Pub Date : 2021-10-19DOI: 10.15446/RECOLMA.V55N1.99098
Abdeslam Talha, Mohamed Saad Bouh ELEMINE VALL
In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.
{"title":"Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces","authors":"Abdeslam Talha, Mohamed Saad Bouh ELEMINE VALL","doi":"10.15446/RECOLMA.V55N1.99098","DOIUrl":"https://doi.org/10.15446/RECOLMA.V55N1.99098","url":null,"abstract":"In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.","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":"47520776","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 : 2021-01-25DOI: 10.15446/recolma.v54n2.93846
Franqui Cárdenas
It is proved that if an uncountable cardinal κ has an ineffable subset of weakly compact cardinals, then κ is a weakly compact cardinal, and if κ has an ineffable subset of Ramsey (Rowbottom, Jónsson, ineffable or subtle) cardinals, then κ is a Ramsey (Rowbottom, J'onsson, ineffable or subtle) cardinal.
{"title":"Ineffable limits of weakly compact cardinals and similar results","authors":"Franqui Cárdenas","doi":"10.15446/recolma.v54n2.93846","DOIUrl":"https://doi.org/10.15446/recolma.v54n2.93846","url":null,"abstract":"It is proved that if an uncountable cardinal κ has an ineffable subset of weakly compact cardinals, then κ is a weakly compact cardinal, and if κ has an ineffable subset of Ramsey (Rowbottom, Jónsson, ineffable or subtle) cardinals, then κ is a Ramsey (Rowbottom, J'onsson, ineffable or subtle) cardinal.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44047153","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 : 2021-01-25DOI: 10.15446/recolma.v54n2.93842
T. Amouzegar
En esta nota nosotros introducimos los módulos L-⊕-suplementados, una generalizacion de los módulos ⊕-suplementados. Un módulo M se dice I-⊕-suplementado si para cada φ ∈ EndR (M), existe un sumando directo L de M tal que Imφ + L = M y Imφ ∩ L « L. Se demuestra que si M es un módulo I-⊕-suplementado con la condición D3 , entonces cada sumando directo de M es I-⊕-suplementado. Demostramos que si M = M1 ⊕ M2 es I-⊕-suplementado tal que M1 y M2 son proyectivos relativos, entonces M1 y M2 son I-⊕-suplementados. Estudiamos algunos anillos cuyos modulos son I-⊕-suplementados.
在本说明中，我们介绍了补充L-⊕模块，这是补充L-⊕模块的推广。模块M I -⊕据说-suplementado如果对于每个φ∈EndR (M)、一个加数直接升米,以致ImφIm + L = Mφ∩升«L .证明如果M是一个模块I -⊕-suplementado直接与D3条件,那么每一个加数M是I -⊕-suplementado。我们证明了如果M = M1⊕M2是I-⊕-补充，使M1和M2是相对射影，那么M1和M2是I-⊕-补充。我们研究了一些模为I-⊕-补充的环。
{"title":"On L-O-supplemented modules","authors":"T. Amouzegar","doi":"10.15446/recolma.v54n2.93842","DOIUrl":"https://doi.org/10.15446/recolma.v54n2.93842","url":null,"abstract":"En esta nota nosotros introducimos los módulos L-⊕-suplementados, una generalizacion de los módulos ⊕-suplementados. Un módulo M se dice I-⊕-suplementado si para cada φ ∈ EndR (M), existe un sumando directo L de M tal que Imφ + L = M y Imφ ∩ L « L. Se demuestra que si M es un módulo I-⊕-suplementado con la condición D3 , entonces cada sumando directo de M es I-⊕-suplementado. Demostramos que si M = M1 ⊕ M2 es I-⊕-suplementado tal que M1 y M2 son proyectivos relativos, entonces M1 y M2 son I-⊕-suplementados. Estudiamos algunos anillos cuyos modulos son I-⊕-suplementados.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43222498","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 : 2021-01-24DOI: 10.15446/recolma.v54n2.93833
P. Danchev
We prove that any square nilpotent matrix over a field is a difference of two idempotent matrices as well as that any square matrix over an algebraically closed field is a sum of a nilpotent square-zero matrix and a diagonalizable matrix. We further apply these two assertions to a variation of π-regular rings. These results somewhat improve on establishments due to Breaz from Linear Algebra & amp; Appl. (2018) and Abyzov from Siberian Math. J. (2019) as well as they also refine two recent achievements due to the present author, published in Vest. St. Petersburg Univ. - Ser. Math., Mech. & amp; Astr. (2019) and Chebyshevskii Sb. (2019), respectively.
{"title":"Certain Properties of Square Matrices over Fields with Applications to Rings","authors":"P. Danchev","doi":"10.15446/recolma.v54n2.93833","DOIUrl":"https://doi.org/10.15446/recolma.v54n2.93833","url":null,"abstract":"We prove that any square nilpotent matrix over a field is a difference of two idempotent matrices as well as that any square matrix over an algebraically closed field is a sum of a nilpotent square-zero matrix and a diagonalizable matrix. We further apply these two assertions to a variation of π-regular rings. These results somewhat improve on establishments due to Breaz from Linear Algebra & amp; Appl. (2018) and Abyzov from Siberian Math. J. (2019) as well as they also refine two recent achievements due to the present author, published in Vest. St. Petersburg Univ. - Ser. Math., Mech. & amp; Astr. (2019) and Chebyshevskii Sb. (2019), respectively.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283901","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 : 2021-01-24DOI: 10.15446/recolma.v54n2.93841
S. M. Tabatabaie, A. Bagheri Salec
Let K be a locally compact hypergroup. In this paper, among other results we give a sufficient condition for the inclusion LΦ1w (K) * LΦ2w (K) ⊆ LΦ1w (K) to hold. Also, as an application, we provide a new sufficient condition for the weighted Orlicz space LΦw (K) to be a convolution Banach algebra.
{"title":"Convolution of Two Weighted Orlicz Spaces on Hypergroups","authors":"S. M. Tabatabaie, A. Bagheri Salec","doi":"10.15446/recolma.v54n2.93841","DOIUrl":"https://doi.org/10.15446/recolma.v54n2.93841","url":null,"abstract":"Let K be a locally compact hypergroup. In this paper, among other results we give a sufficient condition for the inclusion LΦ1w (K) * LΦ2w (K) ⊆ LΦ1w (K) to hold. Also, as an application, we provide a new sufficient condition for the weighted Orlicz space LΦw (K) to be a convolution Banach algebra.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46850912","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 : 2021-01-20DOI: 10.15446/recolma.v54n2.93828
Duv'an Cardona
In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the L∞-BMO boundedness for pseudo-multipliers of the harmonic oscillator. The H1-L1 continuity for Hermite multipliers also is investigated.
{"title":"L-BMO bounds for pseudo-multipliers associated with the harmonic oscillator","authors":"Duv'an Cardona","doi":"10.15446/recolma.v54n2.93828","DOIUrl":"https://doi.org/10.15446/recolma.v54n2.93828","url":null,"abstract":"In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the L∞-BMO boundedness for pseudo-multipliers of the harmonic oscillator. The H1-L1 continuity for Hermite multipliers also is investigated.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45759785","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 : 2021-01-19DOI: 10.15446/recolma.v56n2.108370
J. Mantilla, Wilson Olaya-Le'on, J. L. Ram'irez
A superdiagonal composition is one in which the i-th part or summand is of size greater than or equal to i. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In particular, we give generating functions and explicit combinatorial formulas involving binomial coefficients and Stirling numbers of the first kind.
{"title":"Palindromic and Colored Superdiagonal Compositions","authors":"J. Mantilla, Wilson Olaya-Le'on, J. L. Ram'irez","doi":"10.15446/recolma.v56n2.108370","DOIUrl":"https://doi.org/10.15446/recolma.v56n2.108370","url":null,"abstract":"A superdiagonal composition is one in which the i-th part or summand is of size greater than or equal to i. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In particular, we give generating functions and explicit combinatorial formulas involving binomial coefficients and Stirling numbers of the first kind.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47102380","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 : 2020-02-06DOI: 10.15446/recolma.v55n2.102612
A. Bingham
Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of ‘3-primality’ -primality with respect to ternary multiplication- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fields Q(√-n), n > 0, with odd discriminant and whose ring of integers admits unique factorization. We also describe how to determine representations of numbers as ternary products and related algorithms for usual primality testing and integer factorization.
{"title":"Ternary arithmetic, factorization, and the class number one problem","authors":"A. Bingham","doi":"10.15446/recolma.v55n2.102612","DOIUrl":"https://doi.org/10.15446/recolma.v55n2.102612","url":null,"abstract":"Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of ‘3-primality’ -primality with respect to ternary multiplication- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fields Q(√-n), n > 0, with odd discriminant and whose ring of integers admits unique factorization. We also describe how to determine representations of numbers as ternary products and related algorithms for usual primality testing and integer factorization.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47500821","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 : 2020-01-01DOI: 10.15446/recolma.v54n1.89789
J. C. García, R. Hidalgo
Let S be a connected Riemann surface and let φ: S → Ĉ bebranched covering map of nite type. If n ≥ 2,then we describe a simple geometrical necessary and sucient condition for the existence of some n-th root, that is, a meromorphic map ψ: S → Ĉ such that φ = ψn.
{"title":"On n-th roots of meromorphic maps","authors":"J. C. García, R. Hidalgo","doi":"10.15446/recolma.v54n1.89789","DOIUrl":"https://doi.org/10.15446/recolma.v54n1.89789","url":null,"abstract":"Let S be a connected Riemann surface and let φ: S → Ĉ bebranched covering map of nite type. If n ≥ 2,then we describe a simple geometrical necessary and sucient condition for the existence of some n-th root, that is, a meromorphic map ψ: S → Ĉ such that φ = ψn.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42022666","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 : 2020-01-01DOI: 10.15446/recolma.v54n1.89788
Mohamed Louzari, A. Reyes
In this paper, we characterize the units of skew PBW extensions over compatible rings. With this aim, we recall the transfer of the property of being 2-primal for these extensions. As a consequence of our treatment, the results established here generalize those corresponding for commutative rings and Ore extensions of injective type. In this way, we present new results for several noncommutative rings of polynomial type not considered before in the literature.
{"title":"Minimal prime ideals of skew PBW extensions over 2-primal compatible rings","authors":"Mohamed Louzari, A. Reyes","doi":"10.15446/recolma.v54n1.89788","DOIUrl":"https://doi.org/10.15446/recolma.v54n1.89788","url":null,"abstract":"In this paper, we characterize the units of skew PBW extensions over compatible rings. With this aim, we recall the transfer of the property of being 2-primal for these extensions. As a consequence of our treatment, the results established here generalize those corresponding for commutative rings and Ore extensions of injective type. In this way, we present new results for several noncommutative rings of polynomial type not considered before in the literature.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47123310","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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