Mathematical Notes最新文献_第2页

On Damping a Control System of Arbitrary Order with Global Aftereffect on a Tree 论阻尼树上具有全局效应的任意阶控制系统

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050249

S. A. Buterin

引用次数: 0

Stability of a Traveling Wave on a Saddle-Node Trajectory 鞍节点轨迹上的行波稳定性

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050286

L. A. Kalyakin

引用次数: 0

Basis Property of the Haar System in Weighted Lebesgue Spaces with Variable Exponent 具有可变指数的加权勒贝格空间中的哈尔系统的基础属性

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050109

M. G. Magomed-Kasumov

引用次数: 0

On the Convergence of Generalized Pseudo-Spectrum 论广义伪谱的收敛性

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050316

M. A. Mansouri, A. Khellaf, H. Guebbai

引用次数: 0

On the Unique Solvability of Nonlocal Problems for Abstract Singular Equations 论抽象奇异方程非局部问题的唯一可解性

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050067

A. V. Glushak

引用次数: 0

Synchronization in a Ring of Oscillators with Delayed Feedback 具有延迟反馈的环形振荡器中的同步问题

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050298

A. A. Kashchenko

引用次数: 0

Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces 与搜索函数族相关的函数的零点。公设空间映射的重合与定点推论

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050304

A. É. Kurbanov, T. N. Fomenko

{"title":"Zeros of a Functional Associated with a Family of Search Functionals. Corollaries for Coincidence and Fixed Points of Mappings of Metric Spaces","authors":"A. É. Kurbanov, T. N. Fomenko","doi":"10.1134/s0001434624050304","DOIUrl":"https://doi.org/10.1134/s0001434624050304","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The study of the zero existence problem for a nonnegative set-valued functional on a metric space is continued. The zero existence problem for a functional related by a certain <span>(theta)</span>-continuity condition to a parametric family of <span>((alpha,beta))</span>-search functionals on an open subset of a metric space is examined. A theorem containing several sufficient conditions for this functional to have zeros is proved. </p><p> As corollaries of this result, theorems on the existence of coincidence and fixed points are also proved for set-valued mappings related by the <span>(theta)</span>-continuity condition to families of set-valued mappings with the property that the existence of coincidence and fixed points in an open subset of a metric space is preserved under parameter variation. For uniformly convex metric spaces, analogs of M. Edelstein’s 1972 asymptotic center theorem and M. Frigon’s 1996 fixed point theorem for nonexpansive mappings of Banach spaces are obtained and compared with the main results of the paper. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Class of Quasilinear Equations with Hilfer Derivatives 一类具有希尔弗导数的准线性方程

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050171

V. E. Fedorov, A. S. Skorynin

{"title":"A Class of Quasilinear Equations with Hilfer Derivatives","authors":"V. E. Fedorov, A. S. Skorynin","doi":"10.1134/s0001434624050171","DOIUrl":"https://doi.org/10.1134/s0001434624050171","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the solvability of a Cauchy type problem for linear and quasilinear equations with Hilfer fractional derivatives solved for the higher-order derivative. The linear operator acting on the unknown function in the equation is assumed to be bounded. The unique solvability of the Cauchy type problem for a linear inhomogeneous equation is proved. Using the resulting solution formula, we reduce the Cauchy type problem for the quasilinear differential equation to an integro-differential equation of the form <span>(y=G(y))</span>. Under the local Lipschitz condition for the nonlinear operator in the equation, the contraction property of the operator <span>(G)</span> in a suitably chosen metric function space on a sufficiently small interval is proved. Thus, we prove a theorem on the existence of a unique local solution of the Cauchy type problem for the quasilinear equation. The result on the unique global solvability of this problem is obtained by proving the contraction property of a sufficiently high power of the operator <span>(G)</span> in a special function space on the original interval provided that the Lipschitz condition is satisfied for the nonlinear operator in the equation. We use the general results to study Cauchy type problems for a quasilinear system of ordinary differential equations and for a quasilinear system of integro-differential equations. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotic Expansions for the Stationary Moments of a Modified Renewal-Reward Process with Dependent Components 有依赖成分的修正奖赏过程静态矩的渐近展开

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s000143462405033x

Aynura Poladova, Salih Tekin, Tahir Khaniyev

{"title":"Asymptotic Expansions for the Stationary Moments of a Modified Renewal-Reward Process with Dependent Components","authors":"Aynura Poladova, Salih Tekin, Tahir Khaniyev","doi":"10.1134/s000143462405033x","DOIUrl":"https://doi.org/10.1134/s000143462405033x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, a modification of a renewal-reward process <span>(X(t))</span> with dependent components is mathematically constructed and the stationary characteristics of this process are studied. Stochastic processes with dependent components have rarely been studied in the literature owing to their complex mathematical structure. We partially fill the gap by studying the effect of the dependence assumption on the stationary properties of the process <span>(X(t))</span>. To this end, first, we obtain explicit formulas for the ergodic distribution and the stationary moments of the process. Then we analyze the asymptotic behavior of the stationary moments of the process by using the basic results of the renewal theory and the Laplace transform method. Based on the analysis, we obtain two-term asymptotic expansions of the stationary moments. Moreover, we present two-term asymptotic expansions for the expectation, variance, and standard deviation of the process <span>(Xleft(tright))</span>. Finally, the asymptotic results obtained are examined in special cases. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis 论带有中继滞后的非自主系统的一种振荡解

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050080

V. V. Yevstafyeva

{"title":"On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis","authors":"V. V. Yevstafyeva","doi":"10.1134/s0001434624050080","DOIUrl":"https://doi.org/10.1134/s0001434624050080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider an <span>(n)</span>-dimensional system of first-order ordinary differential equations with a constant matrix having real, simple, and nonzero eigenvalues, with a discontinuous nonlinearity of two-position relay type with positive hysteresis and a continuous bounded perturbation function. We study continuous two-point oscillatory solutions with a certain period for the representative point to be returned to the switching hyperplane in the state space. When solving the Cauchy problem with initial condition at the switching point, we use the fitting method. We construct a system of transcendental equations for the switching instants and points. We prove a criterion for the existence and uniqueness of a solution with some fixed return period. For a system in the canonical form with diagonal matrix and with feedback vector of a special form, we obtain conditions for the solvability of a system of transcendental equations for the first switching instant for a given return period and formulas for the switching points. For a three-dimensional system, we give a numerical example to illustrate the theoretical results. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0