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Transactions of A Razmadze Mathematical Institute最新文献

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Integral equations of the third kind for the case of piecewise monotone coefficients 分段单调系数情况下的第三类积分方程
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.05.002
D. Shulaia
{"title":"Integral equations of the third kind for the case of piecewise monotone coefficients","authors":"D. Shulaia","doi":"10.1016/j.trmi.2017.05.002","DOIUrl":"10.1016/j.trmi.2017.05.002","url":null,"abstract":"<div><p>We examine the third kind integral equations in Hölder class. The coefficients of the equations are piecewise strictly monotone functions having simple zeros. By singular integral equations theory, for solvability of considered equations, we give the necessary and sufficient conditions. Finding a solution is reduced to solving a regular integral equation of second kind.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 396-410"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.05.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43546395","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
Coupled systems of Caputo type fractional Δ-difference boundary value problems at resonance 耦合系统的Caputo型分数阶Δ-difference共振边值问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.03.005
Yousef Gholami, Kazem Ghanbari
{"title":"Coupled systems of Caputo type fractional Δ-difference boundary value problems at resonance","authors":"Yousef Gholami,&nbsp;Kazem Ghanbari","doi":"10.1016/j.trmi.2017.03.005","DOIUrl":"10.1016/j.trmi.2017.03.005","url":null,"abstract":"<div><p>The main research line of this paper is concerned with the existence and uniqueness of solutions for a certain class of coupled systems of Caputo type fractional <span><math><mi>Δ</mi></math></span>-difference boundary value problems at resonance. To this aim, we use coincidence degree theory to obtain existence results and impose growth controlling conditions on nonlinearities, uniqueness results will be concluded. At the end by means of an illustrative example the obtained main results will be implemented.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 332-349"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.03.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44094040","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
A non-dense subspace in Mqp with 1 Mqp中1<q<p<∞的非稠密子空间
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.05.001
Yoshihiro Sawano
{"title":"A non-dense subspace in Mqp with 1<q<p<∞","authors":"Yoshihiro Sawano","doi":"10.1016/j.trmi.2017.05.001","DOIUrl":"10.1016/j.trmi.2017.05.001","url":null,"abstract":"<div><p>The Morrey space <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> is disproved dense in <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> if <span><math><mn>1</mn><mo>&lt;</mo><mi>q</mi><mo>&lt;</mo><mover><mrow><mi>q</mi></mrow><mrow><mo>̃</mo></mrow></mover><mo>&lt;</mo><mi>p</mi></math></span>.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 379-380"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.05.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48106746","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: 9
On Riesz summability factors of Fourier series 傅里叶级数的Riesz可和因子
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.06.003
Şebnem Yildiz
{"title":"On Riesz summability factors of Fourier series","authors":"Şebnem Yildiz","doi":"10.1016/j.trmi.2017.06.003","DOIUrl":"10.1016/j.trmi.2017.06.003","url":null,"abstract":"<div><p>In this paper, a main theorem dealing with <span><math><mo>|</mo><mover><mrow><mi>N</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mo>|</mo></mrow><mrow><mi>k</mi></mrow></msub></math></span> summability method has been generalized for <span><math><mi>φ</mi><mo>−</mo><mo>|</mo><mover><mrow><mi>N</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>;</mo><mi>δ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>k</mi></mrow></msub></math></span> summability by using different and general summability factors of Fourier series.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 328-331"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.06.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48681394","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: 9
Conservation of time scale for one-dimensional pulsating flow 一维脉动流的时间尺度守恒
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.07.001
G. Aptsiauri
{"title":"Conservation of time scale for one-dimensional pulsating flow","authors":"G. Aptsiauri","doi":"10.1016/j.trmi.2017.07.001","DOIUrl":"10.1016/j.trmi.2017.07.001","url":null,"abstract":"<div><p>In the work by analysis of one-dimensional unsteady flows, based on the fundamental law of conservation with application of Fourier series is shown that in the presence of periodic, steady pulsations along the flow, the main frequency as well as all higher frequencies remain constant and only the amplitude of oscillations is changed that is in full agreement with the results of analysis of more complex three-dimensional flows. Thus, is confirmed the validity of the principle of conservation of frequencies or time scale along the flow. So, is obtained very interesting result for turbulence problem solution.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 253-256"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.07.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41582125","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
New generalizations of Popoviciu type inequalities via new green functions and Fink’s identity 基于新格林函数和Fink恒等式的波波维西乌型不等式的新推广
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.04.003
Saad Ihsan Butt , Nasir Mehmood , Josip Pečarić
{"title":"New generalizations of Popoviciu type inequalities via new green functions and Fink’s identity","authors":"Saad Ihsan Butt ,&nbsp;Nasir Mehmood ,&nbsp;Josip Pečarić","doi":"10.1016/j.trmi.2017.04.003","DOIUrl":"10.1016/j.trmi.2017.04.003","url":null,"abstract":"<div><p>We formulate new identities involving new Green functions. Inequality of Popoviciu, which was improved by Vasić and Stanković (1976), is generalized by using newly introduced Green functions. We utilize Fink’s identity along with new Green’s function to generalize the known Popoviciu’s inequality from convex functions to higher order convex functions. Then we construct linear functionals from the generalized identities and formulate the monotonicity of these functionals utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are computed.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 293-303"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.04.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47214506","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: 12
Mathematical problems of thermoelasticity of bodies with microstructure and microtemperatures 具有微观结构和微温度的物体热弹性数学问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.04.002
L. Giorgashvili, S. Zazashvili
{"title":"Mathematical problems of thermoelasticity of bodies with microstructure and microtemperatures","authors":"L. Giorgashvili,&nbsp;S. Zazashvili","doi":"10.1016/j.trmi.2017.04.002","DOIUrl":"10.1016/j.trmi.2017.04.002","url":null,"abstract":"<div><p>The paper deals with the linear theory of thermoelasticity for elastic isotropic microstretch materials with microtemperatures and microdilatations. For the differential equations of pseudo-oscillations the fundamental matrix is constructed explicitly in terms of elementary functions. With the help of the corresponding Green identities the general integral representation formula of solutions by means of generalized layer and Newtonian potentials are derived. The basic Dirichlet and Neumann type boundary value problems are formulated in appropriate function spaces and the uniqueness theorems are proved. The existence theorems for classical solutions are established by using the potential method.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 350-378"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.04.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41447444","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
Application of Sinc-Galerkin method for solving a nonlinear inverse parabolic problem c- galerkin方法在求解非线性逆抛物问题中的应用
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.05.003
A. Zakeri, A.H. Salehi Shayegan, S. Sakaki
{"title":"Application of Sinc-Galerkin method for solving a nonlinear inverse parabolic problem","authors":"A. Zakeri,&nbsp;A.H. Salehi Shayegan,&nbsp;S. Sakaki","doi":"10.1016/j.trmi.2017.05.003","DOIUrl":"10.1016/j.trmi.2017.05.003","url":null,"abstract":"<div><p>In this paper, using Sinc-Galerkin and Levenberg–Marquardt methods a stable numerical solution is obtained to a nonlinear inverse parabolic problem. Due to this, this problem is reduced to a parameter approximation problem. To approximate unknown parameters, we consider an optimization problem where objective function is minimized by Levenberg–Marquardt method. This objective function is obtained by using Sinc-Galerkin method and the overposed measured data. Finally, some numerical examples are given to demonstrate the accuracy and reliability of the proposed method.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 411-423"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.05.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48947231","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
Method of fundamental solutions for mixed and crack type problems in the classical theory of elasticity 经典弹性理论中混合和裂纹型问题的基本解方法
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.04.004
Tengiz Buchukuri , Otar Chkadua , David Natroshvili
{"title":"Method of fundamental solutions for mixed and crack type problems in the classical theory of elasticity","authors":"Tengiz Buchukuri ,&nbsp;Otar Chkadua ,&nbsp;David Natroshvili","doi":"10.1016/j.trmi.2017.04.004","DOIUrl":"10.1016/j.trmi.2017.04.004","url":null,"abstract":"<div><p>We analyse some new aspects concerning application of the fundamental solution method to the basic three-dimensional boundary value problems, mixed transmission problems, and also interior and interfacial crack type problems for steady state oscillation equations of the elasticity theory. First we present existence and uniqueness theorems of weak solutions and derive the corresponding norm estimates in appropriate function spaces. Afterwards, by means of the columns of Kupradze’s fundamental solution matrix special systems of vector functions are constructed explicitly. The linear independence and completeness of these systems are proved in appropriate Sobolev–Slobodetskii and Besov function spaces. It is shown that the problem of construction of approximate solutions to the basic and mixed boundary value problems and to the interior and interfacial crack problems can be reduced to the problems of approximation of the given boundary vector functions by elements of the linear spans of the corresponding complete systems constructed by the fundamental solution vectors. By this approach the approximate solutions of the boundary value and transmission problems are represented in the form of linear combinations of the columns of the fundamental solution matrix with appropriately chosen poles distributed outside the domain under consideration. The unknown coefficients of the linear combinations are defined by the approximation conditions of the corresponding boundary and transmission data.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 264-292"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.04.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47670689","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: 11
2-adic cofiltration of SO3(Q) SO3的二进共滤(Q)
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.06.001
Tengiz Bokelavadze , Raffaello Caserta
{"title":"2-adic cofiltration of SO3(Q)","authors":"Tengiz Bokelavadze ,&nbsp;Raffaello Caserta","doi":"10.1016/j.trmi.2017.06.001","DOIUrl":"10.1016/j.trmi.2017.06.001","url":null,"abstract":"<div><p>We prove that the group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math></span> of rational rotations is the inverse limit of a family of finite solvable groups of order <span><math><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn><mi>k</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></math></span>, whose <span><math><mn>2</mn></math></span>-Sylow subgroups have nilpotency class <span><math><mn>2</mn><mi>k</mi><mo>−</mo><mn>3</mn></math></span>, exponent <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, and Frattini subgroups coinciding with the commutator subgroups, and we give generators for these groups.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"171 3","pages":"Pages 257-263"},"PeriodicalIF":0.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.06.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47418380","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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