{"title":"Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs","authors":"A. V. Nadutkina, A. N. Tikhomirov, D. A. Timushev","doi":"10.1134/s1055134424020056","DOIUrl":"https://doi.org/10.1134/s1055134424020056","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the spectra of random weighted bipartite graphs. We establish that, under\u0000specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution\u0000function of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur\u0000distribution function.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198431","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}
{"title":"On Alternating Semigroups of Endomorphisms of a Groupoid","authors":"A. V. Litavrin","doi":"10.1134/s1055134424020032","DOIUrl":"https://doi.org/10.1134/s1055134424020032","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the bipolar type of the composition for pairs of endomorphisms of a groupoid\u0000and introduce the notion of an alternating pair of endomorphisms. For such a pair, the bipolar\u0000type of the composition is represented in terms of the bipolar types of the initial endomorphisms.\u0000We suggest an explicit formula for this representation. We also introduce alternating and special\u0000alternating semigroups of endomorphisms of a groupoid so that every pair of endomorphisms from\u0000an alternating semigroup is alternating. For every groupoid, we prove that the base set of\u0000endomorphisms of the first type is a special alternating semigroup with identity (i.e., a monoid).\u0000For isomorphic groupoids <span>(G)</span> and\u0000<span>(G^{prime } )</span>, we prove that every special alternating semigroup\u0000of endomorphisms of <span>(G)</span> is isomorphic to\u0000a suitable special alternating semigroup of endomorphisms of <span>(G^{prime } )</span>.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192902","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}
{"title":"On a Piecewise Constant Control for Nonlinear Differential Equations in a Banach Space","authors":"A. A. Sedipkov","doi":"10.1134/s105513442402007x","DOIUrl":"https://doi.org/10.1134/s105513442402007x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the problem on controlling solutions of nonlinear differential equations with\u0000unstable equilibrium states. We assume that the operator of the linearized problem is bounded\u0000and its spectrum is located in the right half-plane. We prove that there exists a control such that\u0000the solution remains in a prescribed neighborhood of an equilibrium state as long as required.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192961","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}
{"title":"An Inverse Problem for a Hyperbolic Integro-Differential Equation in a Bounded Domain","authors":"J. Sh. Safarov, D. K. Durdiev, A. A. Rakhmonov","doi":"10.1134/s1055134424020068","DOIUrl":"https://doi.org/10.1134/s1055134424020068","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the inverse problem of finding the kernel of the integral term in an\u0000integro-differential equation. The problem of finding the memory kernel in the wave process is\u0000reduced to a nonlinear Volterra integral equation of the first kind of convolution type, which is in\u0000turn reduced under some assumptions to a Volterra integral equation of the second kind. Using\u0000the method of contraction mappings, we prove the unique solvability of the problem in the space\u0000of continuous functions with weighted norms and obtain an estimate of the conditional stability of\u0000the solution.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192964","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}
I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov
{"title":"Negative Numberings in Admissible Sets. II","authors":"I. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov","doi":"10.1134/s1055134424010024","DOIUrl":"https://doi.org/10.1134/s1055134424010024","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We describe constructions that are used in the proof of the main result of the first part of\u0000the article. They are based on automorphisms and properties of the Cantor space.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"115 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098709","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}
V. G. Bardakov, B. B. Chuzhinov, I. A. Emelyanenkov, M. E. Ivanov, T. A. Kozlovskaya, V. E. Leshkov
{"title":"Set-Theoretical Solutions of the $$n$$ -Simplex Equation","authors":"V. G. Bardakov, B. B. Chuzhinov, I. A. Emelyanenkov, M. E. Ivanov, T. A. Kozlovskaya, V. E. Leshkov","doi":"10.1134/s1055134424010012","DOIUrl":"https://doi.org/10.1134/s1055134424010012","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The <span>(n )</span>-simplex equation was introduced by Zamolodchikov\u0000as a generalization of the Yang–Baxter equation which becomes the <span>(2 )</span>-simplex equation in this terms. In the present\u0000article, we suggest general approaches to construction of solutions of the <span>(n )</span>-simplex equation, describe certain types of\u0000solutions, and introduce an operation that allows us to construct, under certain conditions,\u0000a solution of the <span>((n + m + k))</span>-simplex equation from solutions of the\u0000<span>((n + k) )</span>-simplex equation and <span>((m + k) )</span>-simplex equation. We consider the tropicalization\u0000of rational solutions and discuss its generalizations. We prove that a solution of the\u0000<span>(n )</span>-simplex equation on <span>(G )</span> can be constructed from solutions of this equation\u0000on <span>(H )</span> and <span>(K )</span> if <span>(G )</span> is an extension of a group <span>(H )</span> by a group <span>(K )</span>. We also find solutions of the parametric\u0000Yang–Baxter equation on <span>(H)</span> with parameters in\u0000<span>(K )</span>. We introduce ternary algebras for studying\u0000the 3-simplex equation and present examples of such algebras that provide us with solutions of\u0000the 3-simplex equation. We find all elementary verbal solutions of the 3-simplex equation on a free\u0000group. <span>(|| )</span>\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098777","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}
{"title":"Lipschitz Images of Open Sets on Sub-Lorentzian Structures","authors":"M. B. Karmanova","doi":"10.1134/s1055134424010036","DOIUrl":"https://doi.org/10.1134/s1055134424010036","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We prove a sub-Lorentzian analog of the area formula for intrinsically Lipschitz mappings\u0000of open subsets of Carnot groups of arbitrary depth with a sub-Lorentzian structure introduced on\u0000the image space.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098734","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}
{"title":"Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind","authors":"","doi":"10.1134/s1055134424010048","DOIUrl":"https://doi.org/10.1134/s1055134424010048","url":null,"abstract":"<span> <h3>Abstract</h3> <p> We consider the problem on optimal quadrature formulas for curvilinear integrals of the first kind that are exact for constant functions. This problem is reduced to the minimization problem for a quadratic form in many variables whose matrix is symmetric and positive definite. We prove that the objective quadratic function attains its minimum at a single point of the corresponding multi-dimensional space. Hence, for a prescribed set of nodes, there exists a unique optimal quadrature formula over a closed smooth contour, i.e., a formula with the least possible norm of the error functional in the conjugate space. We show that the tuple of weights of the optimal quadrature formula is a solution of a special nondegenerate system of linear algebraic equations. </p> </span>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098730","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}
{"title":"An Approach to Constructing Explicit Estimators in Nonlinear Regression","authors":"Yu. Yu. Linke, I. S. Borisov","doi":"10.1134/s1055134423040065","DOIUrl":"https://doi.org/10.1134/s1055134423040065","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the problem of constructing explicit consistent estimators of finite-dimensional\u0000parameters of nonlinear regression models using various nonparametric kernel estimators.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"234 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628377","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}
{"title":"The Generating Function is Rational for the Number of Rooted Forests in a Circulant Graph","authors":"U. P. Kamalov, A. B. Kutbaev, A. D. Mednykh","doi":"10.1134/s1055134423040041","DOIUrl":"https://doi.org/10.1134/s1055134423040041","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the generating function <span>(Phi )</span> for the number\u0000<span>(f_{Gamma }(n) )</span> of rooted spanning forests in the circulant graph\u0000<span>(Gamma )</span>, where <span>(Phi (x)= sum _{n=1}^{infty } f_{Gamma }(n) x^n)</span> and either <span>(Gamma =C_n(s_1,s_2,dots ,s_k) )</span> or <span>(Gamma =C_{2n}(s_1,s_2,dots ,s_k,n) )</span>. We show that <span>(Phi )</span> is a rational function with integer coefficients that\u0000satisfies the condition <span>(Phi (x)=-Phi (1/x) )</span>. We illustrate this result by a series of examples.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138628449","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}
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