Mathematische Nachrichten最新文献

{"title":"On non-Hopf Ricci-pseudosymmetric hypersurfaces in \u0000 \u0000 \u0000 C\u0000 \u0000 P\u0000 2\u0000 \u0000 \u0000 $mathbb {C}P^{2}$\u0000 and \u0000 \u0000 \u0000 C\u0000 \u0000 H\u0000 2\u0000 \u0000 \u0000 $mathbb {C}H^{2}$","authors":"Qianshun Cui,&nbsp;Zejun Hu","doi":"10.1002/mana.202300463","DOIUrl":"https://doi.org/10.1002/mana.202300463","url":null,"abstract":"<p>In this paper, we study an open problem raised by Cecil and Ryan [<i>Geometry of Hypersurfaces</i>, Springer Monographs in Mathematics, p. 531] which asked whether there exist non-Hopf Ricci-pseudosymmetric hypersurfaces in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}P^{2}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}H^{2}$</annotation>\u0000 </semantics></math>. As our main results, we first prove the nonexistence of non-Hopf Ricci-pseudosymmetric hypersurfaces of the constant type in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}H^{2}$</annotation>\u0000 </semantics></math>. Then, we prove the existence of non-Hopf Ricci-pseudosymmetric hypersurfaces of the constant type in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}P^{2}$</annotation>\u0000 </semantics></math>. Finally, applying the preceding results and sharpening Theorem 4.1 of Wang and Zhang [<i>J. Geom. Phys</i>. <b>181</b> (2022), 104648], we prove the nonexistence of non-Hopf weakly Einstein hypersurfaces with constant norm of Riemannian curvature tensor in both <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}P^{2}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {C}H^{2}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"527-547"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397235","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":"Construction of the log-convex minorant of a sequence \u0000 \u0000 \u0000 \u0000 {\u0000 \u0000 M\u0000 α\u0000 \u0000 }\u0000 \u0000 \u0000 α\u0000 ∈\u0000 \u0000 N\u0000 0\u0000 d\u0000 \u0000 \u0000 \u0000 $lbrace M_alpha rbrace _{alpha in mathbb {N}_0^d}$","authors":"Chiara Boiti,&nbsp;David Jornet,&nbsp;Alessandro Oliaro,&nbsp;Gerhard Schindl","doi":"10.1002/mana.202400135","DOIUrl":"https://doi.org/10.1002/mana.202400135","url":null,"abstract":"&lt;p&gt;We give a simple construction of the log-convex minorant of a sequence &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;M&lt;/mi&gt;\u0000 &lt;mi&gt;α&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;α&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$lbrace M_alpha rbrace _{alpha in mathbb {N}_0^d}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and consequently extend to the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;annotation&gt;$d$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional case the well-known formula that relates a log-convex sequence &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;M&lt;/mi&gt;\u0000 &lt;mi&gt;p&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;p&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$lbrace M_prbrace _{pin mathbb {N}_0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to its associated function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$omega _M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, that is, &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;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;sup&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;exp&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;m","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"456-477"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397231","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":"Partitions in real quadratic fields","authors":"David Stern,&nbsp;Mikuláš Zindulka","doi":"10.1002/mana.202300480","DOIUrl":"https://doi.org/10.1002/mana.202300480","url":null,"abstract":"<p>We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such that there exists an element with exactly 1–5, 7, and 11 partitions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"548-566"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300480","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397242","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":"Curvature of quaternionic skew-Hermitian manifolds and bundle constructions","authors":"Ioannis Chrysikos,&nbsp;Vicente Cortés,&nbsp;Jan Gregorovič","doi":"10.1002/mana.202400301","DOIUrl":"https://doi.org/10.1002/mana.202400301","url":null,"abstract":"<p>This paper is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Hermitian manifolds <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M, Q, omega)$</annotation>\u0000 </semantics></math>. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic connections and we study qualitative properties of the induced Ricci tensor. Then, we proceed with bundle constructions over such a manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M, Q, omega)$</annotation>\u0000 </semantics></math>. In particular, we prove the existence of almost hypercomplex skew-Hermitian structures on the Swann bundle over <i>M</i> and investigate their integrability.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"87-112"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400301","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120095","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":"Laplacian with singular drift in a critical borderline case","authors":"D. Kinzebulatov","doi":"10.1002/mana.202400098","DOIUrl":"https://doi.org/10.1002/mana.202400098","url":null,"abstract":"<p>We establish well-posedness and regularity results for parabolic diffusion equation on the torus in the case when the singularities of a general drift reach the critical magnitude. The latter dictates the need to work in an Orlicz space situated between all <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"511-526"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397233","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":"Embedded trace operator for infinite metric trees","authors":"Valentina Franceschi,&nbsp;Kiyan Naderi,&nbsp;Konstantin Pankrashkin","doi":"10.1002/mana.202300574","DOIUrl":"https://doi.org/10.1002/mana.202300574","url":null,"abstract":"<p>We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using identifications of the tree boundary with a surface. Our approach unifies some constructions proposed by Maury, Salort, and Vannier for discrete weighted dyadic trees (expansion in orthogonal bases of harmonic functions on the graph and using Haar-type bases on the domain representing the boundary), and by Nicaise and Semin and Joly, Kachanovska, and Semin for fractal metric trees (approximation by finite sections and identification of the boundary with a interval): We show that both machineries give the same trace map, and for a range of parameters we establish the precise Sobolev regularity of the traces. In addition, we introduce new geometric ingredients by proposing an identification with arbitrary Riemannian manifolds. It is shown that any compact manifold admits a suitable multiscale decomposition and, therefore, can be identified with a metric tree boundary in the context of trace theorems.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"190-243"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300574","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120065","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":"The first eigenvalue of one-dimensional elliptic operators with killing","authors":"Kang Dai,&nbsp;Xiaobin Sun,&nbsp;Jian Wang,&nbsp;Yingchao Xie","doi":"10.1002/mana.202400331","DOIUrl":"https://doi.org/10.1002/mana.202400331","url":null,"abstract":"<p>In this paper, we investigate the first eigenvalue for one-dimensional elliptic operators with killing. Two-sided approximation procedures and basic estimates of the first eigenvalue are given in both the half line and the whole line. The proofs are based on the <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-transform, Chen's dual variational formulas, and the split technique. In particular, a few examples are presented to illustrate the power of our results.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"282-311"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120097","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":"Decay character and global existence for weakly coupled system of semilinear \u0000 \u0000 σ\u0000 $sigma$\u0000 -evolution damped equations with time-dependent damping","authors":"Cung The Anh,&nbsp;Phan Duc An,&nbsp;Pham Trieu Duong","doi":"10.1002/mana.202400243","DOIUrl":"https://doi.org/10.1002/mana.202400243","url":null,"abstract":"<p>In this article, we investigate the existence and decay rate of the global solution to the coupled system of semilinear structurally damped <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-evolution equations with time-dependent damping in the so-called effective cases\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"478-510"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397234","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":"Averaging principle on semi-axis for semi-linear differential equations","authors":"David Cheban","doi":"10.1002/mana.202300392","DOIUrl":"https://doi.org/10.1002/mana.202300392","url":null,"abstract":"<p>We establish an averaging principle on the real semi-axis for semi-linear equation\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"156-189"},"PeriodicalIF":0.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118142","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":"Well-posedness and inviscid limits for the Keller–Segel–Navier–Stokes system of the parabolic–elliptic type","authors":"Taiki Takeuchi","doi":"10.1002/mana.202300304","DOIUrl":"https://doi.org/10.1002/mana.202300304","url":null,"abstract":"<p>We show the local well-posedness of the Keller–Segel system of the parabolic–elliptic type coupled with the Navier–Stokes system for arbitrary initial data with Sobolev regularities, where the solution is uniformly bounded with respect to the viscosity. We also show the continuous dependence of the solutions with respect to the initial data. As a result of the uniform boundedness of the solutions, we obtain inviscid limits of the system. The proof is mainly based on a priori estimates in the Sobolev spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"53-86"},"PeriodicalIF":0.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117468","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}