Pub Date : 2017-03-12DOI: 10.18270/rcfc.v17i34.2085
Eleonora Catsigeras
We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria, from the logic-formal ones to the non formal ones (but still rational criteria).We illustrate the discussion with concrete examples obtained form the mathematical reseach, particularly from the results that were published in the last 50 years in the mathematical theory of deterministic dynamical systems.
{"title":"CONSISTENCIA, NO TRIVIALIDAD Y REDUNDANCIA EN MATEMÁTICA","authors":"Eleonora Catsigeras","doi":"10.18270/rcfc.v17i34.2085","DOIUrl":"https://doi.org/10.18270/rcfc.v17i34.2085","url":null,"abstract":"We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria, from the logic-formal ones to the non formal ones (but still rational criteria).We illustrate the discussion with concrete examples obtained form the mathematical reseach, particularly from the results that were published in the last 50 years in the mathematical theory of deterministic dynamical systems.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126494410","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}
Pub Date : 2017-03-02DOI: 10.1007/978-3-319-59078-3_3
Konstantin M. Dyakonov
{"title":"Remembering Victor Petrovich Havin","authors":"Konstantin M. Dyakonov","doi":"10.1007/978-3-319-59078-3_3","DOIUrl":"https://doi.org/10.1007/978-3-319-59078-3_3","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128314869","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}
The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no solution is known that is able to take into account all effects such as replacement (limited purchasing of missing stickers) or swapping. In previous papers we have proven that the classical assumptions are not fulfilled in practice. Therefore we define new assumptions that match reality. Based on these assumptions we are able to derive formulae for the mean number of stickers needed (and the associated standard deviation) that are able to take into account all effects that occur in practical collecting. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on elementary calculations. From a practical point of view we consider the Coupon Collector's problem as solved. ----- Das Sammelbilderproblem ist eines der wenigen mathematischen Probleme, die regelmasig in den Schlagzeilen der Nachrichten vorkommen. Dies liegt einerseits an der grosen Popularitat von Fusball-Sammelbildern (Paninimania genannt) und andererseits daran, dass es bisher keine Losung gibt, die alle relevanten Effekte wie Nachkaufen oder Tauschen berucksichtigt. Wir haben bereits nachgewiesen, dass die klassischen Annahmen nicht der Realitat entsprechen. Deshalb stellen wir neue Annahmen auf, die die Praxis besser abbilden. Darauf aufbauend konnen wir Formeln fur die mittlere Anzahl benotigter Bilder (sowie deren Standardabweichung) ableiten, die alle in der Praxis relevanten Effekte berucksichtigen. Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit Hilfe von elementaren Rechnungen bestimmen. Fur praktische Zwecke ist das Sammelbilderproblem damit gelost.
优惠券收集者的问题是为数不多的经常成为新闻头条的数学问题之一。造成这种情况的原因一方面是足球相册的巨大流行(称为“Paninimania”)，另一方面，没有任何已知的解决方案能够考虑到所有的影响，如更换(限制购买丢失的贴纸)或交换。在以前的论文中，我们已经证明了经典假设在实践中是不成立的。因此，我们定义了与现实相符的新假设。基于这些假设，我们能够推导出所需贴纸的平均数量(以及相关的标准偏差)的公式，该公式能够考虑到实际收集中发生的所有影响。因此，收藏家可以估计完成一张专辑的平均成本和它的标准偏差，只是基于基本的计算。从实践的角度来看，我们认为优惠券收集人的问题已经解决。----- Das Sammelbilderproblem ist eines der wenigen mathematischen problem, die regelmasig in den Schlagzeilen der Nachrichten vorkommen。他说:“我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说，我是说。”在现实的世界里，我们有一个伟大的梦想。亚拿门的神阿，我的神阿，我的神阿，我的神阿，我的神阿。Darauf aufbauend konnen与Formeln为die mitere Anzahl benotititer Bilder (sowie deren Standardabweichung) ableiten, die alle在der实践中相关的有效性。Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung(德国)的Hilfe von ementaren rechungen bestmen(德国)。在德国，问题是不可能解决的。
{"title":"A Useful Solution of the Coupon Collector's Problem","authors":"Niklas Braband, Sonja Braband, Malte Braunschweig, Technische Universitat Braunschweig","doi":"10.7795/320.201908","DOIUrl":"https://doi.org/10.7795/320.201908","url":null,"abstract":"The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no solution is known that is able to take into account all effects such as replacement (limited purchasing of missing stickers) or swapping. In previous papers we have proven that the classical assumptions are not fulfilled in practice. Therefore we define new assumptions that match reality. Based on these assumptions we are able to derive formulae for the mean number of stickers needed (and the associated standard deviation) that are able to take into account all effects that occur in practical collecting. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on elementary calculations. From a practical point of view we consider the Coupon Collector's problem as solved. \u0000----- \u0000Das Sammelbilderproblem ist eines der wenigen mathematischen Probleme, die regelmasig in den Schlagzeilen der Nachrichten vorkommen. Dies liegt einerseits an der grosen Popularitat von Fusball-Sammelbildern (Paninimania genannt) und andererseits daran, dass es bisher keine Losung gibt, die alle relevanten Effekte wie Nachkaufen oder Tauschen berucksichtigt. Wir haben bereits nachgewiesen, dass die klassischen Annahmen nicht der Realitat entsprechen. Deshalb stellen wir neue Annahmen auf, die die Praxis besser abbilden. Darauf aufbauend konnen wir Formeln fur die mittlere Anzahl benotigter Bilder (sowie deren Standardabweichung) ableiten, die alle in der Praxis relevanten Effekte berucksichtigen. Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit Hilfe von elementaren Rechnungen bestimmen. Fur praktische Zwecke ist das Sammelbilderproblem damit gelost.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133771706","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}
The liar paradox is widely seen as not a serious problem. I try to explain why this view is mistaken.
人们普遍认为说谎者悖论并不是一个严重的问题。我试图解释为什么这种观点是错误的。
{"title":"The liar paradox is a real problem","authors":"N. Weaver","doi":"10.4288/JAFPOS.25.0_89","DOIUrl":"https://doi.org/10.4288/JAFPOS.25.0_89","url":null,"abstract":"The liar paradox is widely seen as not a serious problem. I try to explain why this view is mistaken.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124242634","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}
Pub Date : 2017-02-04DOI: 10.14477/JHM.2017.30.2.053
Rosalie Hosking
This paper demonstrates how a nineteenth century Japanese votive temple problem known as a sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of =Ohara Toshiaki (?-1828). Our investigation into the solution of =Ohara provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.
{"title":"Solving Sangaku: A Traditional Solution to a Nineteenth Century Japanese Temple Problem","authors":"Rosalie Hosking","doi":"10.14477/JHM.2017.30.2.053","DOIUrl":"https://doi.org/10.14477/JHM.2017.30.2.053","url":null,"abstract":"This paper demonstrates how a nineteenth century Japanese votive temple problem known as a sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of =Ohara Toshiaki (?-1828). Our investigation into the solution of =Ohara provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132796023","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}
Pub Date : 2017-01-15DOI: 10.1007/978-3-319-60039-0_15
T. Sunada
{"title":"Generalized Riemann Sums","authors":"T. Sunada","doi":"10.1007/978-3-319-60039-0_15","DOIUrl":"https://doi.org/10.1007/978-3-319-60039-0_15","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121109287","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}
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real life applications, arise quite naturally and the resulting discussion among non-ideologized, free-minded people offers an opportunity for clarifications.
{"title":"Probability, propensity and probability of propensities (and of probabilities)","authors":"G. D'Agostini","doi":"10.1063/1.4985350","DOIUrl":"https://doi.org/10.1063/1.4985350","url":null,"abstract":"The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real life applications, arise quite naturally and the resulting discussion among non-ideologized, free-minded people offers an opportunity for clarifications.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133246013","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 expository paper written to commemorate Fibonacci Day 2016, we discuss famous relations involving the Fibonacci sequence, the golden ratio, continued fractions and nested radicals, and show how these fit into a more general framework stemming from the quadratic formula.
{"title":"Fibonacci numbers and the golden ratio","authors":"R. Schneider","doi":"10.3840/08003775","DOIUrl":"https://doi.org/10.3840/08003775","url":null,"abstract":"In this expository paper written to commemorate Fibonacci Day 2016, we discuss famous relations involving the Fibonacci sequence, the golden ratio, continued fractions and nested radicals, and show how these fit into a more general framework stemming from the quadratic formula.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129299223","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}
This is a review of genesis of „e-δ" language in works of mathematicians of the 19th century. It shows that although the symbols e and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of e was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [ Sinkevich, 2012d ] of the same author which is slightly redone and translated into English. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:Standardowy; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;}
{"title":"On History of Epsilontics","authors":"Galina Iwanowna Sinkiewicz","doi":"10.14708/AM.V10I0.805","DOIUrl":"https://doi.org/10.14708/AM.V10I0.805","url":null,"abstract":"This is a review of genesis of „e-δ\" language in works of mathematicians of the 19th century. It shows that although the symbols e and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of e was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [ Sinkevich, 2012d ] of the same author which is slightly redone and translated into English. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ \u0000 table.MsoNormalTable \u0000 {mso-style-name:Standardowy; \u0000 mso-tstyle-rowband-size:0; \u0000 mso-tstyle-colband-size:0; \u0000 mso-style-noshow:yes; \u0000 mso-style-priority:99; \u0000 mso-style-parent:\"\"; \u0000 mso-padding-alt:0cm 5.4pt 0cm 5.4pt; \u0000 mso-para-margin-top:0cm; \u0000 mso-para-margin-right:0cm; \u0000 mso-para-margin-bottom:10.0pt; \u0000 mso-para-margin-left:0cm; \u0000 line-height:115%; \u0000 mso-pagination:widow-orphan; \u0000 font-size:11.0pt; \u0000 font-family:\"Calibri\",\"sans-serif\"; \u0000 mso-ascii-font-family:Calibri; \u0000 mso-ascii-theme-font:minor-latin; \u0000 mso-hansi-font-family:Calibri; \u0000 mso-hansi-theme-font:minor-latin; \u0000 mso-bidi-font-family:\"Times New Roman\"; \u0000 mso-bidi-theme-font:minor-bidi; \u0000 mso-fareast-language:EN-US;}","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133659926","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}
Pub Date : 2016-10-03DOI: 10.1007/978-3-030-32808-5_5
G. Jones
{"title":"Paley and the Paley Graphs","authors":"G. Jones","doi":"10.1007/978-3-030-32808-5_5","DOIUrl":"https://doi.org/10.1007/978-3-030-32808-5_5","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121892778","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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