Journal of the London Mathematical Society-Second Series最新文献

{"title":"Twisted rational zeros of linear recurrence sequences","authors":"Yuri Bilu,&nbsp;Florian Luca,&nbsp;Joris Nieuwveld,&nbsp;Joël Ouaknine,&nbsp;James Worrell","doi":"10.1112/jlms.70126","DOIUrl":"https://doi.org/10.1112/jlms.70126","url":null,"abstract":"<p>We introduce the notion of a twisted rational zero of a nondegenerate linear recurrence sequence (LRS). We show that any nondegenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$1/3$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>5</mn>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$-5/3$</annotation>\u0000 </semantics></math> are the only twisted rational zeros that are not integral zeros.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70126","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lipschitz decompositions of domains with bilaterally flat boundaries","authors":"Jared Krandel","doi":"10.1112/jlms.70128","DOIUrl":"https://doi.org/10.1112/jlms.70128","url":null,"abstract":"&lt;p&gt;We study classes of domains in &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;R&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {R}^{d+1}, d geqslant 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with sufficiently flat boundaries that admit a decomposition or covering of bounded overlap by Lipschitz graph domains with controlled total surface area. This study is motivated by the following result proved by Peter Jones as a piece of his proof of the Analyst's Traveling Salesman Theorem in the complex plane: Any simply connected domain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Omega subseteq mathbb {C}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with finite boundary length &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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {H}^1(partial Omega) &lt; infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can be decomposed into Lipschitz graph domains with total boundary length at most &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;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Mmathcal {H}^1(partial Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; 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;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M &gt; 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; independent of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70128","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A presentation of the torus-equivariant quantum \u0000 \u0000 K\u0000 $K$\u0000 -theory ring of flag manifolds of type \u0000 \u0000 A\u0000 $A$\u0000 , Part I: The defining ideal","authors":"Toshiaki Maeno,&nbsp;Satoshi Naito,&nbsp;Daisuke Sagaki","doi":"10.1112/jlms.70095","DOIUrl":"https://doi.org/10.1112/jlms.70095","url":null,"abstract":"<p>We give a presentation of the torus-equivariant (small) quantum <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory ring of flag manifolds of type <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, as the quotient of a polynomial ring by an explicit ideal. This result is the torus-equivariant version of our previous one, which gives a presentation of the nonequivariant quantum <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory ring of flag manifolds of type <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>. However, the method of proof for the torus-equivariant one is entirely different from that for the nonequivariant one; our proof is based on the result in the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Q</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$Q = 0$</annotation>\u0000 </semantics></math> limit, and uses Nakayama-type arguments to upgrade it to the quantum situation. Also, in contrast to the nonequivariant case in which we used the Chevalley formula, we make use of the inverse Chevalley formula for the torus-equivariant <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-group of semi-infinite flag manifolds to obtain relations that yield our presentation.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143689171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fully noncentral Lie ideals and invariant additive subgroups in rings","authors":"Eusebio Gardella,&nbsp;Tsiu-Kwen Lee,&nbsp;Hannes Thiel","doi":"10.1112/jlms.70127","DOIUrl":"https://doi.org/10.1112/jlms.70127","url":null,"abstract":"<p>We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≠</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$ne 2$</annotation>\u0000 </semantics></math> where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solvability and uniqueness of solution of generalized \u0000 \u0000 ★\u0000 $star$\u0000 -Sylvester equations with arbitrary coefficients","authors":"Fernando De Terán,&nbsp;Bruno Iannazzo","doi":"10.1112/jlms.70129","DOIUrl":"https://doi.org/10.1112/jlms.70129","url":null,"abstract":"&lt;p&gt;We analyze the consistency and uniqueness of solution of the generalized &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;★&lt;/mi&gt;\u0000 &lt;annotation&gt;$star$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-Sylvester equation &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;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mi&gt;★&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$AXB+CX^star D=E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with &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;B&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$A,B,C, D$&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;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$E$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; being complex matrices (and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;★&lt;/mi&gt;\u0000 &lt;annotation&gt;$star$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; being either the transpose or the conjugate transpose). In particular, we obtain characterizations for the equation to have at most one solution and to be consistent for any right-hand side. Such characterizations are given in terms of spectral properties of the matrix pencils &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mi&gt;★&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;mtd&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mi&gt;★&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;/mtr&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;/mtr&gt;\u0000 &lt;/mtable&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;annotation&gt;$left[begin{smallmatrix}lambda D^star &amp; B^star A &amp; lambda Cend{smallmatrix}right]$&lt;/annota","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shift orbits for elementary representations of Kronecker quivers","authors":"Daniel Bissinger","doi":"10.1112/jlms.70122","DOIUrl":"https://doi.org/10.1112/jlms.70122","url":null,"abstract":"&lt;p&gt;Let &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;msub&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r in mathbb {N}_{geqslant 3}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We denote by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$K_r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; the wild &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;-Kronecker quiver 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; arrows &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;γ&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/msub&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;/mrow&gt;\u0000 &lt;annotation&gt;$gamma _i colon 1 longrightarrow 2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and consider the action of the group &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;G&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mo&gt;Aut&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_r subseteq operatorname{Aut}(mathbb {Z}^2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; generated by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;⟶&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&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;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational stabilization of degenerate \u0000 \u0000 p\u0000 $p$\u0000 -elasticae","authors":"Tatsuya Miura,&nbsp;Kensuke Yoshizawa","doi":"10.1112/jlms.70096","DOIUrl":"https://doi.org/10.1112/jlms.70096","url":null,"abstract":"<p>A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-elasticae. It was known that in the nondegenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$pin (1,2]$</annotation>\u0000 </semantics></math>, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$pin (2,infty)$</annotation>\u0000 </semantics></math> there emerge uncountably many local minimizers with diverging energy.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Size-Ramsey numbers of graphs with maximum degree three","authors":"Nemanja Draganić,&nbsp;Kalina Petrova","doi":"10.1112/jlms.70116","DOIUrl":"https://doi.org/10.1112/jlms.70116","url":null,"abstract":"&lt;p&gt;The size-Ramsey number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$hat{r}(H)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the smallest number of edges a (host) graph &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; can have, such that for any red/blue colouring 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;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, there is a monochromatic copy of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in &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;. Recently, Conlon, Nenadov and Trujić showed that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a graph on &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; vertices and maximum degree three, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;8&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$hat{r}(H) = O(n^{8/5})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, improving upon the upper bound of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70116","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ergodic averages along sequences of slow growth","authors":"Kaitlyn Loyd,&nbsp;Sovanlal Mondal","doi":"10.1112/jlms.70124","DOIUrl":"https://doi.org/10.1112/jlms.70124","url":null,"abstract":"<p>We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math> denotes the number of prime factors of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$ n$</annotation>\u0000 </semantics></math> counted with multiplicities. It was previously shown that a pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> functions does not hold along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. We classify the strength of this divergence by proving a double-logarithmic pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> functions along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. This contrasts the behavior of Khintchine-type averages, for which, under any weaker form of averaging, there exists a bounded measurable function for which almost everywhere convergence fails. Moreover, we show that certain perturbations of increasing subpolynomial sequences fail to satisfy a pointwise ergodic theorem, yielding natural new examples of such sequences.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70124","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Einstein metrics on aligned homogeneous spaces with two factors","authors":"Jorge Lauret,&nbsp;Cynthia Will","doi":"10.1112/jlms.70120","DOIUrl":"https://doi.org/10.1112/jlms.70120","url":null,"abstract":"&lt;p&gt;Given two homogeneous spaces of the form &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;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_1/K$&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;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_2/K$&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;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_1$&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;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are compact simple Lie groups, we study the existence problem for &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;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_1times G_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-invariant Einstein metrics on the homogeneous space &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;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M=G_1times G_2/K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For the large subclass &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;$mathcal {C}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and nonexistence pieces of &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;$mathcal {C}$&lt;/annotation&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}