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The Fekete-Szego problem by a variational method 用变分方法求解Fekete-Szego问题
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-12-10 DOI: 10.47910/femj202112
Y. Borisova, I. Kolesnikov, S. A. Kopanev, G. Sadritdinova
{"title":"The Fekete-Szego problem by a variational method","authors":"Y. Borisova, I. Kolesnikov, S. A. Kopanev, G. Sadritdinova","doi":"10.47910/femj202112","DOIUrl":"https://doi.org/10.47910/femj202112","url":null,"abstract":"The article is devoted to the well-known Fekete and Szego problem. The paper investigate the problem in sufficient detail using some new observations by the classical method of internal variations, developed at the Tomsk School of Complex Analysis. One particular case is considered. We carried out complete qualitative analysis of the functional-differential equation relative boundary mapping. We completely solved the problem for the real parameter.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"1665 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123893089","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
Tropical sequences associated with the Gale-Robinson sequences 与Gale-Robinson序列相关的热带序列
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-12-10 DOI: 10.47910/femj202121
M. Romanov
{"title":"Tropical sequences associated with the Gale-Robinson sequences","authors":"M. Romanov","doi":"10.47910/femj202121","DOIUrl":"https://doi.org/10.47910/femj202121","url":null,"abstract":"In this paper, tropical sequences associated with some Gale-Robinson sequences are calculated.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117282578","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
Compactness theorems for problems with unknown boundary 未知边界问题的紧性定理
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202109
A. G. Podgaev, T. D. Kulesh
{"title":"Compactness theorems for problems with unknown boundary","authors":"A. G. Podgaev, T. D. Kulesh","doi":"10.47910/femj202109","DOIUrl":"https://doi.org/10.47910/femj202109","url":null,"abstract":"The compactness theorem is proved for sequences of functions that have estimates of the higher derivatives in each subdomain of the domain of definition, divided into parts by a sequence of some curves of class W_2^1. At the same time, in the entire domain of determining summable higher derivatives, these sequences do not have. These results allow us to make limit transitions using approximate solutions in problems with an unknown boundary that describe the processes of phase transitions.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115128610","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
Optimal control of the radiation heat exchange equations for multi-component media 多组分介质辐射换热方程的最优控制
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202110
A. Chebotarev
{"title":"Optimal control of the radiation heat exchange equations for multi-component media","authors":"A. Chebotarev","doi":"10.47910/femj202110","DOIUrl":"https://doi.org/10.47910/femj202110","url":null,"abstract":"An analysis of optimal control problems for nonlinear elliptic equations modeling complex heat transfer with Fresnel conjugation conditions on the discontinuity surfaces of the refractive index is presented. Conditions for the solvability of extremal problems and the nondegeneracy of the optimality system are obtained. For the control problem with boundary observation, the bang-bang property is set.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114410424","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
On the value of the widths of some classes of functions from L_2 关于L_2中若干类函数的宽度值
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202106
M. R. Langarshoev
{"title":"On the value of the widths of some classes of functions from L_2","authors":"M. R. Langarshoev","doi":"10.47910/femj202106","DOIUrl":"https://doi.org/10.47910/femj202106","url":null,"abstract":"In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations of periodic differentiable functions by trigonometric polynomials and generalized moduli of continuity of m-th order in the space L_2. The exact values of various n-widths of classes of functions from L_2 defined by the generalized modus of continuity of the $r$-th derivative of the function f are calculated.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128565945","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
A new subclass of meromorphic function with positive coefficients defined by Hurwitz-Lerch Zeta functions 由Hurwitz-Lerch Zeta函数定义的带正系数亚纯函数的一个新子类
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202102
B. Venkateswarlu, P. Thirupathi Reddy, R. Madhuri Shilpa, Sujatha
{"title":"A new subclass of meromorphic function with positive coefficients defined by Hurwitz-Lerch Zeta functions","authors":"B. Venkateswarlu, P. Thirupathi Reddy, R. Madhuri Shilpa, Sujatha","doi":"10.47910/femj202102","DOIUrl":"https://doi.org/10.47910/femj202102","url":null,"abstract":"In this paper, we introduce and study a new subclass of meromorphic univalent functions defined by Hurwitz-Lerch Zeta function. We obtain coefficient inequalities, extreme points, radius of starlikeness and convexity. Finally we obtain partial sums and neighborhood properties for the class $sigma^*(gamma, k, lambda, b, s).$","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126432274","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
First order necessary optimal conditions in Gursat-Darboux stochastic systems Gursat-Darboux随机系统的一阶必要最优条件
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202108
R. Mastaliyev
{"title":"First order necessary optimal conditions in Gursat-Darboux stochastic systems","authors":"R. Mastaliyev","doi":"10.47910/femj202108","DOIUrl":"https://doi.org/10.47910/femj202108","url":null,"abstract":"For optimal control problems, described by the Gursat-Darboux stochastic system, a number of first-order necessary optimality conditions are formulated and proved, which are the stochastic analogue - the Pontryagin maximum principle, the linearized maximum principle and the Euler equation.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130399438","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
Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model 二维Ising模型居里温度的神经网络预测
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202105
A. Korol, V. Kapitan
{"title":"Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model","authors":"A. Korol, V. Kapitan","doi":"10.47910/femj202105","DOIUrl":"https://doi.org/10.47910/femj202105","url":null,"abstract":"The authors describe a method for determining the critical point of a second-order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training were obtained using Metropolis algorithm for different temperatures. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from 0.1 to 5.0 (in dimensionless units) and determined (the Curie temperature T_c). The accuracy of the obtained results was estimated relative to the Onsager solution for a flat lattice of Ising spins.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133961985","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
Difference methods for solving nonlocal boundary value problems for fractional-order differential convection-diffusion equations with memory effect 具有记忆效应的分数阶微分对流扩散方程非局部边值问题的差分解法
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202101
M. Beshtokov, M. Z. Khudalov
{"title":"Difference methods for solving nonlocal boundary value problems for fractional-order differential convection-diffusion equations with memory effect","authors":"M. Beshtokov, M. Z. Khudalov","doi":"10.47910/femj202101","DOIUrl":"https://doi.org/10.47910/femj202101","url":null,"abstract":"In the present paper, in a rectangular domain, we study nonlocal boundary value problems for one-dimensional in space differential equations of convection-diffusion of fractional order with a memory effect, in which the unknown function appears in the differential expression and at the same time appears under the integral sign. The emergence of the integral term in the equation is associated with the need to take into account the dependence of the instantaneous values of the characteristics of the described object on their respective previous values, i.e. the effect of its prehistory on the current state of the system. For the numerical solution of nonlocal boundary value problems, two-layer monotone difference schemes are constructed that approximate these problems on a uniform grid. Estimates of solutions of problems in differential and difference interpretations are derived by the method of energy inequalities. The obtained a priori estimates imply the uniqueness, as well as the continuous and uniform dependence of the solution on the input data of the problems under consideration and, due to the linearity of the problem under consideration, the convergence of the solution of the difference problem to the solution of the corresponding differential problem with the rate $O(h^2+tau^2)$.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122837716","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
Heat flux in the Langevin model for two particles 两个粒子的朗之万模型中的热通量
Dal'nevostochnyi Matematicheskii Zhurnal Pub Date : 2021-06-18 DOI: 10.47910/femj202103
M. Guzev, A. A. Dmitriev
{"title":"Heat flux in the Langevin model for two particles","authors":"M. Guzev, A. A. Dmitriev","doi":"10.47910/femj202103","DOIUrl":"https://doi.org/10.47910/femj202103","url":null,"abstract":"The analytical representation for the heat flux is obtained on the basis of the constructed solution in a one-dimensional harmonic model for two particles. At $trightarrowinfty$, the amplitude asymptotic behavior of the flow passing through the particle is shown to be determined by the temperature difference between the left and right heat reservoirs, between which the system is located. The dynamic behavior of the thermal characteristic is oscillating in time; its oscillation period is set by the parameter of the system.","PeriodicalId":388451,"journal":{"name":"Dal'nevostochnyi Matematicheskii Zhurnal","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115800431","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
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