Pub Date : 2019-07-01DOI: 10.15446/recolma.v53n2.85538
Irene Erazo, John López, C. Trujillo
Let A = {a1, a2, …, ak} be a set of positive integers with k ≥ 3,such that a1 ≤ a2 ≤ a3 … ak = N. Our problem is to investigate thenumber of triplets (ar, as, at) ∈ A3 with ar < as < at, satisfyingar + as - at < 0 y -ar + as + at > N.In this paper we give an upper bound for the maximum number of such a triplets in an arbitrary set of integers with k elements. We also find the number of triplets satisfying () for some families of sets in order to determine lower bounds for the maximum number of such a triplets that a set with k elements can have.
{"title":"A combinatorial problem that arose in integer B3 Sets","authors":"Irene Erazo, John López, C. Trujillo","doi":"10.15446/recolma.v53n2.85538","DOIUrl":"https://doi.org/10.15446/recolma.v53n2.85538","url":null,"abstract":"Let A = {a1, a2, …, ak} be a set of positive integers with k ≥ 3,such that a1 ≤ a2 ≤ a3 … ak = N. Our problem is to investigate thenumber of triplets (ar, as, at) ∈ A3 with ar < as < at, satisfyingar + as - at < 0 y -ar + as + at > N.In this paper we give an upper bound for the maximum number of such a triplets in an arbitrary set of integers with k elements. We also find the number of triplets satisfying () for some families of sets in order to determine lower bounds for the maximum number of such a triplets that a set with k elements can have.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45896779","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 : 2019-07-01DOI: 10.15446/recolma.v53n2.85536
Bhaskar Srivastava
We give a two independent variable generalization of bilateral eighth order mock theta functions and expressed them as infinite product. On specializing parameters, we have given a continued fraction representation for the generalized function, which I think is a new representation.
{"title":"Generalized Bilateral Eighth Order Mock Theta Functions and Continued Fractions","authors":"Bhaskar Srivastava","doi":"10.15446/recolma.v53n2.85536","DOIUrl":"https://doi.org/10.15446/recolma.v53n2.85536","url":null,"abstract":"We give a two independent variable generalization of bilateral eighth order mock theta functions and expressed them as infinite product. On specializing parameters, we have given a continued fraction representation for the generalized function, which I think is a new representation.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46138487","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 : 2019-07-01DOI: 10.15446/recolma.v53n2.85525
Gustavo Arengas
In the present work, we show how the study of categorical constructions does not have to be done with all the objects of the category, but we can restrict ourselves to work with families of generators. Thus, universal properties can be characterized through iterated families of generators, which leads us in particular to an alternative version of the adjoint functor theorem. Similarly, the properties of relations or subobjects algebra can be investigated by this method. We end with a result that relates various forms of compactness through representable functors of generators.
{"title":"Categorical definitions and properties via generators","authors":"Gustavo Arengas","doi":"10.15446/recolma.v53n2.85525","DOIUrl":"https://doi.org/10.15446/recolma.v53n2.85525","url":null,"abstract":"In the present work, we show how the study of categorical constructions does not have to be done with all the objects of the category, but we can restrict ourselves to work with families of generators. Thus, universal properties can be characterized through iterated families of generators, which leads us in particular to an alternative version of the adjoint functor theorem. Similarly, the properties of relations or subobjects algebra can be investigated by this method. We end with a result that relates various forms of compactness through representable functors of generators.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"84 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41278727","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 : 2019-07-01DOI: 10.15446/recolma.v53n2.85521
D. Mejía, Ismael E. Rivera-Madrid
By coding Polish metric spaces with metrics on countable sets, we propose an interpretation of Polish metric spaces in models of ZFC and extend Mostowski's classical theorem of absoluteness of analytic sets for any Polish metric space in general. In addition, we prove a general version of Shoenfield's absoluteness theorem.
{"title":"Absoluteness theorems for arbitrary Polish spaces","authors":"D. Mejía, Ismael E. Rivera-Madrid","doi":"10.15446/recolma.v53n2.85521","DOIUrl":"https://doi.org/10.15446/recolma.v53n2.85521","url":null,"abstract":"By coding Polish metric spaces with metrics on countable sets, we propose an interpretation of Polish metric spaces in models of ZFC and extend Mostowski's classical theorem of absoluteness of analytic sets for any Polish metric space in general. In addition, we prove a general version of Shoenfield's absoluteness theorem.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42596431","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 : 2019-03-01DOI: 10.15446/recolma.v53nsupl.84084
Shotaro Makisumi
We attempt to give a gentle (though ahistorical) introduction to Koszul duality phenomena for the Hecke category, focusing on the form of this duality studied in joint work [1, 2] of Achar, Riche, Williamson, and the author. We illustrate some key phenomena and constructions for the simplest nontrivial case of (finite) SL2 using Soergel bimodules, a concrete algebraic model of the Hecke category.
{"title":"On monoidal Koszul duality for the Hecke category","authors":"Shotaro Makisumi","doi":"10.15446/recolma.v53nsupl.84084","DOIUrl":"https://doi.org/10.15446/recolma.v53nsupl.84084","url":null,"abstract":"We attempt to give a gentle (though ahistorical) introduction to Koszul duality phenomena for the Hecke category, focusing on the form of this duality studied in joint work [1, 2] of Achar, Riche, Williamson, and the author. We illustrate some key phenomena and constructions for the simplest nontrivial case of (finite) SL2 using Soergel bimodules, a concrete algebraic model of the Hecke category.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/recolma.v53nsupl.84084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41326217","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 : 2019-01-01DOI: 10.15446/RECOLMA.V53N1.81036
M. A. Hammou, E. Azroul, B. Lahmi
This article is devoted to study the existence of weak solutions for the strongly nonlinear p(x)-elliptic problem Our technical approach is based on the recent Berkovits topological degree.
{"title":"Topological degree methods for a Strongly nonlinear p(x)-elliptic problem","authors":"M. A. Hammou, E. Azroul, B. Lahmi","doi":"10.15446/RECOLMA.V53N1.81036","DOIUrl":"https://doi.org/10.15446/RECOLMA.V53N1.81036","url":null,"abstract":"This article is devoted to study the existence of weak solutions for the strongly nonlinear p(x)-elliptic problem Our technical approach is based on the recent Berkovits topological degree.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/RECOLMA.V53N1.81036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67052493","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 : 2019-01-01DOI: 10.15446/RECOLMA.V53N1.81037
R. Estrada
The product of two homogeneous harmonic polynomials is homogeneous, but not harmonic, in general. We give formulas for the Gauss decomposition of the product of two homogeneous harmonic polynomials.
两个齐次调和多项式的乘积通常是齐次的，但不是调和的。给出了两个齐次调和多项式乘积的高斯分解公式。
{"title":"The Gauss decomposition of products of spherical harmonics","authors":"R. Estrada","doi":"10.15446/RECOLMA.V53N1.81037","DOIUrl":"https://doi.org/10.15446/RECOLMA.V53N1.81037","url":null,"abstract":"The product of two homogeneous harmonic polynomials is homogeneous, but not harmonic, in general. We give formulas for the Gauss decomposition of the product of two homogeneous harmonic polynomials.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46906662","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 : 2019-01-01DOI: 10.15446/RECOLMA.V53N1.81042
M. J. Ceballos-Lira, Aroldo Pérez
In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.
{"title":"Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition","authors":"M. J. Ceballos-Lira, Aroldo Pérez","doi":"10.15446/RECOLMA.V53N1.81042","DOIUrl":"https://doi.org/10.15446/RECOLMA.V53N1.81042","url":null,"abstract":"In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/RECOLMA.V53N1.81042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47786284","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 : 2019-01-01DOI: 10.15446/recolma.v53n1.81034
Ana María García Lomeli, Santos Hernández Hernández
Let (Pn)n≥0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n ≥ 0. In this note we study and completely solve the Diophantine equation Pn - 2m = Pn1 - 2m1 in non-negative integers (n, m, n1, m1).
{"title":"Pillai's problem with Padovan numbers and powers of two","authors":"Ana María García Lomeli, Santos Hernández Hernández","doi":"10.15446/recolma.v53n1.81034","DOIUrl":"https://doi.org/10.15446/recolma.v53n1.81034","url":null,"abstract":"Let (Pn)n≥0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n ≥ 0. In this note we study and completely solve the Diophantine equation Pn - 2m = Pn1 - 2m1 in non-negative integers (n, m, n1, m1).","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/recolma.v53n1.81034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67052383","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 : 2019-01-01DOI: 10.15446/RECOLMA.V53N1.81035
H. Al-dweby, M. Darus
In this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.
本文给出了由调和一元函数组成的广义Bernardi积分算子的拟部分和属于相似类的几个条件。
{"title":"Quasi Partial Sums of Harmonic Univalent Functions","authors":"H. Al-dweby, M. Darus","doi":"10.15446/RECOLMA.V53N1.81035","DOIUrl":"https://doi.org/10.15446/RECOLMA.V53N1.81035","url":null,"abstract":"In this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67052475","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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