Pub Date : 2021-02-15DOI: 10.5556/J.TKJM.53.2022.3973
Carlos Gómez
In this article we investigate on the representation of Fibonacci numbers in the form x^a pm x^b pm 1, for x in the sequence of Mersenne and Fermat numbers.
在本文中，我们研究了斐波那契数在梅森和费马数列中的x以x^a pm x^b pm 1的形式的表示。
{"title":"On the Diophantine Equation Fn = x^a pm x^b pm 1 in Mersenne and Fermat Numbers","authors":"Carlos Gómez","doi":"10.5556/J.TKJM.53.2022.3973","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3973","url":null,"abstract":"In this article we investigate on the representation of Fibonacci numbers in the form x^a pm x^b pm 1, for x in the sequence of Mersenne and Fermat numbers.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89951608","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 : 2021-02-06DOI: 10.22541/AU.161264069.97983099/V1
Kuo-Shou Chiu
In this paper, we investigate the models of the impulsive cellular neural network with piecewise alternately advanced and retarded argument of generalized argument (in short IDEPCAG). To ensure the existence, uniqueness and global exponential stability of the equilibrium state, several new sufficient conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEPCAG’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of proposed results. We end the article with a brief conclusion.
{"title":"Analyzing stability of equilibrium points in impulsive neural network models involving generalized piecewise alternately advanced and retarded argument","authors":"Kuo-Shou Chiu","doi":"10.22541/AU.161264069.97983099/V1","DOIUrl":"https://doi.org/10.22541/AU.161264069.97983099/V1","url":null,"abstract":"In this paper, we investigate the models of the impulsive cellular\u0000neural network with piecewise alternately advanced and retarded argument\u0000of generalized argument (in short IDEPCAG). To ensure the existence,\u0000uniqueness and global exponential stability of the equilibrium state,\u0000several new sufficient conditions are obtained, which extend the results\u0000of the previous literature. The method is based on utilizing Banach’s\u0000fixed point theorem and a new IDEPCAG’s Gronwall inequality. The\u0000criteria given are easy to check and when the impulsive effects do not\u0000affect, the results can be extracted from those of the non-impulsive\u0000systems. Typical numerical simulation examples are used to show the\u0000validity and effectiveness of proposed results. We end the article with\u0000a brief conclusion.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83130021","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.52.2021.3519
A. Choucha, D. Ouchenane, K. Zennir
As a continuity to the study by T. A. Apalarain[3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1.
作为T. a . Apalarain[3]研究的延续，我们考虑了在第二个方程中同时存在记忆项和分布延迟项的一维多孔弹性系统。利用众所周知的能量法结合李雅普诺夫泛函方法，我们证明了定理2.1中给出的一般衰减结果。
{"title":"General Decay of Solutions in One-Dimensional Porous-Elastic with Memory and Distributed Delay Term","authors":"A. Choucha, D. Ouchenane, K. Zennir","doi":"10.5556/J.TKJM.52.2021.3519","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3519","url":null,"abstract":"As a continuity to the study by T. A. Apalarain[3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1.","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":"79299677","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.52.2021.3246
C. Lalmalsawma, J. Singh
The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.
{"title":"Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection","authors":"C. Lalmalsawma, J. Singh","doi":"10.5556/J.TKJM.52.2021.3246","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3246","url":null,"abstract":"The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.","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":"80524320","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.52.2021.3373
F. Saeedi, Nafiseh Akbarossadat
Let $L$ be an $n$-Lie algebra over a field $F$. In this paper, we introduce the notion of non-abelian tensor square $Lotimes L$ of $L$ and define the central ideal $Lsquare L$ of it. Using techniques from group theory and Lie algebras, we show that that $Lsquare Lcong L^{ab}square L^{ab}$. Also, we establish the short exact sequence[0lraM(L)lrafrac{Lotimes L}{Lsquare L}lra L^2lra0]and apply it to compute an upper bound for the dimension of non-abelian tensor square of $L$.
{"title":"On the Dimension of Non-Abelian Tensor Squares of $n$-Lie Algebras","authors":"F. Saeedi, Nafiseh Akbarossadat","doi":"10.5556/J.TKJM.52.2021.3373","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3373","url":null,"abstract":"Let $L$ be an $n$-Lie algebra over a field $F$. In this paper, we introduce the notion of non-abelian tensor square $Lotimes L$ of $L$ and define the central ideal $Lsquare L$ of it. Using techniques from group theory and Lie algebras, we show that that $Lsquare Lcong L^{ab}square L^{ab}$. Also, we establish the short exact sequence[0lraM(L)lrafrac{Lotimes L}{Lsquare L}lra L^2lra0]and apply it to compute an upper bound for the dimension of non-abelian tensor square of $L$.","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":"76725600","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.52.2021.3463
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":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":"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":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":"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.52.2021.3326
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":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":"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.52.2021.3563
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":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":"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.52.2021.3521
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":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":"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：