{"title":"On Bass Modules and Semi-V-Modules","authors":"Farid Kourki, R. Tribak","doi":"10.36045/j.bbms.200928","DOIUrl":"https://doi.org/10.36045/j.bbms.200928","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77135660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let D be the open unit disk |x| < R of a complete ultrametric algebraically closed field IK. We define the growth order ρ(f), the growth type σ(f) and the cotype ψ(f) of an analytic function in D and we show that, denoting by q(f, r) the number of zeros of f in the disk |x| ≤ r and putting |f |(r) = sup|x|≤r |f(x)|, the infimum θ(f) of the s such that lim r→R− q(f, r)(R− r) = 0 satisfies θ(f) − 1 ≤ ρ(f) ≤ θ(f) and the infimum of the s such that lim r→R− log(|f |(r))(R− r) = 0 is equal to ρ(f). Moreover, if 0 < ρ(f) < +∞ and 0 < ψ(f) < +∞, then θ(f) = ρ(f) and σ(f) = 0. In residue characteristic zero, then ρ(f ′) = ρ(f), σ(f ′) = σ(f), ψ(f ′) = ψ(f). Suppose IK has characteristic zero. Consider two unbounded analytic functions f, g in D. If ρ(f) 6= ρ(g), then f g has at most two perfectly branched values and if ρ(f) = ρ(g) but σ(f) 6= σ(g), then f g has at most three perfectly branched values; moreover, if 2σ(g) < σ(f), then f g has at most two perfectly branched values. Subject Classification: 12J25; 30D35; 30G06
{"title":"Growth of analytic functions in an ultrametric open disk and branched values","authors":"K. Boussaf, A. Escassut","doi":"10.36045/j.bbms.200707","DOIUrl":"https://doi.org/10.36045/j.bbms.200707","url":null,"abstract":"Let D be the open unit disk |x| < R of a complete ultrametric algebraically closed field IK. We define the growth order ρ(f), the growth type σ(f) and the cotype ψ(f) of an analytic function in D and we show that, denoting by q(f, r) the number of zeros of f in the disk |x| ≤ r and putting |f |(r) = sup|x|≤r |f(x)|, the infimum θ(f) of the s such that lim r→R− q(f, r)(R− r) = 0 satisfies θ(f) − 1 ≤ ρ(f) ≤ θ(f) and the infimum of the s such that lim r→R− log(|f |(r))(R− r) = 0 is equal to ρ(f). Moreover, if 0 < ρ(f) < +∞ and 0 < ψ(f) < +∞, then θ(f) = ρ(f) and σ(f) = 0. In residue characteristic zero, then ρ(f ′) = ρ(f), σ(f ′) = σ(f), ψ(f ′) = ψ(f). Suppose IK has characteristic zero. Consider two unbounded analytic functions f, g in D. If ρ(f) 6= ρ(g), then f g has at most two perfectly branched values and if ρ(f) = ρ(g) but σ(f) 6= σ(g), then f g has at most three perfectly branched values; moreover, if 2σ(g) < σ(f), then f g has at most two perfectly branched values. Subject Classification: 12J25; 30D35; 30G06","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87069487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Relative Choquet boundaries of restriction algebras","authors":"R. I. Hadjigeorgiou","doi":"10.36045/j.bbms.201116","DOIUrl":"https://doi.org/10.36045/j.bbms.201116","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78041773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage","authors":"Khelifa Chadi, M. Selmani","doi":"10.36045/j.bbms.191105","DOIUrl":"https://doi.org/10.36045/j.bbms.191105","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73639335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extremal results on distance Laplacian spectral radius of graphs","authors":"Hongying Lin, Bo Zhou","doi":"10.36045/j.bbms.190405","DOIUrl":"https://doi.org/10.36045/j.bbms.190405","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86531302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"2-nil ideals of commutative rings","authors":"E. Y. Çeli̇kel","doi":"10.36045/j.bbms.201031","DOIUrl":"https://doi.org/10.36045/j.bbms.201031","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88752502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parabolic hypersurfaces with constant mean curvature in Euclidean space","authors":"Mario Hernández, J. Meléndez","doi":"10.36045/j.bbms.200301","DOIUrl":"https://doi.org/10.36045/j.bbms.200301","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85240150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study properties of asymptotic resemblance relations induced by compatible coarse structures on groups. We generalize the notion of asymptotic dimensiongrad for groups with compatible coarse structures and show this notion is coarse invariant. We end by defining the notion of set theoretic coupling for groups with compatible coarse structures and showing this notion is the generalization of the notion of topological coupling for finitely generated groups. We show if two groups with compatible coarse structures admit a set theoretic coupling then they are asymptotic equivalent.
{"title":"Asymptotic resemblance relations on Groups","authors":"Sh. Kalantari","doi":"10.36045/j.bbms.200314","DOIUrl":"https://doi.org/10.36045/j.bbms.200314","url":null,"abstract":"In this paper, we study properties of asymptotic resemblance relations induced by compatible coarse structures on groups. We generalize the notion of asymptotic dimensiongrad for groups with compatible coarse structures and show this notion is coarse invariant. We end by defining the notion of set theoretic coupling for groups with compatible coarse structures and showing this notion is the generalization of the notion of topological coupling for finitely generated groups. We show if two groups with compatible coarse structures admit a set theoretic coupling then they are asymptotic equivalent.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83404252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The celebrated Touchard congruence states that Bn+p ≡ Bn + Bn+1 modulo p, where p is a prime number and Bn denotes the Bell number. In this paper we study divisibility properties of Bn−p and their generalizations involving higher powers of p as well as the r-Bell numbers. In particular, we show a closely relation of the considered problem to the Sun-Zagier congruence, which is additionally improved by deriving a new relation between r-Bell and derangement numbers. Finally, we conclude some results on the period of the Bell numbers modulo p.
{"title":"Backward Touchard congruence","authors":"G. Serafin","doi":"10.36045/j.bbms.210412a","DOIUrl":"https://doi.org/10.36045/j.bbms.210412a","url":null,"abstract":"The celebrated Touchard congruence states that Bn+p ≡ Bn + Bn+1 modulo p, where p is a prime number and Bn denotes the Bell number. In this paper we study divisibility properties of Bn−p and their generalizations involving higher powers of p as well as the r-Bell numbers. In particular, we show a closely relation of the considered problem to the Sun-Zagier congruence, which is additionally improved by deriving a new relation between r-Bell and derangement numbers. Finally, we conclude some results on the period of the Bell numbers modulo p.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78896300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let G be a finite groupoid and α = (Sg, αg)g∈G a unital partial action of group-type of G on a commutative ring S = ⊕y∈G0Sy. We shall prove a Galois correspondence between a class of wide subgroupoids of G and a class of subrings of S. We recover known results for global groupoid actions and we give several examples to illustrate the correspondence.
{"title":"Galois correspondence for group-type partial actions of groupoids","authors":"Dirceu Bagio, Alveri Sant’Ana, Thaísa Tamusiunas","doi":"10.36045/j.bbms.210807","DOIUrl":"https://doi.org/10.36045/j.bbms.210807","url":null,"abstract":"Let G be a finite groupoid and α = (Sg, αg)g∈G a unital partial action of group-type of G on a commutative ring S = ⊕y∈G0Sy. We shall prove a Galois correspondence between a class of wide subgroupoids of G and a class of subrings of S. We recover known results for global groupoid actions and we give several examples to illustrate the correspondence.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90517893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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