Siberian Mathematical Journal最新文献

{"title":"Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries","authors":"S. K. Vodopyanov, S. V. Pavlov","doi":"10.1134/s0037446624030054","DOIUrl":"https://doi.org/10.1134/s0037446624030054","url":null,"abstract":"<p>This article addresses the problem of boundary correspondence\u0000for a sequence of homeomorphisms that\u0000change the capacity of a condenser in a controlled way.\u0000To study the overall boundary behavior of these mappings,\u0000we introduce some capacity metrics\u0000in a sequence of domains with nondegenerate core.\u0000Completions with respect to these metrics add to the domains new points called boundary elements.\u0000As one of the consequences, we obtain not only sufficient conditions for\u0000the global uniform convergence of a sequence of homeomorphisms,\u0000but some applications to elasticity theory as well.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169479","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}

{"title":"The Tricomi–Neumann Problem for a Three-Dimensional Mixed-Type Equation with Singular Coefficients","authors":"A. K. Urinov, K. T. Karimov","doi":"10.1134/s0037446624030224","DOIUrl":"https://doi.org/10.1134/s0037446624030224","url":null,"abstract":"<p>Under study is the Tricomi–Neumann problem for a three-dimensional mixed-type equation\u0000with three singular coefficients in a mixed domain consisting of a quarter of a cylinder and a triangular straight prism.\u0000We prove the unique solvability of the problem in the class of regular solutions by using\u0000the separation of variables in\u0000the hyperbolic part of the mixed domain, which yields the eigenvalue problems\u0000for one-dimensional and two-dimensional equations.\u0000Finding the eigenfunctions of the problems, we use\u0000the formula of the solution of the Cauchy–Goursat problem to construct a solution to the two-dimensional problem.\u0000In result, we find the solutions to eigenvalue problems for the three-dimensional equation in the hyperbolic part.\u0000Using the eigenfunctions and the gluing condition, we derive a nonlocal problem\u0000in the elliptic part of the mixed domain.\u0000To solve the problem in the elliptic part, we reformulate the problem\u0000in the cylindrical coordinate system and separating the variables leads to\u0000the eigenvalue problems for two ordinary differential equations.\u0000We prove a uniqueness theorem by using the completeness property\u0000of the systems of eigenfunctions of these problems and construct\u0000the solution to the problem as the sum of a double series.\u0000Justifying the uniform convergence of the series relies on some\u0000asymptotic estimates for the Bessel functions of the real and imaginary arguments.\u0000These estimates for each summand of the series made it possible to prove the convergence of\u0000the series and its derivatives up to the second order,\u0000as well as establish the existence theorem in the class of regular solutions.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169607","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}

{"title":"The Krein–Milman Theorem for Homogeneous Polynomials","authors":"Z. A. Kusraeva","doi":"10.1134/s0037446624030194","DOIUrl":"https://doi.org/10.1134/s0037446624030194","url":null,"abstract":"<p>This note addresses the problem of recovering a convex set of homogeneous polynomials from the subset of its extreme points,\u0000i.e., the justification of a polynomial version of the classical Krein–Milman theorem.\u0000Not much was done in this direction. The existing papers deal mostly with the description of the extreme points of\u0000the unit ball in the space of homogeneous polynomials in various special cases. Even in the case of linear operators,\u0000the classical Krein–Milman theorem does not work, since closed convex sets of operators turn out to be compact\u0000in some natural topology only in rather special cases. In the 1980s, a new approach to the study of the\u0000extremal structure of convex sets of linear operators was proposed on the basis of the\u0000theory of Kantorovich spaces, which led to an operator form of the Krein–Milman theorem.\u0000Combining the approach with the linearization method for homogeneous polynomials, we obtain a version of the\u0000Krein–Milman theorem for homogeneous polynomials.\u0000Namely, a weakly order bounded, operator convex, and pointwise order closed set <span>( Omega )</span> of\u0000homogeneous polynomials from an arbitrary vector space to a Kantorovich space is\u0000the pointwise order closure of the operator convex hull of the extreme\u0000points of <span>( Omega )</span>.\u0000We also establish Milman’s converse of the Krein–Milman theorem for homogeneous polynomials:\u0000The extreme points of the smallest operator convex pointwise order closed set\u0000including a given set <span>( Omega )</span>\u0000of homogeneous polynomials are pointwise uniform\u0000limits of appropriate nets of mixings in <span>( Omega )</span>.\u0000A mixing of a family of polynomials with the\u0000values in a Kantorovich space is understood as the (infinite) sum of these polynomials\u0000multiplied by pairwise disjoint order projections with sum the identity operator\u0000in the Kantorovich space.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169550","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}

{"title":"Quasi-Baer $ * $ -Ring Characterization of Leavitt Path Algebras","authors":"M. Ahmadi, A. Moussavi","doi":"10.1134/s0037446624030145","DOIUrl":"https://doi.org/10.1134/s0037446624030145","url":null,"abstract":"<p>We say that a graded ring (<span>( * )</span>-ring) <span>( R )</span> is a graded quasi-Baer ring (graded quasi-Baer <span>( * )</span>-ring)\u0000if, for each graded ideal <span>( I )</span> of <span>( R )</span>, the right annihilator of <span>( I )</span> is generated by a homogeneous idempotent (projection).\u0000We prove that a Leavitt path\u0000algebra is quasi-Baer (quasi-Baer <span>( * )</span>) if and only if it is graded quasi-Baer (graded quasi-Baer <span>( * )</span>).\u0000We show that a Leavitt path algebra is quasi-Baer (quasi-Baer <span>( * )</span>) if its zero component is quasi-Baer (quasi-Baer <span>( * )</span>).\u0000However, we give some example that showing that the converse implication fails.\u0000Finally, we characterize the Leavitt path algebras that are quasi-Baer <span>( * )</span>-rings\u0000in terms of the properties of the underlying graph.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169528","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}

{"title":"Recovering a Rapidly Oscillating Lower-Order Coefficient and a Source in a Hyperbolic Equation from Partial Asymptotics of a Solution","authors":"V. B. Levenshtam","doi":"10.1134/s0037446624030200","DOIUrl":"https://doi.org/10.1134/s0037446624030200","url":null,"abstract":"<p>We consider the Cauchy problem for a one-dimensional hyperbolic equation whose lower-order coefficient and right-hand side\u0000oscillate in time with a high frequency and the amplitude of the lower-order coefficient is small.\u0000Under study is the reconstruction of the cofactors of these rapidly oscillating functions independent\u0000of the space variable from a partial asymptotics of a solution at some point of the space.\u0000The classical theory of inverse problems examines the numerous problems of determining unknown sources, and coefficients without\u0000rapid oscillations for various evolutionary equations, where the exact solution\u0000to the direct problem appears in the additional overdetermination condition.\u0000Equations with rapidly oscillating data are often encountered in modeling the physical, chemical, and\u0000other processes that occur in media subjected to high-frequency electromagnetic, acoustic, vibrational, and others fields,\u0000which demonstrates the topicality of perturbation theory problems on the reconstruction of unknown functions\u0000in high-frequency equations.\u0000We give some nonclassical algorithm for solving such problems that lies at the junction of\u0000asymptotic methods and inverse problems. In this case the overdetermination condition involves\u0000a partial asymptotics of solution of a certain length\u0000rather than the exact solution.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169766","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}

{"title":"The Quasivariety $ {mathbf{S}}{mathbf{P}}(L_{6}) $ . II: A Duality Result","authors":"A. O. Basheyeva, M. V. Schwidefsky","doi":"10.1134/s0037446624030029","DOIUrl":"https://doi.org/10.1134/s0037446624030029","url":null,"abstract":"<p>We prove that the category of the complete bi-algebraic (0, 1)-lattices\u0000belonging\u0000to the quasivariety generated by a certain finite lattice with complete\u0000lattice homomorphisms, considered as a concrete category, is dually\u0000equivalent to\u0000the category of certain spaces with an additional structure.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169489","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}

{"title":"On Analogs of Fuhrmann’s Theorem on the Lobachevsky Plane","authors":"A. V. Kostin","doi":"10.1134/s0037446624030182","DOIUrl":"https://doi.org/10.1134/s0037446624030182","url":null,"abstract":"<p>According to Ptolemy’s theorem, the product of the lengths of the diagonals\u0000of a quadrilateral inscribed in a circle on the Euclidean plane equals the sum of the products of the lengths of opposite\u0000sides. This theorem has various generalizations. In one of the\u0000generalizations on the plane, a quadrilateral is replaced with an inscribed hexagon.\u0000In this event the lengths of the sides and long diagonals of an\u0000inscribed hexagon is called Ptolemy’s theorem for a hexagon or Fuhrmann’s theorem. Casey’s theorem\u0000is another generalization of Ptolemy’s theorem.\u0000Four circles tangent to this circle appear instead of four points lying on some fixed circle\u0000whilst the lengths of the sides and diagonals are replaced by the lengths of the segments\u0000tangent to the circles.\u0000If the curvature of the Lobachevsky plane is <span>( -1 )</span>, then in the analogs of the theorems of Ptolemy, Fuhrmann and Casey for\u0000the polygons inscribed in a circle or circles tangent to one circle, the lengths of the\u0000corresponding segments, divided by 2, will be under the signs of hyperbolic sines.\u0000In this paper, we prove some theorems that generalize Casey’s theorem and Fuhrmann’s theorem on the\u0000Lobachevsky plane. The theorems involve six circles\u0000tangent to some line of constant curvature.\u0000We prove the assertions that generalize these theorems for\u0000the lengths of tangent segments. If, in addition to the lengths of the segments of\u0000the geodesic tangents, we consider the lengths of the arcs of the tangent horocycles,\u0000then there is a correspondence between the Euclidean and hyperbolic relations, which\u0000can be most clearly demonstrated if we take a set of horocycles tangent to one line of constant\u0000curvature on the Lobachevsky plane. In this case, if the length of the segment of the geodesic tangent to\u0000the horocycles is <span>( t )</span>, then the length of the “horocyclic” tangent to them is equal to <span>( sinhfrac{t}{2} )</span>. Hence, if the geodesic tangents are connected by a “hyperbolic” relation, then the\u0000“horocyclic” tangents will be connected by the corresponding “Euclidean” relation.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169485","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}

{"title":"On Finite-Dimensional Simple Novikov Algebras of Characteristic  $ p $","authors":"V. N. Zhelyabin, A. S. Zakharov","doi":"10.1134/s0037446624030169","DOIUrl":"https://doi.org/10.1134/s0037446624030169","url":null,"abstract":"<p>Let <span>( N )</span> be a nonassociative finite-dimensional simple Novikov\u0000algebra over an algebraically closed field <span>( F )</span> of characteristic <span>( p&gt;0 )</span>. Then\u0000the right multiplication algebra <span>( R )</span>\u0000is a differential simple algebra\u0000with respect to some derivation <span>( d )</span>. The algebra <span>( N )</span> is isomorphic\u0000to a Novikov algebra <span>( (R,d,R_{x}) )</span>\u0000for some operator of right multiplication by <span>( x )</span> and multiplication\u0000is given by <span>( ucirc w=ud(w)+R_{x}uw )</span>.\u0000Moreover, the algebra <span>( R )</span> is a truncated polynomial algebra.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169614","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}

{"title":"On a Generalized Mizuhara Construction","authors":"A. P. Pozhidaev","doi":"10.1134/s0037446624030091","DOIUrl":"https://doi.org/10.1134/s0037446624030091","url":null,"abstract":"<p>We describe the ideals for Mizuhara extensions and find\u0000some necessary and sufficient conditions for the simplicity of\u0000the direct Mizuhara extension.\u0000Also, we study the Mizuhara construction\u0000for the matrix algebra and Burde algebras.\u0000We construct some various generalizations\u0000of the Mizuhara construction and exhibit some examples\u0000of the simple pre-Lie algebras that are obtained by this\u0000construction; in particular, we construct the simple Witt doubles\u0000<span>( {mathcal{A}}_{d} )</span> and <span>( {mathcal{W}}_{d}({mathcal{A}}) )</span> for a unital associative commutative\u0000algebra <span>( {mathcal{A}} )</span> with derivation <span>( d )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169552","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}

{"title":"Generalization of Artin’s Theorem on the Isotopy of Closed Braids. I","authors":"A. V. Malyutin","doi":"10.1134/s0037446624030078","DOIUrl":"https://doi.org/10.1134/s0037446624030078","url":null,"abstract":"<p>A classical theorem of braid theory, dating back to Artin’s work,\u0000says that\u0000two closed braids in a solid torus are ambient isotopic\u0000if and only if\u0000they represent the same conjugacy class of the braid group.\u0000This theorem can be reformulated\u0000in the framework of link theory\u0000without referring to the group structure.\u0000A link in a surface bundle over the circle is transversal\u0000whenever it covers the circle.\u0000In this terminology,\u0000Artin’s theorem states that\u0000in a solid torus trivially fibered over the circle\u0000transversal links are ambient isotopic\u0000if and only if\u0000they are isotopic in the class of transversal links.\u0000We generalize this result by proving that\u0000(in the piecewise linear category)\u0000transversal links in an arbitrary compact orientable <span>( 3 )</span>-manifold\u0000fibered over the circle with a compact fiber\u0000are ambient isotopic\u0000if and only if\u0000they are isotopic in the class of transversal links.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169529","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}