{"title":"On the Inequalities of Grüss–Čebyshev and Kantorovich: A Probabilistic Approach","authors":"L. Heinrich","doi":"10.4171/em/419","DOIUrl":"https://doi.org/10.4171/em/419","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"172-175"},"PeriodicalIF":0.1,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/419","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48144559","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":"Begegnung zwischen klassischen Mittelwerten und Kegelschnitten","authors":"J. Jäger","doi":"10.4171/em/416","DOIUrl":"https://doi.org/10.4171/em/416","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"137-151"},"PeriodicalIF":0.1,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/416","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49118348","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":"An inequality for cevians and applications","authors":"Martin Lukarevski, D. Marinescu","doi":"10.4171/em/418","DOIUrl":"https://doi.org/10.4171/em/418","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"166-171"},"PeriodicalIF":0.1,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/418","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48684821","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":"A proof of the Schwarz theorem on mixed partial derivatives via elementary approximation theory","authors":"de Camargo, A. Pierro","doi":"10.4171/em/413","DOIUrl":"https://doi.org/10.4171/em/413","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"125-128"},"PeriodicalIF":0.1,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44812210","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}
Yasanthi Kottegoda, A. Mastropietro, Shirley Duong
{"title":"Characteristics of modulo one sequences","authors":"Yasanthi Kottegoda, A. Mastropietro, Shirley Duong","doi":"10.4171/em/410","DOIUrl":"https://doi.org/10.4171/em/410","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"103-113"},"PeriodicalIF":0.1,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/410","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44855731","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":"Ratios, roots, and means: A quartet of convergence tests","authors":"Christopher N. B. Hammond","doi":"10.4171/em/409","DOIUrl":"https://doi.org/10.4171/em/409","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"89-102"},"PeriodicalIF":0.1,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/409","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46687530","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":"Mixtilinear radii and Finsler–Hadwiger inequality","authors":"Martin Lukarevski, G. Wanner","doi":"10.4171/em/412","DOIUrl":"https://doi.org/10.4171/em/412","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"121-124"},"PeriodicalIF":0.1,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/412","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41981535","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":"An application of Euclidean algorithm in cryptanalysis of RSA","authors":"D. Poulakis","doi":"10.4171/em/411","DOIUrl":"https://doi.org/10.4171/em/411","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"114-120"},"PeriodicalIF":0.1,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/411","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47573243","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}
In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $gamma$ covers a planar convex figure $K$, then $operatorname{length}(gamma) geq operatorname{per} (K) - operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.
{"title":"One property of a planar curve whose convex hull covers a given convex figure","authors":"Y. Nikonorov, Y. Nikonorova","doi":"10.4171/EM/458","DOIUrl":"https://doi.org/10.4171/EM/458","url":null,"abstract":"In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $gamma$ covers a planar convex figure $K$, then $operatorname{length}(gamma) geq operatorname{per} (K) - operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42763862","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":"Constructions of isospectral circulant graphs","authors":"Katja Mönius","doi":"10.4171/em/404","DOIUrl":"https://doi.org/10.4171/em/404","url":null,"abstract":"","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"75 1","pages":"45-57"},"PeriodicalIF":0.1,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/404","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48691727","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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