Mathematische Nachrichten最新文献

{"title":"Time Evolution of Elastically Starlike Domains in the Hele-Shaw Flow Problem","authors":"Mihai Aron","doi":"10.1002/mana.70200","DOIUrl":"https://doi.org/10.1002/mana.70200","url":null,"abstract":"<div>\u0000 \u0000 <p>The notion of elasticity and the associated concept of elastically starlike functions are newly introduced in geometric function theory and are developed in this paper. The terminology is motivated by the geometric interpretation of elasticity as a measure of the deformation of level lines under conformal mappings. We investigate the connection between elastically starlike and starlike functions, and we apply these ideas to the Hele-Shaw flow problem with zero surface tension. We show that if the initial fluid domain is starlike and the boundary elasticity is bounded above and below by positive constants depending on the geometry of the initial domain, then this geometric structure is preserved throughout the existence time of the solution.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2452-2471"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Analog of Kida's Formula for Mazur–Tate Elements","authors":"Naman Pratap,&nbsp;Anwesh Ray","doi":"10.1002/mana.70211","DOIUrl":"https://doi.org/10.1002/mana.70211","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We prove an analog of Kida's formula for the Iwasawa invariants of the Mazur–Tate elements attached to elliptic curves over &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {Q}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an odd prime and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L/K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a Galois extension of abelian number fields with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-power Galois group. For an elliptic curve &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$E/mathbb {Q}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we study the Mazur–Tate elements over the finite layers of the cyclotomic &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathbb {Z}_p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-extensions of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We show that the vanishing of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-invariant is preserved in the extension: if the level-&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Mazur–Tate element over &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; has &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mu =0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then the corresponding element over &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; also has &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2652-2679"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extended Sobolev Scale on Non-Compact Manifolds","authors":"Ognjen Milatovic","doi":"10.1002/mana.70194","DOIUrl":"https://doi.org/10.1002/mana.70194","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Adapting the definition of “extended Sobolev scale” on compact manifolds by Mikhailets and Murach to the setting of a (generally non-compact) manifold of bounded geometry &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we define the “extended Sobolev scale” &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H^{varphi }(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a function which is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$RO$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-varying at infinity. With the help of the scale &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H^{varphi }(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we obtain a description of all Hilbert function-spaces that serve as interpolation spaces with respect to a pair of Sobolev spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2359-2383"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Linear Generalization of the Nearly Gorenstein Property, With Applications to Veronese Subalgebras","authors":"Sora Miyashita","doi":"10.1002/mana.70199","DOIUrl":"https://doi.org/10.1002/mana.70199","url":null,"abstract":"<p>We study the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>♮</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(natural)$</annotation>\u0000 </semantics></math> for Cohen–Macaulay semi-standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi-standard graded algebra <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$ R$</annotation>\u0000 </semantics></math> satisfies <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>♮</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(natural)$</annotation>\u0000 </semantics></math>, then its Veronese subalgebras <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$ R^{(k)}$</annotation>\u0000 </semantics></math> are nearly Gorenstein for all sufficiently large <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$ k$</annotation>\u0000 </semantics></math>. We also prove that if a standard graded algebra <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> is nearly Gorenstein so does its Veronese subalgebra <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$R^{(k)}$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$k&gt;0$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2436-2451"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a Class of Integro-Differential Equations Involving Subcritical, Critical, and Supercritical Nonlinearities","authors":"Gelson C. G. dos Santos,&nbsp;Francisco J. S. A. Corrêa,&nbsp;Michele A. S. da Silva","doi":"10.1002/mana.70195","DOIUrl":"https://doi.org/10.1002/mana.70195","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study a class of elliptic problems in the presence of a nonlocal term and a parameter. A careful analysis of the influence of the referred nonlocal term and the parameter on the existence and nonexistence of solution was carried out, where we considered different scenarios. Among our main contributions are: a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Poho</mi>\u0000 <mover>\u0000 <mi>z</mi>\u0000 <mo>̌</mo>\u0000 </mover>\u0000 <mi>aev</mi>\u0000 </mrow>\u0000 <annotation>${rm Poho}check{z}{rm aev}$</annotation>\u0000 </semantics></math> identity for a class of elliptic integro-differential problems (which produces some results of nonexistence of solutions) and an extensive study of the critical nonlocal problem, which includes the study of the double critical case. Some of the main tools used in the research were global and local minimization, mountain pass theorem, concentration compactness principle, sub-supersolution method, and a Carl–Heikkilä fixed point theorem.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2303-2331"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Amenability Constants for Unconditional Sums of Banach Algebras","authors":"Tomasz Kania,&nbsp;Jerzy Ka̧kol","doi":"10.1002/mana.70201","DOIUrl":"https://doi.org/10.1002/mana.70201","url":null,"abstract":"&lt;p&gt;We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$(A_i)_{iin I}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of Banach algebras and a Banach sequence lattice &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;annotation&gt;$I$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-sum &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;⨁&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${bigl (bigoplus _{iin I} A_ibigr)}_{!E}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; carries a natural Banach algebra structure via coordinatewise multiplication. Under the hypothesis that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;sup&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2472-2494"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70201","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity and R-Decomposition","authors":"Ying Liu,&nbsp;Lining Jiang","doi":"10.1002/mana.70171","DOIUrl":"https://doi.org/10.1002/mana.70171","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a complex unital Banach algebra and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Rsubseteq mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a regularity. In order to characterize the accumulation point of the spectrum of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ain mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; associated with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we define &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-decomposition of elements in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and give the conditions to make &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$R^D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; a regularity, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$R^D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the set of elements with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-decomposition. Further, we study the relation between the spectrum of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ain mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; associated with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$R^D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the accumulation point of the spectrum of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ain mathcal {A}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; associated with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"1883-1893"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Matrix-Based Cryptography Using Matrix Norm and Special Integer Sequences","authors":"Melih Göcen,&nbsp;Sümeyye Hacer Büyükakyol","doi":"10.1002/mana.70180","DOIUrl":"https://doi.org/10.1002/mana.70180","url":null,"abstract":"<p>In this paper, a novel matrix-based encryption approach based on the Affine Hill cipher is presented. The key matrix is constructed using the Narayana integer sequence, and the Frobenius norm of the key matrix is used as a scaling factor in the key construction. This approach increases key matrix variation and influences the algebraic structure of the resulting ciphertexts. The security analysis demonstrates that the proposed method yields a larger and more structured key space compared to the classical Hill cipher.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2087-2102"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70180","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inverse Resonance Problems for the Radial Schrödinger Operator","authors":"Xin-Jian Xu,&nbsp;Chuan-Fu Yang,&nbsp;Vjacheslav A. Yurko","doi":"10.1002/mana.70181","DOIUrl":"https://doi.org/10.1002/mana.70181","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider the radial Schrödinger operator on the half-line with angular momentum <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>l</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 <mo>∪</mo>\u0000 <mo>{</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$lin mathbb {N}cup lbrace 0rbrace$</annotation>\u0000 </semantics></math>. Under some conditions on the potentials, we show that the eigenvalues and resonances uniquely determine the radial Schrödinger operator. The methods of proof are based on reducing the inverse resonance problems to the inverse spectral or inverse scattering problems.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2103-2117"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"p-Nuclear Operators on Spaces of Continuous Functions","authors":"Juliusz Stochmal","doi":"10.1002/mana.70189","DOIUrl":"https://doi.org/10.1002/mana.70189","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the relationship between <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-nuclear operators on the space of continuous functions and properties of their representing Borel measures. In particular, we show that a weakly compact operator on the space of scalar-valued continuous functions is <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-nuclear if and only if its representing measure has an appropriate Pettis integrable derivative.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2230-2241"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}