inhomogeneous problems are formulated. To prove these theorems, we apply an approach that uses the theory of divergent series in the sense of Euler, proposed by A.P. Khromov (axiomatic approach). Using this approach, on the basis of formulas for solutions in the form of a series, the formulated main theorems are proved. Further, as an application of the main theorems obtained, we prove a theorem on the existence and uniqueness of a generalized solution of the initial-boundary problem in the presence of a nonzero summable potential and give a formula for the solution in the form of an exponentially convergent series.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132441080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Evasion problem in linear parametric discrete games 线性参数离散对策的回避问题

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-375-382

L. P. Yugai

引用次数: 0

On the theory of entropy suband supersolutions of nonlinear degenerate parabolic equations 非线性退化抛物方程的熵的子解和超解理论

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-306-331

E. Panov

引用次数: 0

Numerical-analytical method for the Burgers equation Burgers方程的数值解析方法

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-208-223

S. I. Bezrodnykh, S. Pikulin

引用次数: 0

On the existence and uniqueness of a positive solution to a boundary-value problem of the Sturm-Liouville type for a nonlinear ordinary differential equation 一类非线性常微分方程Sturm-Liouville型边值问题正解的存在唯一性

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-201-207

G. Abduragimov, P. E. Abduragimova, M. M. Kuramagomedova

引用次数: 0

Some inverse problems of Fourier optics 傅里叶光学的几个反问题

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-332-341

V. E. Petrov

引用次数: 0

Nonlinear optics problem with transformation of a spatial variable and an oblique derivative 具有空间变量变换和斜导数的非线性光学问题

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-276-288

A. Kornuta, V. Lukianenko

引用次数: 0

Mathematical model of ideal free distribution in the predator-prey system 捕食者-猎物系统中理想自由分布的数学模型

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-237-249

P. Zelenchuk, V. Tsybulin

引用次数: 0

Mathematical expectation of the solution of a stochastic multiplicatively perturbed system of differential equations 微分方程随机乘摄动系统解的数学期望

Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-250-262

L. Y. Kabantsova

引用次数: 0