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Weak Solvability of One Model of a Nonlinearly Retarded Fluid in a Thermal Field 热场中非线性迟滞流体模型的弱可解性
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700385
E. I. Kostenko
{"title":"Weak Solvability of One Model of a Nonlinearly Retarded Fluid in a Thermal Field","authors":"E. I. Kostenko","doi":"10.3103/s1066369x24700385","DOIUrl":"https://doi.org/10.3103/s1066369x24700385","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>For the initial-boundary value problem of the dynamics of a thermoviscoelastic medium of Oldroyd type in the planar case, a nonlocal theorem regarding the existence of a weak solution is established.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206017","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
Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator 在 Sturm-Liouville 算子特征值移动的情况下，对带有时变系数的 Korteweg-de Vries 方程进行积分
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x2470035x
U. A. Hoitmetov, T. G. Khasanov
{"title":"Integration of the Korteweg–de Vries Equation with Time-Dependent Coefficients in the Case of Moving Eigenvalues of the Sturm–Liouville Operator","authors":"U. A. Hoitmetov, T. G. Khasanov","doi":"10.3103/s1066369x2470035x","DOIUrl":"https://doi.org/10.3103/s1066369x2470035x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The inverse scattering method is used to integrate the Korteweg–de Vries equation with time-dependent coefficients. We derive the evolution of the scattering data of the Sturm–Liouville operator whose coefficient is a solution of the Korteweg–de Vries equation with time-dependent coefficients. An algorithm for constructing exact solutions of the Korteweg–de Vries equation with time-dependent coefficients is also proposed; we reduce it to the inverse problem of scattering theory for the Sturm–Liouville operator. Examples illustrating the stated algorithm are given.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226342","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
Controlled Frames in n-Hilbert Spaces and Their Tensor Products n-Hilbert 空间中的受控框架及其张量乘积
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700312
P. Ghosh, T. K. Samanta
{"title":"Controlled Frames in n-Hilbert Spaces and Their Tensor Products","authors":"P. Ghosh, T. K. Samanta","doi":"10.3103/s1066369x24700312","DOIUrl":"https://doi.org/10.3103/s1066369x24700312","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The concepts of controlled frame and it’s dual in <span>(n)</span>-Hilbert space have been introduced and then some of their properties are going to be discussed. Also, we study controlled frame in tensor product of <span>(n)</span>-Hilbert spaces and establish a relationship between controlled frame and bounded linear operator in tensor product of <span>(n)</span>-Hilbert spaces. At the end, we consider the direct sum of controlled frames in <span>(n)</span>-Hilbert space.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206012","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
Formula for Regularized Trace of 2m-Order Differential Operator with Periodic Boundary Conditions 具有周期性边界条件的 2m 阶微分算子的正规化轨迹公式
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700373
E. F. Akhmerova, M. A. Rahmatzoda, T. G. Amangildin
{"title":"Formula for Regularized Trace of 2m-Order Differential Operator with Periodic Boundary Conditions","authors":"E. F. Akhmerova, M. A. Rahmatzoda, T. G. Amangildin","doi":"10.3103/s1066369x24700373","DOIUrl":"https://doi.org/10.3103/s1066369x24700373","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We obtain a regularized trace formula for <span>(2m)</span>-order differential operator perturbed by a quasi-differential perturbation and with periodic boundary conditions.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206016","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
Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems 估计自由边界问题中流动区域面积的精确公式
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700361
M. M. Alimov
{"title":"Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems","authors":"M. M. Alimov","doi":"10.3103/s1066369x24700361","DOIUrl":"https://doi.org/10.3103/s1066369x24700361","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206015","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 Multiparameter Family of Solutions to the Volterra Linear Integral Equation of the First Kind 第一类 Volterra 线性积分方程的多参数解族
IF 0.4
Russian Mathematics Pub Date : 2024-08-15 DOI: 10.3103/s1066369x24700348
I. V. Sapronov
{"title":"A Multiparameter Family of Solutions to the Volterra Linear Integral Equation of the First Kind","authors":"I. V. Sapronov","doi":"10.3103/s1066369x24700348","DOIUrl":"https://doi.org/10.3103/s1066369x24700348","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study the Volterra integral equation of the first kind with an integral operator of order <span>(n)</span>, a singularity, and a sufficiently smooth kernel in a certain Banach space with weight. It reduces to an integro-differential equation with two terms in the left-hand side. The first term corresponds to an equation for which an explicitly multiparameter family of solutions is constructed. For the second term we obtain an equation with an operator whose norm in an arbitrary Banach space is arbitrarily small near zero. Such splitting of the integral operator allows constructing a particular and general solutions to the integro-differential equations in the corresponding Banach space in the form of convergent series. Thus, under certain restrictions on the operator pencil corresponding to a given integral operator, a multiparameter family of solutions is constructed for the original integral equation.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206014","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 Existence of an Eigenvalue of the Generalized Friedrichs Model 论广义弗里德里希斯模型特征值的存在性
IF 0.4
Russian Mathematics Pub Date : 2024-08-06 DOI: 10.3103/s1066369x24700257
M. I. Muminov, U. R. Shadiev
{"title":"On the Existence of an Eigenvalue of the Generalized Friedrichs Model","authors":"M. I. Muminov, U. R. Shadiev","doi":"10.3103/s1066369x24700257","DOIUrl":"https://doi.org/10.3103/s1066369x24700257","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a family of bounded self-adjoint matrix operators (generalized Friedrichs models) acting on the direct sum of one-particle and two-particle subspaces of the Fock space. Conditions for the existence of eigenvalues of the matrix operators are obtained.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969000","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 Absolute Convergence of Fourier Series of Almost Periodic Functions 论几乎周期函数傅里叶级数的绝对收敛性
IF 0.4
Russian Mathematics Pub Date : 2024-08-06 DOI: 10.3103/s1066369x24700282
Yu. Kh. Khasanov, F. M. Talbakov
{"title":"On the Absolute Convergence of Fourier Series of Almost Periodic Functions","authors":"Yu. Kh. Khasanov, F. M. Talbakov","doi":"10.3103/s1066369x24700282","DOIUrl":"https://doi.org/10.3103/s1066369x24700282","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a structural characteristic of the function under consideration.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934947","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 Undecidability of Unary Nonnested PFP Operators for One Successor Function Theory 论单继承函数理论的一元非嵌套 PFP 运算符的不可判定性
IF 0.4
Russian Mathematics Pub Date : 2024-08-06 DOI: 10.3103/s1066369x24700300
V. S. Sekorin
{"title":"On Undecidability of Unary Nonnested PFP Operators for One Successor Function Theory","authors":"V. S. Sekorin","doi":"10.3103/s1066369x24700300","DOIUrl":"https://doi.org/10.3103/s1066369x24700300","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We investigate the decidability of first-order logic extensions. For example, it is established in Zolotov’s works that a logic with a unary transitive closure operator for the one successor theory is decidable. We show that in a similar case, a logic with a unary partial fixed point operator is undecidable. For this purpose, we reduce the halting problem for the counter machine to the problem of truth of the underlying formula. This reduction uses only one unary nonnested partial fixed operator that is applied to a universal or existential formula.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934949","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
Variation and λ-Jump Inequalities on Hp Spaces Hp 空间上的变分与λ-跳跃不等式
IF 0.4
Russian Mathematics Pub Date : 2024-08-06 DOI: 10.3103/s1066369x24700233
S. Demir
{"title":"Variation and λ-Jump Inequalities on Hp Spaces","authors":"S. Demir","doi":"10.3103/s1066369x24700233","DOIUrl":"https://doi.org/10.3103/s1066369x24700233","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>(phi in mathcal{S})</span> with <span>(int phi (x){kern 1pt} dx = 1)</span>, and define <span>({{phi }_{t}}(x) = frac{1}{{{{t}^{n}}}}phi left( {frac{x}{t}} right),)</span>\u0000and denote the function family <span>({{{ {{phi }_{t}} * f(x)} }_{{t &gt; 0}}})</span> by <span>(Phi * f(x))</span>. Let <span>(mathcal{J})</span> be a subset of <span>(mathbb{R})</span> (or more generally an ordered index set), and suppose that there exists a constant <span>({{C}_{1}})</span> such that <span>(sumlimits_{t in mathcal{J}} {kern 1pt} {kern 1pt} {text{|}}{{hat {phi }}_{t}}(x){{{text{|}}}^{2}} &lt; {{C}_{1}})</span>\u0000for all <span>(x in {{mathbb{R}}^{n}})</span>. Then</p><p> (i) There exists a constant <span>({{C}_{2}} &gt; 0)</span> such that <span>({text{||}}{{mathcal{V}}_{2}}(Phi * f){text{|}}{{{text{|}}}_{{{{L}^{p}}}}} leqslant {{C}_{2}}{text{||}}f{text{|}}{{{text{|}}}_{{{{H}^{p}}}}},quad frac{n}{{n + 1}} &lt; p leqslant 1)</span> for all <span>(f in {{H}^{p}}({{mathbb{R}}^{n}}))</span>, <span>(frac{n}{{n + 1}} &lt; p leqslant 1)</span>.</p><p> (ii) The λ-jump operator <span>({{N}_{lambda }}(Phi * f))</span> satisfies\u0000<span>({text{||}}lambda {{[{{N}_{lambda }}(Phi * f)]}^{{1/2}}}{text{|}}{{{text{|}}}_{{{{L}^{p}}}}} leqslant {{C}_{3}}{text{||}}f{text{|}}{{{text{|}}}_{{{{H}^{p}}}}},quad frac{n}{{n + 1}} &lt; p leqslant 1,)</span> uniformly in <span>(lambda &gt; 0)</span> for some constant <span>({{C}_{3}} &gt; 0)</span>.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934941","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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