Pub Date : 2021-05-19DOI: 10.18273/revint.v39n1-2021004
X. Wang
In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.
{"title":"Soluciones globales para sistema isotérmico con fuente","authors":"X. Wang","doi":"10.18273/revint.v39n1-2021004","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021004","url":null,"abstract":"In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"773 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":"122362161","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.v39n1-2021001
José G. Anaya, Félix Capulín, M. Sánchez Garrido
J. J. Charatonik formulated in 1991 the following problem: What are all mappings that preserve contractibility (noncontractibility) of den-droids? On the other hand, J. J. Charatonik, W. J. Charatonik, and S. Miklos asked in 1990 the following questions (among others related to con-tractibility): What kinds of confluent mappings preserve contractibility of fans? And what kinds of confluent mappings preserve non contractibility of fans? In this paper, we will show some partial answers to these questions. Addition-ally, we will consider these questions with other kinds of families of mappings.
J. J. Charatonik在1991年提出了以下问题:什么是保持den-droids的可收缩性(不可收缩性)的所有映射?另一方面，J. J. Charatonik、W. J. Charatonik和S. Miklos在1990年提出了以下问题(其中包括与可收缩性有关的问题):什么样的融合映射保持了粉丝的可收缩性?什么样的合流映射保持了扇的不可收缩性?在本文中，我们将给出这些问题的部分答案。此外，我们还将用其他类型的映射族来考虑这些问题。
{"title":"Funciones entre dendroides (abanicos) que (no) preservan (no)contractibilidad","authors":"José G. Anaya, Félix Capulín, M. Sánchez Garrido","doi":"10.18273/revint.v39n1-2021001","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021001","url":null,"abstract":"J. J. Charatonik formulated in 1991 the following problem: What are all mappings that preserve contractibility (noncontractibility) of den-droids? On the other hand, J. J. Charatonik, W. J. Charatonik, and S. Miklos asked in 1990 the following questions (among others related to con-tractibility): What kinds of confluent mappings preserve contractibility of fans? And what kinds of confluent mappings preserve non contractibility of fans? In this paper, we will show some partial answers to these questions. Addition-ally, we will consider these questions with other kinds of families of mappings.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"49 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":"126120183","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.v39n1-2021003
Eddye Bustamante, José Jiménez Urrea
In this work we consider equations of the form ∂tu + P(D)u + u^{l}∂xu = 0, where P(D) is a two-dimensional differential operator, and l ∈ N. We prove that if u is a sufficiently smooth solution of the equation, such that suppu(0), suppu(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R0>0 such that suppu(t) ⊂ [-R_0,R_0]×[-R_0,R_0] for every t ∈ [0, T].
{"title":"Propiedades del soporte de soluciones de una clase de ecuaciones de evolución no lineales en dos dimensiones","authors":"Eddye Bustamante, José Jiménez Urrea","doi":"10.18273/revint.v39n1-2021003","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021003","url":null,"abstract":"In this work we consider equations of the form ∂tu + P(D)u + u^{l}∂xu = 0, where P(D) is a two-dimensional differential operator, and l ∈ N. We prove that if u is a sufficiently smooth solution of the equation, such that suppu(0), suppu(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R0>0 such that suppu(t) ⊂ [-R_0,R_0]×[-R_0,R_0] for every t ∈ [0, T].","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":" 32","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132075406","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.v39n1-2021008
N. B. Huamaní, C. Mendes de Jesus
En el presente artículo se estudia el espacio de grafos con pesos, junto con dos operaciones entre estos grafos. Los resultados que se encuentran en este espacio son usados en el estudio de aplicaciones estables de 3-variedades en R3, en particular cuando la 3-variedad es Mn, donde esta variedad es la suma conexa de n-copias de S1×S2 con M0 = S3. Además, se prueban resultados importantes para la construcción de este tipo de aplicaciones.
{"title":"Grafos pesados y aplicaciones estables de 3-variedades en R3","authors":"N. B. Huamaní, C. Mendes de Jesus","doi":"10.18273/revint.v39n1-2021008","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021008","url":null,"abstract":"En el presente artículo se estudia el espacio de grafos con pesos, junto con dos operaciones entre estos grafos. Los resultados que se encuentran en este espacio son usados en el estudio de aplicaciones estables de 3-variedades en R3, en particular cuando la 3-variedad es Mn, donde esta variedad es la suma conexa de n-copias de S1×S2 con M0 = S3. Además, se prueban resultados importantes para la construcción de este tipo de aplicaciones.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"5 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":"131086789","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.v39n1-2021002
A. Castillo, C. Hernández
En este escrito presentamos un estudio de la dualidad de un grupo vía reflexiones. Iniciamos con la demostración de una condición necesaria para que el homomorfismo dual del homomorfismo que va del grupo a su reflexión sea una biyección continua, esto es, que siendo φ: G → ξ(G), sucede que φb: ξ[(G) → Gb es una biyección continua si T ∈ ξ, donde ξ es una subcategoría reflexiva de la categoría de los grupos topológicos y ξ(G) es la reflexión de G. Una vez se tenga la anterior condición se demuestra que Gb ∼= ξ[(G), cuando G es un grupo compacto, o es un grupo topológico Čech completo con φ: G → ξ(G) sobreyectiva y abierta, o un grupo topológico localmente compacto y φ: G → ξ(G) es sobreyectiva y abierta. En el caso del dual de las reflexiones de grupos topológicos metrizables, nos apoyamos en el resultado de Chasco [5] que implica que si G es un grupo topológico abeliano metrizable y H es un subgrupo denso de G, entonces los grupos duales Gb y Hb son topológicamente isomorfos.
{"title":"El dual de la reflexión de un grupo topológico","authors":"A. Castillo, C. Hernández","doi":"10.18273/revint.v39n1-2021002","DOIUrl":"https://doi.org/10.18273/revint.v39n1-2021002","url":null,"abstract":"En este escrito presentamos un estudio de la dualidad de un grupo vía reflexiones. Iniciamos con la demostración de una condición necesaria para que el homomorfismo dual del homomorfismo que va del grupo a su reflexión sea una biyección continua, esto es, que siendo φ: G → ξ(G), sucede que φb: ξ[(G) → Gb es una biyección continua si T ∈ ξ, donde ξ es una subcategoría reflexiva de la categoría de los grupos topológicos y ξ(G) es la reflexión de G. Una vez se tenga la anterior condición se demuestra que Gb ∼= ξ[(G), cuando G es un grupo compacto, o es un grupo topológico Čech completo con φ: G → ξ(G) sobreyectiva y abierta, o un grupo topológico localmente compacto y φ: G → ξ(G) es sobreyectiva y abierta. En el caso del dual de las reflexiones de grupos topológicos metrizables, nos apoyamos en el resultado de Chasco [5] que implica que si G es un grupo topológico abeliano metrizable y H es un subgrupo denso de G, entonces los grupos duales Gb y Hb son topológicamente isomorfos.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"70 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":"128352403","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 : 2021-03-24DOI: 10.18273/revint.v40n1-2022002
Bilel Elbetch, T. Benzekri, D. Massart, T. Sari
This paper is a follow-up to a previous work where we considered a multi-patch model, each patch following a logistic law, the patches being coupled by symmetric migration terms. In this paper we drop the symmetry hypothesis. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities, and depends on the migration terms. Second, we determine, in some particular cases, the conditions under which fragmentation and asymmetrical migration can lead to a total equilibrium population greater or smaller than the sum of the carrying capacities. Finally, for the three-patch model, we show numerically the existence of at least three critical values of the migration rate for which the total equilibrium population equals the sum of the carrying capacities.
{"title":"The multi-patch logistic equation with asymmetric migration","authors":"Bilel Elbetch, T. Benzekri, D. Massart, T. Sari","doi":"10.18273/revint.v40n1-2022002","DOIUrl":"https://doi.org/10.18273/revint.v40n1-2022002","url":null,"abstract":"This paper is a follow-up to a previous work where we considered a multi-patch model, each patch following a logistic law, the patches being coupled by symmetric migration terms. In this paper we drop the symmetry hypothesis. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total population follows a logistic law with a carrying capacity which in general is different from the sum of the n carrying capacities, and depends on the migration terms. Second, we determine, in some particular cases, the conditions under which fragmentation and asymmetrical migration can lead to a total equilibrium population greater or smaller than the sum of the carrying capacities. Finally, for the three-patch model, we show numerically the existence of at least three critical values of the migration rate for which the total equilibrium population equals the sum of the carrying capacities.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121775681","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 : 2020-01-27DOI: 10.18273/revint.v38n1-202002
Eber Lenes, Henry García, Ariel Figueroa, Fabian Mercado
Let N(G) be the number of vertices of the graph G. Let Pl(Bi) be the tree obtained of the path Pl and the trees B1, B2, ..., Bl by identifying the root vertex of Bi with the i-th vertex of Pl. Let Vm n = {Pl(Bi) : N(Pl(Bi)) = n;N(Bi) ≥ 2; l ≥ m}. In this paper, we determine the tree that has the largest α-index among all the trees in Vm n .
设N(G)为图G的顶点数，设Pl(Bi)为路径Pl和树B1, B2，…所得到的树令Vm n = {Pl(Bi): n (Pl(Bi)) = n; n (Bi)≥2;L≥m}。在本文中，我们确定了vmn中所有树中α-索引最大的树。
{"title":"Extremal graphs for α- index","authors":"Eber Lenes, Henry García, Ariel Figueroa, Fabian Mercado","doi":"10.18273/revint.v38n1-202002","DOIUrl":"https://doi.org/10.18273/revint.v38n1-202002","url":null,"abstract":"Let N(G) be the number of vertices of the graph G. Let Pl(Bi) be the tree obtained of the path Pl and the trees B1, B2, ..., Bl by identifying the root vertex of Bi with the i-th vertex of Pl. Let Vm n = {Pl(Bi) : N(Pl(Bi)) = n;N(Bi) ≥ 2; l ≥ m}. In this paper, we determine the tree that has the largest α-index among all the trees in Vm n .","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131459496","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 : 2019-08-30DOI: 10.18273/revint.v37n2-2019001
P. Castillo, S. Gómez
Using the von Neumann analysis as a theoretical tool, an analysisof the stability conditions of some explicit time marching schemes, in com-bination with the spatial discretizationLocal Discontinuous Galerkin(LDG)and high order approximations, is presented. The stabilityconstant, CFL(Courant-Friedrichs-Lewy), is studied as a function of theLDG parametersand the approximation degree. A series of numerical experiments is carriedout to validate the theoretical results.
{"title":"Análisis de Von Neumann para el métodoLocal Discontinuous Galerkin en 1D","authors":"P. Castillo, S. Gómez","doi":"10.18273/revint.v37n2-2019001","DOIUrl":"https://doi.org/10.18273/revint.v37n2-2019001","url":null,"abstract":"Using the von Neumann analysis as a theoretical tool, an analysisof the stability conditions of some explicit time marching schemes, in com-bination with the spatial discretizationLocal Discontinuous Galerkin(LDG)and high order approximations, is presented. The stabilityconstant, CFL(Courant-Friedrichs-Lewy), is studied as a function of theLDG parametersand the approximation degree. A series of numerical experiments is carriedout to validate the theoretical results.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125838904","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 : 2019-07-29DOI: 10.18273/revint.v37n2-2019006
S. Dragomir
Assume thatfandgare continuous onγ,γ⊂Cis a piecewisesmooth path parametrized byz(t), t∈[a, b]fromz(a) =utoz(b) =wwithw6=u, and thecomplex Chebyshev functionalis defined byDγ(f, g) :=1w−u∫γf(z)g(z)dz−1w−u∫γf(z)dz1w−u∫γg(z)dz.In this paper we establish some bounds for the magnitude of the functionalDγ(f, g)under Lipschitzian assumptions for the functionsfandg,and pro-vide a complex version for the well known Chebyshev inequality.
{"title":"On some Chebyshev type inequalities for thecomplex integral","authors":"S. Dragomir","doi":"10.18273/revint.v37n2-2019006","DOIUrl":"https://doi.org/10.18273/revint.v37n2-2019006","url":null,"abstract":"Assume thatfandgare continuous onγ,γ⊂Cis a piecewisesmooth path parametrized byz(t), t∈[a, b]fromz(a) =utoz(b) =wwithw6=u, and thecomplex Chebyshev functionalis defined byDγ(f, g) :=1w−u∫γf(z)g(z)dz−1w−u∫γf(z)dz1w−u∫γg(z)dz.In this paper we establish some bounds for the magnitude of the functionalDγ(f, g)under Lipschitzian assumptions for the functionsfandg,and pro-vide a complex version for the well known Chebyshev inequality.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133985663","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: 10.18273/REVINT.V37N2-2019005
Brenda Lara-Aguilar, O. Osuna, Giovanni Wences
In this work, we prove the existence of periodic solutions forsome enzyme catalysed reaction models subject to periodic substrate input.We also obtain uniqueness and asymptotic stability of the periodic solutionof some classes of reaction equations. Numerical simulations are performedusing specific substrate functions to illustrate our analytical findings.
{"title":"Oscillations in enzymatic reactions withperiodic input","authors":"Brenda Lara-Aguilar, O. Osuna, Giovanni Wences","doi":"10.18273/REVINT.V37N2-2019005","DOIUrl":"https://doi.org/10.18273/REVINT.V37N2-2019005","url":null,"abstract":"In this work, we prove the existence of periodic solutions forsome enzyme catalysed reaction models subject to periodic substrate input.We also obtain uniqueness and asymptotic stability of the periodic solutionof some classes of reaction equations. Numerical simulations are performedusing specific substrate functions to illustrate our analytical findings.","PeriodicalId":402331,"journal":{"name":"Revista Integración","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123864910","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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