Monatshefte fur Mathematik最新文献

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Pair correlations of Halton and Niederreiter Sequences are not Poissonian. Halton序列和Niederreiter序列的对相关不是泊松的。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2021-01-01 Epub Date: 2021-02-13 DOI: 10.1007/s00605-021-01531-x
Roswitha Hofer, Lisa Kaltenböck
{"title":"Pair correlations of Halton and Niederreiter Sequences are not Poissonian.","authors":"Roswitha Hofer,&nbsp;Lisa Kaltenböck","doi":"10.1007/s00605-021-01531-x","DOIUrl":"https://doi.org/10.1007/s00605-021-01531-x","url":null,"abstract":"<p><p>Niederreiter and Halton sequences are two prominent classes of higher-dimensional sequences which are widely used in practice for numerical integration methods because of their excellent distribution qualities. In this paper we show that these sequences-even though they are uniformly distributed-fail to satisfy the stronger property of Poissonian pair correlations. This extends already established results for one-dimensional sequences and confirms a conjecture of Larcher and Stockinger who hypothesized that the Halton sequences are not Poissonian. The proofs rely on a general tool which identifies a specific regularity of a sequence to be sufficient for not having Poissonian pair correlations.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"194 4","pages":"789-809"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-021-01531-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25531808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Diophantine equations in separated variables and polynomial power sums. 分离变量中的 Diophantine方程和多项式幂和。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2021-01-01 Epub Date: 2021-04-30 DOI: 10.1007/s00605-021-01560-6
Clemens Fuchs, Sebastian Heintze
{"title":"Diophantine equations in separated variables and polynomial power sums.","authors":"Clemens Fuchs, Sebastian Heintze","doi":"10.1007/s00605-021-01560-6","DOIUrl":"10.1007/s00605-021-01560-6","url":null,"abstract":"<p><p>We consider Diophantine equations of the shape <math><mrow><mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>g</mi> <mo>(</mo> <mi>y</mi> <mo>)</mo></mrow> </math> , where the polynomials <i>f</i> and <i>g</i> are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (<i>x</i>, <i>y</i>) with a bounded denominator are only possible in trivial cases.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"196 1","pages":"59-65"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550583/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39622553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ebene Geometrie Ebene几何图形
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2021-01-01 DOI: 10.1007/BF01694248
Wolfgang Ludwicki, Michael Rüsing
{"title":"Ebene Geometrie","authors":"Wolfgang Ludwicki, Michael Rüsing","doi":"10.1007/BF01694248","DOIUrl":"https://doi.org/10.1007/BF01694248","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"14 1","pages":"A35"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79993025","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
Finding all S-Diophantine quadruples for a fixed set of primes S. 求所有S-丢番图四元对于一组固定的素数S。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2021-01-01 Epub Date: 2021-07-19 DOI: 10.1007/s00605-021-01605-w
Volker Ziegler
{"title":"Finding all <i>S</i>-Diophantine quadruples for a fixed set of primes <i>S</i>.","authors":"Volker Ziegler","doi":"10.1007/s00605-021-01605-w","DOIUrl":"https://doi.org/10.1007/s00605-021-01605-w","url":null,"abstract":"<p><p>Given a finite set of primes <i>S</i> and an <i>m</i>-tuple <math><mrow><mo>(</mo> <msub><mi>a</mi> <mn>1</mn></msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub><mi>a</mi> <mi>m</mi></msub> <mo>)</mo></mrow> </math> of positive, distinct integers we call the <i>m</i>-tuple <i>S</i>-Diophantine, if for each <math><mrow><mn>1</mn> <mo>≤</mo> <mi>i</mi> <mo><</mo> <mi>j</mi> <mo>≤</mo> <mi>m</mi></mrow> </math> the quantity <math> <mrow><msub><mi>a</mi> <mi>i</mi></msub> <msub><mi>a</mi> <mi>j</mi></msub> <mo>+</mo> <mn>1</mn></mrow> </math> has prime divisors coming only from the set <i>S</i>. For a given set <i>S</i> we give a practical algorithm to find all <i>S</i>-Diophantine quadruples, provided that <math><mrow><mo>|</mo> <mi>S</mi> <mo>|</mo> <mo>=</mo> <mn>3</mn></mrow> </math> .</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"196 3","pages":"617-641"},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-021-01605-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39622554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers. Colombeau广义数的非阿基米德环上的上、下和超极限。
IF 0.8 4区 数学
Monatshefte fur Mathematik Pub Date : 2021-01-01 Epub Date: 2021-07-03 DOI: 10.1007/s00605-021-01590-0
A Mukhammadiev, D Tiwari, G Apaaboah, P Giordano
{"title":"Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers.","authors":"A Mukhammadiev, D Tiwari, G Apaaboah, P Giordano","doi":"10.1007/s00605-021-01590-0","DOIUrl":"10.1007/s00605-021-01590-0","url":null,"abstract":"<p><p>It is well-known that the notion of limit in the sharp topology of sequences of Colombeau generalized numbers <math><mover><mi>R</mi> <mo>~</mo></mover> </math> does not generalize classical results. E.g. the sequence <math> <mrow><mfrac><mn>1</mn> <mi>n</mi></mfrac> <mo>↛</mo> <mn>0</mn></mrow> </math> and a sequence <math> <msub><mrow><mo>(</mo> <msub><mi>x</mi> <mi>n</mi></msub> <mo>)</mo></mrow> <mrow><mi>n</mi> <mo>∈</mo> <mi>N</mi></mrow> </msub> </math> converges <i>if</i> and only if <math> <mrow><msub><mi>x</mi> <mrow><mi>n</mi> <mo>+</mo> <mn>1</mn></mrow> </msub> <mo>-</mo> <msub><mi>x</mi> <mi>n</mi></msub> <mo>→</mo> <mn>0</mn></mrow> </math> . This has several deep consequences, e.g. in the study of series, analytic generalized functions, or sigma-additivity and classical limit theorems in integration of generalized functions. The lacking of these results is also connected to the fact that <math><mover><mi>R</mi> <mo>~</mo></mover> </math> is necessarily not a complete ordered set, e.g. the set of all the infinitesimals has neither supremum nor infimum. We present a solution of these problems with the introduction of the notions of hypernatural number, hypersequence, close supremum and infimum. In this way, we can generalize all the classical theorems for the hyperlimit of a hypersequence. The paper explores ideas that can be applied to other non-Archimedean settings.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"196 1","pages":"163-190"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550461/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39578382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Le rayonnement des corps noirs 黑体的辐射
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2020-11-04 DOI: 10.1007/BF01706970
O. Lummer, R. Dongier, M. Lamotte
{"title":"Le rayonnement des corps noirs","authors":"O. Lummer, R. Dongier, M. Lamotte","doi":"10.1007/BF01706970","DOIUrl":"https://doi.org/10.1007/BF01706970","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"101 1","pages":"A41-A42"},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88963702","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
Naturphilosophie
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2020-04-20 DOI: 10.1007/BF01697911
Hans Hahn
{"title":"Naturphilosophie","authors":"Hans Hahn","doi":"10.1007/BF01697911","DOIUrl":"https://doi.org/10.1007/BF01697911","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"59 1","pages":"A14-A15"},"PeriodicalIF":0.9,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83442215","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: 1
Geometrische Aufgaben 几何任务
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2020-01-01 DOI: 10.1007/BF01832553
Harald Nahrstedt
{"title":"Geometrische Aufgaben","authors":"Harald Nahrstedt","doi":"10.1007/BF01832553","DOIUrl":"https://doi.org/10.1007/BF01832553","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"11 1","pages":"A20"},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77257688","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
Algebraische Gleichungen Algebraische方程
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2020-01-01 DOI: 10.1007/BF01693288
H. Rapp, J. Rapp
{"title":"Algebraische Gleichungen","authors":"H. Rapp, J. Rapp","doi":"10.1007/BF01693288","DOIUrl":"https://doi.org/10.1007/BF01693288","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"120 1","pages":"A37-A38"},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76992530","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 steady stratified purely azimuthal flow representing the Antarctic Circumpolar Current. 代表南极环极洋流的稳定分层纯方位流。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2020-01-01 Epub Date: 2019-09-12 DOI: 10.1007/s00605-019-01332-3
Calin Iulian Martin, Ronald Quirchmayr
{"title":"A steady stratified purely azimuthal flow representing the Antarctic Circumpolar Current.","authors":"Calin Iulian Martin, Ronald Quirchmayr","doi":"10.1007/s00605-019-01332-3","DOIUrl":"10.1007/s00605-019-01332-3","url":null,"abstract":"<p><p>We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are considered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"192 2","pages":"401-407"},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7220887/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37947749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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