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The Golden Anniversary Celebration of the National Association of Mathematicians最新文献

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A discreteness algorithm for 4-punctured sphere groups 四穿孔球群的离散算法
The Golden Anniversary Celebration of the National Association of Mathematicians Pub Date : 2019-10-22 DOI: 10.1090/conm/759/15269
Caleb Ashley
{"title":"A discreteness algorithm for 4-punctured\u0000 sphere groups","authors":"Caleb Ashley","doi":"10.1090/conm/759/15269","DOIUrl":"https://doi.org/10.1090/conm/759/15269","url":null,"abstract":"Let $Gamma$ be a subgroup of $PSL(2,R)$ generated by three parabolic transformations. The main goal of this paper is to present an algorithm to determine whether or not $Gamma$ is discrete. Historically discreteness algorithms have been considered within several broader mathematical paradigms: the discreteness problem, the construction and deformation of hyperbolic structures on surfaces and notions of automata for groups. Each of these approaches yield equivalent results. The second goal of this paper is to give an exposition of the basic ideas needed to interpret these equivalences, emphasizing related works and future directions of inquiry.","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121321503","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}
引用次数: 1
A constructive proof of Masser’s Theorem 马瑟定理的构造性证明
The Golden Anniversary Celebration of the National Association of Mathematicians Pub Date : 2019-08-14 DOI: 10.1090/conm/759/15265
Alexander J. Barrios
{"title":"A constructive proof of Masser’s\u0000 Theorem","authors":"Alexander J. Barrios","doi":"10.1090/conm/759/15265","DOIUrl":"https://doi.org/10.1090/conm/759/15265","url":null,"abstract":"The Modified Szpiro Conjecture, equivalent to the $abc$ Conjecture, states that for each $epsilon>0$, there are finitely many rational elliptic curves satisfying $N_{E}^{6+epsilon}<max!left{ leftvert c_{4}^{3}rightvert,c_{6}^{2}right} $ where $c_{4}$ and $c_{6}$ are the invariants associated to a minimal model of $E$ and $N_{E}$ is the conductor of $E$. We say $E$ is a good elliptic curve if $N_{E}^{6}<max!left{ leftvert c_{4}^{3}rightvert,c_{6}^{2}right} $. Masser showed that there are infinitely many good Frey curves. Here we give a constructive proof of this assertion.","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126042897","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}
引用次数: 2
Catalan and Motzkin integral representations 加泰罗尼亚和莫兹金积分表示
The Golden Anniversary Celebration of the National Association of Mathematicians Pub Date : 2019-01-21 DOI: 10.1090/conm/759/15270
Peter N. McCalla, A. Nkwanta
{"title":"Catalan and Motzkin integral\u0000 representations","authors":"Peter N. McCalla, A. Nkwanta","doi":"10.1090/conm/759/15270","DOIUrl":"https://doi.org/10.1090/conm/759/15270","url":null,"abstract":"We present new proofs of eight integral representations of the Catalan numbers. Then, we create analogous integral representations of the Motzkin numbers and obtain new results. Most integral representations of counting sequences found in the literature are proved by using advanced mathematical techniques. All integral representations in this paper are proved by using standard techniques from integral calculus. Thus, we provide a more simplistic approach of proving integral representations of the Catalan and Motzkin numbers.","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115834994","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}
引用次数: 3
A linear programming method for exponential domination 指数控制的一种线性规划方法
The Golden Anniversary Celebration of the National Association of Mathematicians Pub Date : 2018-01-19 DOI: 10.1090/conm/759/15273
Michael Dairyko, Michael Young
{"title":"A linear programming method for exponential\u0000 domination","authors":"Michael Dairyko, Michael Young","doi":"10.1090/conm/759/15273","DOIUrl":"https://doi.org/10.1090/conm/759/15273","url":null,"abstract":"For a graph G, the set D ⊆V (G) is a porous exponential dominating set if 1 ≤ ∑ d∈D (2) 1−dist(d ,v) for every v ∈ V (G), where dist(d , v) denotes the length of the shortest d v path. The porous exponential dominating number of G, denoted γe (G), is the minimum cardinality of a porous exponential dominating set. For any graph G, a technique is derived to determine a lower bound for γe (G). Specifically for a grid graph H , linear programing is used to sharpen bound found through the lower bound technique. Lower and upper bounds are determined for the porous exponential domination number of the King Grid Kn , the Slant Grid Sn , and the n-dimensional hypercube Qn . AMS 2010 Subject Classification: Primary 05C69; Secondary 90C05","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128221269","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}
引用次数: 1
An overview of mathematical modeling of geometric optics problems involving refraction 涉及折射的几何光学问题的数学建模概述
The Golden Anniversary Celebration of the National Association of Mathematicians Pub Date : 1900-01-01 DOI: 10.1090/conm/759/15263
H. Mawi
{"title":"An overview of mathematical modeling of\u0000 geometric optics problems involving\u0000 refraction","authors":"H. Mawi","doi":"10.1090/conm/759/15263","DOIUrl":"https://doi.org/10.1090/conm/759/15263","url":null,"abstract":"","PeriodicalId":351002,"journal":{"name":"The Golden Anniversary Celebration of the\n National Association of Mathematicians","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127545166","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}
引用次数: 0
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