Pub Date : 2023-04-17DOI: 10.15446/recolma.v56n2.108373
J. López-López, Yesenia Villicaña-Molina
The geometry of certain canonical triangulation of once-punctured torus bundles over the circle is applied to the problem of computing their cusp tori. We are also concerned with the problem of finding the limit points of the set formed by such cusp tori, inside the moduli space of the torus. Our discussion generalizes examples which were elaborated by H. Helling (unpublished) and F. Guéritaud.
{"title":"On cusps of hyperbolic once-punctured torus bundles over the circle","authors":"J. López-López, Yesenia Villicaña-Molina","doi":"10.15446/recolma.v56n2.108373","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108373","url":null,"abstract":"The geometry of certain canonical triangulation of once-punctured torus bundles over the circle is applied to the problem of computing their cusp tori. We are also concerned with the problem of finding the limit points of the set formed by such cusp tori, inside the moduli space of the torus. Our discussion generalizes examples which were elaborated by H. Helling (unpublished) and F. Guéritaud.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46993238","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 : 2023-04-17DOI: 10.15446/recolma.v56n2.108379
A. L. Prins
In this paper, the Fischer matrices of the maximal subgroup G = 21+8+ : (U4(2):2) of U6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8+) = 28 : (U4(2):2), where Z(21+8+) denotes the center of the extra-special 2-group 21+8+. Using this approach, the Fischer matrices and associated ordinary character table of G are computed in an elegantly simple manner. This approach can be used to compute the ordinary character table of any split extension group of the form 21+2n+ :G, n ∈ N, provided the ordinary irreducible characters of 21+2n+ extend to ordinary irreducible characters of its inertia subgroups in 21+2n+:G and also that the Fischer matrices M(gi) of the quotient group 21+2n+ :G/Z(21+2n+) = 22n:G are known for each class representative gi in G.
{"title":"On the Fischer matrices of a group of shape 21+2n + :G","authors":"A. L. Prins","doi":"10.15446/recolma.v56n2.108379","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108379","url":null,"abstract":"In this paper, the Fischer matrices of the maximal subgroup G = 21+8+ : (U4(2):2) of U6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8+) = 28 : (U4(2):2), where Z(21+8+) denotes the center of the extra-special 2-group 21+8+. Using this approach, the Fischer matrices and associated ordinary character table of G are computed in an elegantly simple manner. This approach can be used to compute the ordinary character table of any split extension group of the form 21+2n+ :G, n ∈ N, provided the ordinary irreducible characters of 21+2n+ extend to ordinary irreducible characters of its inertia subgroups in 21+2n+:G and also that the Fischer matrices M(gi) of the quotient group 21+2n+ :G/Z(21+2n+) = 22n:G are known for each class representative gi in G.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43069298","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 : 2023-04-17DOI: 10.15446/recolma.v56n2.108371
Y. Bouhafsi, M. Ech-chad, A. Zouaki
Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A, B ∈ L(H), define the generalized derivation δA, B ∈ L(L(H)) by δA, B(X) = AX - XB. An operator A ∈ L(H) is P-symmetric if AT = TA implies AT* = T* A for all T ∈ C1(H) (trace class operators). In this paper, we give a generalization of P-symmetric operators. We initiate the study of the pairs (A, B) of operators A, B ∈ L(H) such that R(δA, B) W* = R(δA, B) W*, where R(δA, B) W* denotes the ultraweak closure of the range of δA, B. Such pairs of operators are called generalized P-symmetric. We establish a characterization of those pairs of operators. Related properties of P-symmetric operators are also given.
设H是一个可分离的无限维复希尔伯特空间，设L(H)表示H上所有有界线性算子的代数。给定A, B∈L(H)，定义广义导数δA, B∈L(L(H)): δA, B(X) = AX - XB。如果AT = TA意味着对于所有T∈C1(H)(跟踪类算子)AT* = T* A，则算子A∈L(H)是p对称的。本文给出了p对称算子的一个推广。我们研究了算子A, B∈L(H)的(A, B)对，使得R(δA, B) W* = R(δA, B) W*，其中R(δA, B) W*表示δA, B值域的超弱闭包。这种算子对称为广义p对称算子。我们建立了这些算子对的一个表征。给出了p对称算子的相关性质。
{"title":"A Note on the Range of a Derivation","authors":"Y. Bouhafsi, M. Ech-chad, A. Zouaki","doi":"10.15446/recolma.v56n2.108371","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108371","url":null,"abstract":"Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A, B ∈ L(H), define the generalized derivation δA, B ∈ L(L(H)) by δA, B(X) = AX - XB. An operator A ∈ L(H) is P-symmetric if AT = TA implies AT* = T* A for all T ∈ C1(H) (trace class operators). In this paper, we give a generalization of P-symmetric operators. We initiate the study of the pairs (A, B) of operators A, B ∈ L(H) such that R(δA, B) W* = R(δA, B) W*, where R(δA, B) W* denotes the ultraweak closure of the range of δA, B. Such pairs of operators are called generalized P-symmetric. We establish a characterization of those pairs of operators. Related properties of P-symmetric operators are also given.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47966725","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 : 2023-04-17DOI: 10.15446/recolma.v56n2.108374
A. Pethö, L. Szalay
In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.
在本文中，我们给出了丢番图方程F（k）n=±F（k）m的解n
{"title":"Upper bound on the solution to F(2k)n = +F(2k)m with negative subscripts","authors":"A. Pethö, L. Szalay","doi":"10.15446/recolma.v56n2.108374","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108374","url":null,"abstract":"In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F(k)n = ±F(k)m, assuming k is even. Here {F(k)n}n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49361861","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 : 2023-04-17DOI: 10.15446/recolma.v56n2.108383
José Alfonso López Nicolás
We define the concepts of stable sampling set, interpolation set, uniqueness set and complete interpolation set for a quasinormed space of functions and apply these concepts to Paley-Wiener spaces and Bernstein spaces. We obtain a sufficient condition on a uniformly discrete set to be an interpolation set based on a lemma of convergence of series in Paley-Wiener spaces. We also obtain a result of transference, Kadec type, of the property of being a stable sampling set, from a set with this property to other uniformly discrete set, which we apply to Bernstein spaces.
{"title":"On Stable Sampling and Interpolation in Bernstein Spaces","authors":"José Alfonso López Nicolás","doi":"10.15446/recolma.v56n2.108383","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108383","url":null,"abstract":"We define the concepts of stable sampling set, interpolation set, uniqueness set and complete interpolation set for a quasinormed space of functions and apply these concepts to Paley-Wiener spaces and Bernstein spaces. We obtain a sufficient condition on a uniformly discrete set to be an interpolation set based on a lemma of convergence of series in Paley-Wiener spaces. We also obtain a result of transference, Kadec type, of the property of being a stable sampling set, from a set with this property to other uniformly discrete set, which we apply to Bernstein spaces.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43123727","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 : 2023-04-17DOI: 10.15446/recolma.v56n2.108369
C. Cortes, J. D. Hernández
In this work we study the dynamics associated to the interaction of juveniles and adults of the same species, where the harvesting of adults is not allowed when the number of adults is below a critical value. This study is carried out by bifurcation analysis, for a Filippov system, in relation to two parameters: harvesting and protection of the adult species.
{"title":"Population dynamics with protection and harvesting of a species","authors":"C. Cortes, J. D. Hernández","doi":"10.15446/recolma.v56n2.108369","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108369","url":null,"abstract":"In this work we study the dynamics associated to the interaction of juveniles and adults of the same species, where the harvesting of adults is not allowed when the number of adults is below a critical value. This study is carried out by bifurcation analysis, for a Filippov system, in relation to two parameters: harvesting and protection of the adult species.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48127196","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 : 2022-11-02DOI: 10.15446/recolma.v56n1.105613
J. Rodríguez, Mario Velásquez
Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C, defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.
{"title":"Induced character in equivariant K-theory, wreath products and pullback of groups","authors":"J. Rodríguez, Mario Velásquez","doi":"10.15446/recolma.v56n1.105613","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105613","url":null,"abstract":"Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra \u0000FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C, \u0000defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46191930","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 : 2022-11-02DOI: 10.15446/recolma.v56n1.105612
Ali Khalouta
In this work, we suggest a novel iterative method to give approximate solutions of nonlinear wave-like equations of fractional order with variable coefficients. The advantage of the proposed method is the ability to combine two different methods: Shehu transform method and homotopy analysis method, in addition to providing an approximate solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. This method can be called Shehu homotopy analysis method (SHAM). Three different examples are presented to illustrate the preciseness and effectiveness of the proposed method. The numerical results show that the solutions obtained by SHAM are in good agreement with the solutions found in the literature. Furthermore, the results show that this method can be implemented in an easy way and therefore can be used to solve other nonlinear fractional partial differential equations.
{"title":"A novel iterative method to solve nonlinear wave-like equations of fractional order with variable coefficients","authors":"Ali Khalouta","doi":"10.15446/recolma.v56n1.105612","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105612","url":null,"abstract":"In this work, we suggest a novel iterative method to give approximate solutions of nonlinear wave-like equations of fractional order with variable coefficients. The advantage of the proposed method is the ability to combine two different methods: Shehu transform method and homotopy analysis method, in addition to providing an approximate solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. This method can be called Shehu homotopy analysis method (SHAM). Three different examples are presented to illustrate the preciseness and effectiveness of the proposed method. The numerical results show that the solutions obtained by SHAM are in good agreement with the solutions found in the literature. Furthermore, the results show that this method can be implemented in an easy way and therefore can be used to solve other nonlinear fractional partial differential equations.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"17 5-6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41290675","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 : 2022-11-02DOI: 10.15446/recolma.v56n1.105617
Christo Kriel, E. Mphako-Banda
We show that the problem of counting the number of flats of size k for a cycle matroid of a complete graph is equivalent to the problem of counting the number of partitions of an integer k into triangular numbers. In addition, we give some values of k such that there is no flat of size k in a cycle matroid of a complete graph of order k. Finally, we give a minimum bound for the number of values, k, for which there are no flats of size k in the given cycle matroid.
{"title":"Sizes of flats of cycle matroids of complete graphs","authors":"Christo Kriel, E. Mphako-Banda","doi":"10.15446/recolma.v56n1.105617","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105617","url":null,"abstract":"We show that the problem of counting the number of flats of size k for a cycle matroid of a complete graph is equivalent to the problem of counting the number of partitions of an integer k into triangular numbers. In addition, we give some values of k such that there is no flat of size k in a cycle matroid of a complete graph of order k. Finally, we give a minimum bound for the number of values, k, for which there are no flats of size k in the given cycle matroid.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46087845","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 : 2022-11-02DOI: 10.15446/recolma.v56n1.105620
S. Mehry
Let Rm = Fq [y] = /〈ym - 1〉, where m|q - 1. In this paper, we obtain the structure of linear and cyclic codes over Rm. Also, we introduce a preserving-orthogonality Gray map from Rm to Fmq. Among the main results, we obtain the exact structure of self-orthogonal cyclic codes over Rm to introduce parameters of quantum codes from cyclic codes over Rm.
{"title":"On quantum codes from codes over Rm","authors":"S. Mehry","doi":"10.15446/recolma.v56n1.105620","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105620","url":null,"abstract":"Let Rm = Fq [y] = /〈ym - 1〉, where m|q - 1. In this paper, we obtain the structure of linear and cyclic codes over Rm. Also, we introduce a preserving-orthogonality Gray map from Rm to Fmq. Among the main results, we obtain the exact structure of self-orthogonal cyclic codes over Rm to introduce parameters of quantum codes from cyclic codes over Rm.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47839807","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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