Pub Date : 2021-04-13DOI: 10.5556/J.TKJM.53.2022.3729
M. Lone, Mohamd Saleem Lone, M. Shahid
In the present paper, we form a sharp inequality for a doubly warped product submanifold of a Riemannian manifold of nearly quasi-constant curvature.
本文给出了近似准常曲率黎曼流形的双翘曲积子流形的一个尖锐不等式。
{"title":"Doubly Warped Product Submanifolds of a Riemannian Manifold of Nearly Quasi-constant Curvature","authors":"M. Lone, Mohamd Saleem Lone, M. Shahid","doi":"10.5556/J.TKJM.53.2022.3729","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3729","url":null,"abstract":"\u0000\u0000\u0000In the present paper, we form a sharp inequality for a doubly warped product submanifold of a Riemannian manifold of nearly quasi-constant curvature. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78800898","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 : 2021-04-13DOI: 10.5556/J.TKJM.53.2022.3295
M. Pitchaimani, A. S. Devi
In this article, a mathematical model to study the dynamics of HIV-TB coinfection with two time delays is proposed and analyzed. We compute the basic reproduction number for each disease (HIV and TB) which acts as a threshold parameters. The disease dies out when the basic reproduction number of both diseases are less than unity and persists when the basic reproduction number of atleast one of the disease is greater than unity. A numerical study on the model is also performed to investigate the influence of certain key parameters on the spread of the disease. Mathematical analysis of our model shows that switching co-infection (HIV and TB) to single infection (HIV) can be achieved by imposing treatment for both the disease simultaneously as TB eradication is made possible with effective treatment.
{"title":"Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays","authors":"M. Pitchaimani, A. S. Devi","doi":"10.5556/J.TKJM.53.2022.3295","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3295","url":null,"abstract":"In this article, a mathematical model to study the dynamics of HIV-TB coinfection with two time delays is proposed and analyzed. We compute the basic reproduction number for each disease (HIV and TB) which acts as a threshold parameters. The disease dies out when the basic reproduction number of both diseases are less than unity and persists when the basic reproduction number of atleast one of the disease is greater than unity. A numerical study on the model is also performed to investigate the influence of certain key parameters on the spread of the disease. Mathematical analysis of our model shows that switching co-infection (HIV and TB) to single infection (HIV) can be achieved by imposing treatment for both the disease simultaneously as TB eradication is made possible with effective treatment.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79109533","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 : 2021-04-11DOI: 10.5556/J.TKJM.53.2022.3893
Argha Ghosh, Samiran Das
We introduce the notions of strongly $lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $lambda$-statistically convergent sequences are strongly $lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $lambda$-statistically pre-Cauchy but not strongly $lambda$-statistically convergent.
{"title":"Strongly $lambda$-Statistically and Strongly Vallée-Poussin Pre-Cauchy Sequences in Probabilistic Metric Spaces","authors":"Argha Ghosh, Samiran Das","doi":"10.5556/J.TKJM.53.2022.3893","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3893","url":null,"abstract":"We introduce the notions of strongly $lambda$-statistically pre-Cauchy and strongly Vall´ee-Poussin pre-Cauchy sequences in probabilistic metric spaces endowed with strong topology. And we show that these two new notions are equivalent. Strongly $lambda$-statistically convergent sequences are strongly $lambda$-statistically pre-Cauchy sequences, and we give an example to show that there is a sequence in a probabilistic metric space which is strongly $lambda$-statistically pre-Cauchy but not strongly $lambda$-statistically convergent.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83321326","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.53.2022.3296
Farah Balaadich, E. Azroul
We prove an existence result for solutions of nonlinear p-Laplacian systems with data in generalized form: { −divΦ(Du−Θ(u)) = f(x, u,Du) in Ω u = 0 on ∂Ω by the theory of Young measures.
利用杨氏测度理论证明了在∂Ω上的Ω u = 0中数据为广义形式{−divΦ(Du−Θ(u)) = f(x, u,Du)的非线性p-拉普拉斯系统解的存在性。
{"title":"Elliptic Systems of $p$-Laplacian Type","authors":"Farah Balaadich, E. Azroul","doi":"10.5556/J.TKJM.53.2022.3296","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3296","url":null,"abstract":"We prove an existence result for solutions of nonlinear p-Laplacian systems with data in generalized form: { −divΦ(Du−Θ(u)) = f(x, u,Du) in Ω u = 0 on ∂Ω by the theory of Young measures.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79786639","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.52.2021.3523
L. Volkmann
Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on a digraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfying the condition that $sum_{xin N^-[v]}f(x)ge 1$ for each $vin V(D)$, where $N^-[v]$ consists of $v$ and allvertices of $D$ from which arcs go into $v$. The weight of a WSRDF $f$ is $sum_{vin V(D)}f(v)$. The weak signed Roman domination number $gamma_{wsR}(D)$ of $D$ is the minimum weight of a WSRDF on $D$. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on $gamma_{wsR}(D)$. In addition, we determine the weak signed Roman domination number of some classesof digraphs.
{"title":"Weak Signed Roman Domination in Digraphs","authors":"L. Volkmann","doi":"10.5556/J.TKJM.52.2021.3523","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3523","url":null,"abstract":"Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on a digraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfying the condition that $sum_{xin N^-[v]}f(x)ge 1$ for each $vin V(D)$, where $N^-[v]$ consists of $v$ and allvertices of $D$ from which arcs go into $v$. The weight of a WSRDF $f$ is $sum_{vin V(D)}f(v)$. The weak signed Roman domination number $gamma_{wsR}(D)$ of $D$ is the minimum weight of a WSRDF on $D$. In this paper we initiate the study of the weak signed Roman domination number of digraphs, and we present different bounds on $gamma_{wsR}(D)$. In addition, we determine the weak signed Roman domination number of some classesof digraphs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78488400","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.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":"28 1","pages":""},"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":"120 1","pages":""},"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":"36 1","pages":""},"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":"2 1","pages":""},"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":"54 1","pages":""},"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}
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