Pub Date : 2018-07-01DOI: 10.15446/RECOLMA.V52N2.77160
G. Ossandón, Ricardo Castro Santis
This study assesses the effects of migration on the dynamics of a species population. It is considered that the species in its natural state and without the presence of migration exhibits Allee effect. This work also considers migration as a density-dependent function, which, from a maximum rate, decreases to a minimum of zero when the population reaches its carrying capacity.
{"title":"Population Dynamics with Density-Dependent Immigrations and Allee effect","authors":"G. Ossandón, Ricardo Castro Santis","doi":"10.15446/RECOLMA.V52N2.77160","DOIUrl":"https://doi.org/10.15446/RECOLMA.V52N2.77160","url":null,"abstract":"This study assesses the effects of migration on the dynamics of a species population. It is considered that the species in its natural state and without the presence of migration exhibits Allee effect. This work also considers migration as a density-dependent function, which, from a maximum rate, decreases to a minimum of zero when the population reaches its carrying capacity.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43993745","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 : 2018-07-01DOI: 10.15446/RECOLMA.V52N2.77157
M. Bracamonte, J. Gimenez, J. Medina
We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.
引入了互强凸函数的概念，给出了它们的一些例子和性质。我们还证明了定义在实区间[a, b]上的两个实数函数f和g，满足对所有x, y∈[a, b]和t∈[0,1]，如果存在一个互强凸函数h: [a, b]→R使得对所有x∈[a, b]， f (x)≤h(x)≤g(x)。最后，我们得到了互强凸函数的一个近似凸性结果;即证明了该类函数的Hyers-Ulam型的稳定性结果。
{"title":"Sandwich theorem for reciprocally strongly convex functions","authors":"M. Bracamonte, J. Gimenez, J. Medina","doi":"10.15446/RECOLMA.V52N2.77157","DOIUrl":"https://doi.org/10.15446/RECOLMA.V52N2.77157","url":null,"abstract":"We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42587659","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 : 2018-07-01DOI: 10.15446/RECOLMA.V52N2.77161
Aldo Guzmán-Sáen, M. Xicoténcatl
We give an alternative proof of the Bullett-Macdonald identity for the Steenrod squares, which is in turn equivalent to the Adem relations. The main idea is to show that the iterated total squaring operation S2: Hn(X) → H4n(X × BZ2 × BZ2) is the restriction of a total fourth-power operation T : Hn(X) → H4n(X × BΣ4).
{"title":"A proof of the Adem relations","authors":"Aldo Guzmán-Sáen, M. Xicoténcatl","doi":"10.15446/RECOLMA.V52N2.77161","DOIUrl":"https://doi.org/10.15446/RECOLMA.V52N2.77161","url":null,"abstract":"We give an alternative proof of the Bullett-Macdonald identity for the Steenrod squares, which is in turn equivalent to the Adem relations. The main idea is to show that the iterated total squaring operation S2: Hn(X) → H4n(X × BZ2 × BZ2) is the restriction of a total fourth-power operation T : Hn(X) → H4n(X × BΣ4).","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43690752","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 : 2018-07-01DOI: 10.15446/RECOLMA.V52N2.77156
A. Tsarev
Let τ be a subgroup functor such that all subgroups of every finite group G contained in τ(G) are subnormal in G. In this paper, we give a simple proof of the fact that the lattice of all τ-closed totally composition formations of finite groups is inductive.
{"title":"Inductive lattices of totally composition formations","authors":"A. Tsarev","doi":"10.15446/RECOLMA.V52N2.77156","DOIUrl":"https://doi.org/10.15446/RECOLMA.V52N2.77156","url":null,"abstract":"Let τ be a subgroup functor such that all subgroups of every finite group G contained in τ(G) are subnormal in G. In this paper, we give a simple proof of the fact that the lattice of all τ-closed totally composition formations of finite groups is inductive.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44774661","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 : 2018-06-14DOI: 10.15446/recolma.v53nsupl.84083
Daniel López-Aguayo
In this paper we give an overview of a generalization, introduced by R. Bautista and the author, of the theory of mutation of quivers with potential developed in 2007 by Derksen-Weyman-Zelevinsky. This new construction allows us to consider finite dimensional semisimple F-algebras, where F is any field. We give a brief account of the results concerning this generalization and its main consequences.
{"title":"Cyclic derivations, species realizations and potentials","authors":"Daniel López-Aguayo","doi":"10.15446/recolma.v53nsupl.84083","DOIUrl":"https://doi.org/10.15446/recolma.v53nsupl.84083","url":null,"abstract":"In this paper we give an overview of a generalization, introduced by R. Bautista and the author, of the theory of mutation of quivers with potential developed in 2007 by Derksen-Weyman-Zelevinsky. This new construction allows us to consider finite dimensional semisimple F-algebras, where F is any field. We give a brief account of the results concerning this generalization and its main consequences.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/recolma.v53nsupl.84083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45922913","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 : 2017-07-20DOI: 10.15446/RECOLMA.V52N2.77154
Alfred Dolich, John Goodrick
We characterize all ordered Abelian groups whose first-order theory in the language {+, <, 0} is strongly dependent. The main result of this note was obtained independently by Halevi and Hasson [7] and Farré [5].
{"title":"A Characterization of Strongly Dependent Ordered Abelian Groups","authors":"Alfred Dolich, John Goodrick","doi":"10.15446/RECOLMA.V52N2.77154","DOIUrl":"https://doi.org/10.15446/RECOLMA.V52N2.77154","url":null,"abstract":"We characterize all ordered Abelian groups whose first-order theory in the language {+, <, 0} is strongly dependent. The main result of this note was obtained independently by Halevi and Hasson [7] and Farré [5].","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41504041","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 : 2005-08-17DOI: 10.15446/recolma.v56n1.105611
H. Figueroa, Jose M. Gracia-Bondia, Joseph C. Varilly
This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.
{"title":"Faà di Bruno Hopf algebras","authors":"H. Figueroa, Jose M. Gracia-Bondia, Joseph C. Varilly","doi":"10.15446/recolma.v56n1.105611","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105611","url":null,"abstract":"This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2005-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67052084","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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