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Monatshefte fur Mathematik最新文献

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On Weyl products and uniform distribution modulo one. 关于Weyl积和模1的均匀分布。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2018-01-01 Epub Date: 2017-09-26 DOI: 10.1007/s00605-017-1100-8
Christoph Aistleitner, Gerhard Larcher, Friedrich Pillichshammer, Sumaia Saad Eddin, Robert F Tichy
{"title":"On Weyl products and uniform distribution modulo one.","authors":"Christoph Aistleitner, Gerhard Larcher, Friedrich Pillichshammer, Sumaia Saad Eddin, Robert F Tichy","doi":"10.1007/s00605-017-1100-8","DOIUrl":"10.1007/s00605-017-1100-8","url":null,"abstract":"<p><p>In the present paper we study the asymptotic behavior of trigonometric products of the form <math> <mrow><msubsup><mo>∏</mo> <mrow><mi>k</mi> <mo>=</mo> <mn>1</mn></mrow> <mi>N</mi></msubsup> <mn>2</mn> <mo>sin</mo> <mrow><mo>(</mo> <mi>π</mi> <msub><mi>x</mi> <mi>k</mi></msub> <mo>)</mo></mrow> </mrow> </math> for <math><mrow><mi>N</mi> <mo>→</mo> <mi>∞</mi></mrow> </math> , where the numbers <math><mrow><mi>ω</mi> <mo>=</mo> <msubsup><mrow><mo>(</mo> <msub><mi>x</mi> <mi>k</mi></msub> <mo>)</mo></mrow> <mrow><mi>k</mi> <mo>=</mo> <mn>1</mn></mrow> <mi>N</mi></msubsup> </mrow> </math> are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points <math><mi>ω</mi></math> , thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97-118, 1969). Furthermore, we consider the special cases when the points <math><mi>ω</mi></math> are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-017-1100-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37377943","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: 12
Quadrics and Scherk towers. 二次曲线和舍尔克塔。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2018-01-01 Epub Date: 2017-07-03 DOI: 10.1007/s00605-017-1075-5
S Fujimori, U Hertrich-Jeromin, M Kokubu, M Umehara, K Yamada
{"title":"Quadrics and Scherk towers.","authors":"S Fujimori,&nbsp;U Hertrich-Jeromin,&nbsp;M Kokubu,&nbsp;M Umehara,&nbsp;K Yamada","doi":"10.1007/s00605-017-1075-5","DOIUrl":"https://doi.org/10.1007/s00605-017-1075-5","url":null,"abstract":"<p><p>We investigate the relation between quadrics and their Christoffel duals on the one hand, and certain zero mean curvature surfaces and their Gauss maps on the other hand. To study the relation between timelike minimal surfaces and the Christoffel duals of 1-sheeted hyperboloids we introduce para-holomorphic elliptic functions. The curves of type change for real isothermic surfaces of mixed causal type turn out to be aligned with the real curvature line net.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-017-1075-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37164208","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: 3
Theoretische Betrachtungen 理论Betrachtungen
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-12-31 DOI: 10.1007/BF01692220
{"title":"Theoretische Betrachtungen","authors":"","doi":"10.1007/BF01692220","DOIUrl":"https://doi.org/10.1007/BF01692220","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88941801","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
Oeuvres mathématiques d' Évariste Galois evariste Galois的数学作品
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-05-31 DOI: 10.1007/BF01695090
Évariste Galois
{"title":"Oeuvres mathématiques d' Évariste Galois","authors":"Évariste Galois","doi":"10.1007/BF01695090","DOIUrl":"https://doi.org/10.1007/BF01695090","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89625311","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: 25
On semidiscrete constant mean curvature surfaces and their associated families. 半离散常平均曲率曲面及其相关族。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-01-01 Epub Date: 2016-05-23 DOI: 10.1007/s00605-016-0929-6
Wolfgang Carl
{"title":"On semidiscrete constant mean curvature surfaces and their associated families.","authors":"Wolfgang Carl","doi":"10.1007/s00605-016-0929-6","DOIUrl":"https://doi.org/10.1007/s00605-016-0929-6","url":null,"abstract":"<p><p>The present paper studies semidiscrete surfaces in three-dimensional Euclidean space within the framework of integrable systems. In particular, we investigate semidiscrete surfaces with constant mean curvature along with their associated families. The notion of mean curvature introduced in this paper is motivated by a recently developed curvature theory for quadrilateral meshes equipped with unit normal vectors at the vertices, and extends previous work on semidiscrete surfaces. In the situation of vanishing mean curvature, the associated families are defined via a Weierstrass representation. For the general cmc case, we introduce a Lax pair representation that directly defines associated families of cmc surfaces, and is connected to a semidiscrete [Formula: see text]-Gordon equation. Utilizing this theory we investigate semidiscrete Delaunay surfaces and their connection to elliptic billiards.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-016-0929-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34832703","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: 4
Unconventional height functions in simultaneous Diophantine approximation. 在同时的丢番图近似中，非常规高度函数。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-01-01 Epub Date: 2016-10-18 DOI: 10.1007/s00605-016-0983-0
Lior Fishman, David Simmons
{"title":"Unconventional height functions in simultaneous Diophantine approximation.","authors":"Lior Fishman,&nbsp;David Simmons","doi":"10.1007/s00605-016-0983-0","DOIUrl":"https://doi.org/10.1007/s00605-016-0983-0","url":null,"abstract":"<p><p>Simultaneous Diophantine approximation is concerned with the approximation of a point <math><mrow><mi>x</mi> <mo>∈</mo> <msup><mi>R</mi> <mi>d</mi></msup> </mrow> </math> by points <math><mrow><mi>r</mi> <mo>∈</mo> <msup><mi>Q</mi> <mi>d</mi></msup> </mrow> </math> , with a view towards jointly minimizing the quantities <math><mrow><mo>‖</mo> <mi>x</mi> <mo>-</mo> <mi>r</mi> <mo>‖</mo></mrow> </math> and <math><mrow><mi>H</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo></mrow> </math> . Here <math><mrow><mi>H</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo></mrow> </math> is the so-called \"standard height\" of the rational point <math><mi>r</mi></math> . In this paper the authors ask: What changes if we replace the standard height function by a different one? As it turns out, this change leads to dramatic differences from the classical theory and requires the development of new methods. We discuss three examples of nonstandard height functions, computing their exponents of irrationality as well as giving more precise results. A list of open questions is also given.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-016-0983-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37816115","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: 3
Operator differential-algebraic equations with noise arising in fluid dynamics. 流体力学中带有噪声的算子微分代数方程。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-01-01 Epub Date: 2016-05-24 DOI: 10.1007/s00605-016-0931-z
Robert Altmann, Tijana Levajković, Hermann Mena
{"title":"Operator differential-algebraic equations with noise arising in fluid dynamics.","authors":"Robert Altmann,&nbsp;Tijana Levajković,&nbsp;Hermann Mena","doi":"10.1007/s00605-016-0931-z","DOIUrl":"https://doi.org/10.1007/s00605-016-0931-z","url":null,"abstract":"<p><p>We study linear semi-explicit stochastic operator differential algebraic equations (DAEs) for which the constraint equation is given in an explicit form. In particular, this includes the Stokes equations arising in fluid dynamics. We combine a white noise polynomial chaos expansion approach to include stochastic perturbations with deterministic regularization techniques. With this, we are able to include Gaussian noise and stochastic convolution terms as perturbations in the differential as well as in the constraint equation. By the application of the polynomial chaos expansion method, we reduce the stochastic operator DAE to an infinite system of deterministic operator DAEs for the stochastic coefficients. Since the obtained system is very sensitive to perturbations in the constraint equation, we analyze a regularized version of the system. This then allows to prove the existence and uniqueness of the solution of the initial stochastic operator DAE in a certain weighted space of stochastic processes.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-016-0931-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37782392","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
Analysis of carries in signed digit expansions. 有符号数字扩展中的携带分析。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2017-01-01 Epub Date: 2016-06-10 DOI: 10.1007/s00605-016-0917-x
Clemens Heuberger, Sara Kropf, Helmut Prodinger
{"title":"Analysis of carries in signed digit expansions.","authors":"Clemens Heuberger, Sara Kropf, Helmut Prodinger","doi":"10.1007/s00605-016-0917-x","DOIUrl":"10.1007/s00605-016-0917-x","url":null,"abstract":"<p><p>The number of positive and negative carries in the addition of two independent random signed digit expansions of given length is analyzed asymptotically for the (<i>q</i>, <i>d</i>)-system and the symmetric signed digit expansion. The results include expectation, variance, covariance between the positive and negative carries and a central limit theorem. Dependencies between the digits require determining suitable transition probabilities to obtain equidistribution on all expansions of given length. A general procedure is described to obtain such transition probabilities for arbitrary regular languages. The number of iterations in von Neumann's parallel addition method for the symmetric signed digit expansion is also analyzed, again including expectation, variance and convergence to a double exponential limiting distribution. This analysis is carried out in a general framework for sequences of generating functions.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7175708/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37890154","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
Compendium der höheren Analysis 微积分整合器
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2016-03-08 DOI: 10.1007/BF01708519
R. Sterneck
{"title":"Compendium der höheren Analysis","authors":"R. Sterneck","doi":"10.1007/BF01708519","DOIUrl":"https://doi.org/10.1007/BF01708519","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72736242","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
Cours de géometrie analytique 分析几何课程
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2016-03-08 DOI: 10.1007/BF01708544
G. Kohn
{"title":"Cours de géometrie analytique","authors":"G. Kohn","doi":"10.1007/BF01708544","DOIUrl":"https://doi.org/10.1007/BF01708544","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2016-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83307395","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: 5
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