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The relation between the gonality and the Clifford index of a chain of cycles 循环链的冈性与克利福德指数之间的关系
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-19 DOI: 10.1007/s00013-024-02049-y
Marc Coppens
{"title":"The relation between the gonality and the Clifford index of a chain of cycles","authors":"Marc Coppens","doi":"10.1007/s00013-024-02049-y","DOIUrl":"https://doi.org/10.1007/s00013-024-02049-y","url":null,"abstract":"<p>For a chain of cycles <span>(Gamma )</span>, we prove that <span>({{,textrm{Cliff},}}(Gamma )={{,textrm{gon},}}(Gamma )-2)</span>.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251397","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
Spherical Logvinenko–Sereda–Kovrijkine type inequality and null-controllability of the heat equation on the sphere 球面罗格维年科-塞雷达-科夫里金式不等式和球面热方程的无效可控性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-17 DOI: 10.1007/s00013-024-02051-4
Alexander Dicke, Ivan Veselić
{"title":"Spherical Logvinenko–Sereda–Kovrijkine type inequality and null-controllability of the heat equation on the sphere","authors":"Alexander Dicke, Ivan Veselić","doi":"10.1007/s00013-024-02051-4","DOIUrl":"https://doi.org/10.1007/s00013-024-02051-4","url":null,"abstract":"<p>It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko–Sereda–Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spectral inequality for the Laplace–Beltrami operator, which, in turn, yields observability and null-controllability with explicit estimates on the control costs for the spherical heat equation that are sharp in the large and in the small time regime.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251438","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
Rationality of extended unipotent characters 扩展单能字符的合理性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-17 DOI: 10.1007/s00013-024-02045-2
Olivier Dudas, Gunter Malle
{"title":"Rationality of extended unipotent characters","authors":"Olivier Dudas, Gunter Malle","doi":"10.1007/s00013-024-02045-2","DOIUrl":"https://doi.org/10.1007/s00013-024-02045-2","url":null,"abstract":"<p>We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof, we use realisations of characters in <span>(ell )</span>-adic cohomology groups of Deligne–Lusztig varieties as well as block theoretic considerations.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251398","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
The canonical trace of determinantal rings 行列式环的典型痕量
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-14 DOI: 10.1007/s00013-024-02047-0
Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi
{"title":"The canonical trace of determinantal rings","authors":"Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate, Vijaylaxmi Trivedi","doi":"10.1007/s00013-024-02047-0","DOIUrl":"https://doi.org/10.1007/s00013-024-02047-0","url":null,"abstract":"<p>We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application, we determine the canonical trace <span>(tr (omega _R))</span> of a Cohen–Macaulay ring <i>R</i> of codimension two, which is generically Gorenstein. It is shown that if the defining ideal <i>I</i> of <i>R</i> is generated by <i>n</i> elements, then <span>(tr (omega _R))</span> is generated by the <span>((n-2))</span>-minors of the Hilbert–Burch matrix of <i>I</i>.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251400","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
The derived dimensions and representation distances of Artin algebras 阿廷代数的导出维数和表示距离
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-11 DOI: 10.1007/s00013-024-02030-9
Junling Zheng, Yingying Zhang
{"title":"The derived dimensions and representation distances of Artin algebras","authors":"Junling Zheng, Yingying Zhang","doi":"10.1007/s00013-024-02030-9","DOIUrl":"https://doi.org/10.1007/s00013-024-02030-9","url":null,"abstract":"<p>There is a well-known class of algebras called Igusa–Todorov algebras which were introduced in relation to the finitistic dimension conjecture. As a generalization of Igusa–Todorov algebras, the new notion of (<i>m</i>, <i>n</i>)-Igusa–Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give methods for constructing (<i>m</i>, <i>n</i>)-Igusa–Todorov algebras. As an application, we present for general Artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206090","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
Almost periodic motions and their stability of the non-autonomous Oseen–Navier–Stokes flows 非自治奥森-纳维尔-斯托克斯流的几乎周期运动及其稳定性
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-09-03 DOI: 10.1007/s00013-024-02044-3
Ngoc Huy Nguyen, Thieu Huy Nguyen, Thi Ngoc Ha Vu
{"title":"Almost periodic motions and their stability of the non-autonomous Oseen–Navier–Stokes flows","authors":"Ngoc Huy Nguyen, Thieu Huy Nguyen, Thi Ngoc Ha Vu","doi":"10.1007/s00013-024-02044-3","DOIUrl":"https://doi.org/10.1007/s00013-024-02044-3","url":null,"abstract":"<p>In this paper, we investigate the existence and stability of almost periodic mild solutions to the non-autonomous Oseen–Navier–Stokes equations (ONSE) in the exterior domain <span>(Omega subset mathbb {R}^3)</span> of a rigid body under the actions of almost periodic external forces. Our method is based on the <span>(L^p-L^q)</span> smoothness of the evolution family corresponding to linearized equations in combination with interpolation spaces and fixed point theorems.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206091","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
Residual growth control for general maps and an approximate inverse function result 一般地图的残差增长控制和近似反函数结果
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-08-30 DOI: 10.1007/s00013-024-02035-4
Mario Amrein
{"title":"Residual growth control for general maps and an approximate inverse function result","authors":"Mario Amrein","doi":"10.1007/s00013-024-02035-4","DOIUrl":"https://doi.org/10.1007/s00013-024-02035-4","url":null,"abstract":"<p>The need to control the residual of a potentially nonlinear function <span>(mathcal {F})</span> arises in several situations in mathematics. For example, computing the zeros of a given map, or the reduction of some cost function during an optimization process are such situations. In this note, we discuss the existence of a curve <span>(tmapsto x(t))</span> in the domain of the nonlinear map <span>(mathcal {F})</span> leading from some initial value <span>(x_0)</span> to a value <i>u</i> such that we are able to control the residual <span>(mathcal {F}(x(t)))</span> based on the value <span>(mathcal {F}(x_0))</span>. More precisely, we slightly extend an existing result from J.W. Neuberger by proving the existence of such a curve, assuming that the directional derivative of <span>(mathcal {F})</span> can be represented by <span>(x mapsto mathcal {A}(x)mathcal {F}(x_0))</span>, where <span>(mathcal {A})</span> is a suitable defined operator. The presented approach covers, in case of <span>(mathcal {A}(x) = -textsf{Id})</span>, some well known results from the theory of so-called <i>continuous Newton methods</i>. Moreover, based on the presented results, we discover an approximate inverse function result.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206092","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 note on the 1-D minimization problem related to solenoidal improvement of the uncertainty principle inequality 与不确定性原理不等式的螺线改进有关的一维最小化问题说明
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-08-28 DOI: 10.1007/s00013-024-02042-5
Naoki Hamamoto
{"title":"A note on the 1-D minimization problem related to solenoidal improvement of the uncertainty principle inequality","authors":"Naoki Hamamoto","doi":"10.1007/s00013-024-02042-5","DOIUrl":"https://doi.org/10.1007/s00013-024-02042-5","url":null,"abstract":"<p>This paper gives a second way to solve the one-dimensional minimization problem of the form : </p><span>$$begin{aligned} min _{fnot equiv 0}frac{displaystyle int limits _0^infty left( f''right) ^2x^{mu +1}dxint limits _0^infty left( {x}^2left( f'right) ^2 -varepsilon f^2right) {{x}}^{mu -1}d{x}}{displaystyle left( int limits _0^infty left( f'right) ^2 {{x}}^{mu }d{x}right) ^2} end{aligned}$$</span><p>for scalar-valued functions <i>f</i> on the half line, where <span>(f')</span> and <span>(f'')</span> are its derivatives and <span>(varepsilon )</span> and <span>(mu )</span> are positive parameters with <span>(varepsilon &lt; frac{mu ^2}{4}.)</span> This problem plays an essential part of the calculation of the best constant in Heisenberg’s uncertainty principle inequality for solenoidal vector fields. The above problem was originally solved by using (generalized) Laguerre polynomial expansion; however, the calculation was complicated and long. In the present paper, we give a simpler method to obtain the same solution, the essential part of which was communicated in Theorem 5.1 of the preprint (Hamamoto, arXiv:2104.02351v4, 2021).</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206094","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
The first two k-invariants of $$textrm{Top}/textrm{O}$$ $$textrm{Top}/textrm{O}$$的前两个k变量
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-08-27 DOI: 10.1007/s00013-024-02036-3
Alexander Kupers
{"title":"The first two k-invariants of $$textrm{Top}/textrm{O}$$","authors":"Alexander Kupers","doi":"10.1007/s00013-024-02036-3","DOIUrl":"https://doi.org/10.1007/s00013-024-02036-3","url":null,"abstract":"<p>We show that the first two <i>k</i>-invariants of <span>(textrm{Top}/textrm{O})</span> vanish and give some applications.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206093","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
The Chermak–Delgado measure as a map on posets 切尔马克-德尔加多度量作为正集上的映射
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2024-08-22 DOI: 10.1007/s00013-024-02015-8
William Cocke, Ryan McCulloch
{"title":"The Chermak–Delgado measure as a map on posets","authors":"William Cocke, Ryan McCulloch","doi":"10.1007/s00013-024-02015-8","DOIUrl":"https://doi.org/10.1007/s00013-024-02015-8","url":null,"abstract":"<p>The Chermak–Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak–Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak–Delgado measure, restricted to the centralizers, is increasing.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142205983","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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