Israel Journal of Mathematics最新文献_第5页

Modulus of continuity for spectral measures of suspension flows over Salem type substitutions 萨伦型置换悬浮流谱测量的连续性模量

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2630-0

Juan Marshall-Maldonado

引用次数: 0

Integrals of groups. II 群的积分二

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2610-4

João Araújo, Peter J. Cameron, Carlo Casolo, Francesco Matucci, Claudio Quadrelli

{"title":"Integrals of groups. II","authors":"João Araújo, Peter J. Cameron, Carlo Casolo, Francesco Matucci, Claudio Quadrelli","doi":"10.1007/s11856-024-2610-4","DOIUrl":"https://doi.org/10.1007/s11856-024-2610-4","url":null,"abstract":"An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G. This paper continues the investigation on integrals of groups started in the work [1]. We study:\u0000<ul>\u0000<li>\u0000A sufficient condition for a bound on the order of an integral for a finite integrable group (Theorem 2.1) and a necessary condition for a group to be integrable (Theorem 3.2).\u0000</li>\u0000<li>\u0000The existence of integrals that are p-groups for abelian p-groups, and of nilpotent integrals for all abelian groups (Theorem 4.1).\u0000</li>\u0000<li>\u0000Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups (Section 5).\u0000</li>\u0000<li>\u0000The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class (Sections 6 and 7).\u0000</li>\u0000<li>\u0000Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups (Section 8.1).\u0000</li>\u0000<li>\u0000Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral (Section 8.2).\u0000</li>\u0000</ul>We end the paper with a number of open problems.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799690","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

Centrality of K2 for Chevalley groups: a pro-group approach 切瓦利组的 K2 中心性：一种支持组的方法

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2608-y

Andrei Lavrenov, Sergey Sinchuk, Egor Voronetsky

引用次数: 0

A quick estimate for the volume of a polyhedron 快速估算多面体的体积

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2615-z

Alexander Barvinok, Mark Rudelson

引用次数: 0

Ramsey numbers of sparse digraphs 稀疏图的拉姆齐数

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2624-y

Jacob Fox, Xiaoyu He, Yuval Wigderson

{"title":"Ramsey numbers of sparse digraphs","authors":"Jacob Fox, Xiaoyu He, Yuval Wigderson","doi":"10.1007/s11856-024-2624-y","DOIUrl":"https://doi.org/10.1007/s11856-024-2624-y","url":null,"abstract":"Burr and Erdős in 1975 conjectured, and Chvátal, Rödl, Szemerédi and Trotter later proved, that the Ramsey number of any bounded degree graph is linear in the number of vertices. In this paper, we disprove the natural directed analogue of the Burr–Erdős conjecture, answering a question of Bucić, Letzter, and Sudakov. If H is an acyclic digraph, the oriented Ramsey number of H, denoted (overrightarrow {{r_1}} (H)), is the least N such that every tournament on N vertices contains a copy of H. We show that for any Δ ≥ 2 and any sufficiently large n, there exists an acyclic digraph H with n vertices and maximum degree Δ such that $$overrightarrow {{r_1}} (H) ge {n^{Omega ({Delta ^{2/3}}/{{log }^{5/3}},Delta )}}.$$This proves that (overrightarrow {{r_1}} (H)) is not always linear in the number of vertices for bounded-degree H. On the other hand, we show that (overrightarrow {{r_1}} (H)) is nearly linear in the number of vertices for typical bounded-degree acyclic digraphs H, and obtain linear or nearly linear bounds for several natural families of bounded-degree acyclic digraphs.For multiple colors, we prove a quasi-polynomial upper bound (overrightarrow {{r_k}} (H) = {2^{{{(log ,n)}^{{O_k}(1)}}}}) for all bounded-de gree acyclic digraphs H on n vertices, where (overrightarrow {{r_k}} (H)) is the least N such that every k-edge-colored tournament on N vertices contains a monochromatic copy of H. For k ≥ 2 and n ≥ 4, we exhibit an acyclic digraph H with n vertices and maximum degree 3 such that (overrightarrow {{r_k}} (H) ge {n^{Omega (log ,n/log log ,n)}}), showing that these Ramsey numbers can grow faster than any polynomial in the number of vertices.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809690","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

Complex Hanner’s inequality for many functions 许多函数的复数汉纳不等式

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2616-y

Jonathan Jenkins, Tomasz Tkocz

引用次数: 0

Complete infinite-time mass aggregation in a quasilinear Keller–Segel system 准线性凯勒-西格尔系统中的完全无限时质量聚集

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2618-9

Michael Winkler

{"title":"Complete infinite-time mass aggregation in a quasilinear Keller–Segel system","authors":"Michael Winkler","doi":"10.1007/s11856-024-2618-9","DOIUrl":"https://doi.org/10.1007/s11856-024-2618-9","url":null,"abstract":"Radially symmetric global unbounded solutions of the chemotaxis system $$left{ {matrix{{{u_t} = nabla cdot (D(u)nabla u) - nabla cdot (uS(u)nabla v),} hfill & {} hfill cr {0 = Delta v - mu + u,} hfill & {mu = {1 over {|Omega |}}int_Omega {u,} } hfill cr } } right.$$ are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0.Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling (m + lambda < 1 - {2 over n}), a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying $${1 over C} cdot {(t + 1)^{{1 over lambda }}} le ||u( cdot ,t)|{|_{{L^infty }(Omega )}} le C cdot {(t + 1)^{{1 over lambda }}},,,{rm{for}},,{rm{all}},,t > 0$$ as well as $$||u( cdot ,,t)|{|_{{L^1}(Omega backslash {B_{{r_0}}}(0))}} to 0,,,{rm{as}},,t to infty ,,,{rm{for}},,{rm{all}},,{r_0} in (0,R)$$ with some C > 0.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885008","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

A quantitative Neumann lemma for finitely generated groups 有限生成群的定量诺依曼定理

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2617-x

Elia Gorokhovsky, Nicolás Matte Bon, Omer Tamuz

引用次数: 0

Sparse reconstruction in spin systems. I: iid spins 自旋系统中的稀疏重构。I: iid 自旋

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2606-0

Pál Galicza, Gábor Pete

引用次数: 0

Multiplicative arithmetic functions and the generalized Ewens measure 乘法算术函数和广义尤文斯量度

IF 1 2区数学

Israel Journal of Mathematics Pub Date : 2024-04-24 DOI: 10.1007/s11856-024-2609-x

Dor Elboim, Ofir Gorodetsky

{"title":"Multiplicative arithmetic functions and the generalized Ewens measure","authors":"Dor Elboim, Ofir Gorodetsky","doi":"10.1007/s11856-024-2609-x","DOIUrl":"https://doi.org/10.1007/s11856-024-2609-x","url":null,"abstract":"Random integers, sampled uniformly from [1, x], share similarities with random permutations, sampled uniformly from Sn. These similarities include the Erdős–Kac theorem on the distribution of the number of prime factors of a random integer, and Billingsley’s theorem on the largest prime factors of a random integer. In this paper we extend this analogy to non-uniform distributions.Given a multiplicative function α: ℕ → ℝ≥0, one may associate with it a measure on the integers in [1, x], where n is sampled with probability proportional to the value α(n). Analogously, given a sequence {θi}i≥1 of non-negative reals, one may associate with it a measure on Sn that assigns to a permutation a probability proportional to a product of weights over the cycles of the permutation. This measure is known as the generalized Ewens measure.We study the case where the mean value of α over primes tends to some positive θ, as well as the weights α(p) ≈ (log p)γ. In both cases, we obtain results in the integer setting which are in agreement with those in the permutation setting.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799580","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