. In the work we consider a class of overdetermined system of second order partial differential equations for one unknown function involving one or two second order derivatives in the right hand side. We find the compatibility conditions and prove theorems on existence and uniqueness of solutions involving at most six arbitrary constants.
{"title":"On compatibility conditions and manilolds of solutions to one class of overdetermined systems of second order partial differential equations","authors":"R. Pirov","doi":"10.13108/2016-8-2-58","DOIUrl":"https://doi.org/10.13108/2016-8-2-58","url":null,"abstract":". In the work we consider a class of overdetermined system of second order partial differential equations for one unknown function involving one or two second order derivatives in the right hand side. We find the compatibility conditions and prove theorems on existence and uniqueness of solutions involving at most six arbitrary constants.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"5 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88819522","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}
In the work we consider a topological module P(a; b) of entire functions, which is the isomorphic image under the Fourier-Laplace transform of the Schwarz space of distributions with compact supports in a finite or infinite interval (a; b) ⊂ R. We prove that each weakly localizable module in P(a; b) is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in C∞(a; b) invariant w.r.t. the differentiation operator.
{"title":"On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis","authors":"N. Abuzyarova","doi":"10.13108/2016-8-3-8","DOIUrl":"https://doi.org/10.13108/2016-8-3-8","url":null,"abstract":"In the work we consider a topological module P(a; b) of entire functions, which is the isomorphic image under the Fourier-Laplace transform of the Schwarz space of distributions with compact supports in a finite or infinite interval (a; b) ⊂ R. We prove that each weakly localizable module in P(a; b) is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in C∞(a; b) invariant w.r.t. the differentiation operator.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"82 1","pages":"8-21"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87175209","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}
. In the present work we study a class of of nonlinear discrete Hammerstein-Volterra equations in a post-critical case. We prove the existence of a one-parametric family of positive solutions in space 𝑙 1 . We describe the set of parameters and establish the monotonic dependence of each solution both in a parameter and a corresponding index.
{"title":"One-parametric family of positive solutions for a class of nonlinear discrete Hammerstein-Volterra equations","authors":"Ermine Oganesovna Azizian, K. Khachatryan","doi":"10.13108/2016-8-1-13","DOIUrl":"https://doi.org/10.13108/2016-8-1-13","url":null,"abstract":". In the present work we study a class of of nonlinear discrete Hammerstein-Volterra equations in a post-critical case. We prove the existence of a one-parametric family of positive solutions in space 𝑙 1 . We describe the set of parameters and establish the monotonic dependence of each solution both in a parameter and a corresponding index.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"3 1","pages":"13-19"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75296166","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}
In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.
{"title":"On convergence of polynomial solutions of minimal surface","authors":"A. A. Klyachin, Irina Vladimirovna Truhliaeva","doi":"10.13108/2016-8-1-68","DOIUrl":"https://doi.org/10.13108/2016-8-1-68","url":null,"abstract":"In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"3 1","pages":"68-78"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76318823","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":"To the solution of a boundary value problem with a parameter for an ordinary differential equations","authors":"S. Aisagaliev, Zhanat Khafizovna Zhunusova","doi":"10.13108/2016-8-2-3","DOIUrl":"https://doi.org/10.13108/2016-8-2-3","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"31 1","pages":"3-13"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90613134","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}
In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.
{"title":"Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis","authors":"N. Abuzyarova","doi":"10.13108/2016-8-1-1","DOIUrl":"https://doi.org/10.13108/2016-8-1-1","url":null,"abstract":"In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"34 1","pages":"3-12"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79994357","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}
Ruslan Khalikovich Karimov, L. M. Kozhevnikova, A. A. Khadzhi
. We establish estimates characterizing the decay rate as | 𝑥 | → ∞ of solutions to the Dirichlet problems in unbounded domains for a certain class of elliptic equations with non-power nonlinearities.
{"title":"Behavior of solutions to elliptic equations with non-power nonlinearities in unbounded domains","authors":"Ruslan Khalikovich Karimov, L. M. Kozhevnikova, A. A. Khadzhi","doi":"10.13108/2016-8-3-95","DOIUrl":"https://doi.org/10.13108/2016-8-3-95","url":null,"abstract":". We establish estimates characterizing the decay rate as | 𝑥 | → ∞ of solutions to the Dirichlet problems in unbounded domains for a certain class of elliptic equations with non-power nonlinearities.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"75 1","pages":"95-108"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88187601","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}
Given an action of a discrete group G on a smooth compact manifold M with a boundary, we consider a class of operators generated by pseudodifferential operators on M and shift operators associated with the group action. For elliptic operators in this class, we obtain a classification up to stable homotopies and show that the group of stable homotopy classes of such problems is isomorphic to the K-group of the crossed product of the algebra of continuous functions on the cotangent bundle over the interior of the manifold and the group G acting on this algebra by automorphisms.
{"title":"Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary","authors":"A. Savin, B. Sternin","doi":"10.13108/2016-8-3-122","DOIUrl":"https://doi.org/10.13108/2016-8-3-122","url":null,"abstract":"Given an action of a discrete group G on a smooth compact manifold M with a boundary, we consider a class of operators generated by pseudodifferential operators on M and shift operators associated with the group action. For elliptic operators in this class, we obtain a classification up to stable homotopies and show that the group of stable homotopy classes of such problems is isomorphic to the K-group of the crossed product of the algebra of continuous functions on the cotangent bundle over the interior of the manifold and the group G acting on this algebra by automorphisms.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"15 1","pages":"122-129"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81196364","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}
A. I. Afonina, I. Kayumov, Alexej Nikolaevich Chuprunov
We consider n identical generalized schemes of allocating particles in cells. We study the probability of the event: for each generalized allocation scheme, there are at most r particles in each cell, where r is a given number. We obtain an asymptotic estimate for this probability and we consider the application of the obtained results to an antinoise coding.
{"title":"On the probability of the event: in $n$ generalized allocation schemes the volume of each cell does not exceed $r$","authors":"A. I. Afonina, I. Kayumov, Alexej Nikolaevich Chuprunov","doi":"10.13108/2016-8-2-14","DOIUrl":"https://doi.org/10.13108/2016-8-2-14","url":null,"abstract":"We consider n identical generalized schemes of allocating particles in cells. We study the probability of the event: for each generalized allocation scheme, there are at most r particles in each cell, where r is a given number. We obtain an asymptotic estimate for this probability and we consider the application of the obtained results to an antinoise coding.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"61 1","pages":"14-21"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72500293","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":"Symmetries and conservation laws for a two-component discrete potentiated Korteweg - de Vries equation","authors":"M. Poptsova, I. Habibullin","doi":"10.13108/2016-8-3-109","DOIUrl":"https://doi.org/10.13108/2016-8-3-109","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"248 1","pages":"109-121"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78172563","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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