Pub Date : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3367
B. S. Ogundare, J. Akingbade
In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.
{"title":"Boundedness and Stability Properties of Solutions of Mathematical Model of Measles.","authors":"B. S. Ogundare, J. Akingbade","doi":"10.5556/J.TKJM.52.2021.3367","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3367","url":null,"abstract":"In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"2 1","pages":"91-112"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85758469","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3047
K. O. Babalola, Mashood Sidiq
Recent studies in the class of Bazilevi$check{c}$ maps as a whole has compelled the development, in this work, of certain complex-parameter integral iterations of Caratheodory maps. The iterations are employed in a similar manner as in cite{BA} to study a certain subfamily of those Bazilevi$check{c}$ maps.
{"title":"Complex-Parameter Integral Iterations of Caratheodory Maps","authors":"K. O. Babalola, Mashood Sidiq","doi":"10.5556/j.tkjm.51.2020.3047","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3047","url":null,"abstract":"Recent studies in the class of Bazilevi$check{c}$ maps as a whole has compelled the development, in this work, of certain complex-parameter integral iterations of Caratheodory maps. The iterations are employed in a similar manner as in cite{BA} to study a certain subfamily of those Bazilevi$check{c}$ maps.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"119 45","pages":"289-301"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72376041","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3087
N. Khan, Talha Usma, M. Aman
Abstract. In this paper, we introduce a new generalization of the Wright function by using an extended beta function and study some classical properties of this function. We establish several formulas involving integral transforms (e.g. Jacobi transform, Gegenbauer transform) and the generalized family of Wright function that does not seem to be reported in the literature even for the basic Wright function. Furthermore, we discuss other results including the recurrence relation, derivative formula, fractional derivative formula and also a partly bilateral and partly unilateral generating relation for the generalized Wright function.
{"title":"Generalized Wright Function and Its Properties Using Extended Beta Function","authors":"N. Khan, Talha Usma, M. Aman","doi":"10.5556/j.tkjm.51.2020.3087","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3087","url":null,"abstract":"Abstract. In this paper, we introduce a new generalization of the Wright function by using an extended beta function and study some classical properties of this function. We establish several formulas involving integral transforms (e.g. Jacobi transform, Gegenbauer transform) and the generalized family of Wright function that does not seem to be reported in the literature even for the basic Wright function. Furthermore, we discuss other results including the recurrence relation, derivative formula, fractional derivative formula and also a partly bilateral and partly unilateral generating relation for the generalized Wright function.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"6 1","pages":"349-363"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75919751","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.2860
Shaibu Osman, O. Makinde, D. Theuri
Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.
{"title":"Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.","authors":"Shaibu Osman, O. Makinde, D. Theuri","doi":"10.5556/j.tkjm.51.2020.2860","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.2860","url":null,"abstract":"Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"96 1","pages":"261-287"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81525195","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3188
F. Pashaie
A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3rightarrowE_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.
Bang yan - chen的一个著名猜想是:双调和欧氏子流形是最小流形。本文研究了伪欧几里德空间E_1^4$上的非退化类时超曲面上的一个扩展条件(即$L_1$-双谐性)。如果满足条件$L_1^2x=0$，则称为$L_1$-双调和，其中$L_1$是与$M_1^3$上的第2平均曲率向量场的第一次变分相关的线性化算子。根据主曲率的多重性，在伪欧几里德空间E_1^4$中，对具有常平均曲率的洛伦兹超曲面，证实了Chen猜想的L_1 -推广。此外，我们还证明了$E_1^4$中不存在固有的$L_1$-双调和$L_1$-有限型连通可定向洛伦兹超曲面。
{"title":"On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$","authors":"F. Pashaie","doi":"10.5556/j.tkjm.51.2020.3188","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3188","url":null,"abstract":"A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3rightarrowE_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"28 1","pages":"313-332"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77161092","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3077
U. De, C. Dey
In the present paper we study three dimensional cosymplectic manifolds admitting almost Ricci solitons. Among others we prove that in a three dimensional compact orientable cosymplectic manifold M^3 withoutboundary an almost Ricci soliton reduces to Ricci soliton under certain restriction on the potential function lambda. As a consequence we obtain several corollaries. Moreover we study gradient almost Ricci solitons.
{"title":"On Three Dimensional Cosymplectic Manifolds Admitting Almost Ricci Solitons","authors":"U. De, C. Dey","doi":"10.5556/j.tkjm.51.2020.3077","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3077","url":null,"abstract":"In the present paper we study three dimensional cosymplectic manifolds admitting almost Ricci solitons. Among others we prove that in a three dimensional compact orientable cosymplectic manifold M^3 withoutboundary an almost Ricci soliton reduces to Ricci soliton under certain restriction on the potential function lambda. As a consequence we obtain several corollaries. Moreover we study gradient almost Ricci solitons.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"51 1","pages":"303-312"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85319834","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 : 2020-11-01DOI: 10.5556/j.tkjm.51.2020.3249
Devipriya Ganeshan, K. Ts
Wireless sensor networks (WSNs) have received wide-ranging considerationdue to their boundless potential in civil and military applications. Maliciousself-replicating codes, known as malware, pose substantial threat to the wireless computing infrastructure. The attacks of the malicious signals in the WSNare epidemic in nature. Biological epidemic models will be helpful to understand the dynamical behavior of the malware attack in WSN. In this paper,A (SEIRS-V) Susceptible - Exposed - Infected - Recovered - Susceptible witha Vaccination compartment, describing the undercurrents of worm propagation with respect to time in wireless sensor network (WSN) is considered. Theanalytical solution of WSN is obtained by Homotopy Perturbation Method.Numerical results are obtained and are graphically interpreted using Maple.The results assures that the dynamics of worm propagation in WSN by theproposed model exhibits rich dynamics.
{"title":"Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method","authors":"Devipriya Ganeshan, K. Ts","doi":"10.5556/j.tkjm.51.2020.3249","DOIUrl":"https://doi.org/10.5556/j.tkjm.51.2020.3249","url":null,"abstract":"Wireless sensor networks (WSNs) have received wide-ranging considerationdue to their boundless potential in civil and military applications. Maliciousself-replicating codes, known as malware, pose substantial threat to the wireless computing infrastructure. The attacks of the malicious signals in the WSNare epidemic in nature. Biological epidemic models will be helpful to understand the dynamical behavior of the malware attack in WSN. In this paper,A (SEIRS-V) Susceptible - Exposed - Infected - Recovered - Susceptible witha Vaccination compartment, describing the undercurrents of worm propagation with respect to time in wireless sensor network (WSN) is considered. Theanalytical solution of WSN is obtained by Homotopy Perturbation Method.Numerical results are obtained and are graphically interpreted using Maple.The results assures that the dynamics of worm propagation in WSN by theproposed model exhibits rich dynamics.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"7 1","pages":"333-347"},"PeriodicalIF":0.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83483134","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 : 2020-10-31DOI: 10.5556/j.tkjm.53.2022.3491
Junesang Choi, N. Khan, T. Usman
A variety of polynomials, their extensions and variants have been extensively investigated, due mainly to their potential applications in diverse research areas. In this paper, we aim to introduce Laguerre-based generalized Apostol type polynomials and investigate some properties and identities involving them. Among them, some differential-recursive relations for the Hermite-Laguerre polynomials, which are expressed in terms of generalized Apostol type numbers and the Laguerre-based generalized Apostol type polynomials, an implicit summation formula and addition-symmetry identities for the Laguerre-based generalized Apostol type polynomials are presented. The results presented here, being very general, are pointed out to reduce to yield some known or new formulas and identities for relatively simple polynomials and numbers.
{"title":"Certain Laguerre-based Generalized Apostol Type Polynomials","authors":"Junesang Choi, N. Khan, T. Usman","doi":"10.5556/j.tkjm.53.2022.3491","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3491","url":null,"abstract":"A variety of polynomials, their extensions and variants have been extensively investigated, due mainly to their potential applications in diverse research areas. In this paper, we aim to introduce Laguerre-based generalized Apostol type polynomials and investigate some properties and identities involving them. Among them, some differential-recursive relations for the Hermite-Laguerre polynomials, which are expressed in terms of generalized Apostol type numbers and the Laguerre-based generalized Apostol type polynomials, an implicit summation formula and addition-symmetry identities for the Laguerre-based generalized Apostol type polynomials are presented. The results presented here, being very general, are pointed out to reduce to yield some known or new formulas and identities for relatively simple polynomials and numbers.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78312427","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 : 2020-10-24DOI: 10.5556/j.tkjm.52.2021.3721
V. Yurko
Non-self-adjoint second-order differential operators on the half-line with indefinite discontinuous weights are studied. Properties of spectral characteristics are established and inverse problems of recovering operators from their spectral characteristics are investigated. For these class of nonlinear inverse problems algorithms for constructing the global solutions are developed, and uniqueness theorems are proved.
{"title":"Recovering Differential Operators on the Half-Line with Indefinite Discontinuous Weights","authors":"V. Yurko","doi":"10.5556/j.tkjm.52.2021.3721","DOIUrl":"https://doi.org/10.5556/j.tkjm.52.2021.3721","url":null,"abstract":"Non-self-adjoint second-order differential operators on the half-line with indefinite discontinuous weights are studied. Properties of spectral characteristics are established and inverse problems of recovering operators from their spectral characteristics are investigated. For these class of nonlinear inverse problems algorithms for constructing the global solutions are developed, and uniqueness theorems are proved.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75291016","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 : 2020-10-24DOI: 10.5556/j.tkjm.52.2021.3645
Shueh-Inn Hu, Thakyin Hu
Suppose $X$ is a Banach space and $K$ is a compact convex subset of $X$. Let $mathcal{F}$ be a commutative family of continuous affine mappings of $K$ into $K$. It follows from Markov-Kakutani Theorem that $mathcal{F}$ has a common fixed point in $K$. Suppose now $(CC(X), h)$ is the corresponding hyperspace of $X$ containing all compact, convex subsets of $X$ endowed with Hausdorff metric $h$. We shall prove the above version of Markov-Kakutani Theorem is valid on the hyperspace $(CC(X), h)$.
{"title":"Markov-Kakutani Theorem on Hyperspace of a Banach Space","authors":"Shueh-Inn Hu, Thakyin Hu","doi":"10.5556/j.tkjm.52.2021.3645","DOIUrl":"https://doi.org/10.5556/j.tkjm.52.2021.3645","url":null,"abstract":"Suppose $X$ is a Banach space and $K$ is a compact convex subset of $X$. Let $mathcal{F}$ be a commutative family of continuous affine mappings of $K$ into $K$. It follows from Markov-Kakutani Theorem that $mathcal{F}$ has a common fixed point in $K$. Suppose now $(CC(X), h)$ is the corresponding hyperspace of $X$ containing all compact, convex subsets of $X$ endowed with Hausdorff metric $h$. We shall prove the above version of Markov-Kakutani Theorem is valid on the hyperspace $(CC(X), h)$.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81372993","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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