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On applications of Faà-di-Bruno formula 论Faà-di-Bruno公式的应用
IF 0.5
Ufa Mathematical Journal Pub Date : 2017-01-01 DOI: 10.13108/2017-9-3-131
A. Shabat, Magomed Khochalaevich Efendiev
{"title":"On applications of Faà-di-Bruno formula","authors":"A. Shabat, Magomed Khochalaevich Efendiev","doi":"10.13108/2017-9-3-131","DOIUrl":"https://doi.org/10.13108/2017-9-3-131","url":null,"abstract":"In the work we construct two modifications of the classical Faà-di-Bruno formula. We consider the applications of these formulae in the integrability theory for nonlinear partial differential equations. We discuss the problem on integration by parts in the Gelfand-Olver-Sanders formal variational calculus.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"22 1","pages":"131-136"},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90851667","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: 4
G{aa}rding inequality for higher order elliptic operators with a non-power degeneration and its applications 非幂退化高阶椭圆算子的G{aa}定不等式及其应用
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-51
S. A. Iskhokov, M. G. Gadoev, I. Yakushev
{"title":"G{aa}rding inequality for higher order elliptic operators with a non-power degeneration and its applications","authors":"S. A. Iskhokov, M. G. Gadoev, I. Yakushev","doi":"10.13108/2016-8-1-51","DOIUrl":"https://doi.org/10.13108/2016-8-1-51","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"99 1","pages":"51-67"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85904340","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
Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential 第三painlev<s:1>方程和具有莫尔斯势的非平稳时间Schrödinger方程的可积性的量子方面
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-136
B. Suleimanov
{"title":"Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential","authors":"B. Suleimanov","doi":"10.13108/2016-8-3-136","DOIUrl":"https://doi.org/10.13108/2016-8-3-136","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"24 1","pages":"136-154"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82984614","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: 4
On Frech`{e}t differentiability of cost functional in optimal control of coefficients of elliptic equations 椭圆方程系数最优控制中代价泛函的french ' {e}t可微性
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-79
A. Manapova, F. Lubyshev
{"title":"On Frech`{e}t differentiability of cost functional in optimal control of coefficients of elliptic equations","authors":"A. Manapova, F. Lubyshev","doi":"10.13108/2016-8-1-79","DOIUrl":"https://doi.org/10.13108/2016-8-1-79","url":null,"abstract":"In the work we consider nonlinear optimal control problems for semi-linear elliptic equations with discontinuous data and solutions (states) with controls in the boundary conditions of conjugation of heterogeneous media and in the right hand side of the state equation. We prove the differentiability and Lipshitz continuity for the grid analogue of the cost functional for extremum problems.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"79-96"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90178342","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
The asymptotic formulae in the problem on constructing hyperbolicity and stability regions of dynamical systems 构造动力系统双曲域和稳定域问题的渐近公式
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-58
L. S. Ibragimova, I. Mustafina, M. Yumagulov
{"title":"The asymptotic formulae in the problem on constructing hyperbolicity and stability regions of dynamical systems","authors":"L. S. Ibragimova, I. Mustafina, M. Yumagulov","doi":"10.13108/2016-8-3-58","DOIUrl":"https://doi.org/10.13108/2016-8-3-58","url":null,"abstract":"The paper proposes a new general method allowing us to study the problem on constructing hyperbolicity and stability regions for nonlinear dynamical systems. The method is based on a modification of the method by M. Rozo for studying the stability of linear systems with periodic coefficients depending on a small parameter and on the asymptotic formulae in the perturbation theory of linear operators. We obtain approximate formulae describing the boundary of hyperbolicity and stability regions. As an example, we provide the scheme for constructing the stability regions for Mathieu equation.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"58-78"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83036813","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: 4
Darboux transformations in the inverse scattering problem 逆散射问题中的达布变换
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-42
Mukhtar Shamil'evich Badakhov, A. Shabat
{"title":"Darboux transformations in the inverse scattering problem","authors":"Mukhtar Shamil'evich Badakhov, A. Shabat","doi":"10.13108/2016-8-4-42","DOIUrl":"https://doi.org/10.13108/2016-8-4-42","url":null,"abstract":"As it is known, Darboux transformations play a key role in applications in ISP. In the paper we expose the theory of such transformations for the Schrödinger equations with compactly supported potential, which are not necessarily smooth. We study a new class of transformations connected with the zeroes of the reflection coefficient located at conjugated points in the complex plane.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"47 1","pages":"42-51"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88184319","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: 3
Some results on generalized relative orders of meromorphic functions 关于亚纯函数的广义相对阶的一些结果
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-95
D. Kumar, Biswas Tanmay, Das Pranab
{"title":"Some results on generalized relative orders of meromorphic functions","authors":"D. Kumar, Biswas Tanmay, Das Pranab","doi":"10.13108/2016-8-2-95","DOIUrl":"https://doi.org/10.13108/2016-8-2-95","url":null,"abstract":"In this paper we discuss some growth rates of compositions of entire and meromorphic functions on the base of generalized relative order and generalized relative lower order of meromorphic functions with respect to entire functions.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"95-103"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89433750","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: 3
On the expansion of a meromorphic function in partial fractions 亚纯函数在部分分式中的展开式
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-104
Maergoiz Lev Sergeevich
{"title":"On the expansion of a meromorphic function in partial fractions","authors":"Maergoiz Lev Sergeevich","doi":"10.13108/2016-8-2-104","DOIUrl":"https://doi.org/10.13108/2016-8-2-104","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"41 1","pages":"104-111"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76580879","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
On decay of solution to linear parabolic equation with double degeneracy 双简并线性抛物型方程解的衰减
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-35
V. F. Vil'danova
{"title":"On decay of solution to linear parabolic equation with double degeneracy","authors":"V. F. Vil'danova","doi":"10.13108/2016-8-1-35","DOIUrl":"https://doi.org/10.13108/2016-8-1-35","url":null,"abstract":". We obtain the upper bound for the decay rate of the solution to the Dirichlet initial boundary value problem for a linear parabolic second order equation with a double degeneracy 𝜇 ( 𝑥 ) 𝑢 𝑡 = ( 𝜌 ( 𝑥 ) 𝑎 𝑖𝑗 ( 𝑡, 𝑥 ) 𝑢 𝑥 𝑖 ) 𝑥 𝑗 in an unbounded domain. For a wide class of revolution domains we prove a lower bound. We adduce the examples showing that the upper and lower bounds are in some sense sharp. We prove the unique solvability of the problem in an unbounded domain by Galerkin’s approximations method.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"50 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78270630","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
Inverting of generalized Riemann - Liouville operator by means of integral Laplace transform 广义Riemann - Liouville算子的积分拉普拉斯变换反演
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-41
I. I. Bavrin, O. Yaremko
{"title":"Inverting of generalized Riemann - Liouville operator by means of integral Laplace transform","authors":"I. I. Bavrin, O. Yaremko","doi":"10.13108/2016-8-3-41","DOIUrl":"https://doi.org/10.13108/2016-8-3-41","url":null,"abstract":"We employ the integral Laplace transform to invert the generalized RiemannLiouville operator in a closed form. We establish that the inverse generalized RiemannLiouville operator is a differential or integral-differential operator. We establish a relation between Riemann-Liouville operator and Temlyakov-Bavrin operator. We provide new examples of generalized Riemann-Liouville operator.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"19 1","pages":"41-48"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83778492","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
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