{"title":"*-Weyl Curvature Tensor within the Framework of Sasakian and $(kappa,mu)$-Contact Manifolds","authors":"V. Venkatesha, H. Kumara","doi":"10.5556/J.TKJM.52.2021.3440","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3440","url":null,"abstract":"The object of the present paper is to study $*$-Weyl curvature tensor within the framework of Sasakian and $(kappa,mu)$-contact manifolds.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89594316","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 : 2021-02-05DOI: 10.5556/J.TKJM.52.2021.3714
M. Y. Baba, M. Saleem, Abdur Raheem
In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.
{"title":"P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53","authors":"M. Y. Baba, M. Saleem, Abdur Raheem","doi":"10.5556/J.TKJM.52.2021.3714","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3714","url":null,"abstract":"In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88708577","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 : 2021-02-04DOI: 10.5556/J.TKJM.52.2021.3271
M. Nunokawa, J. Sokół
We consider univalent functions, analytic in the unit disc $ |z|<1$in the complex plane ${mathbb{C}}$ which map $ |z|<1$ onto a domainwith some nice property. The purpose of this paper is to find somenew conditions for strong starlikeness and some related results.
{"title":"Strongly Starlike Functions and Related Classes","authors":"M. Nunokawa, J. Sokół","doi":"10.5556/J.TKJM.52.2021.3271","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3271","url":null,"abstract":"We consider univalent functions, analytic in the unit disc $ |z|<1$in the complex plane ${mathbb{C}}$ which map $ |z|<1$ onto a domainwith some nice property. The purpose of this paper is to find somenew conditions for strong starlikeness and some related results.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77274681","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 : 2021-02-04DOI: 10.5556/J.TKJM.52.2021.3209
Guangyu Zhao
We study a variety of basic properties of the principal eigenvalue of a perturbed fractional Laplace operator and weakly coupled cooperative systems involving fractional Laplace operators. Our work extends a number of well-known properties regarding the principal eigenvalues of linear second-order elliptic operators with Dirichlet boundary condition to perturbed fractional Laplace operators. The establish results are also utilized to investigate the spatio-temporary dynamics of population models.
{"title":"The Principal Eigenvalue Problems for Perturbed Fractional Laplace Operators","authors":"Guangyu Zhao","doi":"10.5556/J.TKJM.52.2021.3209","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3209","url":null,"abstract":"We study a variety of basic properties of the principal eigenvalue of a perturbed fractional Laplace operator and weakly coupled cooperative systems involving fractional Laplace operators. Our work extends a number of well-known properties regarding the principal eigenvalues of linear second-order elliptic operators with Dirichlet boundary condition to perturbed fractional Laplace operators. The establish results are also utilized to investigate the spatio-temporary dynamics of population models.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78574260","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 : 2021-02-04DOI: 10.5556/J.TKJM.52.2021.3270
H. K. Nigam, Supriya Rani
In the present paper, we establish a theorem on best approximation of a function g ∈ Bqλ(Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1.
{"title":"Approximation of Functions in Besov Space","authors":"H. K. Nigam, Supriya Rani","doi":"10.5556/J.TKJM.52.2021.3270","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3270","url":null,"abstract":"In the present paper, we establish a theorem on best approximation of a function g ∈ Bqλ(Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76691835","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3298
K. Roy, M. Saha, Ismat Beg
We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.
{"title":"Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space","authors":"K. Roy, M. Saha, Ismat Beg","doi":"10.5556/J.TKJM.52.2021.3298","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3298","url":null,"abstract":"We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86571732","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3241
R. Hasenauer, Bethany Kubik
Given a ring $R$, an ideal $I$ of $R$, and an element $ain I$, we say $a=lambda b_1cdots b_k$ is a $tau_I$-factorization of $a$ if $lambda$ is any unit and $b_1equivcdotsequiv b_kpmod{I}$. In this paper, we investigate the $tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.
{"title":"$tau$-Atomicity and Quotients of Size Four","authors":"R. Hasenauer, Bethany Kubik","doi":"10.5556/J.TKJM.52.2021.3241","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3241","url":null,"abstract":"Given a ring $R$, an ideal $I$ of $R$, and an element $ain I$, we say $a=lambda b_1cdots b_k$ is a $tau_I$-factorization of $a$ if $lambda$ is any unit and $b_1equivcdotsequiv b_kpmod{I}$. In this paper, we investigate the $tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91334473","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3276
H. M. Abood, M. Y. Abass
In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further, the conditions required for this to be an Einstein manifold have been determined.
{"title":"A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type","authors":"H. M. Abood, M. Y. Abass","doi":"10.5556/J.TKJM.52.2021.3276","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3276","url":null,"abstract":"In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further, the conditions required for this to be an Einstein manifold have been determined.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80165514","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3330
H. Akhadkulov, F. Alsharari, T. Y. Ying
In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.
{"title":"Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations","authors":"H. Akhadkulov, F. Alsharari, T. Y. Ying","doi":"10.5556/J.TKJM.52.2021.3330","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3330","url":null,"abstract":"In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75084884","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 : 2021-02-02DOI: 10.5556/J.TKJM.52.2021.3254
R. Khoeilar, M. Chellali, H. Karami, S. M. Sheikholeslami
For a positive integer $k$, a subset $D$ of vertices in a digraph $overrightarrow{G}$ is a $k$-dominating set if every vertex not in $D$ has at least $k$ direct predecessors in $D.$ The $k$-domination number is the minimum cardinality among all $k$-dominating sets of $overrightarrow{G}$. The game $k$-domination number of a simple and undirected graph is defined by the following game. Two players, $mathcal{A}$ and $mathcal{D}$, orient the edges of the graph alternately until all edges are oriented. Player $mathcal{D}$ starts the game, and his goal is to decrease the $k$-domination number of the resulting digraph, while $mathcal{A}$ is trying to increase it. The game $k$-domination number of the graph $G$ is the $k$-domination number of the directed graph resulting from this game. This is well defined if we suppose that both players follow their optimal strateries. We are mainly interested in the study of the game $2$-domination number, where some upper bounds will be presented. We also establish a Nordhaus-Gaddum bound for the game $2$-domination number of a graph and its complement.
{"title":"Game $k$-Domination Number of Graphs","authors":"R. Khoeilar, M. Chellali, H. Karami, S. M. Sheikholeslami","doi":"10.5556/J.TKJM.52.2021.3254","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3254","url":null,"abstract":"For a positive integer $k$, a subset $D$ of vertices in a digraph $overrightarrow{G}$ is a $k$-dominating set if every vertex not in $D$ has at least $k$ direct predecessors in $D.$ The $k$-domination number is the minimum cardinality among all $k$-dominating sets of $overrightarrow{G}$. The game $k$-domination number of a simple and undirected graph is defined by the following game. Two players, $mathcal{A}$ and $mathcal{D}$, orient the edges of the graph alternately until all edges are oriented. Player $mathcal{D}$ starts the game, and his goal is to decrease the $k$-domination number of the resulting digraph, while $mathcal{A}$ is trying to increase it. The game $k$-domination number of the graph $G$ is the $k$-domination number of the directed graph resulting from this game. This is well defined if we suppose that both players follow their optimal strateries. We are mainly interested in the study of the game $2$-domination number, where some upper bounds will be presented. We also establish a Nordhaus-Gaddum bound for the game $2$-domination number of a graph and its complement.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89538660","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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