Journal of the London Mathematical Society-Second Series最新文献_第7页

First-order asymptotic perturbation theory for extensions of symmetric operators 对称算子扩展的一阶渐近扰动理论

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-11 DOI: 10.1112/jlms.13005

Yuri Latushkin, Selim Sukhtaiev

{"title":"First-order asymptotic perturbation theory for extensions of symmetric operators","authors":"Yuri Latushkin, Selim Sukhtaiev","doi":"10.1112/jlms.13005","DOIUrl":"https://doi.org/10.1112/jlms.13005","url":null,"abstract":"This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness, we use a version of resolvent difference identity for two arbitrary self-adjoint extensions that facilitates asymptotic analysis of resolvent operators via first-order expansion for the family of Lagrangian planes associated with perturbed operators. Specifically, we derive a Riccati-type differential equation and the first-order asymptotic expansion for resolvents of self-adjoint extensions determined by smooth one-parameter families of Lagrangian planes. This asymptotic perturbation theory yields a symplectic version of the abstract Kato selection theorem and Hadamard–Rellich-type variational formula for slopes of multiple eigenvalue curves bifurcating from an eigenvalue of the unperturbed operator. The latter, in turn, gives a general infinitesimal version of the celebrated formula equating the spectral flow of a path of self-adjoint extensions and the Maslov index of the corresponding path of Lagrangian planes. Applications are given to quantum graphs, periodic Kronig–Penney model, elliptic second-order partial differential operators with Robin boundary conditions, and physically relevant heat equations with thermal conductivity.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429889","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}

引用次数: 0

Codimension two mean curvature flow of entire graphs 整图的二维平均曲率流

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-10 DOI: 10.1112/jlms.13000

Andreas Savas Halilaj, Knut Smoczyk

{"title":"Codimension two mean curvature flow of entire graphs","authors":"Andreas Savas Halilaj, Knut Smoczyk","doi":"10.1112/jlms.13000","DOIUrl":"https://doi.org/10.1112/jlms.13000","url":null,"abstract":"We consider the graphical mean curvature flow of maps <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbf {f}:{mathbb {R}^{m}}rightarrow {mathbb {R}^{n}}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mgeqslant 2$</annotation>\u0000 </semantics></math>, and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbf {f}:{mathbb {R}^{m}} rightarrow {mathbb {R}^{2}}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$mgeqslant 2$</annotation>\u0000 </semantics></math>, we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429928","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}

引用次数: 0

Colouring versus density in integers and Hales–Jewett cubes 整数和黑尔斯-祖耶特立方体中的着色与密度关系

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-10 DOI: 10.1112/jlms.12987

Christian Reiher, Vojtěch Rödl, Marcelo Sales

{"title":"Colouring versus density in integers and Hales–Jewett cubes","authors":"Christian Reiher, Vojtěch Rödl, Marcelo Sales","doi":"10.1112/jlms.12987","DOIUrl":"https://doi.org/10.1112/jlms.12987","url":null,"abstract":"We construct for every integer <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$kgeqslant 3$</annotation>\u0000 </semantics></math> and every real <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>k</mi>\u0000 </mfrac>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mu in (0, frac{k-1}{k})$</annotation>\u0000 </semantics></math> a set of integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mi>X</mi>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>μ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$X=X(k, mu)$</annotation>\u0000 </semantics></math> which, when coloured with finitely many colours, contains a monochromatic <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-term arithmetic progression, whilst every finite <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>⊆</mo>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <annotation>$Ysubseteq X$</annotation>\u0000 </semantics></math> has a subset <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 <mo>⊆</mo>\u0000 <mi>Y</mi>\u0000 </mrow>\u0000 <annotation>$Zsubseteq Y$</annotation>\u0000 </semantics></math> of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>Z</mi>\u0000 <mo>|</mo>\u0000 <mo>⩾</mo>\u0000 <mi>μ</mi>\u0000 <mo>|</mo>\u0000 <mi>Y</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|Z|geqslant mu |Y|$</annotation>\u0000 </semantics></math> that is free of arithmetic progressions of length <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>. T","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 5","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12987","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429927","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}

引用次数: 0

Least energy solutions for a class of ( p 1 , p 2 ) $(p_{1}, p_{2})$ -Kirchhoff-type problems in R N $mathbb {R}^{N}$ with general nonlinearities 具有一般非线性的 R N $mathbb {R}^{N}$ 中一类 ( p 1 , p 2 ) $(p_{1}, p_{2})$ -Kirchhoff-type 问题的最小能量解法

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-07 DOI: 10.1112/jlms.13004

Vincenzo Ambrosio

{"title":"Least energy solutions for a class of \u0000 \u0000 \u0000 (\u0000 \u0000 p\u0000 1\u0000 \u0000 ,\u0000 \u0000 p\u0000 2\u0000 \u0000 )\u0000 \u0000 $(p_{1}, p_{2})$\u0000 -Kirchhoff-type problems in \u0000 \u0000 \u0000 R\u0000 N\u0000 \u0000 $mathbb {R}^{N}$\u0000 with general nonlinearities","authors":"Vincenzo Ambrosio","doi":"10.1112/jlms.13004","DOIUrl":"https://doi.org/10.1112/jlms.13004","url":null,"abstract":"We examine the following <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>p</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p_{1}, p_{2})$</annotation>\u0000 </semantics></math>-Kirchhoff-type problem:\u0000\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429514","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}

引用次数: 0

The excedance quotient of the Bruhat order, quasisymmetric varieties, and Temperley–Lieb algebras 布鲁哈特阶的赋形商、准对称品种和滕伯里-里布代数

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-07 DOI: 10.1112/jlms.13007

Nantel Bergeron, Lucas Gagnon

{"title":"The excedance quotient of the Bruhat order, quasisymmetric varieties, and Temperley–Lieb algebras","authors":"Nantel Bergeron, Lucas Gagnon","doi":"10.1112/jlms.13007","DOIUrl":"https://doi.org/10.1112/jlms.13007","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>Q</mi>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$R_n=mathbb {Q}[x_1,x_2,ldots ,x_n]$</annotation>\u0000 </semantics></math> be the ring of polynomials in <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> variables and consider the ideal <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msubsup>\u0000 <mi>QSym</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mo>⊆</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$langle mathrm{QSym}_{n}^{+}rangle subseteq R_n$</annotation>\u0000 </semantics></math> generated by quasisymmetric polynomials without constant term. It was shown by J. C. Aval, F. Bergeron, and N. Bergeron that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <msubsup>\u0000 <mi>QSym</mi>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <mo>⟩</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429515","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}

引用次数: 0

The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform 具有可逆射线变换的流形上大固定频率的各向异性卡尔德龙问题

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-05 DOI: 10.1112/jlms.13006

Shiqi Ma, Suman Kumar Sahoo, Mikko Salo

引用次数: 0

Projective structures with (Quasi-)Hitchin holonomy 具有（准）希钦整体性的投影结构

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-30 DOI: 10.1112/jlms.13003

Daniele Alessandrini, Colin Davalo, Qiongling Li

引用次数: 0

Small-scale distribution of linear patterns of primes 素数线性模式的小范围分布

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-30 DOI: 10.1112/jlms.13001

Mayank Pandey, Katharine Woo

{"title":"Small-scale distribution of linear patterns of primes","authors":"Mayank Pandey, Katharine Woo","doi":"10.1112/jlms.13001","DOIUrl":"https://doi.org/10.1112/jlms.13001","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 <mo>=</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ψ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>⋯</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>ψ</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>:</mo>\u0000 <mo>`</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>t</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Psi =(psi _1,hdots, psi _t):`mathbb {Z}^drightarrow mathbb {R}^t$</annotation>\u0000 </semantics></math> be a system of linear forms with finite complexity. In their seminal paper, Green and Tao showed the following prime number theorem for values of the system <math>\u0000 <semantics>\u0000 <mi>Ψ</mi>\u0000 <annotation>$Psi$</annotation>\u0000 </semantics></math>:\u0000\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.13001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359981","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}

引用次数: 0

Novel non-involutive solutions of the Yang–Baxter equation from (skew) braces 杨-巴克斯特方程的新颖非卷积解来自（倾斜）括号

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-30 DOI: 10.1112/jlms.12999

Anastasia Doikou, Bernard Rybołowicz

{"title":"Novel non-involutive solutions of the Yang–Baxter equation from (skew) braces","authors":"Anastasia Doikou, Bernard Rybołowicz","doi":"10.1112/jlms.12999","DOIUrl":"https://doi.org/10.1112/jlms.12999","url":null,"abstract":"We produce novel non-involutive solutions of the Yang–Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces, they are not necessarily involutive. In the case of two-sided (skew) braces, one can assign such solutions to every element of the set. Novel bijective maps associated to the inverse solutions are also introduced. Moreover, we show that the recently derived Drinfeld twists of the involutive case are still admissible in the non-involutive frame, and we identify the twisted <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-matrices and twisted coproducts. We observe, as in the involutive case, that the underlying quantum algebra is not a quasi-triangular bialgebra, as one would expect, but a quasi-triangular quasi-bialgebra. The same applies to the quantum algebra of the twisted <math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-matrices, contrary to the involutive case.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12999","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359835","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}

引用次数: 0

Automorphism groups of cubic fivefolds and fourfolds 立方五折和四折的自形群

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-27 DOI: 10.1112/jlms.12997

Song Yang, Xun Yu, Zigang Zhu

引用次数: 0