Pub Date : 2021-02-05DOI: 10.5556/J.TKJM.52.2021.3463
M. Izid, Abderrazak El Haimi, A. O. Chahdi
In this paper, we give a new characterization of a k-slant helix which is a generalization of general helix and slant helix. Thereafter, we construct a vector differential equation of the third order to determine the parametric representation of a k-slant helix according to standard frame in Euclidean 3-space. Finally, we apply this method to find the position vector of some examples of 2-slant helix by means of intrinsic equations.
{"title":"Position Vectors of Curves Generalizing General Helices and Slant Helices in Euclidean 3-Space","authors":"M. Izid, Abderrazak El Haimi, A. O. Chahdi","doi":"10.5556/J.TKJM.52.2021.3463","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3463","url":null,"abstract":"In this paper, we give a new characterization of a k-slant helix which is a generalization of general helix and slant helix. Thereafter, we construct a vector differential equation of the third order to determine the parametric representation of a k-slant helix according to standard frame in Euclidean 3-space. Finally, we apply this method to find the position vector of some examples of 2-slant helix by means of intrinsic equations.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90479891","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.52.2021.3253
M. I. Khan
In this paper, a new class of distribution has been characterized through the condi- tional expectations, conditioned on a non-adjacent upper record value. Also an equivalence between the unconditional and conditional expectation is used to characterize the new class of distribution.
{"title":"Characterization of a New Family of Distribution Through Upper Record Values","authors":"M. I. Khan","doi":"10.5556/J.TKJM.52.2021.3253","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3253","url":null,"abstract":"In this paper, a new class of distribution has been characterized through the condi- tional expectations, conditioned on a non-adjacent upper record value. Also an equivalence between the unconditional and conditional expectation is used to characterize the new class of distribution.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73758992","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.52.2021.3563
Ihssane Hay, A. Bnouhachem, T. Rassias
The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.
{"title":"An Iterative Method for a Common Solution of a Combination of the Split Equilibrium Problem, a Finite Family of Nonexpansive Mapping and a Combination of Variational Inequality Problem","authors":"Ihssane Hay, A. Bnouhachem, T. Rassias","doi":"10.5556/J.TKJM.52.2021.3563","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3563","url":null,"abstract":"The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"124 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86434026","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.52.2021.3326
Moytri Sarmah
Let N be a near-ring and I be an ideal of N. The graph of N with respect to I is a graph with V (N ) as vertex set and any two distinct vertices x and y are adjacent if and only if xNy ⊆ I oryNx ⊆ I. This graph is denoted by GI(N). We define the line graph of GI(N) as a graph with each edge of GI (N ) as vertex and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph GI (N ). We denote this graph by L(GI (N )). We have discussed the diameter, girth, clique number, dominating set of L(GI(N)). We have also found conditions for the graph L(GI(N)) to be acycle graph.
{"title":"Line Graph Associated to Graph of a Near-Ring with Respect to an Ideal","authors":"Moytri Sarmah","doi":"10.5556/J.TKJM.52.2021.3326","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3326","url":null,"abstract":"Let N be a near-ring and I be an ideal of N. The graph of N with respect to I is a graph with V (N ) as vertex set and any two distinct vertices x and y are adjacent if and only if xNy ⊆ I oryNx ⊆ I. This graph is denoted by GI(N). We define the line graph of GI(N) as a graph with each edge of GI (N ) as vertex and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph GI (N ). We denote this graph by L(GI (N )). We have discussed the diameter, girth, clique number, dominating set of L(GI(N)). We have also found conditions for the graph L(GI(N)) to be acycle graph.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81336128","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.52.2021.3521
M. Yazdi
In this paper, we propose a new iterative scheme with the help of the gradient- projection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem.
{"title":"A Common Solution of Equilibrium, Constrained Convex Minimization, and Fixed Point Problems","authors":"M. Yazdi","doi":"10.5556/J.TKJM.52.2021.3521","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3521","url":null,"abstract":"\u0000\u0000\u0000In this paper, we propose a new iterative scheme with the help of the gradient- projection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"89 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86575172","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}
{"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":"325 1","pages":""},"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":"1 1","pages":""},"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":"92 1","pages":""},"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":"1 1","pages":""},"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":"8 1","pages":""},"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}
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