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Collective Evolution Under Catastrophes 灾难下的集体进化
4区 数学
American Mathematical Monthly Pub Date : 2023-10-17 DOI: 10.1080/00029890.2023.2261828
Rinaldo B. Schinazi
{"title":"Collective Evolution Under Catastrophes","authors":"Rinaldo B. Schinazi","doi":"10.1080/00029890.2023.2261828","DOIUrl":"https://doi.org/10.1080/00029890.2023.2261828","url":null,"abstract":"AbstractWe introduce the following discrete time model. Each site of N represents an ecological niche and is assigned a fitness in (0,1). All the sites are updated simultaneously at every discrete time. At any given time the environment may be normal with probability p or a catastrophe may occur with probability 1−p. If the environment is normal the fitness of each site is replaced by the maximum of its current fitness and a random number. If there is a catastrophe the fitness of each site is replaced by a random number. We compute the joint fitness distribution of any finite number of sites at any fixed time. We also show convergence of this system to a stationary distribution. This too is computed explicitly.MSC: 60 ACKNOWLEDGMENTThe author wishes to thank two anonymous referees for their careful reading and thoughtful suggestions.Additional informationNotes on contributorsRinaldo B. SchinaziRINALDO B. SCHINAZI received his Ph.D. in statistics at the University of São Paulo. He has been on the faculty at the University of Colorado at Colorado Springs since 1991. He has been teaching mathematics, writing books in mathematical analysis and probability, and doing research in probability.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033020","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
Problems and Solutions 问题与解决方案
4区 数学
American Mathematical Monthly Pub Date : 2023-10-17 DOI: 10.1080/00029890.2023.2266980
Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West
{"title":"Problems and Solutions","authors":"Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West","doi":"10.1080/00029890.2023.2266980","DOIUrl":"https://doi.org/10.1080/00029890.2023.2266980","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032518","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 Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma 凸锥的闭性及Farkas引理的简短证明
4区 数学
American Mathematical Monthly Pub Date : 2023-10-12 DOI: 10.1080/00029890.2023.2261816
Wouter Kager
{"title":"A Short Simple Proof of Closedness of Convex Cones and Farkas’ Lemma","authors":"Wouter Kager","doi":"10.1080/00029890.2023.2261816","DOIUrl":"https://doi.org/10.1080/00029890.2023.2261816","url":null,"abstract":"Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas’ lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas’ lemma from it using well-known arguments.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014636","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 Derivation of the Infinitude of Primes 素数无穷性的推导
4区 数学
American Mathematical Monthly Pub Date : 2023-10-11 DOI: 10.1080/00029890.2023.2261821
Hector Pasten
{"title":"A Derivation of the Infinitude of Primes","authors":"Hector Pasten","doi":"10.1080/00029890.2023.2261821","DOIUrl":"https://doi.org/10.1080/00029890.2023.2261821","url":null,"abstract":"AbstractThe well-known analogy between polynomials and integers breaks down when it comes to considering the polynomial derivative. This is rather unfortunate since derivatives are a powerful tool for doing arithmetic with polynomials. Nevertheless, there are some proposals in the literature for arithmetic analogues of derivatives. In this article we use one of these arithmetic derivatives to give a proof of the infinitude of primes which is analogous to an argument that will be presented for polynomials using polynomial derivatives. We hope that this “differential” proof of the infinitude of primes will help to motivate the reader to look for good notions of arithmetic derivatives.MSC: 11A4111C08 ACKNOWLEDGMENTThis article was possible thanks to the support of ANID Fondecyt Regular Grants 1190442 and 1230507 from Chile. I thank Ricardo Menares and Natalia Garcia-Fritz for valuable feedback on a first version of this article. I also thank the referees and editors for numerous suggestions.Additional informationNotes on contributorsHector PastenHECTOR PASTEN is a Chilean mathematician. He studied at Universidad de Concepción under the supervision of Xavier Vidaux (Chile, 2010) and at Queen’s University under the supervision of Ram Murty (Canada, 2014). Then he was a Benjamin Peirce Fellow at Harvard University (2014-2018). During this period he was also a visiting scholar at the Institute for Advanced Study at Princeton (2015-2016). In 2018 he returned to Chile where he is now an Associate Professor at the Mathematics Department of Pontificia Universidad Católica de Chile. He is interested in number theory and its connections with mathematical logic and analysis.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136097276","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
Tiling with Monotone Polyominos 用单调多聚子平铺
4区 数学
American Mathematical Monthly Pub Date : 2023-10-11 DOI: 10.1080/00029890.2023.2265284
István Tomon
{"title":"Tiling with Monotone Polyominos","authors":"István Tomon","doi":"10.1080/00029890.2023.2265284","DOIUrl":"https://doi.org/10.1080/00029890.2023.2265284","url":null,"abstract":"AbstractA monotone polyomino is a set of grid cells pierced by a continuous monotone function f:[a,b]→R. We prove that the minimum number of monotone polyominos in a tiling of the n×n lattice square is n. Surprisingly, this turns out to be equivalent with the statement that every triangulation of the n×n lattice square into minimum lattice triangles contains at least 2n right angled triangles.MSC: 05B5005B45 ACKNOWLEDGMENTSThe author wishes to thank Christian Richter and the anonymous referees for their useful comments and suggestions.Additional informationNotes on contributorsIstván TomonISTVÁN TOMON received his Ph.D. in mathematics from the University of Cambridge. He spent several years as a postdoctoral student at the EPFL and ETH Zurich. Currently, he is an Associate Professor at Umeå University, pursuing research in combinatorics and related areas.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136098402","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
100 Years Ago This Month in The American Mathematical Monthly 100年前的这个月刊登在美国数学月刊上
4区 数学
American Mathematical Monthly Pub Date : 2023-10-09 DOI: 10.1080/00029890.2023.2261826
Vadim Ponomarenko
{"title":"100 Years Ago This Month in <i>The American Mathematical Monthly</i>","authors":"Vadim Ponomarenko","doi":"10.1080/00029890.2023.2261826","DOIUrl":"https://doi.org/10.1080/00029890.2023.2261826","url":null,"abstract":"\"100 Years Ago This Month in The American Mathematical Monthly.\" The American Mathematical Monthly, ahead-of-print(ahead-of-print), p. 1","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135142103","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 Erdős’s Proof of the Existence of Cages 论Erdős对笼子存在的证明
4区 数学
American Mathematical Monthly Pub Date : 2023-10-05 DOI: 10.1080/00029890.2023.2258742
Vincent Vatter
{"title":"On Erdős’s Proof of the Existence of Cages","authors":"Vincent Vatter","doi":"10.1080/00029890.2023.2258742","DOIUrl":"https://doi.org/10.1080/00029890.2023.2258742","url":null,"abstract":"\"On Erdős’s Proof of the Existence of Cages.\" The American Mathematical Monthly, ahead-of-print(ahead-of-print), p. 1","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135483045","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
The Inverse of a Bad Primitive Root is Not Bad 坏原始根的逆并不坏
4区 数学
American Mathematical Monthly Pub Date : 2023-10-04 DOI: 10.1080/00029890.2023.2257119
V. P. Ramesh, R. Gowtham
{"title":"The Inverse of a Bad Primitive Root is Not Bad","authors":"V. P. Ramesh, R. Gowtham","doi":"10.1080/00029890.2023.2257119","DOIUrl":"https://doi.org/10.1080/00029890.2023.2257119","url":null,"abstract":"\"The Inverse of a Bad Primitive Root is Not Bad.\" The American Mathematical Monthly, ahead-of-print(ahead-of-print), p. 1","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590980","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 Note on Minimal Prime Submodules 关于最小素数子模的一个注记
4区 数学
American Mathematical Monthly Pub Date : 2023-10-03 DOI: 10.1080/00029890.2023.2251353
Ali Reza Naghipour
{"title":"A Note on Minimal Prime Submodules","authors":"Ali Reza Naghipour","doi":"10.1080/00029890.2023.2251353","DOIUrl":"https://doi.org/10.1080/00029890.2023.2251353","url":null,"abstract":"AbstractIn this short note, we give a characterization of the modules with finitely many minimal prime submodules over an arbitrary submodule.MSC: 13C0513A15 AcknowledgmentI would like to thank the referees for their comments and suggestions that helped to improve the paper.Additional informationNotes on contributorsAli Reza NaghipourALI REZA NAGHIPOUR received the Ph.D. degree in Mathematics from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in 2004. He is an Associate Professor of Mathematics at Shahrekord University in Iran. His research interests are in the areas of ring theory and graphs associated to rings.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738857","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
Reviews Once Upon a Prime . By Sarah Hart, Flatiron Books, 2023. 304 pp., ISBN 978-1-250-85088-1, $29.99. The Proof Stage . By Stephen Abbott, Princeton University Press, 2023. 416 pp., ISBN 978-0-691-20608-0, $35.00. 评论 Once Upon a Prime .莎拉-哈特（Sarah Hart）著，Flatiron Books 出版社，2023 年。304 页，ISBN 978-1-250-85088-1，29.99 美元。证明阶段 .作者：斯蒂芬-阿伯特（Stephen Abbott），普林斯顿大学出版社，2023 年。416 页，ISBN 978-0-691-20608-0，35.00 美元。
4区 数学
American Mathematical Monthly Pub Date : 2023-10-02 DOI: 10.1080/00029890.2023.2258050
Pamela Richardson
{"title":"Reviews <i>Once Upon a Prime</i> . By Sarah Hart, Flatiron Books, 2023. 304 pp., ISBN 978-1-250-85088-1, $29.99. <i>The Proof Stage</i> . By Stephen Abbott, Princeton University Press, 2023. 416 pp., ISBN 978-0-691-20608-0, $35.00.","authors":"Pamela Richardson","doi":"10.1080/00029890.2023.2258050","DOIUrl":"https://doi.org/10.1080/00029890.2023.2258050","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135896018","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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