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Admissibility and Unification in the Modal Logics Related to S4.2 与 S4.2 有关的模态逻辑中的可接受性和统一性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2024-01-01 DOI: 10.1134/s0037446624010154
{"title":"Admissibility and Unification in the Modal Logics Related to S4.2","authors":"","doi":"10.1134/s0037446624010154","DOIUrl":"https://doi.org/10.1134/s0037446624010154","url":null,"abstract":"<h3>Abstract</h3> <p>We study unification and admissibility for an infinite class of modal logics. Conditions superimposed to these logics are to be decidable, Kripke complete, and generated by the classes of rooted frames possessing the greatest clusters of states (in particular, these logics extend modal logic S4.2). Given such logic <span> <span>( L )</span> </span> and each formula <span> <span>( alpha )</span> </span> unifiable in <span> <span>( L )</span> </span>, we construct a unifier <span> <span>( sigma )</span> </span> for <span> <span>( alpha )</span> </span> in <span> <span>( L )</span> </span>, where <span> <span>( sigma )</span> </span> verifies admissibility in <span> <span>( L )</span> </span> of arbitrary inference rules <span> <span>( alpha/beta )</span> </span> with a switched-modality conclusions <span> <span>( beta )</span> </span> (i.e., <span> <span>( sigma )</span> </span> solves the admissibility problem for such rules).</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769981","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 the Existence of Radially Symmetric Solutions for the $ p $ -Laplace Equation with Strong Gradient Nonlinearities 强梯度非线性$ p $ -Laplace方程径向对称解的存在性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060162
Ar. S. Tersenov
{"title":"On the Existence of Radially Symmetric Solutions for the $ p $ -Laplace Equation with Strong Gradient Nonlinearities","authors":"Ar. S. Tersenov","doi":"10.1134/s0037446623060162","DOIUrl":"https://doi.org/10.1134/s0037446623060162","url":null,"abstract":"<p>We consider the Dirichlet problem for the <span>( p )</span>-Laplace equation\u0000in presence of a gradient not satisfying the Bernstein–Nagumo type condition.\u0000We define some class of gradient nonlinearities,\u0000for which we prove the existence of a radially symmetric solution with a Hölder continuous derivative.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"601 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507163","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
Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems 拟线性双曲型系统的有限时间镇定及指数稳定性
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060101
N. A. Lyul’ko
{"title":"Finite Time Stabilization to Zero and Exponential Stability of Quasilinear Hyperbolic Systems","authors":"N. A. Lyul’ko","doi":"10.1134/s0037446623060101","DOIUrl":"https://doi.org/10.1134/s0037446623060101","url":null,"abstract":"<p>We consider the asymptotic properties of solutions to the mixed problems\u0000for the quasilinear nonautonomous first-order hyperbolic systems with\u0000two variables in the case of smoothing boundary conditions.\u0000We prove that all smooth solutions to the problem for a decoupled hyperbolic system\u0000stabilize to zero in finite time independently of the initial data.\u0000If the hyperbolic system is coupled then we show that\u0000the zero solution to the quasilinear problem is exponentially stable.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"2 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138543770","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
Regularization of a Distribution Holomorphic in a Parameter 参数全纯分布的正则化
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060137
A. L. Pavlov
{"title":"Regularization of a Distribution Holomorphic in a Parameter","authors":"A. L. Pavlov","doi":"10.1134/s0037446623060137","DOIUrl":"https://doi.org/10.1134/s0037446623060137","url":null,"abstract":"<p>We give sufficient conditions for regularizing a distribution of the form\u0000<span>( a(sigma,lambda)f(lambda) )</span>,\u0000where\u0000<span>( f(lambda) )</span>\u0000is a distribution holomorphic in the parameter <span>( lambda )</span>,\u0000while <span>( a(sigma,lambda) )</span>\u0000is an infinitely differentiable function of <span>( sigma )</span>\u0000outside some closed set <span>( N )</span>\u0000with power singularities of derivatives on <span>( N )</span>\u0000and holomorphic in <span>( lambda )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"610 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507161","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 Locally Finite Subgroups in  $ operatorname{Lim}(N) $ $ operatorname{Lim}(N) $中的局部有限子群
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060150
N. M. Suchkov, A. A. Shlepkin
{"title":"On Locally Finite Subgroups in  $ operatorname{Lim}(N) $","authors":"N. M. Suchkov, A. A. Shlepkin","doi":"10.1134/s0037446623060150","DOIUrl":"https://doi.org/10.1134/s0037446623060150","url":null,"abstract":"<p>Let <span>( G )</span> be the group of all limited permutations of the naturals <span>( N )</span>.\u0000We prove that every countable locally finite group is isomorphic to a subgroup in <span>( G )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533202","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 the Virtual Potency of Automorphism Groups and Split Extensions 关于自同构群和分裂扩展的虚势
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060010
D. N. Azarov
{"title":"On the Virtual Potency of Automorphism Groups and Split Extensions","authors":"D. N. Azarov","doi":"10.1134/s0037446623060010","DOIUrl":"https://doi.org/10.1134/s0037446623060010","url":null,"abstract":"<p>We obtain some sufficient conditions for potency and virtual potency for automorphism\u0000groups and the split extensions of some groups. In particular, considering\u0000a finitely generated group <span>( G )</span> residually <span>( p )</span>-finite for every prime <span>( p )</span>,\u0000we prove that each split extension of <span>( G )</span> by a torsion-free potent group is a potent group,\u0000and if the abelianization rank of <span>( G )</span> is at most 2 then the automorphism group of <span>( G )</span> is virtually\u0000potent. As a corollary, we derive the necessary and sufficient conditions of virtual potency\u0000for certain generalized free products and HNN-extensions.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533183","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
The Quasi-Two-Dimensional Coefficient Inverse Problem for the Wave Equation in a Weakly Horizontally Inhomogeneous Medium with Memory 弱水平非均匀介质中波动方程的准二维系数反问题
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060186
Z. A. Akhmatov, Zh. D. Totieva
{"title":"The Quasi-Two-Dimensional Coefficient Inverse Problem for the Wave Equation in a Weakly Horizontally Inhomogeneous Medium with Memory","authors":"Z. A. Akhmatov, Zh. D. Totieva","doi":"10.1134/s0037446623060186","DOIUrl":"https://doi.org/10.1134/s0037446623060186","url":null,"abstract":"<p>We present the inverse problem of successive determination\u0000of the two unknowns that are a coefficient characterizing\u0000the properties of a medium with weakly horizontal inhomogeneity\u0000and the kernel of an integral operator describing the memory of the medium.\u0000The direct initial-boundary value problem involves the zero data\u0000and the Neumann boundary condition.\u0000The trace of the Fourier image of a solution to the direct problem\u0000on the boundary of the medium serves as additional information.\u0000Studying inverse problems, we assume that the unknown coefficient is expanded\u0000into an asymptotic series in powers of a small parameter.\u0000Also, we construct some method for finding\u0000the coefficient that accounts for the memory of the environment\u0000to within an error of order <span>( O(varepsilon^{2}) )</span>.\u0000At the first stage, we determine\u0000a solution to the direct problem in the zero approximation\u0000and the kernel of the integral operator,\u0000while the inverse problem reduces to an equivalent problem of\u0000solving the system of nonlinear Volterra integral equations of the second kind.\u0000At the second stage, we consider the kernel given and recover\u0000a solution to the direct problem in the first approximation\u0000and the unknown coefficient.\u0000In this case, the solution to the equivalent inverse problem agrees\u0000with a solution to the linear system of Volterra integral equations of the second kind.\u0000We prove some theorems on the unique local solvability of the inverse problems\u0000and present the results of numerical calculations of the kernel and the coefficient.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138533198","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
Almost Convergent 0-1-Sequences and Primes 几乎收敛的0-1序列与素数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060174
N. N. Avdeev
{"title":"Almost Convergent 0-1-Sequences and Primes","authors":"N. N. Avdeev","doi":"10.1134/s0037446623060174","DOIUrl":"https://doi.org/10.1134/s0037446623060174","url":null,"abstract":"<p>We study 0-1-sequences and establish the connection\u0000between the values of the upper and lower Sucheston functional\u0000on such sequence and the set of all possible divisors\u0000of the elements in the sequence support.\u0000If the union of the sets of all simple divisors\u0000of the elements in a 0-1-sequence support is finite then the\u0000sequence is almost convergent to zero. We study the 0-1-sequences\u0000whose support consists exactly of the multiples of\u0000the elements in a given set, and establish some\u0000necessary and sufficient conditions for the upper Sucheston\u0000functional to be equal to 1 on such sequence. We prove that there are\u0000infinitely many sequences at which the lower Sucheston functional\u0000is 1, and the lower Sucheston functional never vanishes at any of\u0000such sequences.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"619 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507157","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
The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups  $ PSL_{3}(2^{m}) $ and  $ PSU_{3}(q^{2}) $ 群$ PSL_{3}(2^{m}) $和$ PSU_{3}(q^{2}) $积为1的最小生成对合数
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s0037446623060058
R. I. Gvozdev, Ya. N. Nuzhin
{"title":"The Minimal Number of Generating Involutions Whose Product Is 1 for the Groups  $ PSL_{3}(2^{m}) $ and  $ PSU_{3}(q^{2}) $","authors":"R. I. Gvozdev, Ya. N. Nuzhin","doi":"10.1134/s0037446623060058","DOIUrl":"https://doi.org/10.1134/s0037446623060058","url":null,"abstract":"<p>Considering the groups <span>( PSL_{3}(2^{m}) )</span> and <span>( PSU_{3}(q^{2}) )</span>, we find the minimal number of generating\u0000involutions whose product is 1. This number is 7 for <span>( PSU_{3}(3^{2}) )</span> and 5 or 6\u0000in the remaining cases.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"613 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507160","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
$ E $ -Rings and Quotient Divisible Abelian Groups $ E $ -环与商可除阿贝尔群
IF 0.5 4区 数学
Siberian Mathematical Journal Pub Date : 2023-11-24 DOI: 10.1134/s003744662306006x
M. N. Zonov, E. A. Timoshenko
{"title":"$ E $ -Rings and Quotient Divisible Abelian Groups","authors":"M. N. Zonov, E. A. Timoshenko","doi":"10.1134/s003744662306006x","DOIUrl":"https://doi.org/10.1134/s003744662306006x","url":null,"abstract":"<p>Under study are the relations between <span>( E )</span>-rings and quotient divisible abelian groups.\u0000We obtain a criterion for the quotient divisibility of the additive group\u0000of an <span>( E )</span>-ring and give a negative solution to the Bowshell and Schultz problem\u0000about the quasidecompositions of <span>( E )</span>-rings.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"557 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507191","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
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