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Transactions of A Razmadze Mathematical Institute最新文献

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Aitken type methods with high efficiency 艾特肯式方法效率高
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.01.001
Pankaj Jain, Kriti Sethi
{"title":"Aitken type methods with high efficiency","authors":"Pankaj Jain,&nbsp;Kriti Sethi","doi":"10.1016/j.trmi.2018.01.001","DOIUrl":"10.1016/j.trmi.2018.01.001","url":null,"abstract":"<div><p>In this paper, we study the iterative method of Aitken type for solving the non-linear equations, in which the interpolation nodes are controlled by variant of Newton method or by a general method of order <span><math><mi>p</mi><mo>.</mo></math></span> By combining such methods with a generalized secant method, it is shown that the order of convergence can be increased to as high as desired and also in the limiting case efficiency of the method is 2. Several numerical examples are provided in support of the theoretical results.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 223-237"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.01.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46923753","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: 4
Several inequalities For log-convex functions 对数凸函数的几个不等式
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.03.004
Merve Avci ArdiÇ , Ahmet Ocak Akdemir , M. Emin Özdemir
{"title":"Several inequalities For log-convex functions","authors":"Merve Avci ArdiÇ ,&nbsp;Ahmet Ocak Akdemir ,&nbsp;M. Emin Özdemir","doi":"10.1016/j.trmi.2018.03.004","DOIUrl":"10.1016/j.trmi.2018.03.004","url":null,"abstract":"<div><p>In this paper, we recall Ostrowski’s inequality, Hadamard’s inequality and the definition of <span><math><mi>l</mi><mi>o</mi><mi>g</mi></math></span>-convex functions. We also mention an useful integral identity in the first part of our study. The second part of our study includes new results. We prove new generalizations for <span><math><mo>log</mo></math></span>-convex functions. Several new Ostrowski type inequalities have been established and some special cases have been given by choosing <span><math><mi>h</mi><mo>=</mo><mn>0</mn></math></span> or <span><math><mi>x</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>.</mo></math></span>\u0000</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 140-145"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.03.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46666669","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
Speeding up the convergence of the Polyak’s Heavy Ball algorithm 加快了Polyak重球算法的收敛速度
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.03.006
Koba Gelashvili, Irina Khutsishvili, Luka Gorgadze, Lela Alkhazishvili
{"title":"Speeding up the convergence of the Polyak’s Heavy Ball algorithm","authors":"Koba Gelashvili,&nbsp;Irina Khutsishvili,&nbsp;Luka Gorgadze,&nbsp;Lela Alkhazishvili","doi":"10.1016/j.trmi.2018.03.006","DOIUrl":"10.1016/j.trmi.2018.03.006","url":null,"abstract":"<div><p>In the presented work, some procedures, usually used in modern algorithms of unconstrained optimization, are added to Polyak’s heavy ball method. Namely, periodical restarts, which guarantees monotonic decrease of the objective function along successive iterates, while restarts involve updating of the step size on the base of line search method.</p><p>For smooth objective functions, the Heavy Ball (briefly HB) and Modified Heavy Ball (briefly MHB) algorithms are described along with the problem of simplifying the form of used line-search algorithm (without changing its content). MHB and the set of test functions are implemented in C++. The set of test functions contains 44 functions, taken from Cuter/st. Solver CG_DESCENT-C-6.8 was used for MHB benchmarking. Test-functions and other materials, related to benchmarking, are uploaded to GitHub: <span>https://github.com/kobage/</span><svg><path></path></svg>.</p><p>In case of smooth and convex objective function, the convergence analysis is concentrated on reducing transformations and their orbits. A concept of reducing transformation allows us to investigate algebraic structure of convergent methods.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 176-188"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.03.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47228417","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
On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity 双孔隙材料粘弹性理论中准静、定常振动方程的解
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.01.002
Maia M. Svanadze
{"title":"On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity","authors":"Maia M. Svanadze","doi":"10.1016/j.trmi.2018.01.002","DOIUrl":"10.1016/j.trmi.2018.01.002","url":null,"abstract":"<div><p>In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic results on the solutions of the quasi-static and steady vibrations equations are obtained. Indeed, the fundamental solutions of the systems of equations of quasi-static and steady vibrations are constructed by elementary functions and their basic properties are established. Green’s formulae and the integral representation of regular solution in the considered theory are obtained. Finally, a wide class of the internal boundary value problems of quasi-static and steady vibrations is formulated and on the basis of Green’s formulae the uniqueness theorems for classical solutions of these problems are proved.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 276-292"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.01.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49047506","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: 4
q-deformation of the square white noise Lie algebra 方形白噪声李代数的q-变形
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.01.005
Sami H. Altoum
{"title":"q-deformation of the square white noise Lie algebra","authors":"Sami H. Altoum","doi":"10.1016/j.trmi.2018.01.005","DOIUrl":"10.1016/j.trmi.2018.01.005","url":null,"abstract":"<div><p>For <span><math><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>, the <span><math><mi>q</mi></math></span>-deformation of the square white noise Lie algebra is introduced using the <span><math><mi>q</mi></math></span>-calculus. A representation of this Lie algebra is given, using the <span><math><mi>q</mi></math></span>-derivative (or Jackson derivative) and the multiplication operator. The free square white noise Lie algebra is defined. Moreover, its representation on the Hardy space is given.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 133-139"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.01.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44204190","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
Lyapunov inequalities of nested fractional boundary value problems and applications 嵌套分数边值问题的Lyapunov不等式及其应用
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-08-01 DOI: 10.1016/j.trmi.2018.03.005
Yousef Gholami
{"title":"Lyapunov inequalities of nested fractional boundary value problems and applications","authors":"Yousef Gholami","doi":"10.1016/j.trmi.2018.03.005","DOIUrl":"10.1016/j.trmi.2018.03.005","url":null,"abstract":"<div><p>In this paper, we study certain classes of nested fractional boundary value problems including both of the Riemann–Liouville and Caputo fractional derivatives. In addition, since we will use the signed-power operators <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>ν</mi></mrow></msub><mi>z</mi><mo>≔</mo><mo>|</mo><mi>z</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>ν</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>z</mi><mo>,</mo><mspace></mspace><mi>ν</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> in the governing equations, so our desired boundary value problems possess half-linear nature. Our investigation theoretically reaches so called Lyapunov inequalities of the considered nested fractional boundary value problems, while in viewpoint of applicability using the obtained Lyapunov inequalities we establish some qualitative behavior criteria for nested fractional boundary value problems such as a disconjugacy criterion that will also be used to establish nonexistence results, upper bound estimation for maximum number of zeros of the nontrivial solutions and distance between consecutive zeros of the oscillatory solutions. Also, considering corresponding nested fractional eigenvalue problems we find spreading interval of the eigenvalues.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 189-204"},"PeriodicalIF":0.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.03.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43456039","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
On the Wiener–Hopf factorization of rational matrices 有理矩阵的Wiener-Hopf分解
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.09.001
Vakhtang Lomadze
{"title":"On the Wiener–Hopf factorization of rational matrices","authors":"Vakhtang Lomadze","doi":"10.1016/j.trmi.2017.09.001","DOIUrl":"10.1016/j.trmi.2017.09.001","url":null,"abstract":"<div><p>The Wiener–Hopf factorization theorem for rational matrices is proved with respect to very general contours using purely algebraic method.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 1","pages":"Pages 73-81"},"PeriodicalIF":0.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.09.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46282881","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
Simplifying differential equations concerning degenerate Bernoulli and Euler numbers 简化关于退化伯努利数和欧拉数的微分方程
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.08.001
Feng Qi , Jing-Lin Wang , Bai-Ni Guo
{"title":"Simplifying differential equations concerning degenerate Bernoulli and Euler numbers","authors":"Feng Qi ,&nbsp;Jing-Lin Wang ,&nbsp;Bai-Ni Guo","doi":"10.1016/j.trmi.2017.08.001","DOIUrl":"10.1016/j.trmi.2017.08.001","url":null,"abstract":"<div><p>In the paper, the authors significantly and meaningfully simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first and second kinds.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 1","pages":"Pages 90-94"},"PeriodicalIF":0.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.08.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44678590","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: 18
Actions of Δ(3,n,k) on projective line Δ(3,n,k)在投影线上的作用
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.09.005
Muhammad Ashiq , Tahir Imran , Muhammad Asad Zaighum
{"title":"Actions of Δ(3,n,k) on projective line","authors":"Muhammad Ashiq ,&nbsp;Tahir Imran ,&nbsp;Muhammad Asad Zaighum","doi":"10.1016/j.trmi.2017.09.005","DOIUrl":"10.1016/j.trmi.2017.09.005","url":null,"abstract":"<div><p>Each conjugacy class of actions of the triangle group <span><math><mi>Δ</mi><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span> over the projective line <span><math><mi>P</mi><mi>L</mi><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></mrow></math></span> can be represented by a coset diagram <span><math><mi>D</mi><mrow><mo>(</mo><mi>θ</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>, where <span><math><mi>θ</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> and <span><math><mi>q</mi></math></span> is a prime number. In this paper, we have considered conjugacy classes which arise from the actions of <span><math><mi>Δ</mi><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>〈</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>:</mo><msup><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><msup><mrow><mi>s</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mrow><mo>(</mo><mi>r</mi><mi>s</mi><mo>)</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup><mo>=</mo><mn>1</mn><mo>〉</mo></mrow></math></span> over <span><math><mi>P</mi><mi>L</mi><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></mrow></math></span>, where <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> is finite field. The points of <span><math><mi>P</mi><mi>L</mi><mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></mrow></math></span> are the elements of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> together with the additional point <span><math><mi>∞</mi><mo>.</mo></math></span>\u0000</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 1","pages":"Pages 1-6"},"PeriodicalIF":0.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.09.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48968228","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
Some differential properties of anisotropic grand Sobolev–Morrey spaces 各向异性大Sobolev-Morrey空间的一些微分性质
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.10.001
Alik M. Najafov , Nilufer R. Rustamova
{"title":"Some differential properties of anisotropic grand Sobolev–Morrey spaces","authors":"Alik M. Najafov ,&nbsp;Nilufer R. Rustamova","doi":"10.1016/j.trmi.2017.10.001","DOIUrl":"10.1016/j.trmi.2017.10.001","url":null,"abstract":"<div><p>In this paper an anisotropic grand Sobolev–Morrey spaces are introduced. With the help of integral representation we study differential and differential-difference properties of functions from these spaces.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 1","pages":"Pages 82-89"},"PeriodicalIF":0.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.10.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44756297","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
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