Pub Date : 2021-03-18DOI: 10.5556/J.TKJM.52.2021.3327
Ashish Pathak, Dileep Kumar
In this paper, a characterization of orthonormal multilevel wavelet families in Sobolev space over a local fields of positive characteristic (Hs(K)) is established. Finally an example is presented.
{"title":"A Characterization of Orthonormal Multilevel Wavelet Families in Sobolev Space over Local Fields of Positive Characteristic","authors":"Ashish Pathak, Dileep Kumar","doi":"10.5556/J.TKJM.52.2021.3327","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3327","url":null,"abstract":"\u0000\u0000\u0000In this paper, a characterization of orthonormal multilevel wavelet families in Sobolev space over a local fields of positive characteristic (Hs(K)) is established. Finally an example is presented. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89523480","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 : 2021-03-16DOI: 10.5556/J.TKJM.53.2022.3946
Vikas Kumar, Rekha Rani, N. Singh
Non-additive entropymeasures are important formany applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability measures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.
{"title":"Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy","authors":"Vikas Kumar, Rekha Rani, N. Singh","doi":"10.5556/J.TKJM.53.2022.3946","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3946","url":null,"abstract":"Non-additive entropymeasures are important formany applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability measures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85120852","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 : 2021-02-26DOI: 10.5556/J.TKJM.53.2022.3579
M. Moosapoor
In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if T is an invertible chaotic or an invertible subspace-chaotic operator, then T, T−n and λT are subspace-recurrent for any positive integer n and any scalar λ with absolute value 1. Also, we state a subspace-recurrence criterion.
{"title":"On Subspace-recurrent Operators","authors":"M. Moosapoor","doi":"10.5556/J.TKJM.53.2022.3579","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3579","url":null,"abstract":"In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if T is an invertible chaotic or an invertible subspace-chaotic operator, then T, T−n and λT are subspace-recurrent for any positive integer n and any scalar λ with absolute value 1. Also, we state a subspace-recurrence criterion.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82215281","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 : 2021-02-21DOI: 10.5556/J.TKJM.53.2022.3250
Akmal Raza, Arshad Khan
An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11, 29].
{"title":"Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method","authors":"Akmal Raza, Arshad Khan","doi":"10.5556/J.TKJM.53.2022.3250","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3250","url":null,"abstract":"An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11, 29].","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83339464","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 : 2021-02-16DOI: 10.5556/J.TKJM.53.2022.3550
A. Naimi, Tellab Brahim, K. Zennir
This paper deals with the existence and uniqueness results for the solution of a Neutral fractional integro-differential problem with nonlocal conditions. Using the Nonlinear alternative for single valued maps, Krasnoselskii’s and Banach fixed point theorems to proof our main results. An example is given to illustrate our main results.
{"title":"Existence and Stability Results for the Solution of Neutral Fractional Integro-Differential Equation with Nonlocal Conditions","authors":"A. Naimi, Tellab Brahim, K. Zennir","doi":"10.5556/J.TKJM.53.2022.3550","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3550","url":null,"abstract":"This paper deals with the existence and uniqueness results for the solution of a Neutral fractional integro-differential problem with nonlocal conditions. Using the Nonlinear alternative for single valued maps, Krasnoselskii’s and Banach fixed point theorems to proof our main results. An example is given to illustrate our main results.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76081688","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 : 2021-02-15DOI: 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":"1 1","pages":""},"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":"74 1","pages":""},"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.52.2021.3246
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":"5 1","pages":""},"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.52.2021.3519
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":"104 1","pages":""},"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.52.2021.3373
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":"43 1","pages":""},"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}
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