Advances in Mathematics最新文献

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Diffusion limit with optimal convergence rate of classical solutions to the Vlasov-Maxwell-Boltzmann system Vlasov-Maxwell-Boltzmann系统经典解的最优收敛速率扩散极限

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.aim.2026.110800

Tong Yang , Mingying Zhong

We study the diffusion limit of the classical solution to the Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. By introducing a new decomposition of the solution to identify the essential components for generating the initial layer, we prove the convergence and establish the optimal convergence rate of the classical solution to the VMB system to the solution of the Navier-Stokes-Maxwell system based on the spectral analysis.

研究了初始数据接近全局麦克斯韦线的Vlasov-Maxwell-Boltzmann （VMB）系统经典解的扩散极限。通过引入一种新的解分解来识别生成初始层的基本分量，证明了VMB系统的经典解对基于谱分析的Navier-Stokes-Maxwell系统解的收敛性，并建立了其最优收敛速率。

引用次数: 0

New results in analysis of Orlicz-Lorentz spaces Orlicz-Lorentz空间分析的新结果

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.aim.2026.110808

Luis Bernal-González , Daniel L. Rodríguez-Vidanes , Juan B. Seoane-Sepúlveda , Hyung-Joon Tag

In this article, we investigate the existence of closed vector subspaces (i.e. spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces

Λ_{φ, w}

equipped with the Luxemburg norm. If a family of Orlicz functions

{(φ_{n})}_{n = 1}^{\infty}

satisfies certain order relations with respect to a given Orlicz function φ, the subset of the order-continuous subspace

{(Λ_{φ, w})}_{a}

whose elements do not belong to

⋃_{n = 1}^{\infty} Λ_{φ_{n}, w}

is spaceable, and even maximal-spaceable when φ satisfies the

Δ_{2}

-condition. We also show that this subset is either residual or empty. In addition, sufficient conditions for this subset not being

(α, β)

-spaceable are provided. A similar analysis is also performed on the subset

Λ_{φ, w} ∖ {(Λ_{φ, w})}_{a}

when φ does not satisfy the

Δ_{2}

-condition.

The comparison between different Orlicz-Lorentz spaces is characterized via the generating pairs

(φ, w)

. For a fixed Orlicz function that satisfies the

Δ_{2}^{\infty}

-condition, we provide a characterization of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces with different weights. As a consequence, there are certain subsets of Orlicz-Lorentz spaces on

[0, 1]

for which the lineability problem is not valid. Moreover, various types of

(α, β)

-lineability and pointwise lineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are examined. These results extend a number of previously known results in Orlicz and Lorentz spaces.

在本文中，我们研究了具有卢森堡范数的Orlicz-Lorentz空间Λφ，w的各种非线性子集中的闭向量子空间的存在性（即空间性）。如果一组Orlicz函数（φn）n=1∞对给定的Orlicz函数φ满足一定的序关系，则序连续子空间（Λφ,w）a的子集，其元素不属于∈n=1∞Λφn，w是可空间的，并且当φ满足Δ2-condition时，w是最大可空间的。我们还证明了这个子集要么是残差，要么是空的。此外，给出了该子集不具有（α,β）空间性的充分条件。当φ不满足Δ2-condition时，对子集Λφ，w∈（Λφ,w） A也进行了类似的分析。通过生成对（φ,w）表征了不同Orlicz-Lorentz空间之间的比较。对于满足Δ2∞条件的固定Orlicz函数，给出了不同权值的Orlicz- lorentz空间间的严格不联合奇异包含算子的刻画。因此，在[0,1]上存在Orlicz-Lorentz空间的某些子集，其中线性性问题不成立。此外，还研究了Orlicz-Lorentz空间其他非线性子集上的(α,β)-线性和点向线性性质的各种类型。这些结果扩展了先前在Orlicz和Lorentz空间中已知的一些结果。

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引用次数: 0

Upper bound for the free energy of dilute Bose gases at low temperature 低温下稀玻色气体自由能的上界

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.aim.2026.110825

Florian Haberberger , Christian Hainzl , Benjamin Schlein , Arnaud Triay

We consider a Bose gas at density

ρ > 0

, interacting through a repulsive potential

V \in L^{2} (R^{3})

with scattering length

a > 0

. We prove an upper bound for the free energy of the system, valid at low temperature

T ≲ ρ a

. Combined with the recent lower bound obtained in [18], our estimate resolves the free energy per unit volume up to and including the Lee–Huang–Yang order

a ρ^{2} {(ρ a^{3})}^{1 / 2}

我们考虑密度为ρ>；0的玻色气体，通过散射长度为a>；0的排斥势V∈L2（R3）相互作用。我们证明了系统自由能的上界，在低温T≤ρa时有效。结合[18]中最近得到的下界，我们的估计将单位体积的自由能分解到并包括ρ2(ρa3)1/2的Lee-Huang-Yang阶。

引用次数: 0

Joint distribution of primes in multiple short intervals 多个短区间内素数的联合分布

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-10 DOI: 10.1016/j.aim.2026.110847

Sun-Kai Leung

Assuming the Riemann hypothesis (RH) and the linear independence conjecture (LI), we show that the weighted count of primes in multiple short intervals follows a multivariate Gaussian distribution with weak negative correlations. As an application, we obtain short-interval analogues of many results in the literature on the Shanks–Rényi prime number race, including a sharp phase transition: biased races between primes in short intervals emerge once the number of intervals exceeds an explicit critical threshold. Our result is new even for a single moving interval, particularly under a quantitative formulation of the linear independence conjecture (QLI).

假设黎曼假设（RH）和线性无关猜想（LI），我们证明了多个短区间的质数加权计数服从一个弱负相关的多元高斯分布。作为一个应用，我们得到了许多关于shanks - r尼素数竞赛的文献结果的短区间类比，包括一个尖锐的相变：一旦间隔的数量超过一个明确的临界阈值，短间隔内素数之间的偏竞赛就会出现。我们的结果是新的，即使对于单个移动区间，特别是在线性无关猜想（QLI）的定量表述下。

引用次数: 0

Polynomial ergodic theorems in the spirit of Dunford and Zygmund Dunford和Zygmund精神下的多项式遍历定理

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-13 DOI: 10.1016/j.aim.2026.110859

Dariusz Kosz , Bartosz Langowski , Mariusz Mirek , Paweł Plewa

The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on

L^{p}

p \in (1, \infty)

, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of uniform oscillation estimates for multiparameter polynomial Radon averaging operators. In the proof of our main result we develop flexible Fourier methods that exhibit and handle the so-called “parameters-gluing” phenomenon, an obstruction that arises in studying oscillation and variation inequalities for multiparameter polynomial Radon operators. We will also discuss connections of our main result with a multiparameter variant of the Bellow–Furstenberg problem.

本文的主要目的是证明在Lp， p∈(1,∞)上，对于连续流，具有Dunford和Zygmund精神的某些多参数多项式遍历平均，在范数和点方向上几乎处处收敛。我们将从多参数多项式Radon平均算子的均匀振荡估计的角度，特别注意点向收敛现象的定量方面。在证明我们的主要结果的过程中，我们开发了灵活的傅立叶方法来展示和处理所谓的“参数粘接”现象，这是研究多参数多项式Radon算子的振荡和变化不等式时出现的障碍。我们还将讨论我们的主要结果与Bellow-Furstenberg问题的多参数变体的联系。

引用次数: 0

Systolic lattice extensions of classical Schottky groups 经典Schottky群的收缩格扩展

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-12 DOI: 10.1016/j.aim.2026.110848

Junzhi Huang , Matthew Zevenbergen

We produce lattice extensions of a dense family of classical Schottky subgroups of the isometry group of d-dimensional hyperbolic space. The extensions produced are said to be systolic, since all loxodromic elements with short translation length are conjugate into the Schottky groups. Various corollaries are obtained, in particular showing that for all

d \geq 3

, the set of complex translation lengths realized by systoles of closed hyperbolic d-manifolds is dense inside the set of all possible complex translation lengths. We also consider complex translation lengths in arithmetic hyperbolic d-manifolds, and provide a new way to construct non-arithmetic lattices.

我们给出了d维双曲空间等距群的经典Schottky子群密集族的晶格扩展。所产生的扩展被认为是收缩的，因为所有具有短平移长度的loxodromic元件都共轭到肖特基群中。得到了各种推论，特别是表明当所有d≥3时，封闭双曲d流形的收缩所实现的复平移长度集合在所有可能的复平移长度集合内是稠密的。我们还考虑了算术双曲d流形中的复平移长度，并提供了一种构造非算术格的新方法。

引用次数: 0

On Ulam widths of finitely presented infinite simple groups 有限呈现无限单群的Ulam宽度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.aim.2026.110824

James Hyde , Yash Lodha

A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from 1947 is uniform simplicity. A group G is said to be n-uniformly simple for

n \in N

if for every

f, g \in G ∖ {i d}

, there is a product of no more than n conjugates of g and

g^{- 1}

that equals f. Then G is uniformly simple if it is n-uniformly simple for some

n \in N

, and we refer to the smallest such n as the Ulam width, denoted as

R (G)

. If G is simple but not uniformly simple, one declares

R (G) = \infty

. In this article, we construct for each

n \in N

, a finitely presented infinite simple group G such that

n < R (G) < \infty

. These are the first such examples among the class of finitely presented infinite simple groups. For the class of finitely generated (but not finitely presentable) infinite simple groups, the existence of such examples was settled in the work of Muranov [21]. However, this had remained open for the class of finitely presented infinite simple groups. Our examples are also of type

F_{\infty}

, which means that they are fundamental groups of aspherical CW complexes with finitely many cells in each dimension. Uniformly simple groups are in particular uniformly perfect: there is an

n \in N

such that every element of the group can be expressed as a product of at most n commutators of elements in the group. We also show that the analogous notion of width for uniform perfection is unbounded for our family of finitely presented infinite simple groups. To our knowledge, this is also the first such family.

群论中的一个基本概念是均匀简单性，它起源于1947年乌拉姆和冯·诺伊曼的一篇文章。如果对于每一个f， G∈G∈{id}， G与G−1的共轭之积不超过n，且等于f，则G是一致简单的，如果G对某些n∈n是n一致简单的，我们将最小的n称为Ulam宽度，记为R(G)。如果G是简单的，但不是一致简单的，则声明R(G)=∞。在本文中，我们对每一个n∈n构造一个有限呈现的无限简单群G，使得n<；R(G)<∞。在有限呈现的无限单群中，这是第一个这样的例子。对于有限生成的（但不是有限呈现的）无限单群，这类例子的存在性在Muranov[21]的工作中得到了证明。然而，这对于有限呈现的无限单群类来说仍然是开放的。我们的例子也是F∞型的，这意味着它们是在每个维度上具有有限个细胞的非球面CW复合体的基本群。一致简单群是一致完美的：存在一个n∈n，使得群中的每个元素都可以表示为群中元素的至多n个对易子的乘积。我们还证明了对于有限表示的无限单群族，一致完美的宽度的类似概念是无界的。据我们所知，这也是第一个这样的家庭。

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引用次数: 0

New Brunn–Minkowski and functional inequalities via convexity of entropy 基于熵的凸性的新Brunn-Minkowski和泛函不等式

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-02-04 DOI: 10.1016/j.aim.2026.110841

Gautam Aishwarya , Liran Rotem

We study the connection between the concavity properties of a measure ν and the convexity properties of the associated relative entropy

D (\cdot ‖ ν)

along optimal transport. As a corollary we prove a new dimensional Brunn–Minkowski inequality for centered star-shaped bodies, when the measure ν is log-concave with a p-homogeneous potential (such as the Gaussian measure). Our method allows us to go beyond the usual convexity assumption on the sets that is fundamentally essential for the standard differential-geometric technique in this area.

We then take a finer look at the convexity properties of the Gaussian relative entropy, which yields new functional inequalities. First we obtain curvature and dimensional reinforcements to Otto–Villani's HWI inequality in Gauss space, when restricted to even strongly log-concave measures. As corollaries, we obtain improved versions of Gross' Logarithmic Sobolev inequality and Talagrand's transportation cost inequality in this setting.

我们研究了测度ν的凹凸性与相关相对熵D（⋅‖ν）沿最优输运的凹凸性之间的联系。作为一个推论，我们证明了一个新的维度布伦-闵可夫斯基不等式对于中心星形体，当测量ν是log-凹的p齐次势（如高斯测量）。我们的方法使我们能够超越通常对集合的凸性假设，而凸性假设对于该领域的标准微分几何技术是至关重要的。然后我们仔细研究高斯相对熵的凸性，它产生了新的函数不等式。首先，我们得到了高斯空间中Otto-Villani HWI不等式的曲率和维数增强，当它被限制为偶强对数凹测度时。作为推论，在这种情况下，我们得到了Gross’对数Sobolev不等式和Talagrand’运输成本不等式的改进版本。

引用次数: 0

An explicit derived McKay correspondence for some complex reflection groups of rank two 一类二阶复反射群的显式推导McKay对应

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-01-30 DOI: 10.1016/j.aim.2026.110794

Anirban Bhaduri , Yael Davidov , Eleonore Faber , Katrina Honigs , Peter McDonald , C. Eric Overton-Walker , Dylan Spence

<div><div>In this paper, we explore the derived McKay correspondence for several reflection groups, namely reflection groups of rank two generated by reflections of order two. We prove that for each of the reflection groups <math><mi>G</mi><mo>=</mo><mi>G</mi><mo>(</mo><mn>2</mn><mi>m</mi><mo>,</mo><mi>m</mi><mo>,</mo><mn>2</mn><mo>)</mo></math>, <math><msub><mrow><mi>G</mi></mrow><mrow><mn>12</mn></mrow></msub></math>, <math><msub><mrow><mi>G</mi></mrow><mrow><mn>13</mn></mrow></msub></math>, or <math><msub><mrow><mi>G</mi></mrow><mrow><mn>22</mn></mrow></msub></math>, there is a semiorthogonal decomposition of the following form, where <math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub></math> are the normalizations of the irreducible components of the branch divisor <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>G</mi></math> and <math><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub></math> are exceptional objects:<math><msup><mrow><mi>D</mi></mrow><mrow><mi>G</mi></mrow></msup><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>≅</mo><mo>〈</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>D</mi><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo><mo>…</mo><mo>,</mo><mi>D</mi><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo><mo>,</mo><mi>D</mi><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>G</mi><mo>)</mo><mo>〉</mo><mo>.</mo></math> We verify that the pieces of this decomposition correspond to the irreducible representations of G, verifying the Orbifold Semiorthogonal Decomposition Conjecture of Polishchuk and Van den Bergh. Due to work of Potter on the group <math><mi>G</mi><mo>(</mo><mi>m</mi><mo>,</mo><mi>m</mi><mo>,</mo><mn>2</mn><mo>)</mo></math>, this conjecture is now proven for all finite groups <math><mi>G</mi><mo>≤</mo><mi>GL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math> that are generated by order 2 reflections. Each of these groups contains, as a subgroup of index 2, a distinct finite group <math><mi>H</mi><mo>≤</mo><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math>. A key part of our work is an explicit computation of the action of <math><mi>G</mi><mo>/</mo><mi>H</mi></math> on the H-Hilbert scheme <math><mrow><mtext>H</mtext><mtext>-Hilb</mtext></mrow

本文研究了几种反射群的McKay对应，即由二阶反射生成的二阶反射群。我们证明了对于每一个反射群G=G(2m,m,2), G12, G13，或G22，存在如下形式的半正交分解，其中B1，…，Br是分支因子C2→C2/G的不可约分量的归一化，E1，…，En是例外对象：DG(C2) = < E1，…，En，D(B1)，…，D(Br)，D(C2/G) >。我们证明了这个分解的片段对应于G的不可约表示，验证了Polishchuk和Van den Bergh的轨道半正交分解猜想。由于Potter对群G（m,m,2）的研究，这个猜想现在被证明适用于所有由2阶反射产生的有限群G≤GL（2，C）。这些群中的每一个都包含一个不同的有限群H≤SL(2，C)，作为指标2的子群。我们工作的一个关键部分是G/H对H- hilbert方案H- hilb （C2）的显式计算。

引用次数: 0

On Galois theory of cluster algebras: general and that from Riemann surfaces 关于簇代数的伽罗瓦理论：一般的和来自黎曼曲面的

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-04-01 Epub Date: 2026-01-28 DOI: 10.1016/j.aim.2026.110821

Jinlei Dong, Fang Li

One of the key points in Galois theory via field extensions is to build up a correspondence between subfields of a field and subgroups of its automorphism group, so as to study fields via methods of groups. As an analogue of the Galois theory, we want to discuss the relations between cluster subalgebras of a cluster algebra and subgroups of its automorphism group and then set up the Galois-like method.

In the first part, we build up a Galois map from a skew-symmetrizable cluster algebra

A

to its cluster automorphism group, and introduce notions of Galois-like extensions and Galois extensions. A necessary condition for Galois extensions of a cluster algebra

A

is given, which is also a sufficient condition if

A

has a

D

-stable basis or stable monomial basis with unique expression. Some properties for Galois-like extensions are discussed. It is shown that two subgroups

H_{1}

and

H_{2}

of the automorphism group

Aut A

are conjugate to each other if and only if there exists

f \in Aut A

and two Galois-like extension subalgebras

A (Σ_{1})

A (Σ_{2})

corresponding to

H_{1}

and

H_{2}

such that f is an isomorphism between

A (Σ_{1})

and

A (Σ_{2})

In the second part, as the answers of two conjectures proposed in the first part, for a cluster algebra from a feasible surface, we prove that Galois-like extension subalgebras corresponding to a subgroup of a cluster automorphism group have the same rank. Moreover, it is shown that there are order-preserving reverse Galois maps for these cluster algebras. We also give examples of

D

-stable bases and some discussions on the Galois inverse problem in this part.

伽罗瓦域扩展理论的关键之一是建立域的子域与其自同构群的子群之间的对应关系，从而通过群的方法来研究域。作为伽罗瓦理论的类比，我们讨论了一类聚类代数的聚类子代数与其自同构群的子群之间的关系，并建立了类伽罗瓦方法。在第一部分中，我们建立了从偏对称聚类代数a到它的聚类自同构群的伽罗瓦映射，并引入了类伽罗瓦扩展和伽罗瓦扩展的概念。给出了聚类代数A的伽罗瓦扩展的一个必要条件，同时也是A具有d稳定基或具有唯一表达式的稳定单项式基的充分条件。讨论了类伽罗瓦扩展的一些性质。证明了自同构群AutA的两个子群H1和H2是共轭的当且仅当存在f∈AutA和对应于H1和H2的两个类伽罗司扩展子代数A（Σ1）， A（Σ2），使得f是A（Σ1）和A（Σ2）之间的同构。在第二部分中，作为第一部分中两个猜想的答案，我们从可行曲面上证明了簇自同构群的子群对应的类伽罗瓦扩展子代数具有相同的秩。此外，还证明了这些簇代数存在保序的逆伽罗瓦映射。在这一部分中，我们还给出了d稳定基的例子，并对伽罗瓦逆问题进行了一些讨论。

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