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Archiv der Mathematik最新文献

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On the rank of projective modules
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-20 DOI: 10.1007/s00013-024-02081-y
F.E.A. Johnson
{"title":"On the rank of projective modules","authors":"F.E.A. Johnson","doi":"10.1007/s00013-024-02081-y","DOIUrl":"10.1007/s00013-024-02081-y","url":null,"abstract":"<div><p>Let <i>P</i> be a nonzero projective module over an integral group ring. We consider the question of whether the rank of <i>P</i> is necessarily positive.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"233 - 241"},"PeriodicalIF":0.5,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02081-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184864","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
Poincaré inequality for one-forms on four manifolds with bounded Ricci curvature 具有有界里奇曲率的四流形上单形的波恩卡莱不等式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-20 DOI: 10.1007/s00013-024-02091-w
Shouhei Honda, Andrea Mondino
{"title":"Poincaré inequality for one-forms on four manifolds with bounded Ricci curvature","authors":"Shouhei Honda,&nbsp;Andrea Mondino","doi":"10.1007/s00013-024-02091-w","DOIUrl":"10.1007/s00013-024-02091-w","url":null,"abstract":"<div><p>In this short note, we provide a quantitative global Poincaré inequality for one-forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on the Ricci curvature. This seems to be the first non-trivial result giving such an inequality without any higher curvature assumptions. The proof is based on a Hodge theoretic result on orbifolds, a comparison for fundamental groups, and a spectral convergence with respect to Gromov–Hausdorff convergence, via a degeneration result to orbifolds by Anderson.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"449 - 455"},"PeriodicalIF":0.5,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02091-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621815","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
Nonexistence of certain regular maps of 2-power order
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-17 DOI: 10.1007/s00013-024-02093-8
Yao Tian, Xiaogang Li
{"title":"Nonexistence of certain regular maps of 2-power order","authors":"Yao Tian,&nbsp;Xiaogang Li","doi":"10.1007/s00013-024-02093-8","DOIUrl":"10.1007/s00013-024-02093-8","url":null,"abstract":"<div><p>In a recent paper, Hou et al. conjectured that there exist no regular maps of order <span>(2^n)</span> and of type <span>({2^k,2^s})</span>, where <i>n</i>, <i>k</i>, and <i>s</i> are positive integers satisfying <span>(2le s&lt;k&lt;n-1)</span> and <span>(s+k&gt;n)</span>. In this paper, we give an affirmative answer to this conjecture.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"389 - 394"},"PeriodicalIF":0.5,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622101","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
Correction to: A reciprocity law in function fields
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-17 DOI: 10.1007/s00013-024-02092-9
Yoshinori Hamahata
{"title":"Correction to: A reciprocity law in function fields","authors":"Yoshinori Hamahata","doi":"10.1007/s00013-024-02092-9","DOIUrl":"10.1007/s00013-024-02092-9","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"355 - 356"},"PeriodicalIF":0.5,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02092-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184800","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 the Krull dimension of rings of integer-valued rational functions
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-03 DOI: 10.1007/s00013-024-02086-7
M. M. Chems-Eddin, B. Feryouch, H. Mouanis, A. Tamoussit
{"title":"On the Krull dimension of rings of integer-valued rational functions","authors":"M. M. Chems-Eddin,&nbsp;B. Feryouch,&nbsp;H. Mouanis,&nbsp;A. Tamoussit","doi":"10.1007/s00013-024-02086-7","DOIUrl":"10.1007/s00013-024-02086-7","url":null,"abstract":"<div><p>Let <i>D</i> be an integral domain with quotient field <i>K</i> and <i>E</i> a subset of <i>K</i>. The <i>ring of integer-valued rational functions on</i> <i>E</i> is defined as </p><div><div><span>$$begin{aligned} mathrm {Int^R}(E,D):=lbrace varphi in K(X);; varphi (E)subseteq Drbrace . end{aligned}$$</span></div></div><p>The main goal of this paper is to investigate the Krull dimension of the ring <span>(mathrm {Int^R}(E,D).)</span> Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"243 - 254"},"PeriodicalIF":0.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184674","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
Choquet integrals, Hausdorff content and sparse operators
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-03 DOI: 10.1007/s00013-024-02083-w
Naoya Hatano, Ryota Kawasumi, Hiroki Saito, Hitoshi Tanaka
{"title":"Choquet integrals, Hausdorff content and sparse operators","authors":"Naoya Hatano,&nbsp;Ryota Kawasumi,&nbsp;Hiroki Saito,&nbsp;Hitoshi Tanaka","doi":"10.1007/s00013-024-02083-w","DOIUrl":"10.1007/s00013-024-02083-w","url":null,"abstract":"<div><p>Let <span>(H^d)</span>, <span>(0&lt;d&lt;n)</span>, be the dyadic Hausdorff content of the <i>n</i>-dimensional Euclidean space <span>({{mathbb {R}}}^n)</span>. It is shown that <span>(H^d)</span> counts a Cantor set of the unit cube <span>([0, 1)^n)</span> as <span>(approx 1)</span>, which implies the unboundedness of the sparse operator <span>({{mathcal {A}}}_{{{mathcal {S}}}})</span> on the Choquet space <span>({mathcal L}^p(H^d))</span>, <span>(p&gt;0)</span>. In this paper, the sparse operator <span>({mathcal A}_{{{mathcal {S}}}})</span> is proved to map <span>({{mathcal {L}}}^p(H^d))</span>, <span>(1le p&lt;infty )</span>, into an associate space of the Orlicz-Morrey space <span>({{{mathcal {M}}}^{p'}_{Phi _0}(H^d)}')</span>, <span>(Phi _0(t)=tlog (e+t))</span>. Further, another characterization of those associate spaces is given by means of the tiling <span>({{mathcal {T}}})</span> of <span>({{mathbb {R}}}^n)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"311 - 324"},"PeriodicalIF":0.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184676","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 seminorm characterization of infinite Banach direct sums 无限巴拿赫直接和的半规范表征
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-03 DOI: 10.1007/s00013-024-02080-z
Hojjatollah Samea
{"title":"A seminorm characterization of infinite Banach direct sums","authors":"Hojjatollah Samea","doi":"10.1007/s00013-024-02080-z","DOIUrl":"10.1007/s00013-024-02080-z","url":null,"abstract":"<div><p>In this paper, the notion of a <span>(Delta )</span>-direct sum of a family of Banach spaces indexed by a set <i>I</i>, where <span>(Delta )</span> is a union-closed subnet of <span>(textsf{Fin}(I))</span> (the family of all finite subsets of <i>I</i>), is introduced. A seminorm characterization of <span>(Delta )</span>-direct sums and some results are presented. Necessary and sufficient conditions are found that a direct sum of a family of Banach spaces is a <span>(Delta )</span>-direct sum. Elements of a direct sum of Banach spaces that are <span>(Delta )</span>-sectionally convergent are introduced and studied. Examples of <span>(Delta )</span>-direct sums and applications of <span>(Delta )</span>-direct sums to Fourier analysis on compact groups are given.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"283 - 299"},"PeriodicalIF":0.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184675","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
Lebesgue constants for the Walsh system and the discrepancy of the van der Corput sequence
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-24 DOI: 10.1007/s00013-024-02087-6
Josef Dick, Friedrich Pillichshammer
{"title":"Lebesgue constants for the Walsh system and the discrepancy of the van der Corput sequence","authors":"Josef Dick,&nbsp;Friedrich Pillichshammer","doi":"10.1007/s00013-024-02087-6","DOIUrl":"10.1007/s00013-024-02087-6","url":null,"abstract":"<div><p>In this short note, we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue constants of the Walsh function system that play an important role in approximation theory, and on the other hand, there is the star discrepancy of the van der Corput sequence that plays a prominent role in uniform distribution theory. Over the decades, these two quantities have been examined in great detail independently of each other and important results have been proven. Work in these areas has been carried out independently, but as we show here, they actually coincide. Interestingly, many theorems have been discovered in both areas independently, but some results have only been known in one area but not in the other.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"407 - 414"},"PeriodicalIF":0.5,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02087-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622037","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
Discrete and continuous dynamics of real 3-dimensional nilpotent polynomial vector fields
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-23 DOI: 10.1007/s00013-024-02085-8
Álvaro Castañeda, Salomón Rebollo-Perdomo
{"title":"Discrete and continuous dynamics of real 3-dimensional nilpotent polynomial vector fields","authors":"Álvaro Castañeda,&nbsp;Salomón Rebollo-Perdomo","doi":"10.1007/s00013-024-02085-8","DOIUrl":"10.1007/s00013-024-02085-8","url":null,"abstract":"<div><p>The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by a large class of 3-dimensional nilpotent polynomial vector fields of arbitrary degree. In the discrete case, we prove that each dynamical system has a unique fixed point and there are no 2-cycles. Moreover, either the fixed point is a global attractor or there exists a 3-cycle which is not a repeller. In the continuous setting, we prove that each dynamical system is polynomially integrable. Particularly, it is proved that the global dynamics of some low degree vector fields is completely understood and that there are invariant surfaces foliated by periodic orbits. As far as we know, this last property has not been shown before in the nilpotent context. We achieve our results by using the approach of polynomial automorphisms to obtain simplified conjugated dynamical systems, instead of considering only the usual linear transformations. Finally, we point out some similarities shared by the discrete and continuous dynamical systems, and we formulate some open questions motivated by our results, which are related with the Markus–Yamabe conjecture and the problem of planar limit cycles.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"415 - 434"},"PeriodicalIF":0.5,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621948","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
Linear maps preserving the inclusion of fixed subsets into the local spectrum at some fixed vector
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-12-18 DOI: 10.1007/s00013-024-02078-7
Constantin Costara
{"title":"Linear maps preserving the inclusion of fixed subsets into the local spectrum at some fixed vector","authors":"Constantin Costara","doi":"10.1007/s00013-024-02078-7","DOIUrl":"10.1007/s00013-024-02078-7","url":null,"abstract":"<div><p>For a natural number <span>(n ge 2)</span>, denote by <span>(mathcal {M}_{n})</span> the space of all <span>(ntimes n)</span> matrices over the complex field <span>(mathbb {C})</span>. Let <span>(x_0 in mathbb {C}^{n})</span> be a fixed nonzero vector, and fix also two nonempty subsets <span>(K_1, K_2 subseteq mathbb {C})</span>, each having at most <i>n</i> distinct elements. Under the assumption that <span>(|K_1| le |K_2|)</span>, we characterize linear bijective maps <span>(varphi )</span> on <span>(mathcal {M}_{n})</span> having the property that, for each matrix <i>T</i>, we have that <span>(K_2)</span> is a subset of the local spectrum of <span>(varphi (T))</span> at <span>(x_0 )</span> whenever <span>(K_1 )</span> is a subset of the local spectrum of <i>T</i> at <span>(x_0)</span>. As a corollary, we also characterize linear maps <span>(varphi )</span> on <span>(mathcal {M} _{n})</span> having the property that, for each matrix <i>T</i>, we have that <span>(K_1)</span> is a subset of the local spectrum of <i>T</i> at <span>(x_0)</span> if and only if <span>(K_2)</span> is a subset of the local spectrum of <span>(varphi (T))</span> at <span>(x_0)</span>, without the bijectivity assumption on the map <span>(varphi )</span> and with no assumption made regarding the number of elements of <span>(K_1)</span> and <span>(K_2)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"165 - 176"},"PeriodicalIF":0.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02078-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108624","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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