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Recursion operator for a system with non-rational Lax representation 具有非理性Lax表示的系统的递归算子
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-112
K. Zheltukhin
{"title":"Recursion operator for a system with non-rational Lax representation","authors":"K. Zheltukhin","doi":"10.13108/2016-8-2-112","DOIUrl":"https://doi.org/10.13108/2016-8-2-112","url":null,"abstract":". We consider a hydrodynamic type system, waterbag model, that admits a dispersionless Lax representation with a logarithmic Lax function. Using the Lax representation, we construct a recursion operator of the system. We note that the constructed recursion operator is not compatible with the natural Hamiltonian representation of the system.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"175 1","pages":"112-118"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78463150","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 solutions of second order elliptic equations in cylindrical domains 柱面上二阶椭圆方程的解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-131
A. V. Neklyudov
{"title":"On solutions of second order elliptic equations in cylindrical domains","authors":"A. V. Neklyudov","doi":"10.13108/2016-8-4-131","DOIUrl":"https://doi.org/10.13108/2016-8-4-131","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"19 1","pages":"131-143"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79290141","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
Representation of analytic functions 解析函数的表示
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-3
A. I. Abdulnagimov, A. Krivosheev
{"title":"Representation of analytic functions","authors":"A. I. Abdulnagimov, A. Krivosheev","doi":"10.13108/2016-8-4-3","DOIUrl":"https://doi.org/10.13108/2016-8-4-3","url":null,"abstract":". In this paper we consider exponential series with complex exponents, whose real and imaginary parts are integer. We prove that each function analytical in the vicinity of the closure of a bounded convex domain in the complex plain can be expanded into the above mentioned series and this series converges absolutely inside this domain and uniformly on compact subsets. The result is based on constructing a regular subset with a prescribed angular density of the sequence of all complex numbers, whose real and imaginary parts are integer.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"52 1","pages":"3-23"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78928491","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: 1
Asymptotics for the eigenvalues of a fourth order differential operator in a “degenerate” case 退化情况下四阶微分算子特征值的渐近性
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-79
Kh. K. Ishkin, Khairulla Khabibullovich Murtazin
{"title":"Asymptotics for the eigenvalues of a fourth order differential operator in a “degenerate” case","authors":"Kh. K. Ishkin, Khairulla Khabibullovich Murtazin","doi":"10.13108/2016-8-3-79","DOIUrl":"https://doi.org/10.13108/2016-8-3-79","url":null,"abstract":"In the paper we consider the operator L in L2[0,+∞) generated by the differential expression L(y) = y(4) − 2(p(x)y′)′ + q(x)y and boundary conditions y(0) = y′′(0) = 0 in the “degenerate” case, when the roots of associated characteristic equation has different growth rate at the infinity. Assuming a power growth for functions p and q, under some additional conditions of smoothness and regularity kind, we obtain an asymptotic equation for the spectrum allowing us to write out several first terms in the asymptotic expansion for the eigenvalues of the operator L.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"7 1","pages":"79-94"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82511363","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: 1
Degenerate fractional differential equations in locally convex spaces with a $sigma$-regular pair of operators 用正则算子对退化局部凸空间中的分数阶微分方程
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-98
M. Kostic, V. Fedorov
{"title":"Degenerate fractional differential equations in locally convex spaces with a $sigma$-regular pair of operators","authors":"M. Kostic, V. Fedorov","doi":"10.13108/2016-8-4-98","DOIUrl":"https://doi.org/10.13108/2016-8-4-98","url":null,"abstract":"We consider a degenerate fractional order differential equationDα t Lu(t) = Mu(t) in a Hausdorff sequentially complete locally convex space. Under the p-regularity of the operator pair (L,M), we find the phase space of the equation and the family of its resolving operators. We show that the identity image of the latter coincides with the phase space. We prove an unique solvability theorem and obtain the form of the solution to the Cauchy problem for the corresponding inhomogeneous equation. We give an example of application the obtained abstract results to studying the solvability of the initial boundary value problems for the partial differential equations involving entire functions on an unbounded operator in a Banach space, which is a specially constructed Frechét space. It allows us to consider, for instance, a periodic in a spatial variable x problem for the equation with a shift along x and with a fractional order derivative with respect to time t.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"2007 1","pages":"98-110"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89513257","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: 12
Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula 二维球面上拉普拉斯算子解的性质及轨迹公式
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-22
A. Atnagulov, V. Sadovnichii, Z. Fazullin
{"title":"Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula","authors":"A. Atnagulov, V. Sadovnichii, Z. Fazullin","doi":"10.13108/2016-8-3-22","DOIUrl":"https://doi.org/10.13108/2016-8-3-22","url":null,"abstract":"In the work we study the properties of the resolvent of the Laplace-Beltrami operator on a two-dimensional sphere S2. We obtain the regularized trace formula for the Laplace-Beltrami operator perturbed by the operator of multiplication by a function in W 1 2 (S 2).","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"27 1","pages":"22-40"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73507464","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: 5
On unconditional exponential bases in weak weighted spaces on segment 节上弱加权空间中的无条件指数基
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-88
K. P. Isaev, A. Lutsenko, R. S. Yulmukhametov
{"title":"On unconditional exponential bases in weak weighted spaces on segment","authors":"K. P. Isaev, A. Lutsenko, R. S. Yulmukhametov","doi":"10.13108/2016-8-4-88","DOIUrl":"https://doi.org/10.13108/2016-8-4-88","url":null,"abstract":"We show that the existence of unconditional exponential bases is not determined by the growth characteristics of a weight function. In order to do this, we construct examples of convex weights with arbitrarily slow growth near the boundary such that unconditional exponential bases do not exist in the corresponding space.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"14 1","pages":"88-97"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84267877","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
The problem of Steklov type in a half-cylinder with a small cavity 斯特克洛夫型在半圆柱小腔中的问题
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-62
D. B. Davletov, D. V. Kozhevnikov
{"title":"The problem of Steklov type in a half-cylinder with a small cavity","authors":"D. B. Davletov, D. V. Kozhevnikov","doi":"10.13108/2016-8-4-62","DOIUrl":"https://doi.org/10.13108/2016-8-4-62","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"30 1 1","pages":"62-87"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85528555","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 solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator 带分数阶边界算子的非齐次多谐方程边值问题的可解性
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-155
B. Turmetov
{"title":"On solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator","authors":"B. Turmetov","doi":"10.13108/2016-8-3-155","DOIUrl":"https://doi.org/10.13108/2016-8-3-155","url":null,"abstract":". In this paper we study the solvability of one boundary value problem for an inhomogeneous polyharmonic equation. As a boundary operator, we consider a differen-tiation operator of fractional order in the Hadamard sense. The considered problem is a generalization of the known Neumann problem.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"8 1","pages":"155-170"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82029911","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 resolvent of multi-dimensional operators with frequent alternation of boundary conditions: Critical case 边界条件频繁变换的多维算子的求解:临界情况
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-65
T. F. Sharapov
{"title":"On resolvent of multi-dimensional operators with frequent alternation of boundary conditions: Critical case","authors":"T. F. Sharapov","doi":"10.13108/2016-8-2-65","DOIUrl":"https://doi.org/10.13108/2016-8-2-65","url":null,"abstract":"We consider an elliptic operator in a multi-dimensional domain with frequent alternation of Dirichlet and Robin conditions. We study the case, when the homogenized operator has Robin condition with an additional coefficient generated by the geometry of the alternation. We prove the norm resolvent convergence of the perturbed operator to the homogenized one and obtain the estimate for the convergence rate. We construct the complete asymptotic expansion for the resolvent in the case, when it acts on sufficiently smooth functions.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75161094","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: 2
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