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Bulletin of the Belgian Mathematical Society-Simon Stevin最新文献

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The Khinchin inequality for multiple sums revisited 对多和的钦钦不等式进行了重新考察
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.220831
Anselmo Raposo, Katiuscia B. Teixeira
{"title":"The Khinchin inequality for multiple sums revisited","authors":"Anselmo Raposo, Katiuscia B. Teixeira","doi":"10.36045/j.bbms.220831","DOIUrl":"https://doi.org/10.36045/j.bbms.220831","url":null,"abstract":"We present a self-contained proof of the Khinchin inequality for multiple sums, which avoids advanced results from Probability theory. Not only our new proof is more accessible, but also it sheds lights on some properties of the inequality which may yield further generalizations.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277282","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}
引用次数: 0
On the Classification of Torsion-Free Nil Rings of Rank Two 二阶无扭零环的分类
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.221123
Ryszard R. Andruszkiewicz, Mateusz Woronowicz
{"title":"On the Classification of Torsion-Free Nil Rings of Rank Two","authors":"Ryszard R. Andruszkiewicz, Mateusz Woronowicz","doi":"10.36045/j.bbms.221123","DOIUrl":"https://doi.org/10.36045/j.bbms.221123","url":null,"abstract":"The paper contains the complete classification of nil rings with decomposable torsion-free additive group of rank two and description of nil rings with indecomposable torsion-free additive group of rank two. Moreover, it is shown that an indecomposable non-nil torsion-free abelian group $A$ of rank two supports only nilpotent rings exactly if $A$ is the additive group of a nil ring. Some decomposition criteria for torsion-free abelian groups of rank two are also included.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277084","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}
引用次数: 0
Chain Lemma, Quadratic Forms and Symbol Length 链式引理，二次型和符号长度
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.230123
Adam Chapman, Ilan Levin
{"title":"Chain Lemma, Quadratic Forms and Symbol Length","authors":"Adam Chapman, Ilan Levin","doi":"10.36045/j.bbms.230123","DOIUrl":"https://doi.org/10.36045/j.bbms.230123","url":null,"abstract":"We want to bound the symbol length of classes in ${_{2^{m-1}}Br}(F)$ which are represented by tensor products of 5 or 6 cyclic algebras of degree $2^m$. The main ingredients are the chain lemma for quadratic forms, a form of a generalized Clifford invariant and Pfister's and Rost's descriptions of 12- and 14-dimensional forms in $I^3 F$.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277086","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}
引用次数: 0
A best possible upper bound for the complete elliptic integral of the first kind 第一类完全椭圆积分的最佳可能上界
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.230228
Zhong-Xuan Mao, Lan-Xiang Yu, Jun-Yi Li, Jing-Feng Tian
{"title":"A best possible upper bound for the complete elliptic integral of the first kind","authors":"Zhong-Xuan Mao, Lan-Xiang Yu, Jun-Yi Li, Jing-Feng Tian","doi":"10.36045/j.bbms.230228","DOIUrl":"https://doi.org/10.36045/j.bbms.230228","url":null,"abstract":"In this paper, we establish a sufficient and necessary condition for a function involving the inverse hyperbolic tangent function as a best possible upper bound for the complete elliptic integral of the first kind. Equivalently, we obtain a lower bound involving the arithmetic mean and logarithmic mean for the Gauss arithmetic-geometric mean. This provides a positive answer to a conjecture proposed by Yang, Song and Chu in 2014.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277085","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}
引用次数: 0
Primes in coverings of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation 杨-巴克斯特方程不可分解对合集合论解复盖中的素数
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.230429
Wolfgang Rump
{"title":"Primes in coverings of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation","authors":"Wolfgang Rump","doi":"10.36045/j.bbms.230429","DOIUrl":"https://doi.org/10.36045/j.bbms.230429","url":null,"abstract":"Jan Okniński raised the question whether the primes dividing the size $n$ of a finite indecomposable set-theoretic solution to the Yang-Baxter equation are related to the primes dividing the order of the associated permutation group. With Cedó he proved that both prime sets are equal if $n$ is square-free. We characterize equality and prove that surjective morphisms of solutions admit a canonical factorization into a covering and a morphism given by a brace ideal. The existence of solutions with non-equality of the prime sets is reduced to irretractable solutions. It is proved that non-equality is possible, and a minimal example is constructed..","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277080","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}
引用次数: 0
A characterization of minimal Lagrangian submanifolds of the nearly Kähler $G times G$ 近似Kähler $G 乘以G$的极小拉格朗日子流形的表征
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.220331
Rodrigo Aguilar-Suárez, Gabriel Ruiz-Hernández
{"title":"A characterization of minimal Lagrangian submanifolds of the nearly Kähler $G times G$","authors":"Rodrigo Aguilar-Suárez, Gabriel Ruiz-Hernández","doi":"10.36045/j.bbms.220331","DOIUrl":"https://doi.org/10.36045/j.bbms.220331","url":null,"abstract":"We investigate Lagrangian submanifolds in the nearly Kähler manifold $G times G$. First we review the construction of a nearly Kähler structure on the Lie group product $G times G$, where $G$ is a Lie group with a bi-invariant metric. This construction was proposed by K. Sekigawa to E. Abbena and S. Garbiero. An example of this construction is the homogeneous nearly Kähler manifold $mathbb{S}^{3}times mathbb{S}^{3}$, where $G=mathbb{S}^{3}$ with its standard metric. It is known that this construction on $G times G$ gives a nearly Kähler structure. To get our main result, we extend the notion of angle functions of a Lagrangian submanifold proposed by B. Dioos, L. Vrancken and X. Wang in the case of $mathbb{S}^{3}times mathbb{S}^{3}$. These angle functions are useful to characterize minimal Lagrangian submanifolds in the NK manifold $G times G$. We prove our main result: a Lagrangian submanifold is minimal if and only if the sum of its angle functions is constant. We give five examples of Lagrangian submanifolds: three canonical examples and other two examples using an element in the center of $G$.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277083","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}
引用次数: 0
On $P$-spaces and $G_{delta}$-sets in the absence of the Axiom of Choice 在没有选择公理的$P$-空间和$G_{delta}$-集合上
4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI: 10.36045/j.bbms.230117
Kyriakos Keremedis, AliReza Olfati, Eliza Wajch
{"title":"On $P$-spaces and $G_{delta}$-sets in the absence of the Axiom of Choice","authors":"Kyriakos Keremedis, AliReza Olfati, Eliza Wajch","doi":"10.36045/j.bbms.230117","DOIUrl":"https://doi.org/10.36045/j.bbms.230117","url":null,"abstract":"A $P$-space is a topological space whose every $G_{delta}$-set is open. In this article, basic properties of $P$-spaces are investigated in the absence of the Axiom of Choice. New weaker forms of the Axiom of Choice, all relevant to $P$-spaces or to countable intersections of $G_{delta}$-sets, are introduced for applications. Special subrings of rings of continuous real functions are applied. New notions of a quasi Baire space and a strongly (quasi) Baire space are introduced. Several independence results are obtained. For instance, it is shown in $mathbf{ZF}$ that if $G_{delta}$-modifications of Tychonoff spaces are $P$-spaces, then every denumerable family of denumerable sets has a multiple choice function. In $mathbf{ZF}$, a zero-dimensional subspace of $mathbb{R}$ may fail to be strongly zero-dimensional, and countable intersections of $G_{delta}$-sets of $mathbb{R}$ may fail to be $G_{delta}$-sets. New open problems are posed. Partial answers to some of them are given.","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277078","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}
引用次数: 1
Asymptotics of the eigenvalues of a fourth order differential operator with eigenvalue dependent and periodic boundary conditions 具有特征值相关和周期边界条件的四阶微分算子的渐近性
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-07-31 DOI: 10.36045/j.bbms.210416a
B. Moletsane, Bertin Zinsou
{"title":"Asymptotics of the eigenvalues of a fourth order differential operator with eigenvalue dependent and periodic boundary conditions","authors":"B. Moletsane, Bertin Zinsou","doi":"10.36045/j.bbms.210416a","DOIUrl":"https://doi.org/10.36045/j.bbms.210416a","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72426173","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}
引用次数: 0
Asymptotic Behavior of a Periodic Sequence of Nonexpansive Mappings with Applications 一类非扩张映射周期序列的渐近性质及其应用
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-07-31 DOI: 10.36045/j.bbms.220607
M. Hashemi, H. Khatibzadeh
{"title":"Asymptotic Behavior of a Periodic Sequence of Nonexpansive Mappings with Applications","authors":"M. Hashemi, H. Khatibzadeh","doi":"10.36045/j.bbms.220607","DOIUrl":"https://doi.org/10.36045/j.bbms.220607","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82430803","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}
引用次数: 0
Surgery on ${rm Aut}(F_2)$ ${rm Aut}(F_2)$的手术
IF 0.5 4区 数学
Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-07-31 DOI: 10.36045/j.bbms.210809
Sylvain Barré, Mikael Pichot
{"title":"Surgery on ${rm Aut}(F_2)$","authors":"Sylvain Barré, Mikael Pichot","doi":"10.36045/j.bbms.210809","DOIUrl":"https://doi.org/10.36045/j.bbms.210809","url":null,"abstract":"","PeriodicalId":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85593883","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}
引用次数: 0
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