Pub Date : 2021-12-06DOI: 10.5556/j.tkjm.53.2022.3494
Maryam Salehnejad, M. Azhini
Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces.
{"title":"Vector Variational Inequalities In G-Convex Spaces","authors":"Maryam Salehnejad, M. Azhini","doi":"10.5556/j.tkjm.53.2022.3494","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3494","url":null,"abstract":"\u0000\u0000\u0000Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73045487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-20DOI: 10.5556/j.tkjm.54.2023.3830
Bhawna Kohli
In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.
{"title":"Optimality Conditions Using Convexifactors for a Multiobjective Fractional Bilevel Programming Problem","authors":"Bhawna Kohli","doi":"10.5556/j.tkjm.54.2023.3830","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3830","url":null,"abstract":"In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"165 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91251127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-14DOI: 10.5556/j.tkjm.53.2022.3644
A. Zivari-kazempour, M. Valaei
In this paper, we prove that if $varphi:mathcal{R}longrightarrowmathcal{R}'$ is an $n$-Jordan homomorphism, where $mathcal{R}$ has a unit $e$, then the map $alongmapsto varphi(e)^{n-2}varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.
{"title":"Characterization of $n$-Jordan Homomorphisms on Rings","authors":"A. Zivari-kazempour, M. Valaei","doi":"10.5556/j.tkjm.53.2022.3644","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3644","url":null,"abstract":"In this paper, we prove that if $varphi:mathcal{R}longrightarrowmathcal{R}'$ is an $n$-Jordan homomorphism, where $mathcal{R}$ has a unit $e$, then the map $alongmapsto varphi(e)^{n-2}varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80884219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-13DOI: 10.5556/j.tkjm.54.2023.3971
A. Montes
In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem.
{"title":"Existence of Periodic Traveling Wave Solutions for a K-P-Boussinesq Type System","authors":"A. Montes","doi":"10.5556/j.tkjm.54.2023.3971","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3971","url":null,"abstract":"In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"40 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87506313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.5556/j.tkjm.54.2023.3943
Abdulhamit Ekinci, S. Temir
In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. cite{Thakur}, Ullahand Arschad cite{UA}.
{"title":"Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces","authors":"Abdulhamit Ekinci, S. Temir","doi":"10.5556/j.tkjm.54.2023.3943","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3943","url":null,"abstract":"In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. cite{Thakur}, Ullahand Arschad cite{UA}.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"27 6","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72453545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.5556/j.tkjm.54.2023.4085
A. Uçum, Ç. Camcı, K. Ilarslan
In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.
{"title":"A New Approach to Mannheim Curve in Euclidean 3-Space","authors":"A. Uçum, Ç. Camcı, K. Ilarslan","doi":"10.5556/j.tkjm.54.2023.4085","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4085","url":null,"abstract":"In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"190 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79758774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.
{"title":"The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations","authors":"Kanognudge Wuttanachamsri, Nattapol Oangwatcharaparkan","doi":"10.5556/j.tkjm.54.2023.3738","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3738","url":null,"abstract":"In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. \u0000However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. \u0000The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. \u0000We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. \u0000Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. \u0000The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82175906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.5556/j.tkjm.54.2023.4069
M. Azis
The anisotropic-diffusion convection equation of spatiallyvariable coefficients which is relevant for functionally graded mediais discussed in this paper to find numerical solutions by using acombined Laplace transform and boundary element method. The variablecoefficients equation is transformed to a constant coefficients equation.The constant coefficients equation is then Laplace-transformed sothat the time variable vanishes. The Laplace-transformed equationis consequently written in a pure boundary integral equation whichinvolves a time-free fundamental solution. The boundary integral equationis therefore employed to find numerical solutions using a standardboundary element method. Finally the results obtained are inverselytransformed numerically using the Stehfest formula to get solutionsin the time variable. The combined Laplace transform and boundaryelement method is easy to be implemented, efficient and accurate forsolving unsteady problems of anisotropic functionally graded mediagoverned by the diffusion convection equation.
{"title":"Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow","authors":"M. Azis","doi":"10.5556/j.tkjm.54.2023.4069","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4069","url":null,"abstract":"The anisotropic-diffusion convection equation of spatiallyvariable coefficients which is relevant for functionally graded mediais discussed in this paper to find numerical solutions by using acombined Laplace transform and boundary element method. The variablecoefficients equation is transformed to a constant coefficients equation.The constant coefficients equation is then Laplace-transformed sothat the time variable vanishes. The Laplace-transformed equationis consequently written in a pure boundary integral equation whichinvolves a time-free fundamental solution. The boundary integral equationis therefore employed to find numerical solutions using a standardboundary element method. Finally the results obtained are inverselytransformed numerically using the Stehfest formula to get solutionsin the time variable. The combined Laplace transform and boundaryelement method is easy to be implemented, efficient and accurate forsolving unsteady problems of anisotropic functionally graded mediagoverned by the diffusion convection equation.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82049402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-08DOI: 10.5556/j.tkjm.54.2023.4136
Tapatee Sahoo, B. Davvaz, Harikrishnan Panackal, B. S. Kedukodi, S. P. Kuncham
Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important properties and obtain equivalent conditions for the relative essential ideals (or $N$-subgroups) involving the quotient. Further, we derive results on direct sums, complement ideals of $N$-groups and obtain their properties under homomorphism.
{"title":"Relative Essential Ideals in N-groups","authors":"Tapatee Sahoo, B. Davvaz, Harikrishnan Panackal, B. S. Kedukodi, S. P. Kuncham","doi":"10.5556/j.tkjm.54.2023.4136","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4136","url":null,"abstract":"Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important properties and obtain equivalent conditions for the relative essential ideals (or $N$-subgroups) involving the quotient. Further, we derive results on direct sums, complement ideals of $N$-groups and obtain their properties under homomorphism.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85059311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-07DOI: 10.5556/j.tkjm.54.2023.4120
S. Pirzada, Saleem Khan
Let $G$ be a connected graph with $n$ vertices, $m$ edges and having diameter $d$. The distance Laplacian matrix $D^{L}$ is defined as $D^L=$Diag$(Tr)-D$, where Diag$(Tr)$ is the diagonal matrix of vertex transmissions and $D$ is the distance matrix of $G$. The distance Laplacian eigenvalues of $G$ are the eigenvalues of $D^{L}$ and are denoted by $delta_{1}, ~delta_{1},~dots,delta_{n}$. In this paper, we obtain (a) the upper bounds for the sum of $k$ largest and (b) the lower bounds for the sum of $k$ smallest non-zero, distance Laplacian eigenvalues of $G$ in terms of order $n$, diameter $d$ and Wiener index $W$ of $G$. We characterize the extremal cases of these bounds. As a consequence, we also obtain the bounds for the sum of the powers of the distance Laplacian eigenvalues of $G$.
{"title":"On the Sum of Distance Laplacian Eigenvalues of Graphs","authors":"S. Pirzada, Saleem Khan","doi":"10.5556/j.tkjm.54.2023.4120","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4120","url":null,"abstract":"Let $G$ be a connected graph with $n$ vertices, $m$ edges and having diameter $d$. The distance Laplacian matrix $D^{L}$ is defined as $D^L=$Diag$(Tr)-D$, where Diag$(Tr)$ is the diagonal matrix of vertex transmissions and $D$ is the distance matrix of $G$. The distance Laplacian eigenvalues of $G$ are the eigenvalues of $D^{L}$ and are denoted by $delta_{1}, ~delta_{1},~dots,delta_{n}$. In this paper, we obtain (a) the upper bounds for the sum of $k$ largest and (b) the lower bounds for the sum of $k$ smallest non-zero, distance Laplacian eigenvalues of $G$ in terms of order $n$, diameter $d$ and Wiener index $W$ of $G$. We characterize the extremal cases of these bounds. As a consequence, we also obtain the bounds for the sum of the powers of the distance Laplacian eigenvalues of $G$.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89536436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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