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ONE CASE OF EXTENDED BOUNDARY VALUE PROBLEM OF THE MEMBRANE THEORY OF CONVEX SHELLS BY I. N. VEKUA i. n. vekua关于凸壳膜理论扩展边值问题的一个例子
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/j3.art.2018.5471
E. Tyurikov
{"title":"ONE CASE OF EXTENDED BOUNDARY VALUE PROBLEM OF THE MEMBRANE THEORY OF CONVEX SHELLS BY I. N. VEKUA","authors":"E. Tyurikov","doi":"10.15393/j3.art.2018.5471","DOIUrl":"https://doi.org/10.15393/j3.art.2018.5471","url":null,"abstract":"In this paper we obtain results related to the membrane theory of convex shells with piecewise smooth boundary of its median surface. Within this theory we study the problem of realisation of the momentless tense state of equilibrium of the thin elastic shell, the median surface of which is a part of an ovaloid of the strictly positive Gaussian curvature. Development of this theory is based on the usage of generalized analytic functions and is needed for the extended statement of the basic boundary problem. We provide such a further development for a shell with a simply connected median surface using the Riemann–Gilbert special boundary condition. In the paper we identify surface classes for which the index of the corresponding discontinuous boundary condition is efficiently calculated and find sufficent boundary conditions for quasi-correctness of the basic boundary problem in the geometric form.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"128 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76397926","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
The interpolation problem in the spaces of analytical functions of finite order in the half-plane 半平面上有限阶解析函数空间内插问题
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/J3.ART.2018.5170
K. Malyutin, Alexander L. Gusev
{"title":"The interpolation problem in the spaces of analytical functions of finite order in the half-plane","authors":"K. Malyutin, Alexander L. Gusev","doi":"10.15393/J3.ART.2018.5170","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5170","url":null,"abstract":"The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ > 1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"75 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86417363","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 problem of determining parameters in the Schwarz equation 关于Schwarz方程中参数的确定问题
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/J3.ART.2018.5411
I. Kolesnikov
{"title":"On the problem of determining parameters in the Schwarz equation","authors":"I. Kolesnikov","doi":"10.15393/J3.ART.2018.5411","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5411","url":null,"abstract":"P. P. Kufarev’s method makes it possible to reduce the problem of determining the parameters in the Schwarz-Christoffel integral to the problem of successive solutions of systems of ordinary differential equations. B. G. Baibarin obtained a generalization of this method for the problem of determining parameters (preimages of vertices and accessory parameters) in the Schwarz differential equation, whose solution is a holomorphic univalent mapping from the upper half-plane onto a circular-arc polygon. This paper specifies the initial condition for the system of differential equations for the parameters of the Schwarz equation obtained by B. G. Baibarin. This method is used to solve the problem of determining the accessory parameters for some particular mappings.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87780506","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: 6
On entire functions with given asymptotic behavior 具有给定渐近性质的整个函数
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/J3.ART.2018.5451
K. P. Isaev
{"title":"On entire functions with given asymptotic behavior","authors":"K. P. Isaev","doi":"10.15393/J3.ART.2018.5451","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5451","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"47 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86894780","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
On the heat integral identity for unbounded functions 无界函数的热积分恒等式
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/j3.art.2018.5470
A. Biryuk, A. Svidlov, E. Silchenko
{"title":"On the heat integral identity for unbounded functions","authors":"A. Biryuk, A. Svidlov, E. Silchenko","doi":"10.15393/j3.art.2018.5470","DOIUrl":"https://doi.org/10.15393/j3.art.2018.5470","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75160400","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
SINGULAR POINTS FOR THE SUM OF A SERIES OF EXPONENTIAL MONOMIALS 一系列指数单项式和的奇异点
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/J3.ART.2018.5310
O. Krivosheeva, A. Krivosheev
{"title":"SINGULAR POINTS FOR THE SUM OF A SERIES OF EXPONENTIAL MONOMIALS","authors":"O. Krivosheeva, A. Krivosheev","doi":"10.15393/J3.ART.2018.5310","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5310","url":null,"abstract":"A problem of distribution of singular points for sums of series of exponential monomials on the boundary of its convergence domain is studied. The influence of a multiple sequence Λ = {λk, nk}k=1 of the series in the presence of singular points on the arc of the boundary, the ends of which are located at a certain distance R from each other, is investigated. In this regard, the condensation indices of the sequence and the relative multiplicity of its points are considered. It is proved that the finiteness of the condensation index and the zero relative multiplicity are necessary for the existence of singular points of the series sum on the R-arc. It is also proved that for one of the sequence classes Λ, these conditions give a criterion. Special cases of this result are the well-known results for the singular points of the sums of the Taylor and Dirichlet series, obtained by J. Hadamard, E. Fabry, G. Pólya, W.H.J. Fuchs, P. Malliavin, V. Bernstein and A. F. Leont’ev, etc.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85025756","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
Beltrami equations revisited: Marcinkiewicz exponents and Painleve-type theorem 重新审视贝尔特拉米方程:Marcinkiewicz指数和painleve型定理
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/j3.art.2018.5431
D. Katz
{"title":"Beltrami equations revisited: Marcinkiewicz exponents and Painleve-type theorem","authors":"D. Katz","doi":"10.15393/j3.art.2018.5431","DOIUrl":"https://doi.org/10.15393/j3.art.2018.5431","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"28 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83598643","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
On solvability of the boundary value problems for the inhomogeneous elliptic equations on noncompact Riemannian manifolds 非紧黎曼流形上非齐次椭圆方程边值问题的可解性
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-09-01 DOI: 10.15393/J3.ART.2018.5330
A. Losev, E. Mazepa
{"title":"On solvability of the boundary value problems for the inhomogeneous elliptic equations on noncompact Riemannian manifolds","authors":"A. Losev, E. Mazepa","doi":"10.15393/J3.ART.2018.5330","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5330","url":null,"abstract":"We study questions of existence and belonging to a given functional class of solutions of the inhomogeneous elliptic equations ∆u − c(x)u = g(x), where c(x) > 0, g(x) are Hölder fuctions on a noncompact Riemannian manifold M without boundary. In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique is essentially based on an approach from the papers by E. A. Mazepa and S. A. Korol’kov connected with an introduction of equivalency classes of functions and representations. We investigate the relationship between the existence of solutions of this equation on M and outside some compact set B ⊂ M with the same growth \"at infinity\".","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"92 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84054150","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
Inequalities for some basic hypergeometric functions 一些基本超几何函数的不等式
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-08-15 DOI: 10.15393/j3.art.2019.5210
S. Kalmykov, D. Karp
{"title":"Inequalities for some basic hypergeometric functions","authors":"S. Kalmykov, D. Karp","doi":"10.15393/j3.art.2019.5210","DOIUrl":"https://doi.org/10.15393/j3.art.2019.5210","url":null,"abstract":"We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"41 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75510988","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
Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes 类稳定过程生成McKean-Vlasov型SPDEs的正则性和灵敏度
IF 0.6
Problemy Analiza-Issues of Analysis Pub Date : 2018-08-13 DOI: 10.15393/j3.art.2018.5250
V. Kolokoltsov, M. Troeva
{"title":"Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes","authors":"V. Kolokoltsov, M. Troeva","doi":"10.15393/j3.art.2018.5250","DOIUrl":"https://doi.org/10.15393/j3.art.2018.5250","url":null,"abstract":"In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86284580","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
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