Pub Date : 2022-11-02DOI: 10.15446/recolma.v56n1.105621
H. Díaz-Marín, O. Osuna
In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.
{"title":"On the invariant rational curves of a certain family of polynomial differential equations","authors":"H. Díaz-Marín, O. Osuna","doi":"10.15446/recolma.v56n1.105621","DOIUrl":"https://doi.org/10.15446/recolma.v56n1.105621","url":null,"abstract":"In this work, we present sufficient conditions to determine if the limit cycles of certain differential systems in the plane are algebraic or not. In particular, we obtain criteria such that the limit cycles of equations derived from predatory prey models with rational functional response are necessarily transcendental ovals.","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":"49058718","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102690
J. Sánchez-Guevara
The aim of this paper is to construct an E∞-operad inducing an E∞-coalgebra structure on chain complexes with integer coefficients, which is an alternative description to the E∞-coalgebra by the Barrat-Eccles operad.
{"title":"E-infinity coalgebra structure on chain complexes with integer coefficients","authors":"J. Sánchez-Guevara","doi":"10.15446/recolma.v55n2.102690","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102690","url":null,"abstract":"The aim of this paper is to construct an E∞-operad inducing an E∞-coalgebra structure on chain complexes with integer coefficients, which is an alternative description to the E∞-coalgebra by the Barrat-Eccles operad.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43690670","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102509
Gabriela Hinojosa, R. Valdez
We say that a topological space N is a cubical n-manifold if it is a topological manifold of dimension n contained in the n-skeleton of the canonical cubulation of Rn+2. For instance, any smooth n-knot Sn → Rn+2 can be deformed by an ambient isotopy into a cubical n-knot. An open question is the following: Is any closed, oriented, cubical n-manifold N in Rn+2, n > 2, smoothable? If the response is positive, we could give a discrete description of any smooth n-manifold; in particular, if we can stablish that for smooth n-knots, that fact can be useful to define invariants. One of the main dificulties to answer the above question lies in the understanding of how N looks at each vertex of the canonical cubulation. In this paper, we analyze all possible combinatorial behaviors around any vertex of any cubical manifold of dimension n, via the study of the cycles on the complete graph K2n.
{"title":"Combinatorial description around any vertex of a cubical n-manifold","authors":"Gabriela Hinojosa, R. Valdez","doi":"10.15446/recolma.v55n2.102509","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102509","url":null,"abstract":"We say that a topological space N is a cubical n-manifold if it is a topological manifold of dimension n contained in the n-skeleton of the canonical cubulation of Rn+2. For instance, any smooth n-knot Sn → Rn+2 can be deformed by an ambient isotopy into a cubical n-knot. An open question is the following: Is any closed, oriented, cubical n-manifold N in Rn+2, n > 2, smoothable? If the response is positive, we could give a discrete description of any smooth n-manifold; in particular, if we can stablish that for smooth n-knots, that fact can be useful to define invariants. One of the main dificulties to answer the above question lies in the understanding of how N looks at each vertex of the canonical cubulation. In this paper, we analyze all possible combinatorial behaviors around any vertex of any cubical manifold of dimension n, via the study of the cycles on the complete graph K2n.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43778920","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102739
L. Corredor, Adrien Deloro
A streamlined exposition of Frécon's theorem on non-existence of bad groups of Morley rank 3. Systematising ideas by Poizat and Wagner, we avoid incidence geometries and use group actions instead; the proof becomes short and completely elementary.
{"title":"A self-contained guide to Frécon's theorem","authors":"L. Corredor, Adrien Deloro","doi":"10.15446/recolma.v55n2.102739","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102739","url":null,"abstract":"A streamlined exposition of Frécon's theorem on non-existence of bad groups of Morley rank 3. Systematising ideas by Poizat and Wagner, we avoid incidence geometries and use group actions instead; the proof becomes short and completely elementary.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44829858","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102677
R. Tavoni, Paulo F. A. Mancera, R. F. Camargo
This paper presents a stability analysis of a differential equations model related to the cancer treatment with an oncolytic virus in its classical and fractional version via Caputo derivatives. Numerical simulations of three possible scenarios are presented and support the discussions on the advantages of using fractional modeling.
{"title":"Stability analysis of a fractional virotherapy model for cancer treatment","authors":"R. Tavoni, Paulo F. A. Mancera, R. F. Camargo","doi":"10.15446/recolma.v55n2.102677","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102677","url":null,"abstract":"This paper presents a stability analysis of a differential equations model related to the cancer treatment with an oncolytic virus in its classical and fractional version via Caputo derivatives. Numerical simulations of three possible scenarios are presented and support the discussions on the advantages of using fractional modeling.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43760775","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102622
Nada Bouazila, H. Guebbai, W. Merchela
In this paper, we build a Newton-like sequence to approach the zero of a nonlinear Fréchet differentiable function defined in Hilbert space. This new iterative sequence uses the concept of the adjoint operator, which makes it more manageable in practice compared to the one developed by Kantorovich which requires the calculation of the inverse operator in each iteration. Because the calculation of the adjoint operator is easier compared to the calculation of the inverse operator which requires in practice solving a system of linear equations, our new method makes the calculation of the term of our new sequence easier and more convenient for numerical approximations. We provide an a priori convergence theorem of this sequence, where we use hypotheses equivalent to those constructed by Kantorovich, and we show that our new iterative sequence converges towards the solution.
{"title":"New linearization method for nonlinear problems in Hilbert space","authors":"Nada Bouazila, H. Guebbai, W. Merchela","doi":"10.15446/recolma.v55n2.102622","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102622","url":null,"abstract":"In this paper, we build a Newton-like sequence to approach the zero of a nonlinear Fréchet differentiable function defined in Hilbert space. This new iterative sequence uses the concept of the adjoint operator, which makes it more manageable in practice compared to the one developed by Kantorovich which requires the calculation of the inverse operator in each iteration. Because the calculation of the adjoint operator is easier compared to the calculation of the inverse operator which requires in practice solving a system of linear equations, our new method makes the calculation of the term of our new sequence easier and more convenient for numerical approximations. We provide an a priori convergence theorem of this sequence, where we use hypotheses equivalent to those constructed by Kantorovich, and we show that our new iterative sequence converges towards the solution.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42730897","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 : 2022-05-18DOI: 10.15446/recolma.v55n2.102513
A. Shukurov, Afet Jabrailova
A result from the recent paper of the first named author on frame properties of iterates of the multiplication operator Tφf = φf implies in particular that a system of the form {φn}∞n=0 cannot be a frame in L2(a, b). The classical exponential system shows that the situation changes drastically when one considers systems of the form {φn}∞n=-∞ instead of {φn}∞n=0. This note is dedicated to the characterization of all frames of the form {φn}∞n=-∞ coming from iterates of the multiplication operator Tφ. It is shown in this note that this problem can be reduced to the following one: Problem. Find (or describe a class of ) all real-valued functions α for which {einα(·)}+∞n=-∞ is a frame in L2(a, b). In this note we give a partial answer to this problem. To our knowledge, in the general statement, this problem remains unanswered not only for frame, but also for Schauder and Riesz basicity properties and even for orthonormal basicity of systems of the form {einα(·)}+∞n=-∞.
{"title":"On frames that are iterates of a multiplication operator","authors":"A. Shukurov, Afet Jabrailova","doi":"10.15446/recolma.v55n2.102513","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102513","url":null,"abstract":"A result from the recent paper of the first named author on frame properties of iterates of the multiplication operator Tφf = φf implies in particular that a system of the form {φn}∞n=0 cannot be a frame in L2(a, b). The classical exponential system shows that the situation changes drastically when one considers systems of the form {φn}∞n=-∞ instead of {φn}∞n=0. This note is dedicated to the characterization of all frames of the form {φn}∞n=-∞ coming from iterates of the multiplication operator Tφ. It is shown in this note that this problem can be reduced to the following one: \u0000Problem. Find (or describe a class of ) all real-valued functions α for which {einα(·)}+∞n=-∞ is a frame in L2(a, b). \u0000In this note we give a partial answer to this problem. \u0000To our knowledge, in the general statement, this problem remains unanswered not only for frame, but also for Schauder and Riesz basicity properties and even for orthonormal basicity of systems of the form {einα(·)}+∞n=-∞.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47374405","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 : 2021-10-19DOI: 10.15446/RECOLMA.V55N1.99097
Jorge Moreno, E. Pineda, W. Urbina
The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd, on Gaussian variable Lebesgue spaces Lp(.) (γd); under a condition of regularity on p(.) following [5] and [8]. As an immediate consequence of that result, the Lp(.) (γd)-boundedness of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd is obtained. Another consequence of that result is the Lp(.) (γd)-boundedness of the Poisson-Hermite semigroup and the Lp(.) (γd)- boundedness of the Gaussian Bessel potentials of order β > 0.
{"title":"Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences","authors":"Jorge Moreno, E. Pineda, W. Urbina","doi":"10.15446/RECOLMA.V55N1.99097","DOIUrl":"https://doi.org/10.15446/RECOLMA.V55N1.99097","url":null,"abstract":"The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd, on Gaussian variable Lebesgue spaces Lp(.) (γd); under a condition of regularity on p(.) following [5] and [8]. As an immediate consequence of that result, the Lp(.) (γd)-boundedness of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd is obtained. Another consequence of that result is the Lp(.) (γd)-boundedness of the Poisson-Hermite semigroup and the Lp(.) (γd)- boundedness of the Gaussian Bessel potentials of order β > 0.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48269991","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 : 2021-10-19DOI: 10.15446/RECOLMA.V55N1.99095
Edilberto Arroyo-Ortiz
We present a basis of p-adic wavelets for Sobolev-type spaces consisting of eigenvectors of certain pseudodifferential operators. Our result extends a well-known result due to S. Kozyrev.
{"title":"A note on the p-adic Kozyrev wavelets basis","authors":"Edilberto Arroyo-Ortiz","doi":"10.15446/RECOLMA.V55N1.99095","DOIUrl":"https://doi.org/10.15446/RECOLMA.V55N1.99095","url":null,"abstract":"We present a basis of p-adic wavelets for Sobolev-type spaces consisting of eigenvectors of certain pseudodifferential operators. Our result extends a well-known result due to S. Kozyrev.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49483059","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 : 2021-10-19DOI: 10.15446/recolma.v55n1.99096
H. Díaz-Marín, O. Osuna
In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.
{"title":"Periodic solutions for a model of tumor volume with anti-angiogenic periodic treatment","authors":"H. Díaz-Marín, O. Osuna","doi":"10.15446/recolma.v55n1.99096","DOIUrl":"https://doi.org/10.15446/recolma.v55n1.99096","url":null,"abstract":"In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49603124","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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