Pub Date : 2023-03-28DOI: 10.5556/j.tkjm.55.2024.5031
A. Ayoade, N. Nyerere, M. Ibrahim
Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.
{"title":"An epidemic model for control and possible elimination of Lassa fever","authors":"A. Ayoade, N. Nyerere, M. Ibrahim","doi":"10.5556/j.tkjm.55.2024.5031","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5031","url":null,"abstract":"Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79241851","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 : 2023-03-26DOI: 10.5556/j.tkjm.55.2024.4821
C. Feng
In this paper, a class of nonlinear predator-prey models with three discrete delays is considered. By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system, two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays. Some numerical simulations are provided to illustrate our theoretical prediction.
{"title":"Existence of positive periodic solutions for a predator-prey model","authors":"C. Feng","doi":"10.5556/j.tkjm.55.2024.4821","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.4821","url":null,"abstract":"In this paper, a class of nonlinear predator-prey models with three discrete delays is considered.\u0000By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system,\u0000two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained.\u0000It is found that under suitable conditions on the parameters, time delay affects the stability of the system.\u0000The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays.\u0000Some numerical simulations are provided to illustrate our theoretical prediction.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88939022","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 : 2023-03-15DOI: 10.5556/j.tkjm.55.2024.5066
Gizem Koprulu Karakas, B. Şahin
The purpose of this paper is to study triharmonic curves along Riemannian submersions from Riemannian manifolds onto Riemannian manifolds. We obtain necessary and sufficient conditions for a triharmonic curve on the total manifoldof Riemannian submersion from a space form ( respectively, a complex space form) to a Riemannian manifold to be triharmonic curve on the base manifold. The above research problem is also studied in the complex setting of the manifoldon which the Riemannian submersion is defined. In addition, we give several results involving curvature conditions for a triharmonic curves along Riemannian submersions.
{"title":"Triharmonic curves along Riemannian submersions","authors":"Gizem Koprulu Karakas, B. Şahin","doi":"10.5556/j.tkjm.55.2024.5066","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5066","url":null,"abstract":"The purpose of this paper is to study triharmonic curves along Riemannian submersions from Riemannian manifolds onto Riemannian manifolds. We obtain necessary and sufficient conditions for a triharmonic curve on the total manifoldof Riemannian submersion from a space form ( respectively, a complex space form) to a Riemannian manifold to be triharmonic curve on the base manifold. The above research problem is also studied in the complex setting of the manifoldon which the Riemannian submersion is defined. In addition, we give several results involving curvature conditions for a triharmonic curves along Riemannian submersions.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76738754","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 : 2023-03-13DOI: 10.5556/j.tkjm.55.2024.3913
L. Saha
For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $displaystylemax_{vin V(G)}f(v)$ and the emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $displaystylemin_{f}{~span_f(G)}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $kin{n-1, n-2,n-3}$ in different approach but simple way.
{"title":"A different approach for multi-level distance labellings of path structure networks","authors":"L. Saha","doi":"10.5556/j.tkjm.55.2024.3913","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.3913","url":null,"abstract":"For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $displaystylemax_{vin V(G)}f(v)$ and the emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $displaystylemin_{f}{~span_f(G)}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $kin{n-1, n-2,n-3}$ in different approach but simple way.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76828829","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 : 2022-11-15DOI: 10.5556/j.tkjm.54.2023.4954
Foko Kamseu Maturin, D. David, Abel Nguelemo Kenfack, Woukeng Jean Louis
This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.
{"title":"Viscosity solutions for the relativistic inhomogeneous Vlasov equation in Schwarzschild outer space-time in the presence of the Yang-Mills field","authors":"Foko Kamseu Maturin, D. David, Abel Nguelemo Kenfack, Woukeng Jean Louis","doi":"10.5556/j.tkjm.54.2023.4954","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4954","url":null,"abstract":"This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75444667","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 : 2022-11-14DOI: 10.5556/j.tkjm.54.2023.4876
F. Pashaie
Biconservative submanifolds, with important role in mathematical physics and differential geometry, arise as the conservative stress-energy tensor associated to the variational problem of biharmonic submanifolds. Many examples of biconservative hypersurfaces have constant mean curvature. A famous conjecture of Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null mean curvature. Inspired by Chen conjecture, we study biconservative Lorentz submanifolds of the Minkowski spaces. Although the conjecture has not been generally confirmed, it has been proven in many cases, and this has led to its spread to various types of submenifolds. As an extension, we consider a advanced version of the conjecture (namely, $L_1$-conjecture) on Lorentz hypersurfaces of the pseudo-Euclidean space $mathbb{M}^5 :=mathbb{E}^5_1$ (i.e. the Minkowski 5-space). We show every $L_1$-biconservative Lorentz hypersurface of $mathbb{M}^5$ with constant mean curvature and at least three principal curvatures has constant second mean curvature.
{"title":"Biconservative Lorentz Hypersurfaces with at Least Three Principal Curvatures","authors":"F. Pashaie","doi":"10.5556/j.tkjm.54.2023.4876","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4876","url":null,"abstract":"Biconservative submanifolds, with important role in mathematical physics and differential geometry, arise as the conservative stress-energy tensor associated to the variational problem of biharmonic submanifolds. Many examples of biconservative hypersurfaces have constant mean curvature. A famous conjecture of Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null mean curvature. Inspired by Chen conjecture, we study biconservative Lorentz submanifolds of the Minkowski spaces. Although the conjecture has not been generally confirmed, it has been proven in many cases, and this has led to its spread to various types of submenifolds. As an extension, we consider a advanced version of the conjecture (namely, $L_1$-conjecture) on Lorentz hypersurfaces of the pseudo-Euclidean space $mathbb{M}^5 :=mathbb{E}^5_1$ (i.e. the Minkowski 5-space). We show every $L_1$-biconservative Lorentz hypersurface of $mathbb{M}^5$ with constant mean curvature and at least three principal curvatures has constant second mean curvature.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81755974","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 : 2022-10-20DOI: 10.5556/j.tkjm.54.2023.4865
Monika Swami, S. Rathee
In the recent work, a new hybrid technique for computing the common solution of fixed point of a finite family of two non-expansive mapping and variational inequality problem for inverse strongly monotone mapping in a real Hilbert space is provided. We also demonstrate the convergence of the hybrid approach using an example.
{"title":"Algorithm for Finite Family of Variational Inequality with Fixed Point of Two Non-expansive Mappings","authors":"Monika Swami, S. Rathee","doi":"10.5556/j.tkjm.54.2023.4865","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4865","url":null,"abstract":"In the recent work, a new hybrid technique for computing the common solution of fixed point of a finite family of two non-expansive mapping and variational inequality problem for inverse strongly monotone mapping in a real Hilbert space is provided. We also demonstrate the convergence of the hybrid approach using an example.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85418114","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 : 2022-10-15DOI: 10.5556/j.tkjm.54.2023.4966
L. Shahbaz
In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S.
{"title":"Adjoint Relations Between the Category of Poset Acts and Some Other Categories","authors":"L. Shahbaz","doi":"10.5556/j.tkjm.54.2023.4966","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4966","url":null,"abstract":"In this paper, first the congruences in the category PosAct-S of all poset acts over a pomonoid S; an S-act in the category Pos of all posets, with action preserving monotone maps between them, are introduced. Then, we study the existence of the free and cofree objects in the category PosAct-S. More precisely, we consider all forgetful functors between this category and the categories Pos-S of all S-posets, Pos of all posets, Act-S of all S-acts, and Set of all sets, and we study the existence of their left and right adjoints. It is shown that the category Pos-S is a full reflective and coreflective subcategory of PosAct-S.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82685186","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 : 2022-10-14DOI: 10.5556/j.tkjm.54.2023.4175
Wakjira Tolassa Gobena, G. Duressa
This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.
{"title":"Fitted Operator Average Finite Difference Method for Singularly Perturbed Delay Parabolic Reaction Diffusion Problems with Non-Local Boundary Conditions","authors":"Wakjira Tolassa Gobena, G. Duressa","doi":"10.5556/j.tkjm.54.2023.4175","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4175","url":null,"abstract":"This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81124628","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 : 2022-10-14DOI: 10.5556/j.tkjm.54.2023.4061
M. Rashid
Some power inequalities for the numerical radius based on the recent Dragomir extension of Furuta's inequality are established. Some particular cases are also provided. Moreover, we get an improvement of the H"older-McCarthy operator inequality in the case when $rgeq 1$ and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.
{"title":"Refinements of Some Numerical Radius Inequalities for Hilbert Space Operators","authors":"M. Rashid","doi":"10.5556/j.tkjm.54.2023.4061","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4061","url":null,"abstract":"Some power inequalities for the numerical radius based on the recent Dragomir extension of Furuta's inequality are established. Some particular cases are also provided. Moreover, we get an improvement of the H\"older-McCarthy operator inequality in the case when $rgeq 1$ and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79978613","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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