Pub Date : 2021-04-08DOI: 10.5556/J.TKJM.53.2022.3853
Burhan Selçuk
This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as kt blows up at the same finite time and lower bound estimates of the quenching time of the equation kt = (kn)xx + (1 − k)−α, (x,t) ∈ (0,L) × (0,T) with (kn)x (0,t) = 0, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k(x,0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants. Second, we obtain that finite time queching on the boundary, as well as kt blows up at the same finite time and a local existence resultbythehelpofsteadystateoftheequationkt =(kn)xx,(x,t)∈(0,L)×(0,T)with (kn)x (0,t) = (1 − k(0,t))−α, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k (x, 0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants.
{"title":"Quenching for Porous Medium Equations","authors":"Burhan Selçuk","doi":"10.5556/J.TKJM.53.2022.3853","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3853","url":null,"abstract":"\u0000\u0000\u0000This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as kt blows up at the same finite time and lower bound estimates of the quenching time of the equation kt = (kn)xx + (1 − k)−α, (x,t) ∈ (0,L) × (0,T) with (kn)x (0,t) = 0, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k(x,0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants. Second, we obtain that finite time queching on the boundary, as well as kt blows up at the same finite time and a local existence resultbythehelpofsteadystateoftheequationkt =(kn)xx,(x,t)∈(0,L)×(0,T)with (kn)x (0,t) = (1 − k(0,t))−α, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k (x, 0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83638236","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 : 2021-04-08DOI: 10.5556/J.TKJM.52.2021.3233
Pradip Mandal, Y. Mandal, S. Hui
ThesubmanifoldsofSasakianmanifoldswithaconcurrentvectorfieldhavebeen studied. Applications of such submanifolds to Ricci solitons and Yamabe solitons has also been showed.
{"title":"Submanifolds of Sasakian Manifolds with Concurrent Vector Field","authors":"Pradip Mandal, Y. Mandal, S. Hui","doi":"10.5556/J.TKJM.52.2021.3233","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3233","url":null,"abstract":"\u0000\u0000\u0000ThesubmanifoldsofSasakianmanifoldswithaconcurrentvectorfieldhavebeen studied. Applications of such submanifolds to Ricci solitons and Yamabe solitons has also been showed. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89045432","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 : 2021-04-07DOI: 10.5556/J.TKJM.53.2022.3436
S. Leeratanavalee, Jukkrit Daengsaen
Any relational hypersubstitution for algebraic systems of type (τ, τ ′) = ((mi)i∈I , (nj)j∈J) is a mapping which maps anymi-ary operation symbol to anmi-ary term and maps any njary relational symbol to an nj-ary relational term preserving arities, where I, J are indexed sets. Some algebraic properties of themonoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’s relations on the regular part of this monoid of a particular type (τ, τ ′) = ((m), (n)), wherem,n ≥ 2.
{"title":"Green’s Relations on Regular Elements of Semigroup of Relational Hypersubstitutions for Algebraic Systems of Type ((m), (n))","authors":"S. Leeratanavalee, Jukkrit Daengsaen","doi":"10.5556/J.TKJM.53.2022.3436","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3436","url":null,"abstract":"Any relational hypersubstitution for algebraic systems of type (τ, τ ′) = ((mi)i∈I , (nj)j∈J) is a mapping which maps anymi-ary operation symbol to anmi-ary term and maps any njary relational symbol to an nj-ary relational term preserving arities, where I, J are indexed sets. Some algebraic properties of themonoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’s relations on the regular part of this monoid of a particular type (τ, τ ′) = ((m), (n)), wherem,n ≥ 2.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80083567","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 : 2021-04-04DOI: 10.5556/J.TKJM.53.2022.3761
D. Dey
In the present paper, we characterize Ricci symmetric almost Kenmotsu manifolds under several constraints and proved that they are Einstein manifolds. As a consequence, we obtain several corollaries. Finally, an illustrative example is presented to verify our results.
{"title":"On The Ricci Symmetry of Almost Kenmotsu Manifolds","authors":"D. Dey","doi":"10.5556/J.TKJM.53.2022.3761","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3761","url":null,"abstract":"\u0000\u0000\u0000In the present paper, we characterize Ricci symmetric almost Kenmotsu manifolds under several constraints and proved that they are Einstein manifolds. As a consequence, we obtain several corollaries. Finally, an illustrative example is presented to verify our results. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89365444","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 : 2021-03-22DOI: 10.5556/J.TKJM.53.2022.3638
G. Duressa, M. Woldaregay
In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using implicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.
{"title":"Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations","authors":"G. Duressa, M. Woldaregay","doi":"10.5556/J.TKJM.53.2022.3638","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3638","url":null,"abstract":"In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using implicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90756516","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 : 2021-03-18DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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