We introduce and study C-groups and mixed C-groups of bounded linear operators on non-archimedean Banach spaces. Our main result extends some existing theorems on this topic. In contrast with the classical setting, the parameter of a given C-group (or mixed C-group) belongs to a clopen ball Ωr of the ground field K. As an illustration, we discuss the solvability of some homogeneous p-adic differential equations for C-groups and inhomogeneous p-adic differential equations for mixed C-groups when α = −1. Examples are given to support our work.
{"title":"$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces","authors":"A. El amrani, A. Blali, J. Ettayb","doi":"10.33044/revuma.2074","DOIUrl":"https://doi.org/10.33044/revuma.2074","url":null,"abstract":"We introduce and study C-groups and mixed C-groups of bounded linear operators on non-archimedean Banach spaces. Our main result extends some existing theorems on this topic. In contrast with the classical setting, the parameter of a given C-group (or mixed C-group) belongs to a clopen ball Ωr of the ground field K. As an illustration, we discuss the solvability of some homogeneous p-adic differential equations for C-groups and inhomogeneous p-adic differential equations for mixed C-groups when α = −1. Examples are given to support our work.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42907682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Cabrera Martínez, Suitberto Cabrera García, Iztok Peterin, Ismael G. Yero
. A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D . The total domi- nating set D is called a total co-independent dominating set if the subgraph induced by V ( G ) − D is edgeless. The minimum cardinality among all total co-independent dominating sets of G is the total co-independent domination number of G . In this article we study the total co-independent domination number of the join, strong, lexicographic, direct and rooted products of graphs.
{"title":"The total co-independent domination number of some graph operations","authors":"A. Cabrera Martínez, Suitberto Cabrera García, Iztok Peterin, Ismael G. Yero","doi":"10.33044/revuma.1652","DOIUrl":"https://doi.org/10.33044/revuma.1652","url":null,"abstract":". A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D . The total domi- nating set D is called a total co-independent dominating set if the subgraph induced by V ( G ) − D is edgeless. The minimum cardinality among all total co-independent dominating sets of G is the total co-independent domination number of G . In this article we study the total co-independent domination number of the join, strong, lexicographic, direct and rooted products of graphs.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43483849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Studies of the dynamics of predator-prey systems are abundant in the literature. In an attempt to account for more realistic models, previous studies have opted for the use of discrete predator-prey systems with ratio-dependent functional response. In the present research we go a step further with the inclusion of impulsive effects in the dynamics. More concretely, by assuming that the coefficients involved in the system and the impulses are peri- odic, we obtain sufficient conditions for the existence of periodic solutions. We present some numerical examples to illustrate the effectiveness of our results.
{"title":"Positive periodic solutions of a discrete ratio-dependent predator-prey model with impulsive effects","authors":"C. Duque, J. L. Herrera Diestra","doi":"10.33044/revuma.2058","DOIUrl":"https://doi.org/10.33044/revuma.2058","url":null,"abstract":". Studies of the dynamics of predator-prey systems are abundant in the literature. In an attempt to account for more realistic models, previous studies have opted for the use of discrete predator-prey systems with ratio-dependent functional response. In the present research we go a step further with the inclusion of impulsive effects in the dynamics. More concretely, by assuming that the coefficients involved in the system and the impulses are peri- odic, we obtain sufficient conditions for the existence of periodic solutions. We present some numerical examples to illustrate the effectiveness of our results.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42963721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. An important problem in the variety of Heyting algebras H is to find new characterizations which allow us to determinate if a given H ∈ H is linear or Stone. In this work we present two Heyting algebras, H ns and H snl , such that: (a) a Heyting algebra H is a Stone–Heyting algebra if and only if H ns cannot be embedded in H , and (b) H is a linear Heyting algebra if and only if neither H ns nor H snl can be embedded in H .
{"title":"A characterization of Stone and linear Heyting algebras","authors":"A. Petrovich, Carlos Scirica","doi":"10.33044/revuma.2052","DOIUrl":"https://doi.org/10.33044/revuma.2052","url":null,"abstract":". An important problem in the variety of Heyting algebras H is to find new characterizations which allow us to determinate if a given H ∈ H is linear or Stone. In this work we present two Heyting algebras, H ns and H snl , such that: (a) a Heyting algebra H is a Stone–Heyting algebra if and only if H ns cannot be embedded in H , and (b) H is a linear Heyting algebra if and only if neither H ns nor H snl can be embedded in H .","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44998431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. A commutative ring R is said to be a Baer ring if for each a ∈ R , ann( a ) is generated by an idempotent element b ∈ R . In this paper, we extend the notion of a Baer ring to modules in terms of weak idempotent elements defined in a previous work by Jayaram and Tekir. Let R be a commutative ring with a nonzero identity and let M be a unital R -module. M is said to be a Baer module if for each m ∈ M there exists a weak idempotent element e ∈ R such that ann R ( m ) M = eM . Various examples and properties of Baer modules are given. Also, we characterize a certain class of modules/submodules such as von Neumann regular modules/prime submodules in terms of Baer modules.
。如果对每个A∈R, ann(A)由幂等元素b∈R生成，则称交换环R为Baer环。在本文中，我们将Baer环的概念推广到由Jayaram和Tekir在之前的工作中定义的弱幂等元构成的模。设R是一个具有非零单位元的交换环，设M是一个一元R模。如果对于每个M∈M，存在一个弱幂等元素e∈R，使得R (M) M = eM，则M是Baer模。给出了贝尔模的各种例子和性质。此外，我们还用Baer模描述了一类模/子模，如von Neumann正则模/素子模。
{"title":"On Baer modules","authors":"C. Jayaram, Ünsal Tekir, Suat Koç","doi":"10.33044/revuma.1741","DOIUrl":"https://doi.org/10.33044/revuma.1741","url":null,"abstract":". A commutative ring R is said to be a Baer ring if for each a ∈ R , ann( a ) is generated by an idempotent element b ∈ R . In this paper, we extend the notion of a Baer ring to modules in terms of weak idempotent elements defined in a previous work by Jayaram and Tekir. Let R be a commutative ring with a nonzero identity and let M be a unital R -module. M is said to be a Baer module if for each m ∈ M there exists a weak idempotent element e ∈ R such that ann R ( m ) M = eM . Various examples and properties of Baer modules are given. Also, we characterize a certain class of modules/submodules such as von Neumann regular modules/prime submodules in terms of Baer modules.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let R be a commutative ring and M an R-module. The M -intersection graph of ideals of R is an undirected simple graph, denoted by GM (R), whose vertices are non-zero proper ideals of R and two distinct vertices are adjacent if and only if IM ∩ JM 6= 0. In this article, we focus on how certain graph theoretic parameters of GM (R) depend on the properties of both R and M . Specifically, we derive a necessary and sufficient condition for R and M such that the M -intersection graph GM (R) is either connected or complete. Also, we classify all R-modules according to the diameter value of GM (R). Further, we characterize rings R for which GM (R) is perfect or Hamiltonian or pancyclic or planar. Moreover, we show that the graph GM (R) is weakly perfect and cograph.
{"title":"On the module intersection graph of ideals of rings","authors":"T. Asir, Arun Kumar, Alveera Mehdi","doi":"10.33044/revuma.1936","DOIUrl":"https://doi.org/10.33044/revuma.1936","url":null,"abstract":"Let R be a commutative ring and M an R-module. The M -intersection graph of ideals of R is an undirected simple graph, denoted by GM (R), whose vertices are non-zero proper ideals of R and two distinct vertices are adjacent if and only if IM ∩ JM 6= 0. In this article, we focus on how certain graph theoretic parameters of GM (R) depend on the properties of both R and M . Specifically, we derive a necessary and sufficient condition for R and M such that the M -intersection graph GM (R) is either connected or complete. Also, we classify all R-modules according to the diameter value of GM (R). Further, we characterize rings R for which GM (R) is perfect or Hamiltonian or pancyclic or planar. Moreover, we show that the graph GM (R) is weakly perfect and cograph.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69487317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The $mathfrak{A}$-principal real hypersurfaces in complex quadrics","authors":"T. Loo","doi":"10.33044/revuma.1917","DOIUrl":"https://doi.org/10.33044/revuma.1917","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69487303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The space of infinite partitions of $mathbb{N}$ as a topological Ramsey space","authors":"J. C. Cano, C. A. Di Prisco","doi":"10.33044/revuma.2869","DOIUrl":"https://doi.org/10.33044/revuma.2869","url":null,"abstract":"","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41510329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zoran Maksimovic, Aleksandar Lj. Savić, M. Bogdanovic
This paper is devoted to solving the weakly convex dominating set problem and the convex dominating set problem for some classes of planar graphs—convex polytopes. We consider all classes of convex polytopes known from the literature and present exact values of weakly convex and convex domination number for all classes, namely An, Bn, Cn, Dn, En, Rn, R′′ n, Qn, Sn, S′′ n , Tn, T ′′ n and Un. When n is up to 26, the values are confirmed by using the exact method, while for greater values of n theoretical proofs are given.
研究了一类平面图-凸多面体的弱凸控制集问题和凸控制集问题。我们考虑了文献中已知的所有凸多面体的类，并给出了所有类的弱凸和凸控制数的精确值，即An, Bn, Cn, Dn, En, Rn, R ' n, Qn, Sn, S ' n, Tn, T ' n和Un。当n≤26时，用精确方法确定，当n大于26时，给出理论证明。
{"title":"The convex and weak convex domination number of convex polytopes","authors":"Zoran Maksimovic, Aleksandar Lj. Savić, M. Bogdanovic","doi":"10.33044/revuma.1739","DOIUrl":"https://doi.org/10.33044/revuma.1739","url":null,"abstract":"This paper is devoted to solving the weakly convex dominating set problem and the convex dominating set problem for some classes of planar graphs—convex polytopes. We consider all classes of convex polytopes known from the literature and present exact values of weakly convex and convex domination number for all classes, namely An, Bn, Cn, Dn, En, Rn, R′′ n, Qn, Sn, S′′ n , Tn, T ′′ n and Un. When n is up to 26, the values are confirmed by using the exact method, while for greater values of n theoretical proofs are given.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43096780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Some of the spectral distance related parameters (cospectrality, spectral eccentricity, and spectral diameter with respect to an arbitrary graph matrix) are determined in one particular set of graphs. According to these results, the spectral distances connected with the adjacency matrix and the corresponding distance related parameters are computed in some sets of trees. Examples are provided of graphs whose spectral distances related to the adjacency matrix, the Laplacian and the signless Laplacian matrix are mutually equal. The conjecture related to the spectral diameter of the set of connected regular graphs with respect to the adjacency matrix is disproved using graph energy.
{"title":"Spectral distances in some sets of graphs","authors":"Irena M. Jovanović","doi":"10.33044/revuma.1755","DOIUrl":"https://doi.org/10.33044/revuma.1755","url":null,"abstract":"Some of the spectral distance related parameters (cospectrality, spectral eccentricity, and spectral diameter with respect to an arbitrary graph matrix) are determined in one particular set of graphs. According to these results, the spectral distances connected with the adjacency matrix and the corresponding distance related parameters are computed in some sets of trees. Examples are provided of graphs whose spectral distances related to the adjacency matrix, the Laplacian and the signless Laplacian matrix are mutually equal. The conjecture related to the spectral diameter of the set of connected regular graphs with respect to the adjacency matrix is disproved using graph energy.","PeriodicalId":54469,"journal":{"name":"Revista De La Union Matematica Argentina","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45701783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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