Mathematische Nachrichten最新文献

{"title":"Effects of degeneracy and functional response on the bifurcation and positive solutions for a diffusion model","authors":"Yunfeng Jia,&nbsp;Jingjing Wang,&nbsp;Jianhua Wu","doi":"10.1002/mana.70094","DOIUrl":"https://doi.org/10.1002/mana.70094","url":null,"abstract":"<p>This paper studies a diffusive competition model with degeneracy and Holling-II functional response in spatially heterogeneous environment. First, we discuss the structures and stability of steady-state bifurcation solutions. Then, the existence, nonexistence, and multiplicity of steady-state solutions are established. We conclude that there exist two critical values induced by the spatial degeneracy and the functional response, respectively, such that when the growth rate of one of the competition species is between these two critical values, the model behaves drastically and some qualitative changes occur, which is in sharp contrast to the well-studied classical models. In addition, it is found that the boundary condition also has important effects on the critical value. These show that not only degeneracy but also the combination of functional response and boundary condition have important influences on the model, especially on the structures of bifurcations and the existence of steady-state solutions. Finally, the asymptotic behavior and global attractor of positive solutions for the parabolic system are investigated, which enrich the study of dynamical behavior for the model.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 2","pages":"397-432"},"PeriodicalIF":0.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146136196","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 note on the Brill–Noether loci of small codimension in moduli space of stable bundles","authors":"Pritthijit Biswas,&nbsp;Jaya N. N. Iyer","doi":"10.1002/mana.70101","DOIUrl":"https://doi.org/10.1002/mana.70101","url":null,"abstract":"&lt;p&gt;Let &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; be a smooth projective curve of genus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;annotation&gt;$g$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; over the field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {C}$&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;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M_{X}(2,L)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote the moduli space of stable rank 2 vector bundles on &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; with fixed determinant &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; of degree &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$2g-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Consider the Brill–Noether subvariety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$W^{1}_{X}(2,L)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &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;M&lt;/mi&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M_{X}(2,L)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; which parameterizes stable vector bundles having at least two linearly independent global sections. In this paper, for generic &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;/annotat","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 2","pages":"480-489"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140189","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":"Generalized Campanato space over non-homogeneous space and its applications","authors":"Yuxun Zhang,&nbsp;Jiang Zhou","doi":"10.1002/mana.70098","DOIUrl":"https://doi.org/10.1002/mana.70098","url":null,"abstract":"<p>The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John–Nirenberg inequality and equivalent characterizations. As applications, the boundedness of fractional type Marcinkiewicz integral and its commutator on generalized Morrey space over non-homogeneous space is obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"270-289"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941831","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":"Fractional Volterra-type operators from Bergman spaces to Hardy spaces","authors":"Xiang Fang,&nbsp;Feng Guo,&nbsp;Shengzhao Hou,&nbsp;Xiaolin Zhu","doi":"10.1002/mana.70095","DOIUrl":"https://doi.org/10.1002/mana.70095","url":null,"abstract":"<p>A new family of Volterra-type operators <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <mi>φ</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>·</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathfrak {V}_{alpha,beta }^{varphi }(cdot)$</annotation>\u0000 </semantics></math> based on bona fide fractional calculus is introduced in [12] by constructing analytic paraproducts acting on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mi>D</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$H(mathbb {D})$</annotation>\u0000 </semantics></math> and their boundedness between Hardy spaces is characterized for certain parameter ranges there. This paper is a natural companion to [12] in the sense that it characterizes those <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math>’s such that <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <mi>φ</mi>\u0000 </msubsup>\u0000 <annotation>$mathfrak {V}_{alpha,beta }^{varphi }$</annotation>\u0000 </semantics></math> is bounded from weighted Bergman spaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>L</mi>\u0000 <mi>a</mi>\u0000 <mi>p</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>d</mi>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>γ</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L_a^p(dA_gamma)$</annotation>\u0000 </semantics></math> to Hardy spaces <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <annotation>$H^q$</annotation>\u0000 </semantics></math> for the range\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"224-247"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930826","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":"Zeta functions of quadratic lattices of a hyperbolic plane","authors":"Daejun Kim,&nbsp;Seok Hyeong Lee,&nbsp;Seungjai Lee","doi":"10.1002/mana.70102","DOIUrl":"https://doi.org/10.1002/mana.70102","url":null,"abstract":"<p>In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane—that is, a nondegenerate isotropic quadratic space of dimension 2. We derive explicit formulas for the associated zeta functions and obtain a combinatorial way to compute them. Their analytic properties lead to the intriguing consequence that a large proportion of proper classes are one-lattice classes.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"290-311"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941833","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":"First moments of \u0000 \u0000 \u0000 GL\u0000 (\u0000 3\u0000 )\u0000 ×\u0000 GL\u0000 (\u0000 2\u0000 )\u0000 \u0000 ${{mathrm{GL}}}(3)times {{mathrm{GL}}}(2)$\u0000 and \u0000 \u0000 \u0000 GL\u0000 (\u0000 2\u0000 )\u0000 \u0000 $ {{mathrm{GL}}}(2)$\u0000 \u0000 \u0000 L\u0000 $L$\u0000 -functions and their applications","authors":"Fei Hou","doi":"10.1002/mana.70099","DOIUrl":"https://doi.org/10.1002/mana.70099","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a self-dual Hecke–Maaß form for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;GL&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathrm{GL}}(3)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; underlying the symmetric square lift of a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;GL&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathrm{GL}}(2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-newform of square-free level and trivial nebentypus. In this paper, we are interested in the first moments of the central values of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;GL&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mi&gt;GL&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$rm GL(3)times GL(2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; &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;-functions and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;GL&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$rm GL(2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; &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;-functions. As a result, we obtain an estimate for the first moment for &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;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L(1/2, Fotimes f)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in a family, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is of the level &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$q^2$&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 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 2","pages":"316-342"},"PeriodicalIF":0.8,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140188","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 weighted eigenvalue problem for mixed local and nonlocal operators with potential","authors":"Radhakrishnan Lakshmi,&nbsp;Ratan Kr. Giri,&nbsp;Sekhar Ghosh","doi":"10.1002/mana.70093","DOIUrl":"https://doi.org/10.1002/mana.70093","url":null,"abstract":"<p>We study an <i>indefinite weighted eigenvalue problem</i> for an operator of <i>mixed-type</i> (that includes both the classical <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math><i>-Laplacian</i> and the <i>fractional</i> <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math><i>-Laplacian</i>) in a bounded open subset <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Omega subset mathbb {R}^N ,(Nge 2)$</annotation>\u0000 </semantics></math> with <i>Lipschitz boundary</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 </mrow>\u0000 <annotation>$partial Omega$</annotation>\u0000 </semantics></math>, which is given by\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 2","pages":"367-396"},"PeriodicalIF":0.8,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146140190","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":"Geometric logarithmic Hardy and Hardy–Poincaré inequalities on stratified groups","authors":"Marianna Chatzakou","doi":"10.1002/mana.70097","DOIUrl":"https://doi.org/10.1002/mana.70097","url":null,"abstract":"&lt;p&gt;We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any open set &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Msubset {mathbb {G}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a stratified group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathbb {G}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, provided the validity of the Hardy inequality in this setting, where the so-called “weight” is regarded to be any measurable nonnegative function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;w&lt;/mi&gt;\u0000 &lt;annotation&gt;$w$&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;M&lt;/mi&gt;\u0000 &lt;annotation&gt;$M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Provided the legitimacy of the latter for some &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;w&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M,w$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we also show an inequality that is an extension of the ‘generalized Poincaré inequality’ introduced by Beckner with the addition of the weight &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;w&lt;/mi&gt;\u0000 &lt;annotation&gt;$w$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and this is referred to as the “geometric Hardy-Poincaré inequality.” The aforesaid inequalities become explicit in the case where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M={mathbb {G}}^{+}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the half-space of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathbb {G}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;w&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;dist&lt;/mtext&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$w(cdot)={text{dist}(cdot,partial mathbb {G}^","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"248-269"},"PeriodicalIF":0.8,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941803","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":"Large-time behavior in a two-species chemotaxis-competition system with nonlocal nonlinear growth terms","authors":"Zhan Jiao,&nbsp;Irena Jadlovská,&nbsp;Tongxing Li","doi":"10.1002/mana.70041","DOIUrl":"https://doi.org/10.1002/mana.70041","url":null,"abstract":"<p>This paper deals with a two-species chemotaxis-competition system in a setting that not only accounts for a class of nonlinear variants of the chemotactic cross-diffusion processes, but also involves an external source describing a superlinear growth effect under nonlocal resource consumption. Apart from that, the considered chemoattractant is assumed to be produced according to a fairly general power law. We first confirm the global existence and boundedness of classical solutions to an associated Neumann initial-boundary value problem under some appropriate parameter conditions. Moreover, it is shown that these global bounded solutions converge to the spatially homogeneous coexistence state as time tends to infinity.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"5-34"},"PeriodicalIF":0.8,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941806","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":"Families of singular algebraic varieties that are rationally elliptic spaces","authors":"A. Libgober","doi":"10.1002/mana.70092","DOIUrl":"https://doi.org/10.1002/mana.70092","url":null,"abstract":"<p>We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy types with all hypersurfaces having a nef canonical or anti-canonical class. In the Appendix, we show that such an infinite family of smooth rationally elliptic 3-folds does not exist.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 1","pages":"214-223"},"PeriodicalIF":0.8,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941830","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}