Acta Mathematica Sinica-English Series最新文献_第8页

Variable Degeneracy of Planar Graphs without Chorded 6-Cycles 无弦 6 循环平面图的可变退化性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2245-8

Hui Hui Fang, Dan Jun Huang, Tao Wang, Wei Fan Wang

{"title":"Variable Degeneracy of Planar Graphs without Chorded 6-Cycles","authors":"Hui Hui Fang, Dan Jun Huang, Tao Wang, Wei Fan Wang","doi":"10.1007/s10114-024-2245-8","DOIUrl":"10.1007/s10114-024-2245-8","url":null,"abstract":"<div>A cover of a graph G is a graph H with vertex set V (H) = ∪v∈V(G) Lv, where Lv = {v} × [s], and the edge set M = ∪uv∈E(G) Muv, where Muv is a matching between Lu and Lv. A vertex set T ⊆ V (H) is a transversal of H if ∣T ∩ Lv∣ = 1 for each v ∈ V(G). Let f be a nonnegative integer valued function on the vertex-set of H. If for any nonempty subgraph Γ of H[T], there exists a vertex x ∈ V (H) such that d(x) < f(x), then T is called a strictly f-degenerate transversal. In this paper, we give a sufficient condition for the existence of strictly f-degenerate transversal for planar graphs without chorded 6-cycles. As a consequence, every planar graph without subgraphs isomorphic to the configurations is DP-4-colorable.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2735 - 2750"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694744","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}

引用次数: 0

On the Centralizers of Rescaling Separating Differentiable Vector Fields 论重缩分微分矢量场的中心点

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3170-6

Bo Han, Xiao Wen

{"title":"On the Centralizers of Rescaling Separating Differentiable Vector Fields","authors":"Bo Han, Xiao Wen","doi":"10.1007/s10114-024-3170-6","DOIUrl":"10.1007/s10114-024-3170-6","url":null,"abstract":"<div>In this paper, we introduce a new concept of expansiveness, similar to the separating property. Specifically, we consider a compact Riemannian manifold M without boundary and a C1 vector field X on M, which generates a flow φt on M. We say that X is rescaling separating on a compact invariant set Λ of X if there is a constant δ > 0 such that, for any x, y ∈ Λ, if d(φt(x), φt(y)) ≤ δ∥X (φt(x))∥ for all t ∈ ℝ, then y ∈ Orb(x). We prove that if X is rescaling separating on Λ and every singularity of X in Λ is hyperbolic, then any C1 vector field Y, whose flow commutes with φt on Λ, must be collinear to X on Λ. As applications of this result, we show that the centralizer of a rescaling separating C1 vector field without nonhyperbolic singularity is quasi-trivial. We also proved that there is an open and dense set ({cal U} subset {{cal X}^{1}}(M)) such that for any star vector field (X in {cal U}), the centralizer of X is collinear to X on the chain recurrent set of X.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2671 - 2683"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694743","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}

引用次数: 0

The Scattered Range Problem of Elementary Operators on ({cal B}({cal H})) 初等算子在({cal B}({cal H}))上的散射范围问题

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3346-0

Peng Cao, Cun Wang

引用次数: 0

A Weak ∞-Functor in Morse Theory 莫尔斯理论中的弱∞矢量

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2523-5

Shan Zhong Sun, Chen Xi Wang

引用次数: 0

Characterizations of Weighted Besov Spaces with Variable Exponents 具有可变指数的加权贝索夫空间的特征

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2623-2

Sheng Rong Wang, Peng Fei Guo, Jing Shi Xu

引用次数: 0

Compactness of Extremals for Trudinger-Moser Functionals on the Unit Ball in ℝ2 ℝ2中单位球上特鲁丁格-莫泽函数极值的紧凑性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3046-9

Wei Wei Shan, Xiao Meng Li

{"title":"Compactness of Extremals for Trudinger-Moser Functionals on the Unit Ball in ℝ2","authors":"Wei Wei Shan, Xiao Meng Li","doi":"10.1007/s10114-024-3046-9","DOIUrl":"10.1007/s10114-024-3046-9","url":null,"abstract":"<div>Let (mathbb{B}) be a unit ball in ℝ2, (W_{0}^{1,2}(mathbb{B})) be the standard Sobolev space. For any ϵ > 0, de Figueiredo, do Ó, dos Santons, Yang and Zhu proved the existence of extremals of a Trudinger-Moser inequality in the unit ball. Precisely, <div><div>$$mathop {sup }limits_{u in W_0^{1,2}left( mathbb{B} right),int_mathbb{B} {|nabla u{|^2}dx le 1} } int_mathbb{B} {{{left| x right|}^{2epsilon }}{rm{e}^{4pi left( {1 + epsilon } right){u^2}}}} dx$$</div></div> can be attained by some radially symmetric function (u_{epsilon}in W_{0}^{1,2}(mathbb{B})) with (int_{mathbb{B}}vertnabla u_{epsilon}vert^{2}dx=1). In this note, we concern the compactness of the function family {uϵ}ϵ>0 and prove that up to a subsequence uϵ converges to some function u\u00000 in (C^{1}(overline{mathbb{B}})) as ϵ → 0. Furthermore, u0 is an extremal function of the supremum <div><div>$$mathop {sup }limits_{u in W_0^{1,2}left( mathbb{B} right),int_mathbb{B} {|nabla u{|^2}dx le 1} } int_{mathbb{B}}rm{e}^{4pi u^{2}}dx.$$</div></div> Let us explain the result in geometry. Denote (omega_{0}=dx_{1}^{2}+dx_{2}^{2}) be the standard Euclidean metric. Define a conical metric (omega_{epsilon}=vert xvert^{2epsilon}omega_{0}) for (xinmathbb{B}). Then the extremal family {u\u0000ϵ}ϵ>0 of the following Trudinger-Moser functionals <div><div>$$int_{mathbb{B}}rm{e}^{4pi(1+epsilon)u^{2}}dv_{w_{epsilon}}$$</div></div> under the constraint (uin W_{0}^{1,2}(mathbb{B})) and (int_{mathbb{B}}vertnabla_{omega_{epsilon}u}vert^{2}dv_{omega_{epsilon}}leq 1) is compact as ϵ → 0.</div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2840 - 2854"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694742","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}

引用次数: 0

On pj-rank of Even K-groups of Rings of Integers 论整数环偶数 K 群的 pj 级

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-10-15 DOI: 10.1007/s10114-024-1312-5

Meng Fai Lim

引用次数: 0

Completeness of Induced Cotorsion Pairs in Representation Categories of Rooted Quivers 有根四元组表示范畴中诱导共旋对的完备性

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-07-18 DOI: 10.1007/s10114-024-3041-1

Zhen Xing Di, Li Ping Li, Li Liang, Fei Xu

引用次数: 0

On Some Sums Involving Small Arithmetic Functions 论涉及小算术函数的一些和

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-07-18 DOI: 10.1007/s10114-024-2129-y

Wen Guang Zhai

引用次数: 0

Supnorm Estimates for ({bar partial}) on Product Domains in ℂn ℂn中积域上$${bar partial}$ 的超矩形估计值

IF 0.8 3区数学

Acta Mathematica Sinica-English Series Pub Date : 2024-07-18 DOI: 10.1007/s10114-024-2463-0

Martino Fassina, Yi Fei Pan

引用次数: 0