{"title":"Monotone versus non-monotone projective operators","authors":"J. P. Aguilera, P. D. Welch","doi":"10.1112/blms.13194","DOIUrl":"https://doi.org/10.1112/blms.13194","url":null,"abstract":"<p>For a class of operators <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>, let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>Γ</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|Gamma |$</annotation>\u0000 </semantics></math> denote the closure ordinal of <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>-inductive definitions. We give upper bounds on the values of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <msubsup>\u0000 <mi>Σ</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mi>o</mi>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$|Sigma ^{1,mon}_{2n+1}|$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <msubsup>\u0000 <mi>Π</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mi>o</mi>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$|Pi ^{1,mon}_{2n+2}|$</annotation>\u0000 </semantics></math> under the assumption that all projective sets of reals are determined, significantly improving the known results. In particular, the bounds show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <msubsup>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"256-264"},"PeriodicalIF":0.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143115892","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":"Algebraically overtwisted tight 3-manifolds from \u0000 \u0000 \u0000 +\u0000 1\u0000 \u0000 $+1$\u0000 surgeries","authors":"Youlin Li, Zhengyi Zhou","doi":"10.1112/blms.13211","DOIUrl":"https://doi.org/10.1112/blms.13211","url":null,"abstract":"<p>We execute Avdek's algorithm to find many algebraically overtwisted and tight 3-manifolds by contact <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$+1$</annotation>\u0000 </semantics></math> surgeries. In particular, we show that a contact <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$1/k$</annotation>\u0000 </semantics></math> surgery on the standard contact 3-sphere along any Legendrian positive torus knot with the maximal Thurston–Bennequin invariant yields an algebraically overtwisted and tight 3-manifold, where <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> is a positive integer.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"534-550"},"PeriodicalIF":0.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362383","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":"The master relation for polynomiality and equivalences of integrable systems","authors":"Xavier Blot, Adrien Sauvaget, Sergey Shadrin","doi":"10.1112/blms.13215","DOIUrl":"https://doi.org/10.1112/blms.13215","url":null,"abstract":"<p>We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin–Zhang hierarchies associated to different versions of cohomological field theories as well as their equivalences to the corresponding double ramification hierarchies.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"599-604"},"PeriodicalIF":0.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13215","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143363079","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 infinite Dyson Brownian motion with \u0000 \u0000 \u0000 β\u0000 =\u0000 2\u0000 \u0000 $beta =2$\u0000 does not have a spectral gap","authors":"Kohei Suzuki","doi":"10.1112/blms.13204","DOIUrl":"https://doi.org/10.1112/blms.13204","url":null,"abstract":"<p>We prove that the Dirichlet forms associated with the unlabelled infinite Dyson Brownian motion with the inverse temperature <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$beta =2$</annotation>\u0000 </semantics></math> do not have a spectral gap.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"426-431"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13204","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362337","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":"Constructions of superabundant tropical curves in higher genus","authors":"Sae Koyama","doi":"10.1112/blms.13209","DOIUrl":"https://doi.org/10.1112/blms.13209","url":null,"abstract":"<p>We construct qualitatively new examples of superabundant tropical curves which are non-realisable in genuses 3 and 4. These curves are in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>${mathbb {R}}^3$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>${mathbb {R}}^4$</annotation>\u0000 </semantics></math>, respectively, and have properties resembling canonical embeddings of genus 3 and 4 algebraic curves. In particular, the genus 3 example is a degree 4 planar tropical curve, and the genus 4 example is contained in the product of a tropical line and a tropical conic. They have excess dimension of deformation space equal to 1. Non-realisability follows by combining this with a dimension calculation for the corresponding space of logarithmic curves.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"490-509"},"PeriodicalIF":0.8,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143363043","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}
Ruth Charney, Matthew Cordes, Antoine Goldsborough, Alessandro Sisto, Stefanie Zbinden
{"title":"(Non-)existence of Cannon–Thurston maps for Morse boundaries","authors":"Ruth Charney, Matthew Cordes, Antoine Goldsborough, Alessandro Sisto, Stefanie Zbinden","doi":"10.1112/blms.13207","DOIUrl":"https://doi.org/10.1112/blms.13207","url":null,"abstract":"<p>We show that the Morse boundary exhibits interesting examples of both the existence and non-existence of Cannon–Thurston maps for normal subgroups, in contrast with the hyperbolic case.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"463-471"},"PeriodicalIF":0.8,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143363042","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":"Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities","authors":"Bogdan-Vasile Matioc, Christoph Walker","doi":"10.1112/blms.13206","DOIUrl":"https://doi.org/10.1112/blms.13206","url":null,"abstract":"<p>It is shown that semilinear parabolic evolution equations <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>u</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <mi>A</mi>\u0000 <mi>u</mi>\u0000 <mo>+</mo>\u0000 <mi>f</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$u^{prime }=Au+f(t,u)$</annotation>\u0000 </semantics></math> featuring Hölder continuous nonlinearities <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ f=f(t,u)$</annotation>\u0000 </semantics></math> with at most linear growth possess global strong solutions for a general class of initial data. The abstract results are applied to a recent model describing front propagation in bushfires and in the context of a reaction–diffusion system.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"444-462"},"PeriodicalIF":0.8,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Octonionic Hahn–Banach theorem for para-linear functionals","authors":"Qinghai Huo, Guangbin Ren","doi":"10.1112/blms.13208","DOIUrl":"https://doi.org/10.1112/blms.13208","url":null,"abstract":"<p>Goldstine and Horwitz introduced the octonionic Hilbert space in 1964, sparking extensive research into octonionic linear operators. A recent discovery unveiled a significant characteristic of octonionic Hilbert spaces: an axiom, once deemed insurmountable, has been found not to be independent of other axioms. This discovery gives rise to a novel concept known as octonionic para-linear functionals. The purpose of this paper is to establish the octonionic Hahn–Banach theorem for para-linear functionals. Due to the non-associativity, the submodule generalized by an element <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$xin X$</annotation>\u0000 </semantics></math> is no longer of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>O</mi>\u0000 <mo>{</mo>\u0000 <mi>x</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {O}lbrace xrbrace$</annotation>\u0000 </semantics></math>. This phenomenon makes it difficult to apply the octonionic Hahn–Banach theorem if the theorem holds only for functionals defined on octonionic submodules. In this paper, we introduce a notion of <i>para-linear functionals on real subspaces</i> and establish the octonionic Hahn–Banach theorem for such functionals. Then we apply it to obtain some valuable corollaries and discuss the reflexivity of Banach <span></span><math>\u0000 <semantics>\u0000 <mi>O</mi>\u0000 <annotation>$mathbb {O}$</annotation>\u0000 </semantics></math>-modules.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"472-489"},"PeriodicalIF":0.8,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The sparse circular law, revisited","authors":"Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney","doi":"10.1112/blms.13199","DOIUrl":"https://doi.org/10.1112/blms.13199","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$A_n$</annotation>\u0000 </semantics></math> be an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>×</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$ntimes n$</annotation>\u0000 </semantics></math> matrix with iid entries distributed as Bernoulli random variables with parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$p = p_n$</annotation>\u0000 </semantics></math>. Rudelson and Tikhomirov, in a beautiful and celebrated paper, show that the distribution of eigenvalues of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>·</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$A_n cdot (pn)^{-1/2}$</annotation>\u0000 </semantics></math> is approximately uniform on the unit disk as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math> as long as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$pn rightarrow infty$</annotation>\u0000 </semantics></math>, which is the natural necessary condition. In this paper, we give a much simpler proof of this result, in its full generality, using a perspective we developed in our recent proof of the existence of the limiting spectral law when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mi>n</mi>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"330-358"},"PeriodicalIF":0.8,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362894","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
