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Transactions of A Razmadze Mathematical Institute最新文献

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On the homogeneity test based on the kernel-type estimators of a distribution density 基于分布密度核估计的均匀性检验
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.07.005
Petre Babilua, Elizbar Nadaraya
{"title":"On the homogeneity test based on the kernel-type estimators of a distribution density","authors":"Petre Babilua,&nbsp;Elizbar Nadaraya","doi":"10.1016/j.trmi.2018.07.005","DOIUrl":"https://doi.org/10.1016/j.trmi.2018.07.005","url":null,"abstract":"<div><p>The test of homogeneity is constructed by using kernel-type estimators of a distribution density. The limit power of the constructed test is found for close Pitman-type alternatives. The constructed test is compared with Pearson’s <span><math><mi>X</mi><mi>u</mi></math></span>-square test.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 318-331"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.07.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136519693","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
Bayesian inverse problems with partial observations 部分观测的贝叶斯反问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.09.002
Shota Gugushvili, Aad W. van der Vaart, Dong Yan
{"title":"Bayesian inverse problems with partial observations","authors":"Shota Gugushvili,&nbsp;Aad W. van der Vaart,&nbsp;Dong Yan","doi":"10.1016/j.trmi.2018.09.002","DOIUrl":"10.1016/j.trmi.2018.09.002","url":null,"abstract":"<div><p>We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical Gaussian sequence model. Upon placing the truncated series prior on the unknown parameter, we show that as the number of observations <span><math><mi>n</mi><mo>→</mo><mi>∞</mi><mo>,</mo></math></span> the corresponding posterior distribution contracts around the true parameter at a rate depending on the smoothness of the true parameter and the prior, and the ill-posedness degree of the problem. Correct combinations of these values lead to optimal posterior contraction rates (up to logarithmic factors). Similarly, the frequentist coverage of Bayesian credible sets is shown to be dependent on a combination of smoothness of the true parameter and the prior, and the ill-posedness of the problem. Oversmoothing priors lead to zero coverage, while undersmoothing priors produce highly conservative results. Finally, we illustrate our theoretical results by numerical examples.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 388-403"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.09.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48703925","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
Invex programming problems with equality and inequality constraints 具有等式和不等式约束的逆规划问题
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.04.001
A.K. Das , R. Jana , Deepmala
{"title":"Invex programming problems with equality and inequality constraints","authors":"A.K. Das ,&nbsp;R. Jana ,&nbsp;Deepmala","doi":"10.1016/j.trmi.2018.04.001","DOIUrl":"10.1016/j.trmi.2018.04.001","url":null,"abstract":"<div><p>The class of functions is known as invex function (invariant convex) in the literature and the name derives from the fact that the convex like property of such functions remains invariant under all diffeomorphisms of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> into <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>.</mo></math></span> A noteworthy result here is that the class of invex functions is precisely the class of differentiable functions whose stationary points are global minimizers. We revisit some of the important results obtained by Hanson and Martin and extend them to constrained minimization problems with equality constraints in addition to inequality constraints. We address some conditions by which a function is invex. We propose a result to solve pseudo-invex programming problem with the help of an equivalent programming problem.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 361-371"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.04.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48176128","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: 6
Melting and viscous dissipation effects on MHD flow over a moving surface with constant heat source 恒热源移动表面上MHD流动的熔化和粘滞耗散效应
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.03.007
B. Venkateswarlu , P.V. Satya Narayana , Nainaru Tarakaramu
{"title":"Melting and viscous dissipation effects on MHD flow over a moving surface with constant heat source","authors":"B. Venkateswarlu ,&nbsp;P.V. Satya Narayana ,&nbsp;Nainaru Tarakaramu","doi":"10.1016/j.trmi.2018.03.007","DOIUrl":"10.1016/j.trmi.2018.03.007","url":null,"abstract":"<div><p>The effects of viscous dissipation and heat source on MHD flow and heat transfer from a warm, electrically conducting fluid to melting surface parallel to a constant free stream are investigated numerically. This model constitutes highly non-linear governing equations which are transformed using similarity variables and are then solved by fourth order Runge–Kutta scheme along with shooting method. The influence of the various interesting parameters on the velocity and temperature fields within the boundary layer is discussed and explained graphically. It is noticed that the melting phenomenon rises the skin friction coefficient and declines the Nusselt number at the solid interface.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 619-630"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.03.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43222459","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: 27
Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results 用不动点结果证明一类具有无界时滞的中立型微分问题的存在唯一性
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.08.006
Azhar Hussain, Tanzeela Kanwal
{"title":"Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results","authors":"Azhar Hussain,&nbsp;Tanzeela Kanwal","doi":"10.1016/j.trmi.2018.08.006","DOIUrl":"10.1016/j.trmi.2018.08.006","url":null,"abstract":"<div><p>Jleli and Samet (2018) introduced a new metric space and named it as <span><math><mi>F</mi></math></span>-space. In this paper we consider the notion of <span><math><mi>α</mi></math></span>-<span><math><mi>ψ</mi></math></span>-contraction in the setting of <span><math><mi>F</mi></math></span>-metric spaces. We present some fixed point and coupled fixed point results in the generalized setting. Moreover, our purpose in this paper is to concerned with the solution of nonlinear neutral differential equation <span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>a</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>b</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mi>r</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>c</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mi>r</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span></span></span>with unbounded delay using fixed point theory in <span><math><mi>F</mi></math></span>-metric space.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 481-490"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.08.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43501933","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: 42
Nonparametric density estimation based on the scaled Laplace transform inversion 基于尺度拉普拉斯变换反演的非参数密度估计
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.09.003
Fairouz Elmagbri, Robert M. Mnatsakanov
{"title":"Nonparametric density estimation based on the scaled Laplace transform inversion","authors":"Fairouz Elmagbri,&nbsp;Robert M. Mnatsakanov","doi":"10.1016/j.trmi.2018.09.003","DOIUrl":"10.1016/j.trmi.2018.09.003","url":null,"abstract":"<div><p>New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 440-447"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.09.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44576204","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 functionals of the Wiener process in a Banach space Banach空间中Wiener过程的泛函
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.07.007
Badri Mamporia , Omar Purtukhia
{"title":"On functionals of the Wiener process in a Banach space","authors":"Badri Mamporia ,&nbsp;Omar Purtukhia","doi":"10.1016/j.trmi.2018.07.007","DOIUrl":"10.1016/j.trmi.2018.07.007","url":null,"abstract":"<div><p>In development of stochastic analysis in a Banach space one of the main problem is to establish the existence of the stochastic integral from predictable Banach space valued (operator valued) random process. In the problem of representation of the Wiener functional as a stochastic integral we are faced with an inverse problem: we have the stochastic integral as a Banach space valued random element and we are looking for a suitable predictable integrand process. There are positive results only for a narrow class of Banach spaces with special geometry (UMD Banach spaces). We consider this problem in a general Banach space for a Gaussian functional.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 420-428"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.07.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48758324","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
Representations of functionals on absolute weighted spaces and adjoint operators 绝对加权空间上泛函的表示与伴随算子
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2017.10.003
Mehmet Ali Sarıgöl
{"title":"Representations of functionals on absolute weighted spaces and adjoint operators","authors":"Mehmet Ali Sarıgöl","doi":"10.1016/j.trmi.2017.10.003","DOIUrl":"10.1016/j.trmi.2017.10.003","url":null,"abstract":"<div><p>In the present paper, we establish general representations of continuous linear functionals, which play important roles in Functional Analysis, of the absolute weighted spaces which have recently been introduced in Sarıgöl (2016, 2011), and also determine their norms. Further making use of this we give adjoint operators of matrix mappings defined on these spaces.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 539-544"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2017.10.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55644023","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
Tension spline method for solution of Fitzhugh–Nagumo equation 求解Fitzhugh-Nagumo方程的张力样条法
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.02.001
H.S. Shekarabi , M. Aqamohamadi , J. Rashidinia
{"title":"Tension spline method for solution of Fitzhugh–Nagumo equation","authors":"H.S. Shekarabi ,&nbsp;M. Aqamohamadi ,&nbsp;J. Rashidinia","doi":"10.1016/j.trmi.2018.02.001","DOIUrl":"10.1016/j.trmi.2018.02.001","url":null,"abstract":"<div><p>One of the most widely studied biological systems with excitable behavior is neural communication by nerve cells via electrical signaling. The Fitzhugh–Nagumo equation is a simplification of the Hodgin–Huxley model (Hodgin and Huxley, 1952) [<span>24</span>] for the membrane potential of a nerve axon. In this paper we developed a three time-level implicit method by using tension spline function. The resulting equations are solved by a tri-diagonal solver. We described the mathematical formulation procedure in detail. The stability of the presented method is investigated. Results of numerical experiments verify the theoretical behavior of the orders of convergence.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 571-581"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.02.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43207363","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
Forks, noodles and the Burau representation for n=4 叉子，面条和局表示为n=4
IF 0.2
Transactions of A Razmadze Mathematical Institute Pub Date : 2018-12-01 DOI: 10.1016/j.trmi.2018.05.001
A. Beridze , P. Traczyk
{"title":"Forks, noodles and the Burau representation for n=4","authors":"A. Beridze ,&nbsp;P. Traczyk","doi":"10.1016/j.trmi.2018.05.001","DOIUrl":"10.1016/j.trmi.2018.05.001","url":null,"abstract":"<div><p>The reduced Burau representation is a natural action of the braid group <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on the first homology group <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub><mo>;</mo><mi>Z</mi><mo>)</mo></mrow></math></span> of a suitable infinite cyclic covering space <span><math><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub></math></span> of the <span><math><mi>n</mi></math></span>-punctured disc <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. It is known that the Burau representation is faithful for <span><math><mi>n</mi><mo>≤</mo><mn>3</mn></math></span>\u0000and that it is not faithful for <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>. We use forks and noodles homological techniques and Bokut–Vesnin generators to analyze the problem for <span><math><mi>n</mi><mo>=</mo><mn>4</mn></math></span>. We present a Conjecture implying faithfulness and a Lemma explaining the implication. We give some arguments suggesting why we expect the Conjecture to be true. Also, we give some geometrically calculated examples and information about data gathered using a C<span>++</span> program.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 337-353"},"PeriodicalIF":0.2,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.05.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43434718","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: 6
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