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Transactions of A Razmadze Mathematical Institute最新文献

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Estimation of multianisotropic kernels and their application to the embedding theorems 多各向异性核的估计及其在嵌入定理中的应用
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-04-01 DOI: 10.1016/j.trmi.2016.12.005
Garnik Karapetyan, Mikael Arakelian
{"title":"Estimation of multianisotropic kernels and their application to the embedding theorems","authors":"Garnik Karapetyan,&nbsp;Mikael Arakelian","doi":"10.1016/j.trmi.2016.12.005","DOIUrl":"10.1016/j.trmi.2016.12.005","url":null,"abstract":"<div><p>In the current paper we consider an integral representation of functions and embedding theorems of multianisotropic Sobolev spaces in the three-dimensional case when the completely regular polyhedron has an arbitrary number of anisotropic vertices. This work generalizes results obtained in Karapetyan (in press) and Karapetyan (2016). Particularly, in Karapetyan (in press) the two-dimensional case was fully solved and in Karapetyan (2016) analogous results were obtained for the case of one anisotropic vertex. The problem takes root from various works of Sobolev, particularly, Sobolev (1938) and Sobolev (0000) <span>[4]</span>, <span>[5]</span>. Related results were obtained by many authors and can be found in Besov et al. (1967), Reshetnyak (1971), Smith (1961), Nikolsky (0000) and Il’in (1967) <span>[6]</span>, <span>[7]</span>, <span>[8]</span>, <span>[9]</span>, <span>[10]</span>. The monograph (Besov, 1978) contains an overview of the problem. The results obtained in this paper are based on a generalization of regularization by a quasi-homogeneous polynomial (see Uspenskii (1972) and Karapetyan (1990) <span>[11]</span>, <span>[12]</span>).</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.12.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55644192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Elastoplastic problem for a plate with partially unknown boundary 边界部分未知板的弹塑性问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-04-01 DOI: 10.1016/j.trmi.2017.01.004
Zurab Abashidze
{"title":"Elastoplastic problem for a plate with partially unknown boundary","authors":"Zurab Abashidze","doi":"10.1016/j.trmi.2017.01.004","DOIUrl":"10.1016/j.trmi.2017.01.004","url":null,"abstract":"<div><p>In this paper there is considered the Elastoplastic problem for infinite plate, that is weakened by two identical square holes. The boundaries of the holes are partially unknown contours. The plate is in a stressed state, a region of plasticity contains only unknown parts of holes contours and does not spread inside of the plate. Applying the theory of functions of a complex variable and the conformal mapping theory the problem is reduced to a boundary value problem of the analytic function theory and the solution of this problem is obtained, the unknown parts of the holes contours are defined.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.01.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47243863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Duality of fully measurable grand Lebesgue space 完全可测大勒贝格空间的对偶性
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-04-01 DOI: 10.1016/j.trmi.2016.12.003
Pankaj Jain , Monika Singh , Arun Pal Singh
{"title":"Duality of fully measurable grand Lebesgue space","authors":"Pankaj Jain ,&nbsp;Monika Singh ,&nbsp;Arun Pal Singh","doi":"10.1016/j.trmi.2016.12.003","DOIUrl":"10.1016/j.trmi.2016.12.003","url":null,"abstract":"<div><p>In this paper, we prove a Hölder’s type inequality for fully measurable grand Lebesgue spaces, which involves the notion of fully measurable small Lebesgue spaces. It is proved that these spaces are non-reflexive rearrangement invariant Banach function spaces. Moreover, under certain continuity assumptions, along with several properties of fully measurable small Lebesgue spaces, we establish Levi’s theorem for monotone convergence and that grand and small spaces are associated to each other.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.12.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43749079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Stochastic differential equations in a Banach space driven by the cylindrical Wiener process 圆柱维纳过程驱动的巴拿赫空间中的随机微分方程
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-04-01 DOI: 10.1016/j.trmi.2016.10.003
Badri Mamporia
{"title":"Stochastic differential equations in a Banach space driven by the cylindrical Wiener process","authors":"Badri Mamporia","doi":"10.1016/j.trmi.2016.10.003","DOIUrl":"10.1016/j.trmi.2016.10.003","url":null,"abstract":"<div><p>Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of <span><math><mi>p</mi></math></span>-absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are given.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.10.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44721759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp weighted bounds for the Hilbert transform of odd and even functions 奇偶函数希尔伯特变换的尖锐加权界
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-04-01 DOI: 10.1016/j.trmi.2016.07.005
Jérôme Gilles , Alexander Meskhi
{"title":"Sharp weighted bounds for the Hilbert transform of odd and even functions","authors":"Jérôme Gilles ,&nbsp;Alexander Meskhi","doi":"10.1016/j.trmi.2016.07.005","DOIUrl":"10.1016/j.trmi.2016.07.005","url":null,"abstract":"<div><p>Our aim is to establish sharp weighted bounds for the Hilbert transform of odd and even functions in terms of the mixed type characteristics of weights. These bounds involve <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> type characteristics. As a consequence, we obtain weighted bounds in terms of so-called Andersen–Muckenhoupt type characteristics.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.07.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45084548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unilateral contact problems with a friction 带有摩擦的单侧接触问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI: 10.1016/j.trmi.2016.09.003
Avtandil Gachechiladze, Roland Gachechiladze
{"title":"Unilateral contact problems with a friction","authors":"Avtandil Gachechiladze,&nbsp;Roland Gachechiladze","doi":"10.1016/j.trmi.2016.09.003","DOIUrl":"10.1016/j.trmi.2016.09.003","url":null,"abstract":"<div><p>The boundary contact problem for a micropolar homogeneous elastic hemitropic medium with a friction is investigated. Here, on a part of the elastic medium surface with a friction, instead of a normal component of force stress there is prescribed the normal component of the displacement vector. We give their mathematical formulation of the Problem in the form of spatial variational inequalities. We consider two cases, the so-called coercive case (when elastic medium is fixed along some part of the boundary) and semi-coercive case (the boundary is not fixed). Based on our variational inequality approach, we prove the existence and uniqueness theorems and show that solutions continuously depend on the data of the original problem. In the semi-coercive case, the necessary condition of solvability of the corresponding contact problem is written out explicitly. This condition under certain restrictions is sufficient, as well.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.09.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55643961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dirichlet problem for Laplace–Beltrami equation on hypersurfaces—FEM approximation 超曲面上Laplace-Beltrami方程的Dirichlet问题-有限元逼近
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI: 10.1016/j.trmi.2016.07.003
Tengiz Buchukuri , Roland Duduchava , George Tephnadze
{"title":"Dirichlet problem for Laplace–Beltrami equation on hypersurfaces—FEM approximation","authors":"Tengiz Buchukuri ,&nbsp;Roland Duduchava ,&nbsp;George Tephnadze","doi":"10.1016/j.trmi.2016.07.003","DOIUrl":"10.1016/j.trmi.2016.07.003","url":null,"abstract":"<div><p>We consider Dirichlet boundary value problem for Laplace–Beltrami Equation On Hypersurface <span><math><mi>S</mi></math></span>, when the Laplace–Beltrami operator on the surface is described explicitly in terms of Günter’s differential operators. Using the calculus of Günter’s tangential differential operators on hypersurfaces we establish Finite Element Method for the considered boundary value problem and obtain approximate solution in explicit form.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.07.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55643822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed boundary value problems of pseudo-oscillations of generalized thermo-electro-magneto-elasticity theory for solids with interior cracks 含内裂纹固体广义热电磁弹性理论伪振动的混合边值问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI: 10.1016/j.trmi.2016.09.001
Tengiz Buchukuri , Otar Chkadua , David Natroshvili
{"title":"Mixed boundary value problems of pseudo-oscillations of generalized thermo-electro-magneto-elasticity theory for solids with interior cracks","authors":"Tengiz Buchukuri ,&nbsp;Otar Chkadua ,&nbsp;David Natroshvili","doi":"10.1016/j.trmi.2016.09.001","DOIUrl":"10.1016/j.trmi.2016.09.001","url":null,"abstract":"<div><p>We investigate the mixed boundary value problems of the generalized thermo-electro-magneto-elasticity theory for homogeneous anisotropic solids with interior cracks. Using the potential methods and theory of pseudodifferential equations on manifolds with boundary we prove the existence and uniqueness of solutions. We analyse the asymptotic behaviour and singularities of the mechanical, electric, magnetic, and thermal fields near the crack edges and near the curves, where different types of boundary conditions collide. In particular, for some important classes of anisotropic media we derive explicit expressions for the corresponding stress singularity exponents and demonstrate their dependence on the material parameters. The questions related to the so called oscillating singularities are treated in detail as well.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.09.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55643942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
The second Darboux problem for the wave equation with integral nonlinearity 具有积分非线性的波动方程的第二类达布问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI: 10.1016/j.trmi.2016.09.002
Sergo Kharibegashvili , Otar Jokhadze
{"title":"The second Darboux problem for the wave equation with integral nonlinearity","authors":"Sergo Kharibegashvili ,&nbsp;Otar Jokhadze","doi":"10.1016/j.trmi.2016.09.002","DOIUrl":"10.1016/j.trmi.2016.09.002","url":null,"abstract":"<div><p>For a one-dimensional wave equation with integral nonlinearity, the second Darboux problem is considered for which the questions on the existence and uniqueness of a global solution are investigated.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.09.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55643953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Some problems of oscillation and stability of prestressed shells of rotation close to cylindrical ones, with an elastic filler and under the action of temperature 温度作用下带弹性填料的接近圆柱形旋转预应力壳的振动与稳定性问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI: 10.1016/j.trmi.2016.06.002
Sergo Kukudzhanov
{"title":"Some problems of oscillation and stability of prestressed shells of rotation close to cylindrical ones, with an elastic filler and under the action of temperature","authors":"Sergo Kukudzhanov","doi":"10.1016/j.trmi.2016.06.002","DOIUrl":"10.1016/j.trmi.2016.06.002","url":null,"abstract":"<div><p>The present paper investigates natural oscillations and stability of shells of revolution which are close by their form to cylindrical ones, with elastic filler and under the action of meridional forces, external pressure and temperature. The shell is assumed to be thin and elastic. A filler is simulated by an elastic base. The shells of positive and negative Gaussian curvature are considered. Formulas for finding the least frequencies and a form of wave formation are written out. The questions dealing with the higher frequencies and stability of shells of revolution are studied, and formulas for critical loadings are also written out.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.06.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55643704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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