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A survey on Lyapunov functions for epidemic compartmental models. 流行病区室模型的李雅普诺夫函数综述。
Bollettino della Unione matematica italiana (2008) Pub Date : 2023-06-06 DOI: 10.1007/s40574-023-00368-6
Nicolò Cangiotti, Marco Capolli, Mattia Sensi, Sara Sottile
{"title":"A survey on Lyapunov functions for epidemic compartmental models.","authors":"Nicolò Cangiotti,&nbsp;Marco Capolli,&nbsp;Mattia Sensi,&nbsp;Sara Sottile","doi":"10.1007/s40574-023-00368-6","DOIUrl":"10.1007/s40574-023-00368-6","url":null,"abstract":"<p><p>In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, and provide a commentary on their use. Our aim is to provide a comprehensive starting point to readers who are attempting to prove global stability of systems of ODEs. The focus is on mathematical epidemiology, however some of the functions and strategies presented in this paper can be adapted to a wider variety of models, such as prey-predator or rumor spreading.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10242238/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10073739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Prime numbers in typical continued fraction expansions. 典型的连续分数展开中的素数。
Bollettino della Unione matematica italiana (2008) Pub Date : 2023-01-01 Epub Date: 2023-02-28 DOI: 10.1007/s40574-023-00349-9
Tanja I Schindler, Roland Zweimüller
{"title":"Prime numbers in typical continued fraction expansions.","authors":"Tanja I Schindler,&nbsp;Roland Zweimüller","doi":"10.1007/s40574-023-00349-9","DOIUrl":"10.1007/s40574-023-00349-9","url":null,"abstract":"<p><p>We study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10203034/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9528295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$pi _1$$end{document}π1 of Miranda moduli spaces of elliptic surfaces documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$pi _1$$end{document}π1 of Miranda moduli spaces of elliptic surfaces
Bollettino della Unione matematica italiana (2008) Pub Date : 2021-06-28 DOI: 10.1007/s40574-021-00297-2
Michael Lönne
{"title":"documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$pi _1$$end{document}π1 of Miranda moduli spaces of elliptic surfaces","authors":"Michael Lönne","doi":"10.1007/s40574-021-00297-2","DOIUrl":"https://doi.org/10.1007/s40574-021-00297-2","url":null,"abstract":"","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76231870","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
Local singular characteristics on R 2. r2上的局部奇异特征。
Bollettino della Unione matematica italiana (2008) Pub Date : 2021-01-01 Epub Date: 2021-02-22 DOI: 10.1007/s40574-021-00279-4
Piermarco Cannarsa, Wei Cheng
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Local singular characteristics on <ns0:math> <ns0:msup><ns0:mrow><ns0:mi>R</ns0:mi></ns0:mrow> <ns0:mn>2</ns0:mn></ns0:msup></ns0:math>.","authors":"Piermarco Cannarsa,&nbsp;Wei Cheng","doi":"10.1007/s40574-021-00279-4","DOIUrl":"https://doi.org/10.1007/s40574-021-00279-4","url":null,"abstract":"<p><p>The singular set of a viscosity solution to a Hamilton-Jacobi equation is known to propagate, from any noncritical singular point, along singular characteristics which are curves satisfying certain differential inclusions. In the literature, different notions of singular characteristics were introduced. However, a general uniqueness criterion for singular characteristics, not restricted to mechanical systems or problems in one space dimension, is missing at the moment. In this paper, we prove that, for a Tonelli Hamiltonian on <math> <msup><mrow><mi>R</mi></mrow> <mn>2</mn></msup> </math> , two different notions of singular characteristics coincide up to a bi-Lipschitz reparameterization. As a significant consequence, we obtain a uniqueness result for the class of singular characteristics that was introduced by Khanin and Sobolevski in the paper [On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations. <i>Arch. Ration. Mech. Anal.</i>, 219(2):861-885, 2016].</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40574-021-00279-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25415646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
On transfer homomorphisms of Krull monoids. 关于Krull单群的转移同态。
Bollettino della Unione matematica italiana (2008) Pub Date : 2021-01-01 Epub Date: 2021-06-28 DOI: 10.1007/s40574-021-00301-9
Alfred Geroldinger, Florian Kainrath
{"title":"On transfer homomorphisms of Krull monoids.","authors":"Alfred Geroldinger,&nbsp;Florian Kainrath","doi":"10.1007/s40574-021-00301-9","DOIUrl":"https://doi.org/10.1007/s40574-021-00301-9","url":null,"abstract":"<p><p>Every Krull monoid has a transfer homomorphism onto a monoid of zero-sum sequences over a subset of its class group. This transfer homomorphism is a crucial tool for studying the arithmetic of Krull monoids. In the present paper, we strengthen and refine this tool for Krull monoids with finitely generated class group.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40574-021-00301-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39732059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Epidemic evolution models to the test of Covid-19. 检验Covid-19的流行病演化模型。
Bollettino della Unione matematica italiana (2008) Pub Date : 2020-01-01 Epub Date: 2020-08-03 DOI: 10.1007/s40574-020-00252-7
Primo Brandi, Rita Ceppitelli, Anna Salvadori
{"title":"Epidemic evolution models to the test of Covid-19.","authors":"Primo Brandi,&nbsp;Rita Ceppitelli,&nbsp;Anna Salvadori","doi":"10.1007/s40574-020-00252-7","DOIUrl":"https://doi.org/10.1007/s40574-020-00252-7","url":null,"abstract":"<p><p>We illustrate a suitable adaptation and modification of classical epidemic evolution models that proves helpful in the study of Covid-19 spread in Italy.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40574-020-00252-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38399009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A characterization of seminormal C-monoids. 半正规c -一元群的一个性质。
Bollettino della Unione matematica italiana (2008) Pub Date : 2019-01-01 Epub Date: 2019-02-09 DOI: 10.1007/s40574-019-00194-9
Alfred Geroldinger, Qinghai Zhong
{"title":"A characterization of seminormal C-monoids.","authors":"Alfred Geroldinger,&nbsp;Qinghai Zhong","doi":"10.1007/s40574-019-00194-9","DOIUrl":"https://doi.org/10.1007/s40574-019-00194-9","url":null,"abstract":"<p><p>It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.</p>","PeriodicalId":72440,"journal":{"name":"Bollettino della Unione matematica italiana (2008)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40574-019-00194-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37773499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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