Pub Date : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3298
K. Roy, M. Saha, Ismat Beg
We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.
{"title":"Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space","authors":"K. Roy, M. Saha, Ismat Beg","doi":"10.5556/J.TKJM.52.2021.3298","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3298","url":null,"abstract":"We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"82 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86571732","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3241
R. Hasenauer, Bethany Kubik
Given a ring $R$, an ideal $I$ of $R$, and an element $ain I$, we say $a=lambda b_1cdots b_k$ is a $tau_I$-factorization of $a$ if $lambda$ is any unit and $b_1equivcdotsequiv b_kpmod{I}$. In this paper, we investigate the $tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.
{"title":"$tau$-Atomicity and Quotients of Size Four","authors":"R. Hasenauer, Bethany Kubik","doi":"10.5556/J.TKJM.52.2021.3241","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3241","url":null,"abstract":"Given a ring $R$, an ideal $I$ of $R$, and an element $ain I$, we say $a=lambda b_1cdots b_k$ is a $tau_I$-factorization of $a$ if $lambda$ is any unit and $b_1equivcdotsequiv b_kpmod{I}$. In this paper, we investigate the $tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91334473","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3276
H. M. Abood, M. Y. Abass
In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further, the conditions required for this to be an Einstein manifold have been determined.
{"title":"A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type","authors":"H. M. Abood, M. Y. Abass","doi":"10.5556/J.TKJM.52.2021.3276","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3276","url":null,"abstract":"In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further, the conditions required for this to be an Einstein manifold have been determined.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80165514","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 : 2021-02-03DOI: 10.5556/J.TKJM.52.2021.3330
H. Akhadkulov, F. Alsharari, T. Y. Ying
In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.
{"title":"Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations","authors":"H. Akhadkulov, F. Alsharari, T. Y. Ying","doi":"10.5556/J.TKJM.52.2021.3330","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3330","url":null,"abstract":"In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75084884","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 : 2021-02-02DOI: 10.5556/J.TKJM.52.2021.3254
R. Khoeilar, M. Chellali, H. Karami, S. M. Sheikholeslami
For a positive integer $k$, a subset $D$ of vertices in a digraph $overrightarrow{G}$ is a $k$-dominating set if every vertex not in $D$ has at least $k$ direct predecessors in $D.$ The $k$-domination number is the minimum cardinality among all $k$-dominating sets of $overrightarrow{G}$. The game $k$-domination number of a simple and undirected graph is defined by the following game. Two players, $mathcal{A}$ and $mathcal{D}$, orient the edges of the graph alternately until all edges are oriented. Player $mathcal{D}$ starts the game, and his goal is to decrease the $k$-domination number of the resulting digraph, while $mathcal{A}$ is trying to increase it. The game $k$-domination number of the graph $G$ is the $k$-domination number of the directed graph resulting from this game. This is well defined if we suppose that both players follow their optimal strateries. We are mainly interested in the study of the game $2$-domination number, where some upper bounds will be presented. We also establish a Nordhaus-Gaddum bound for the game $2$-domination number of a graph and its complement.
{"title":"Game $k$-Domination Number of Graphs","authors":"R. Khoeilar, M. Chellali, H. Karami, S. M. Sheikholeslami","doi":"10.5556/J.TKJM.52.2021.3254","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3254","url":null,"abstract":"For a positive integer $k$, a subset $D$ of vertices in a digraph $overrightarrow{G}$ is a $k$-dominating set if every vertex not in $D$ has at least $k$ direct predecessors in $D.$ The $k$-domination number is the minimum cardinality among all $k$-dominating sets of $overrightarrow{G}$. The game $k$-domination number of a simple and undirected graph is defined by the following game. Two players, $mathcal{A}$ and $mathcal{D}$, orient the edges of the graph alternately until all edges are oriented. Player $mathcal{D}$ starts the game, and his goal is to decrease the $k$-domination number of the resulting digraph, while $mathcal{A}$ is trying to increase it. The game $k$-domination number of the graph $G$ is the $k$-domination number of the directed graph resulting from this game. This is well defined if we suppose that both players follow their optimal strateries. We are mainly interested in the study of the game $2$-domination number, where some upper bounds will be presented. We also establish a Nordhaus-Gaddum bound for the game $2$-domination number of a graph and its complement.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"76 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89538660","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4087
Hongming You, Kaijen Cheng
In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.
{"title":"Mathematical Analysis of Intraguild Interactions among Hosts, Parasitoids and Predators","authors":"Hongming You, Kaijen Cheng","doi":"10.5556/J.TKJM.52.2021.4087","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4087","url":null,"abstract":"In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"122 1","pages":"171-187"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83503772","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4029
Jong-Shenq Guo
In this paper, we present some recent developments on the application of Schauder’s fixed point theorem to the existence of traveling waves for some three-species predator-prey systems. The existence of traveling waves of predator-prey systems is closely related to the invasion phenomenon of some alien species to the habitat of aboriginal species. Three different three-species predator-prey models with different invaded and invading states are presented. In this paper, we focus on the methodology of deriving the convergence of stale tail of wave profiles.
{"title":"Traveling Wave Solutions for Some Three-Species Predator-Prey Systems","authors":"Jong-Shenq Guo","doi":"10.5556/J.TKJM.52.2021.4029","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4029","url":null,"abstract":"In this paper, we present some recent developments on the application of Schauder’s fixed point theorem to the existence of traveling waves for some three-species predator-prey systems. The existence of traveling waves of predator-prey systems is closely related to the invasion phenomenon of some alien species to the habitat of aboriginal species. Three different three-species predator-prey models with different invaded and invading states are presented. In this paper, we focus on the methodology of deriving the convergence of stale tail of wave profiles.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"29 1","pages":"25-36"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77224079","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.4016
S. Hsu, I. Sun
In this paper we consider a mathematical model of two host species competing for a single -limited resource mediated by parasites. Each host population is divided into susceptible and infective population. We assume that species 1 has the lowest break-even concentration with respect to nutrient, when there is no parasite. Thus species 1 is a superior competitor that outcompetes species 2. When parasites present, the competitive outcome is determined by the contact rate of the superior competitor. We analyze the model by finding the conditions for the existence of various equilibria and doing their stability analysis. Two bifurcation diagrams are presented. The first one is in $beta_1$-$beta_2$ plane (See Figure 3) and the second one is in $R^{(0)}$-line (See Figure 4).
{"title":"Competition of Two Host Species for a Single-Limited Resource Mediated by Parasites","authors":"S. Hsu, I. Sun","doi":"10.5556/J.TKJM.52.2021.4016","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.4016","url":null,"abstract":"In this paper we consider a mathematical model of two host species competing for a single -limited resource mediated by parasites. Each host population is divided into susceptible and infective population. We assume that species 1 has the lowest break-even concentration with respect to nutrient, when there is no parasite. Thus species 1 is a superior competitor that outcompetes species 2. When parasites present, the competitive outcome is determined by the contact rate of the superior competitor. We analyze the model by finding the conditions for the existence of various equilibria and doing their stability analysis. Two bifurcation diagrams are presented. The first one is in $beta_1$-$beta_2$ plane (See Figure 3) and the second one is in $R^{(0)}$-line (See Figure 4).","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"4 1","pages":"1-18"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82078757","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3280
Hilal Ahmad, A. Alhevaz, M. Baghipur, Gui-Xian Tian
For a simple connected graph $G$, the convex linear combinations $D_{alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{alpha}(G)=alpha Tr(G)+(1-alpha)D(G)$, $0leq alphaleq 1$. As $D_{0}(G)=D(G)$, $2D_{frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$ and $D_{alpha}(G)-D_{beta}(G)=(alpha-beta)D^{L}(G)$, this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. In this paper, we study the spectral properties of the generalized distance matrix $D_{alpha}(G)$. We obtain some lower and upper bounds for the generalized distance spectral radius, involving different graph parameters and characterize the extremal graphs. Further, we obtain upper and lower bounds for the maximal and minimal entries of the $ p $-norm normalized Perron vector corresponding to spectral radius $ partial(G) $ of the generalized distance matrix $D_{alpha}(G)$ and characterize the extremal graphs.
{"title":"Bounds for Generalized Distance Spectral Radius and the Entries of the Principal Eigenvector","authors":"Hilal Ahmad, A. Alhevaz, M. Baghipur, Gui-Xian Tian","doi":"10.5556/J.TKJM.52.2021.3280","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3280","url":null,"abstract":"For a simple connected graph $G$, the convex linear combinations $D_{alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{alpha}(G)=alpha Tr(G)+(1-alpha)D(G)$, $0leq alphaleq 1$. As $D_{0}(G)=D(G)$, $2D_{frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$ and $D_{alpha}(G)-D_{beta}(G)=(alpha-beta)D^{L}(G)$, this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. In this paper, we study the spectral properties of the generalized distance matrix $D_{alpha}(G)$. We obtain some lower and upper bounds for the generalized distance spectral radius, involving different graph parameters and characterize the extremal graphs. Further, we obtain upper and lower bounds for the maximal and minimal entries of the $ p $-norm normalized Perron vector corresponding to spectral radius $ partial(G) $ of the generalized distance matrix $D_{alpha}(G)$ and characterize the extremal graphs.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"30 2","pages":"69-89"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72408753","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 : 2021-01-31DOI: 10.5556/J.TKJM.52.2021.3430
Peter D. Johnson, Alexis Krumpelman
The Babai numbers and the upper chromatic number are parameters that can be assigned to any metric space. They can, therefore, be assigned to any connected simple graph. In this paper we make progress in the theory of the first Babai number and the upper chromatic number in the simple graph setting, with emphasis on graphs of diameter 2.
{"title":"On the Babai and Upper Chromatic Numbers of Graphs of Diameter 2","authors":"Peter D. Johnson, Alexis Krumpelman","doi":"10.5556/J.TKJM.52.2021.3430","DOIUrl":"https://doi.org/10.5556/J.TKJM.52.2021.3430","url":null,"abstract":"The Babai numbers and the upper chromatic number are parameters that can be assigned to any metric space. They can, therefore, be assigned to any connected simple graph. In this paper we make progress in the theory of the first Babai number and the upper chromatic number in the simple graph setting, with emphasis on graphs of diameter 2.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"46 1","pages":"113-123"},"PeriodicalIF":0.6,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80086162","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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