Andriy Yaroslavovych Khrystiyanyn, O. S. Vyshyns'kyi
{"title":"Growth regularity for the arguments of meromorphic in $mathbb Csetminus{0}$ functions of completely regular growth","authors":"Andriy Yaroslavovych Khrystiyanyn, O. S. Vyshyns'kyi","doi":"10.13108/2017-9-1-123","DOIUrl":"https://doi.org/10.13108/2017-9-1-123","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87421331","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}
We study the solvability of the inverse problems on finding a solution u(x, t) and an unknown coefficient c for a telegraph equation utt −Δu+ cu = f(x, t). We prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.
研究了电报方程utt−Δu+ cu = f(x, t)的u(x, t)和未知系数c的反问题的可解性，证明了正则解的存在性定理。问题的特点是所考虑的一类方程存在新的超定条件。
{"title":"Determination of parameters in telegraph equation","authors":"A. I. Kozhanov, R. R. Safiullova","doi":"10.13108/2017-9-1-62","DOIUrl":"https://doi.org/10.13108/2017-9-1-62","url":null,"abstract":"We study the solvability of the inverse problems on finding a solution u(x, t) and an unknown coefficient c for a telegraph equation utt −Δu+ cu = f(x, t). We prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78927869","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":"Representation of functions in locally convex subspaces of $A^infty (D)$ by series of exponentials","authors":"K. P. Isaev, K. Trounov, R. S. Yulmukhametov","doi":"10.13108/2017-9-3-48","DOIUrl":"https://doi.org/10.13108/2017-9-3-48","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89470976","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 operators generated by the second order matrix linear symmetric quasi-differential expression on the set [1 , + ∞ ), where 𝑃 − 1 ( 𝑥 ), 𝑄 ( 𝑥 ) are Hermitian matrix functions and 𝑅 ( 𝑥 ) is a complex matrix function of order 𝑛 with entries 𝑝 𝑖𝑗 ( 𝑥 ) , 𝑞 𝑖𝑗 ( 𝑥 ) , 𝑟 𝑖𝑗 ( 𝑥 ) ∈ 𝐿 1 𝑙𝑜𝑐 [1 , + ∞ ) ( 𝑖, 𝑗 = 1 , 2 , . . . , 𝑛 ). We describe the minimal closed symmetric operator 𝐿 0 generated by this expression in the Hilbert space 𝐿 2 𝑛 [1 , + ∞ ). For this operator we prove an analogue of the Orlov’s theorem on the deficiency index of linear scalar differential operators.
{"title":"On deficiency index for some second order vector differential operators","authors":"I. N. Braeutigam, K. A. Mirzoev, T. Safonova","doi":"10.13108/2017-9-1-18","DOIUrl":"https://doi.org/10.13108/2017-9-1-18","url":null,"abstract":". In this paper we consider the operators generated by the second order matrix linear symmetric quasi-differential expression on the set [1 , + ∞ ), where 𝑃 − 1 ( 𝑥 ), 𝑄 ( 𝑥 ) are Hermitian matrix functions and 𝑅 ( 𝑥 ) is a complex matrix function of order 𝑛 with entries 𝑝 𝑖𝑗 ( 𝑥 ) , 𝑞 𝑖𝑗 ( 𝑥 ) , 𝑟 𝑖𝑗 ( 𝑥 ) ∈ 𝐿 1 𝑙𝑜𝑐 [1 , + ∞ ) ( 𝑖, 𝑗 = 1 , 2 , . . . , 𝑛 ). We describe the minimal closed symmetric operator 𝐿 0 generated by this expression in the Hilbert space 𝐿 2 𝑛 [1 , + ∞ ). For this operator we prove an analogue of the Orlov’s theorem on the deficiency index of linear scalar differential operators.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82364494","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":"On one Leontiev-Levin theorem","authors":"A. Krivosheev, A. F. Kuzhaev","doi":"10.13108/2017-9-3-87","DOIUrl":"https://doi.org/10.13108/2017-9-3-87","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85581186","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":"On continuity and differentiability of the maximum values of functions","authors":"V. Klyachin","doi":"10.13108/2017-9-4-54","DOIUrl":"https://doi.org/10.13108/2017-9-4-54","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90208463","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}
. The paper is devoted to developing a geometric approach to the theory of approximate equations (including ODEs and PDEs) and their symmetries. We introduce dual Lie algebras, manifolds over dual numbers and dual Lie group. We describe some constructions applied for these objects. On the basis of these constructions, we show how one can formulate basic concepts and methods in the theory of approximate equations and their symmetries. The proofs of many general results here can be obtained almost immediately from classical ones, unlike the methods used for studying the approximate equations.
{"title":"On geometry of solutions to approximate equations and their symmetries","authors":"V. Gorbatsevich","doi":"10.13108/2017-9-2-40","DOIUrl":"https://doi.org/10.13108/2017-9-2-40","url":null,"abstract":". The paper is devoted to developing a geometric approach to the theory of approximate equations (including ODEs and PDEs) and their symmetries. We introduce dual Lie algebras, manifolds over dual numbers and dual Lie group. We describe some constructions applied for these objects. On the basis of these constructions, we show how one can formulate basic concepts and methods in the theory of approximate equations and their symmetries. The proofs of many general results here can be obtained almost immediately from classical ones, unlike the methods used for studying the approximate equations.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81935770","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":"Analogue of Tricomi problem for characteristically loaded hyperbolic-parabolic equation with variable coefficients","authors":"K. U. Khubiev","doi":"10.13108/2017-9-2-92","DOIUrl":"https://doi.org/10.13108/2017-9-2-92","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88517571","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 Q-homeomorphisms w.r.t p-modulus on the complex plane as p > 2. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.
{"title":"Lower bounds for the area of the image of a circle","authors":"B. Klishchuk, R. Salimov","doi":"10.13108/2017-9-2-55","DOIUrl":"https://doi.org/10.13108/2017-9-2-55","url":null,"abstract":"In the work we consider Q-homeomorphisms w.r.t p-modulus on the complex plane as p > 2. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82814463","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":"“Quantizations” of isomonodromic Hamilton system $H^{frac{7}{2}+1}$","authors":"V. A. Pavlenko, B. Suleimanov","doi":"10.13108/2017-9-4-97","DOIUrl":"https://doi.org/10.13108/2017-9-4-97","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73226279","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：