Pub Date : 2022-03-01DOI: 10.18273/revint.v40n1-2022004
N. B. Huamaní, Joice S. do Nascimento, A. Condori
Caterpillar trees, or simply Caterpillar, are trees such that when we remove all their leaves (or end edge) we obtain a path. The number of nonisomorphic caterpillars with n ≥ 2 edges is 2n−3 + 2⌊(n−3)/2⌋. Using a new sum of graphs, introduced in this paper, we provided a new proof of this result.
{"title":"A new sum of graphs and caterpillar trees","authors":"N. B. Huamaní, Joice S. do Nascimento, A. Condori","doi":"10.18273/revint.v40n1-2022004","DOIUrl":"https://doi.org/10.18273/revint.v40n1-2022004","url":null,"abstract":"Caterpillar trees, or simply Caterpillar, are trees such that when we remove all their leaves (or end edge) we obtain a path. The number of nonisomorphic caterpillars with n ≥ 2 edges is 2n−3 + 2⌊(n−3)/2⌋. Using a new sum of graphs, introduced in this paper, we provided a new proof of this result.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131111217","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 : 2022-01-08DOI: 10.18273/revint.v40n1-2022001
D. Mej'ia, Y. Kiriu
Let q be a prime. We classify the odd primes p ≠ q such that the equation x2 ≡ q (mod p) has a solution, concretely, we find a subgroup L4q of the multiplicative group U4q of integers relatively prime with 4q (modulo 4q) such that x2 ≡ q (mod p) has a solution iff p ≡ c (mod 4q) for some c ∈ L4q. Moreover, L4q is the only subgroup of U4q of half order containing −1. Considering the ring Z[√2], for any odd prime p it is known that the equation x2 ≡ 2 (mod p) has a solution iff the equation x2 −2y2 = p has a solution in the integers. We ask whether this can be extended in the context of Z[n√2] with n ≥2, namely: for any prime p ≡ 1 (mod n), is it true that xn ≡ 2 (mod p) has a solution iff the equation D2n(x0, . . . , xn−1) = p has a solution in the integers? Here D2n(x̄) represents the norm of the field extension Q(n√2) of Q. We solve some weak versions of this problem, where equality with p is replaced by 0 (mod p) (divisible by p), and the “norm" Drn(x̄) is considered for any r ∈ Z in the place of 2.
{"title":"Some notes about power residues modulo prime","authors":"D. Mej'ia, Y. Kiriu","doi":"10.18273/revint.v40n1-2022001","DOIUrl":"https://doi.org/10.18273/revint.v40n1-2022001","url":null,"abstract":"Let q be a prime. We classify the odd primes p ≠ q such that the equation x2 ≡ q (mod p) has a solution, concretely, we find a subgroup L4q of the multiplicative group U4q of integers relatively prime with 4q (modulo 4q) such that x2 ≡ q (mod p) has a solution iff p ≡ c (mod 4q) for some c ∈ L4q. Moreover, L4q is the only subgroup of U4q of half order containing −1. Considering the ring Z[√2], for any odd prime p it is known that the equation x2 ≡ 2 (mod p) has a solution iff the equation x2 −2y2 = p has a solution in the integers. We ask whether this can be extended in the context of Z[n√2] with n ≥2, namely: for any prime p ≡ 1 (mod n), is it true that xn ≡ 2 (mod p) has a solution iff the equation D2n(x0, . . . , xn−1) = p has a solution in the integers? Here D2n(x̄) represents the norm of the field extension Q(n√2) of Q. We solve some weak versions of this problem, where equality with p is replaced by 0 (mod p) (divisible by p), and the “norm\" Drn(x̄) is considered for any r ∈ Z in the place of 2.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133925619","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 : 2021-10-08DOI: 10.18273/revint.v39n2-20210004
W. Sánchez, R. Pérez, H. Martínez
In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.
{"title":"Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal","authors":"W. Sánchez, R. Pérez, H. Martínez","doi":"10.18273/revint.v39n2-20210004","DOIUrl":"https://doi.org/10.18273/revint.v39n2-20210004","url":null,"abstract":"In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115961105","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 : 2021-10-08DOI: 10.18273/revint.v39n2-2021002
Rafael Gaitan Ospina
En este artículo, se presenta la construcción de una teoría de homología general en la categoría de los grupos abelianos en el sentido de R. Ruiz, definida en su texto Introducción a la Teoría de Homología General [22], para categorías en general, la cual satisface una axiomática similar a la presentada por Eilenberg y Steenrod para teorías de homología en categorías admisibles de parejas de espacios topológicos (X, A) [3]. Esta teoría de homología general en los grupos abelianos se construyó por medio de un Esqueleto Homoto-Homológico, definido en este trabajo, mostrando sus conexiones con categorías monoidales y categorías simpliciales.
{"title":"Esqueleto Homoto-Homológico en la Categoría de los Grupos Abelianos","authors":"Rafael Gaitan Ospina","doi":"10.18273/revint.v39n2-2021002","DOIUrl":"https://doi.org/10.18273/revint.v39n2-2021002","url":null,"abstract":"En este artículo, se presenta la construcción de una teoría de homología general en la categoría de los grupos abelianos en el sentido de R. Ruiz, definida en su texto Introducción a la Teoría de Homología General [22], para categorías en general, la cual satisface una axiomática similar a la presentada por Eilenberg y Steenrod para teorías de homología en categorías admisibles de parejas de espacios topológicos (X, A) [3]. Esta teoría de homología general en los grupos abelianos se construyó por medio de un Esqueleto Homoto-Homológico, definido en este trabajo, mostrando sus conexiones con categorías monoidales y categorías simpliciales.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"92 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128019798","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 : 2021-10-08DOI: 10.18273/revint.v39n2-2021003
O. Osuna, Jose Geiser Villavicencio Pulido
We analyze the evolution of an infectious disease if infectious individuals are treated or isolated. The analysis of the model shows catastrophic scenarios for the population in which bringing R0 below 1 is not enough to decrease the number of infectious individuals. Finally, we show three scenarios for the behavior of the model solutions in which multiple endemic equilibria exist.
{"title":"La aplicación simultanea de intervenciones de control puede llevar a escenarios catastróficos para la población","authors":"O. Osuna, Jose Geiser Villavicencio Pulido","doi":"10.18273/revint.v39n2-2021003","DOIUrl":"https://doi.org/10.18273/revint.v39n2-2021003","url":null,"abstract":"We analyze the evolution of an infectious disease if infectious individuals are treated or isolated. The analysis of the model shows catastrophic scenarios for the population in which bringing R0 below 1 is not enough to decrease the number of infectious individuals. Finally, we show three scenarios for the behavior of the model solutions in which multiple endemic equilibria exist.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124579743","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 : 2021-10-08DOI: 10.18273/revint.v39n2-20210005
Carlos Arias, R. Pérez, H. Martínez
En este artículo, proponemos un nuevo algoritmo tipo Newton inexacto para resolver el problema de complementariedad horizontal mediante su reformulación como un problema de minimización restricto. El algoritmo usa la estrategia de combinar una dirección Newton inexacta con su proyección sobre el conjunto factible; esta última opción solo se usa cuando se necesita garantizar factibilidad. Además, presentamos un análisis teórico y numérico del nuevo algoritmo.
{"title":"Un algoritmo Newton inexacto para complementariedad horizontal","authors":"Carlos Arias, R. Pérez, H. Martínez","doi":"10.18273/revint.v39n2-20210005","DOIUrl":"https://doi.org/10.18273/revint.v39n2-20210005","url":null,"abstract":"En este artículo, proponemos un nuevo algoritmo tipo Newton inexacto para resolver el problema de complementariedad horizontal mediante su reformulación como un problema de minimización restricto. El algoritmo usa la estrategia de combinar una dirección Newton inexacta con su proyección sobre el conjunto factible; esta última opción solo se usa cuando se necesita garantizar factibilidad. Además, presentamos un análisis teórico y numérico del nuevo algoritmo.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123094954","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 : 2021-10-08DOI: 10.18273/revint.v39n2-2021001
Aníbal Coronel, E. Lozada
En este artículo presentamos una prueba corta y elemental de la siguiente desigualdad algebraico-trigonométrica de tipo Laub-Ilani: cos(xy) + cos(yx) ≥ cos(xx) + cos(yy) para x, y ∈ [0, π/2] que fue conjeturada por Özban [‘New algebraic-trigonometric inequalities of Laub-Ilani type’, Bull. Aust. Math. Soc. 96 (2017), 87–97] y recientemente probada por Matejíčka [‘Proof of one open inequality of Laub-Ilani type’, Journal of Mathematical Inequalities, 14 (2020), 83–98]. La prueba se basa en las propiedades de las funciones potenciales-exponenciales y trigonométricas.
在本文中,介绍一个简短的测试和训练不平等algebraico-trigonométrica Laub-Ilani型:因为科(yx)≥(xy) +科(yy)科(xx) + x, y∈[0,π/ 2]受到conjeturadaÖzban[‘New type algebraic-trigonometric 2006 of Laub-Ilani, Bull。奥斯特。Math。Soc 96(2017年),87—97]最近得到Matejíčka[‘Proof of one open inequality of Laub-Ilani type、Journal of Mathematical不平等、14(2020年),83—98]。证明是基于幂指数函数和三角函数的性质。
{"title":"Una nueva prueba para una conjetura de Özban","authors":"Aníbal Coronel, E. Lozada","doi":"10.18273/revint.v39n2-2021001","DOIUrl":"https://doi.org/10.18273/revint.v39n2-2021001","url":null,"abstract":"En este artículo presentamos una prueba corta y elemental de la siguiente desigualdad algebraico-trigonométrica de tipo Laub-Ilani: cos(xy) + cos(yx) ≥ cos(xx) + cos(yy) para x, y ∈ [0, π/2] que fue conjeturada por Özban [‘New algebraic-trigonometric inequalities of Laub-Ilani type’, Bull. Aust. Math. Soc. 96 (2017), 87–97] y recientemente probada por Matejíčka [‘Proof of one open inequality of Laub-Ilani type’, Journal of Mathematical Inequalities, 14 (2020), 83–98]. La prueba se basa en las propiedades de las funciones potenciales-exponenciales y trigonométricas.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134234764","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 : 2021-10-08DOI: 10.18273/revint.v39n2-2021006
Juan Angoa Amador, Agustín Contreras Carreto, Jesús González Sandoval
In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms M and epimorphisms E for any topological category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some M−coreflective subcategories of a topological category. We pay special attention to projective structures.
{"title":"(E,M)−estructuras inducidas en categorías topológicas","authors":"Juan Angoa Amador, Agustín Contreras Carreto, Jesús González Sandoval","doi":"10.18273/revint.v39n2-2021006","DOIUrl":"https://doi.org/10.18273/revint.v39n2-2021006","url":null,"abstract":"In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms M and epimorphisms E for any topological category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some M−coreflective subcategories of a topological category. We pay special attention to projective structures.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115821395","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 : 2021-10-08DOI: 10.18273/revint.v39n2-2021007
Danilo García Hernández, Oscar Mario Londoño Duque, Yeisson Acevedo, Gabriel Loaiza
We obtain the complete classification of the Lie symmetry group and the optimal system’s generating operators associated with a particular case of the generalized Kummer - Schwarz equation. Using those operators we characterize all invariant solutions, alternative solutions were found for the equation studied and the Lie algebra associated with the symmetry group is classified.
{"title":"Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie","authors":"Danilo García Hernández, Oscar Mario Londoño Duque, Yeisson Acevedo, Gabriel Loaiza","doi":"10.18273/revint.v39n2-2021007","DOIUrl":"https://doi.org/10.18273/revint.v39n2-2021007","url":null,"abstract":"We obtain the complete classification of the Lie symmetry group and the optimal system’s generating operators associated with a particular case of the generalized Kummer - Schwarz equation. Using those operators we characterize all invariant solutions, alternative solutions were found for the equation studied and the Lie algebra associated with the symmetry group is classified.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129368135","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 : 2021-05-19DOI: 10.18273/revint.v39n1-2021007
Héctor Suárez, Duban Cáceres, Armando Reyes
In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslander-regular algebra has trivial homological determinant. For A = σ(R) a graded skew PBW extension over a connected algebra R, we compute its P-determinant and the inverse of σ. In the particular case of quasi-commutative skew PBW extensions over Koszul Artin-Schelter regular algebras, we show explicitly the connection between the Nakayama automorphism of the ring of coefficients and the extension. Finally, we give conditions to guarantee that A is Calabi-Yau. We provide illustrative examples of the theory concerning algebras of interest in noncommutative algebraic geometry and noncommutative differential geometry.
{"title":"Algunos tipos especiales de determinantes en extensiones PBW torcidas graduadas","authors":"Héctor Suárez, Duban Cáceres, Armando Reyes","doi":"10.18273/revint.v39n1-2021007","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021007","url":null,"abstract":"In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslander-regular algebra has trivial homological determinant. For A = σ(R) a graded skew PBW extension over a connected algebra R, we compute its P-determinant and the inverse of σ. In the particular case of quasi-commutative skew PBW extensions over Koszul Artin-Schelter regular algebras, we show explicitly the connection between the Nakayama automorphism of the ring of coefficients and the extension. Finally, we give conditions to guarantee that A is Calabi-Yau. We provide illustrative examples of the theory concerning algebras of interest in noncommutative algebraic geometry and noncommutative differential geometry.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133698821","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：