Pub Date : 2018-09-01DOI: 10.15393/j3.art.2018.5471
E. Tyurikov
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.
{"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}
Pub Date : 2018-09-01DOI: 10.15393/J3.ART.2018.5170
K. Malyutin, Alexander L. Gusev
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.
{"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}
Pub Date : 2018-09-01DOI: 10.15393/J3.ART.2018.5411
I. Kolesnikov
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.
P. P. Kufarev方法使Schwarz-Christoffel积分中参数的确定问题简化为常微分方程系统的连续解问题成为可能。B. G. Baibarin对Schwarz微分方程中参数(顶点和辅助参数的原像)的确定问题进行了推广，该问题的解是上半平面到圆弧多边形的全纯一元映射。本文给出了B. G. Baibarin所得到的Schwarz方程参数的微分方程组的初始条件。该方法用于解决某些特定映射的附件参数确定问题。
{"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}
Pub Date : 2018-09-01DOI: 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}
Pub Date : 2018-09-01DOI: 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}
Pub Date : 2018-09-01DOI: 10.15393/J3.ART.2018.5310
O. Krivosheeva, A. Krivosheev
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.
研究了指数单项式级数和在收敛域边界上的奇异点分布问题。研究了在边界弧上存在两端相距一定距离R的奇点时，多重序列Λ = {Λ k, nk}k=1对序列的影响。在这方面，考虑了序列的凝聚指数和它的点的相对多重性。证明了r -弧上级数和的奇点存在的必要条件是凝结指数的有限性和相对多重性为零。还证明了对于其中一个序列类Λ，这些条件给出了一个判据。这个结果的特殊情况是由J. Hadamard, E. Fabry, G. Pólya, W.H.J. Fuchs, P. Malliavin, V. Bernstein和A. F. Leont 'ev等人得到的关于Taylor和Dirichlet级数和的奇点的著名结果。
{"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}
Pub Date : 2018-09-01DOI: 10.15393/J3.ART.2018.5330
A. Losev, E. Mazepa
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".
研究了一类非齐次椭圆方程(∆u−c(x)u = g(x)解的存在性问题，其中c(x) > 0, g(x)是无界非紧黎曼流形M上的Hölder函数。本文提出了一种求任意非紧黎曼流形上椭圆型线性方程和拟线性方程边值问题解的方法。我们的技术本质上是基于E. A. Mazepa和S. A. Korol 'kov论文中的一种方法，该方法与函数和表示的等价类的介绍有关。我们研究了该方程在M上与具有相同增长“在无穷远处”的紧集B∧M外解的存在性之间的关系。
{"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}
Pub Date : 2018-08-15DOI: 10.15393/j3.art.2019.5210
S. Kalmykov, D. Karp
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.
{"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}
Pub Date : 2018-08-13DOI: 10.15393/j3.art.2018.5250
V. Kolokoltsov, M. Troeva
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.
{"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}
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