{"title":"President's Report 2023","authors":"Leo Creedon","doi":"10.18235/0005492","DOIUrl":"https://doi.org/10.18235/0005492","url":null,"abstract":"IDB Report of the President 2023.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"48 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139536201","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}
{"title":"From CT scans to 4-manifold topology via neutral geometry","authors":"B. Guilfoyle","doi":"10.33232/BIMS.0091.9.32","DOIUrl":"https://doi.org/10.33232/BIMS.0091.9.32","url":null,"abstract":"In this survey paper the ultrahyperbolic equation in dimension four is discussed from a geometric, analytic and topological point of view. The geometry centres on the canonical neutral metric on the space of oriented geodesics of 3-dimensional space-forms, the analysis discusses a mean value theorem for solutions of the equation and presents a new solution of the Cauchy problem over a certain family of null hypersurfaces, while the topology relates to generalizations of codimension two foliations of 4-manifolds.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127387778","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}
{"title":"Segre's theorem on ovals in Desarguesian projective planes","authors":"P. Browne, S. Dougherty, Padraig 'O Cath'ain","doi":"10.33232/bims.0091.37.47","DOIUrl":"https://doi.org/10.33232/bims.0091.37.47","url":null,"abstract":"Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract algebra, provides a complete and self-contained proof. All necessary pre-requisites, principally evaluation of homogeneous polynomials at projective points and Desargues' theorem are presented in full. While following the broad outline of Segre's proof, careful parameterisation of certain tangent lines results in shorter and simpler computations than the original.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125163520","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}
{"title":"Modular Metric Spaces","authors":"H. Abobaker, R. Ryan","doi":"10.33232/bims.0080.35.44","DOIUrl":"https://doi.org/10.33232/bims.0080.35.44","url":null,"abstract":". We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134043143","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}
{"title":"Weighted Sylvester sums on the Frobenius set","authors":"T. Komatsu, Yuancao Zhang","doi":"10.33232/bims.0087.35.44","DOIUrl":"https://doi.org/10.33232/bims.0087.35.44","url":null,"abstract":"Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $sum_{nin{rm NR}(a,b)}lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134214081","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}
{"title":"Locally Nilpotent Linear Groups","authors":"A. Detinko, D. Flannery, Martin L. Newell","doi":"10.33232/bims.0056.37.51","DOIUrl":"https://doi.org/10.33232/bims.0056.37.51","url":null,"abstract":"This article examines aspects of the theory of locally nilpotent linear groups. We also present a new clas- sification result for locally nilpotent linear groups over an arbitrary field F.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121280731","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}
{"title":"Derangements and Continued Fractions for $e$","authors":"P. Lynch","doi":"10.33232/bims.0087.45.50","DOIUrl":"https://doi.org/10.33232/bims.0087.45.50","url":null,"abstract":"Several continued fraction expansions for $e$ have been produced by an automated conjecture generator (ACG) called emph{The Ramanujan Machine}. Some of these were already known, some have recently been proved and some remain unproven. While an ACG can produce interesting putative results, it gives very limited insight into their significance. In this paper, we derive an elegant continued fraction expansion, equivalent to a result from the Ramanujan Machine, using the sequence of ratios of factorials to subfactorials or derangement numbers.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115907693","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}
{"title":"Linear Dynamical Systems","authors":"Clifford Gilmore","doi":"10.33232/BIMS.0086.47.78","DOIUrl":"https://doi.org/10.33232/BIMS.0086.47.78","url":null,"abstract":"This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and distributional chaos, and hypercyclic algebras.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128656099","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}
{"title":"Hermitian Morita Theory: a Matrix Approach","authors":"D. W. Lewis, T. Unger","doi":"10.33232/bims.0062.37.41","DOIUrl":"https://doi.org/10.33232/bims.0062.37.41","url":null,"abstract":"(all forms are assumed to be nonsingular) which respect isometries,orthogonal sums and hyperbolic forms.In this note we describe these correspondences explicitly. In par-ticular we give a matrix description of Morita equivalence which doesnot seem to be generally known. Other explicit descriptions can befound in [3, 4, 5]. The subject is often treated in a more abstractmanner, such as in [1] and [2, Chap. I, §9].2. ScalingLet M be a right M","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124763112","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}
{"title":"Homogeneous manifolds whose geodesics are orbits. Recent results and some open problems","authors":"A. Arvanitoyeorgos","doi":"10.33232/bims.0079.5.29","DOIUrl":"https://doi.org/10.33232/bims.0079.5.29","url":null,"abstract":"A homogeneous Riemannian manifold $(M=G/K, g)$ is called a space with homogeneous geodesics or a $G$-g.o. space if every geodesic $gamma (t)$ of $M$ is an orbit of a one-parameter subgroup of $G$, that is $gamma(t) = exp(tX)cdot o$, for some non zero vector $X$ in the Lie algebra of $G$. We give an exposition on the subject, by presenting techniques that have been used so far and a wide selection of previous and recent results. \u0000We also present some open problems.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124349224","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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