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Carpathian Journal of Mathematics最新文献

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Unpredictability in Markov chains 马尔可夫链中的不可预测性
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-11-15 DOI: 10.37193/cjm.2022.01.02
M. Akhmet
{"title":"Unpredictability in Markov chains","authors":"M. Akhmet","doi":"10.37193/cjm.2022.01.02","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.02","url":null,"abstract":"We have formalized realizations of Markov chains as conveniently constructed sequences, and explained, why the random dynamics admits the unpredictability, the concept introduced in our papers previously. The method of the domain structured dynamics (dynamics on labels) has been applied. An illustrating example with a proper numerical simulation is provided.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49493512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A two-level based genetic algorithm for solving the soft-clustered vehicle routing problem 一种求解软聚类车辆路径问题的两级遗传算法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-11-15 DOI: 10.37193/cjm.2022.01.09
Ovidiu Cosma, P. Pop, Corina Pop Sitar
{"title":"A two-level based genetic algorithm for solving the soft-clustered vehicle routing problem","authors":"Ovidiu Cosma, P. Pop, Corina Pop Sitar","doi":"10.37193/cjm.2022.01.09","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.09","url":null,"abstract":"The soft-clustered vehicle routing problem (Soft-CluVRP) is a relaxation of the clustered vehicle routing problem (CluVRP), which in turn is a variant of the generalized vehicle routing problem (GVRP). The aim of the Soft-CluVRP is to look for a minimum cost group of routes starting and ending at a given depot to a set of customers partitioned into a priori defined, mutually exclusive and exhaustive clusters, satisfying the capacity constraints of the vehicles and with the supplementary property that all the customers from the same cluster have to be supplied by the same vehicle. The considered optimization problem is NP-hard, that is why we proposed a two-level based genetic algorithm in order to solve it. The computational results reported on a set of existing benchmark instances from the literature, prove that our novel solution approach provides high-quality solutions within acceptable running times.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46009499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Well-posedness of a nonlinear second-order anisotropic reaction-diffusion problem with nonlinear and inhomogeneous dynamic boundary conditions 具有非线性和非齐次动态边界条件的非线性二阶各向异性反应扩散问题的适定性
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-11-15 DOI: 10.37193/cjm.2022.01.08
M. Choban, Costică N. Moroșanu
{"title":"Well-posedness of a nonlinear second-order anisotropic reaction-diffusion problem with nonlinear and inhomogeneous dynamic boundary conditions","authors":"M. Choban, Costică N. Moroșanu","doi":"10.37193/cjm.2022.01.08","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.08","url":null,"abstract":"The paper is concerned with a qualitative analysis for a nonlinear second-order boundary value problem, endowed with nonlinear and inhomogeneous dynamic boundary conditions, extending the types of bounday conditions already studied. Under certain assumptions on the input data: $f_{_1}(t,x)$, $w(t,x)$ and $u_0(x)$, we prove the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a classical solution in the Sobolev space $W^{1,2}_p(Q)$. This extends previous works concerned with nonlinear dynamic boundary conditions, allowing to the present mathematical model to better approximate the real physical phenomena (the anisotropy effects, phase change in $Omega$ and at the boundary $partialOmega$, etc.).","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44850514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems 求解拟单调变分不等式问题的Halpern次梯度外聚算法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-11-15 DOI: 10.37193/cjm.2022.01.20
Pongsakorn Yotkaew, H. Rehman, B. Panyanak, N. Pakkaranang
{"title":"Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems","authors":"Pongsakorn Yotkaew, H. Rehman, B. Panyanak, N. Pakkaranang","doi":"10.37193/cjm.2022.01.20","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.20","url":null,"abstract":"In this paper, we study the numerical solution of the variational inequalities involving quasimonotone operators in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges strongly to a solution. The main advantage of the proposed iterative schemes is that it uses a monotone and non-monotone step size rule based on operator knowledge rather than its Lipschitz constant or some other line search method.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41532640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Center problem for cubic differential systems with the line at infinity of multiplicity four 无穷多倍线为4的三次微分系统的中心问题
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-11-15 DOI: 10.37193/cjm.2022.01.17
A. Suba
{"title":"Center problem for cubic differential systems with the line at infinity of multiplicity four","authors":"A. Suba","doi":"10.37193/cjm.2022.01.17","DOIUrl":"https://doi.org/10.37193/cjm.2022.01.17","url":null,"abstract":"In this paper the center problem for cubic differential systems with the line at infinity of multiplicity four is solved.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46186576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems 求解变分包含的惯性迭代格式及其在Nash-Cournot平衡和图像恢复问题中的应用
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI: 10.37193/cjm.2021.03.01
Jamilu Abubakar, P. Kumam, A. I. Garba, M. Abdullahi, A. Ibrahim, K. Sitthithakerngkiet
{"title":"An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems","authors":"Jamilu Abubakar, P. Kumam, A. I. Garba, M. Abdullahi, A. Ibrahim, K. Sitthithakerngkiet","doi":"10.37193/cjm.2021.03.01","DOIUrl":"https://doi.org/10.37193/cjm.2021.03.01","url":null,"abstract":"Variational inclusion is an important general problem consisting of many useful problems like variational inequality, minimization problem and nonlinear monotone equations. In this article, a new scheme for solving variational inclusion problem is proposed and the scheme uses inertial and relaxation techniques. Moreover, the scheme is self adaptive, that is, the stepsize does not depend on the factorial constants of the underlying operator, instead it can be computed using a simple updating rule. Weak convergence analysis of the iterates generated by the new scheme is presented under mild conditions. In addition, schemes for solving variational inequality problem and split feasibility problem are derived from the proposed scheme and applied in solving Nash-Cournot equilibrium problem and image restoration. Experiments to illustrate the implementation and potential applicability of the proposed schemes in comparison with some existing schemes in the literature are presented.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49361251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On a class of nonlinear nonlocal fractional differential equations 关于一类非线性非局部分数阶微分方程
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI: 10.37193/cjm.2021.03.07
Hossein Fazli, Hongguang Sun, Sima Aghchi, J. Nieto
{"title":"On a class of nonlinear nonlocal fractional differential equations","authors":"Hossein Fazli, Hongguang Sun, Sima Aghchi, J. Nieto","doi":"10.37193/cjm.2021.03.07","DOIUrl":"https://doi.org/10.37193/cjm.2021.03.07","url":null,"abstract":"We investigate the existence of extremal solutions for a class of fractional differential equations in the area of fluid dynamics. By establishing a new comparison theorem and applying the classical monotone iterative approach, we establish sufficient conditions to ensure the existence of the extremal solutions and construct twin convergent monotone explicit iterative schemes. Generalized nonlinear nonlocal Bagley-Torvik equation and generalized Basset equation with nonlinear source functions are some special cases of our discussed problem.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43356726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces p-一致凸度量空间中单值和多值映射的收敛定理
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI: 10.37193/cjm.2021.03.13
Jenjira Puiwong, S. Saejung
{"title":"On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces","authors":"Jenjira Puiwong, S. Saejung","doi":"10.37193/cjm.2021.03.13","DOIUrl":"https://doi.org/10.37193/cjm.2021.03.13","url":null,"abstract":"We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44321190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds Hadamard流形上平衡问题的存在性结果和两步逼近点算法
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI: 10.37193/cjm.2021.03.03
S. Al-Homidan, Q. Ansari, Monirul Islam
{"title":"Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds","authors":"S. Al-Homidan, Q. Ansari, Monirul Islam","doi":"10.37193/cjm.2021.03.03","DOIUrl":"https://doi.org/10.37193/cjm.2021.03.03","url":null,"abstract":"\"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature.\"","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42989463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximate optimality and approximate duality in nonsmooth composite vector optimization 非光滑复合向量优化中的近似最优性和近似对偶性
IF 1.4 4区 数学
Carpathian Journal of Mathematics Pub Date : 2021-07-15 DOI: 10.37193/cjm.2021.03.14
Thanatchaporn Sirichunwijit, R. Wangkeeree, Nithirat Sisarat
{"title":"Approximate optimality and approximate duality in nonsmooth composite vector optimization","authors":"Thanatchaporn Sirichunwijit, R. Wangkeeree, Nithirat Sisarat","doi":"10.37193/cjm.2021.03.14","DOIUrl":"https://doi.org/10.37193/cjm.2021.03.14","url":null,"abstract":"This paper concentrates on studying a nonsmooth composite vector optimization problem (P for brevity). We employ a fuzzy necessary condition for approximate (weakly) efficient solutions of a nonconvex and nonsmooth cone constrained vector optimization problem established in [Choung, T. D. Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization Ann. Oper. Res. (2020), https://doi.org/10.1007/s10479-020-03740-3.] and the a chain rule for generalized differentiation to provide a necessary condition which exhibited in a Fritz-John type for approximate (weakly) efficient solutions of P. Sufficient optimality conditions for approximate (weakly) efficient solutions to P are also provided by means of proposing the use of (strictly) approximately generalized convex composite vector functions with respect to a cone. Moreover, an approximate dual vector problem to P is given and strong and converse duality assertions for approximate (weakly) efficient solutions are proved.","PeriodicalId":50711,"journal":{"name":"Carpathian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45578791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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