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Monatshefte fur Mathematik最新文献

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On generic convergence of successive approximations of mappings with convex and compact point images. 关于具有凸和紧点映象的映射的逐次逼近的一般收敛性。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2022-12-22 DOI: 10.1007/s00605-022-01813-y
Christian Bargetz, Emir Medjic, Katriin Pirk
{"title":"On generic convergence of successive approximations of mappings with convex and compact point images.","authors":"Christian Bargetz,&nbsp;Emir Medjic,&nbsp;Katriin Pirk","doi":"10.1007/s00605-022-01813-y","DOIUrl":"10.1007/s00605-022-01813-y","url":null,"abstract":"<p><p>We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical such mapping and typical points of its domain the sequence of successive approximations is unique and converges to a fixed point of the mapping.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576736/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41240931","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
On azimuthally propagating equatorial atmospheric waves. 关于方位角传播的赤道大气波。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2022-07-08 DOI: 10.1007/s00605-022-01741-x
Calin I Martin
{"title":"On azimuthally propagating equatorial atmospheric waves.","authors":"Calin I Martin","doi":"10.1007/s00605-022-01741-x","DOIUrl":"10.1007/s00605-022-01741-x","url":null,"abstract":"<p><p>We investigate the existence of solutions to a recent model for large-scale equatorial waves, derived recently by an asymptotic method driven by the thin-shell approximation of the Earth's atmosphere in rotating spherical coordinates.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10261202/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9657294","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
The approximate functional equation of some Diophantine series. 一类丢番图级数的近似函数方程。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2023-05-05 DOI: 10.1007/s00605-023-01859-6
Fernando Chamizo, Bruno Martin
{"title":"The approximate functional equation of some Diophantine series.","authors":"Fernando Chamizo,&nbsp;Bruno Martin","doi":"10.1007/s00605-023-01859-6","DOIUrl":"10.1007/s00605-023-01859-6","url":null,"abstract":"<p><p>We prove that a family of Diophantine series satisfies an approximate functional equation. It generalizes a result by Rivoal and Roques and proves an extended version of a conjecture posed in their paper. We also characterize the convergence points.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10363075/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9920046","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: 1
Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. 具有指定因子分解长度的全局域的赋值环上的整值多项式。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2023-01-01 Epub Date: 2023-09-04 DOI: 10.1007/s00605-023-01895-2
Victor Fadinger-Held, Sophie Frisch, Daniel Windisch
{"title":"Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations.","authors":"Victor Fadinger-Held,&nbsp;Sophie Frisch,&nbsp;Daniel Windisch","doi":"10.1007/s00605-023-01895-2","DOIUrl":"10.1007/s00605-023-01895-2","url":null,"abstract":"<p><p>Let <i>V</i> be a valuation ring of a global field <i>K</i>. We show that for all positive integers <i>k</i> and <math><mrow><mn>1</mn><mo><</mo><msub><mi>n</mi><mn>1</mn></msub><mo>≤</mo><mo>⋯</mo><mo>≤</mo><msub><mi>n</mi><mi>k</mi></msub></mrow></math> there exists an integer-valued polynomial on <i>V</i>, that is, an element of <math><mrow><mrow><mspace></mspace><mtext>Int</mtext><mspace></mspace></mrow><mo>(</mo><mi>V</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>f</mi><mo>∈</mo><mi>K</mi><mo>[</mo><mi>X</mi><mo>]</mo><mo>∣</mo><mi>f</mi><mo>(</mo><mi>V</mi><mo>)</mo><mo>⊆</mo><mi>V</mi><mo>}</mo></mrow></math>, which has precisely <i>k</i> essentially different factorizations into irreducible elements of <math><mrow><mrow><mspace></mspace><mtext>Int</mtext><mspace></mspace></mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow></math> whose lengths are exactly <math><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>n</mi><mi>k</mi></msub></mrow></math>. In fact, we show more, namely that the same result holds true for every discrete valuation domain <i>V</i> with finite residue field such that the quotient field of <i>V</i> admits a valuation ring independent of <i>V</i> whose maximal ideal is principal or whose residue field is finite. If the quotient field of <i>V</i> is a purely transcendental extension of an arbitrary field, this property is satisfied. This solves an open problem proposed by Cahen, Fontana, Frisch and Glaz in these cases.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10576700/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41240930","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: 2
Expansion of eigenvalues of the perturbed discrete bilaplacian 扰动离散双placian特征值的展开式
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2022-02-05 DOI: 10.1007/s00605-022-01678-1
S. Kholmatov, Ahmad Khalkhuzhaev, Mardon Pardabaev
{"title":"Expansion of eigenvalues of the perturbed discrete bilaplacian","authors":"S. Kholmatov, Ahmad Khalkhuzhaev, Mardon Pardabaev","doi":"10.1007/s00605-022-01678-1","DOIUrl":"https://doi.org/10.1007/s00605-022-01678-1","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77103075","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
Hyperseries in the non-Archimedean ring of Colombeau generalized numbers. Colombeau广义数的非阿基米德环上的超级数。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2022-01-01 Epub Date: 2021-11-28 DOI: 10.1007/s00605-021-01647-0
Diksha Tiwari, Paolo Giordano
{"title":"Hyperseries in the non-Archimedean ring of Colombeau generalized numbers.","authors":"Diksha Tiwari,&nbsp;Paolo Giordano","doi":"10.1007/s00605-021-01647-0","DOIUrl":"https://doi.org/10.1007/s00605-021-01647-0","url":null,"abstract":"<p><p>This article is the natural continuation of the paper: Mukhammadiev et al. <i>Supremum, infimum and hyperlimits of Colombeau generalized numbers</i> in this journal. Since the ring of Robinson-Colombeau is non-Archimedean and Cauchy complete, a classical series <math> <mrow><msubsup><mo>∑</mo> <mrow><mi>n</mi> <mo>=</mo> <mn>0</mn></mrow> <mrow><mo>+</mo> <mi>∞</mi></mrow> </msubsup> <msub><mi>a</mi> <mi>n</mi></msub> </mrow> </math> of generalized numbers is convergent <i>if</i> and only if <math> <mrow><msub><mi>a</mi> <mi>n</mi></msub> <mo>→</mo> <mn>0</mn></mrow> </math> in the sharp topology. Therefore, this property does not permit us to generalize several classical results, mainly in the study of analytic generalized functions (as well as, e.g., in the study of sigma-additivity in integration of generalized functions). Introducing the notion of hyperseries, we solve this problem recovering classical examples of analytic functions as well as several classical results.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8776721/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39590844","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: 2
Forcing axioms and the complexity of non-stationary ideals. 强迫公理和非定常理想的复杂性。
IF 0.9 4区 数学
Monatshefte fur Mathematik Pub Date : 2022-01-01 Epub Date: 2022-06-27 DOI: 10.1007/s00605-022-01734-w
Sean Cox, Philipp Lücke
{"title":"Forcing axioms and the complexity of non-stationary ideals.","authors":"Sean Cox,&nbsp;Philipp Lücke","doi":"10.1007/s00605-022-01734-w","DOIUrl":"https://doi.org/10.1007/s00605-022-01734-w","url":null,"abstract":"<p><p>We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on <math><msub><mi>ω</mi> <mn>2</mn></msub> </math> and its restrictions to certain cofinalities. Our main result shows that the strengthening <math> <msup><mrow><mi>MM</mi></mrow> <mrow><mo>+</mo> <mo>+</mo></mrow> </msup> </math> of Martin's Maximum does not decide whether the restriction of the non-stationary ideal on <math><msub><mi>ω</mi> <mn>2</mn></msub> </math> to sets of ordinals of countable cofinality is <math><msub><mi>Δ</mi> <mn>1</mn></msub> </math> -definable by formulas with parameters in <math><mrow><mi>H</mi> <mo>(</mo> <msub><mi>ω</mi> <mn>3</mn></msub> <mo>)</mo></mrow> </math> . The techniques developed in the proof of this result also allow us to prove analogous results for the full non-stationary ideal on <math><msub><mi>ω</mi> <mn>2</mn></msub> </math> and strong forcing axioms that are compatible with <math><mi>CH</mi></math> . Finally, we answer a question of S. Friedman, Wu and Zdomskyy by showing that the <math><msub><mi>Δ</mi> <mn>1</mn></msub> </math> -definability of the non-stationary ideal on <math><msub><mi>ω</mi> <mn>2</mn></msub> </math> is compatible with arbitrary large values of the continuum function at <math><msub><mi>ω</mi> <mn>2</mn></msub> </math> .</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9388474/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40632705","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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