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Group noninvariant solutions of the Hénon equation in unbounded domains 无界域hsamnon方程的群非不变解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-01-16 DOI: 10.1016/j.jde.2026.114113

Ryuji Kajikiya

We study the Hénon equation in unbounded domains Ω which are G invariant, where G is a closed subgroup of the orthogonal group. We say that Ω (or

u (x)

) is G invariant if

g (Ω) = Ω

(or

u (g x) = u (x)

) for any

g \in G

. We call

u (x)

a least energy solution if it is a minimizer of the Rayleigh quotient associated with the Hénon equation. We offer sufficient conditions which guarantee that no least energy solution is G invariant.

研究了无界域Ω上G不变的hsamnon方程，其中G是正交群的闭子群。我们说对于任意G∈G，如果G （Ω）=Ω(或u（gx)=u(x)） Ω（或u(x)）是G不变量。我们称u(x)为最小能量解，如果它是与hsamnon方程相关的瑞利商的最小解。给出了保证没有最小能量解是G不变的充分条件。

引用次数: 0

A Class of Fluid-Structure Interaction Problems with Analytical Solutions for the Validation of Numerical Methods 一类流固耦合问题及其数值方法验证的解析解

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics

Pub Date : 2026-01-16 DOI: 10.1007/s00021-025-00999-z

Yongxing Wang, Olivier Pironneau

Analytical solutions to Fluid-Structure Interaction (FSI) problems are almost absent in the literature. However, they are crucial for validation and convergence analysis of numerical methods, as well as for providing insight into the complex coupling dynamics between fluids and solids. In this paper, we derive two analytical and one semi-analytical solutions for three FSI problems, spanning a class of solutions by varying their geometrical and physical parameters. All solutions exhibit complex nonlinear behaviours, which we compare with numerical simulations using a monolithic method. These three FSI problems are described in the cylindrical coordinates, drawing inspiration from Couette flow, with two of them featuring a moving fluid-solid interface and the third incorporating a nonlinear constitutive solid model. To the best of our knowledge, for the first time, we present FSI problems with analytical solutions that include a moving interface.

流固耦合（FSI）问题的解析解在文献中几乎没有。然而，它们对于数值方法的验证和收敛分析以及对流体和固体之间复杂耦合动力学的洞察至关重要。在本文中，我们得到了三个FSI问题的两个解析解和一个半解析解，通过改变它们的几何和物理参数，跨越了一类解。所有解都表现出复杂的非线性行为，我们将其与使用单片方法的数值模拟进行了比较。从Couette flow中得到灵感，在柱坐标中描述了这三个FSI问题，其中两个问题具有移动的流固界面，第三个问题包含非线性本构实体模型。据我们所知，这是我们第一次用包含移动界面的分析解决方案提出FSI问题。

引用次数: 0

Rigidity and reconstruction in matroids of highly connected graphs 高连通图的拟阵的刚性与重构

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-16 DOI: 10.1016/j.jctb.2026.01.003

Dániel Garamvölgyi

A graph matroid family

M

is a family of matroids

M (G)

defined on the edge set of each finite graph G in a compatible and isomorphism-invariant way. We say that

M

has the Whitney property if there is a constant c such that every c-connected graph G is uniquely determined by

M (G)

. Similarly,

M

has the Lovász-Yemini property if there is a constant c such that for every c-connected graph G,

M (G)

has maximal rank among graphs on the same number of vertices.

We show that if

M

is unbounded (that is, there is no absolute constant bounding the rank of

M (G)

for every G), then

M

has the Whitney property if and only if it has the Lovász-Yemini property. We also give a complete characterization of these properties in the bounded case. As an application, we show that if some graph matroid families have the Whitney property, then so does their union. Finally, we show that every 1-extendable graph matroid family has the Lovász-Yemini (and thus the Whitney) property. These results unify and extend a number of earlier results about graph reconstruction from an underlying matroid.

图拟阵族M是在每一个有限图G的边集中以相容且同构不变的方式定义的拟阵族M(G)。我们说M具有惠特尼性质，如果存在一个常数c使得每个c连通图G唯一地由M(G)决定。类似地，如果存在一个常数c，使得对于每个c连通图G， M(G)在具有相同顶点数的图中具有最大秩，则M具有Lovász-Yemini性质。我们证明，如果M是无界的（即，对于每个G， M(G)的秩没有绝对常数的边界），那么M具有惠特尼性质当且仅当它具有Lovász-Yemini性质。在有界情况下，我们也给出了这些性质的完整刻画。作为一个应用，我们证明了如果一些图阵族具有惠特尼性质，那么它们的并集也具有惠特尼性质。最后，我们证明了每一个1-可扩展图矩阵族都具有Lovász-Yemini（因此也是Whitney）性质。这些结果统一并扩展了先前关于从底层矩阵重构图的一些结果。

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引用次数: 0

Construction of large cyclic subspace codes via Sidon spaces with dimensions k and k + 1 维数为k和k的Sidon空间构造大循环子空间码 +

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-16 DOI: 10.1016/j.disc.2026.115008

Yongfeng Niu , Chenyu Zhang , Yansheng Wu , Fagang Li

The research on cyclic subspace codes aims to design coding schemes with larger cardinality and optimal minimum distance to meet the demands of modern communication systems for efficient and reliable coding. This paper investigates the construction problem of cyclic subspace codes, utilizing combinatorial numbers to select the exponent of the irreducible element γ to construct different Sidon spaces, including k-dimensional and

(k + 1)

-dimensional spaces. Subsequently, we consider merging the subspace codes generated by these Sidon spaces, resulting in cyclic subspace codes with larger cardinality. Our construction method effectively increases the cardinality of the code while ensuring optimal minimum distance.

循环子空间码的研究旨在设计具有更大基数和最优最小距离的编码方案，以满足现代通信系统对高效可靠编码的要求。本文研究了循环子空间码的构造问题，利用组合数选择不可约元素γ的指数来构造不同的西顿空间，包括k维和（k+1）维空间。随后，我们考虑合并由这些西顿空间生成的子空间码，得到具有更大基数的循环子空间码。我们的构造方法在保证最优最小距离的同时有效地增加了代码的基数。

引用次数: 0

Implicit-explicit time discretization with complex time for parabolic equations 抛物型方程的复时间隐显时间离散化

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109743

Henghui Tang, Daopeng Yin, Xiaohao Zhang, Liquan Mei

This paper presents a novel high-order time discretization scheme on the time complex plane for parabolic equations. The innovation of this method lies in its ability to straightforwardly construct temporal discretization schemes of arbitrary order while achieving stability comparable to explicit Runge-Kutta methods, and simultaneously enhancing computational efficiency without compromising stability. By employing a matrix construction method, we unify the characterization of the stability region for both ordinary differential equations and partial differential equations. We prove the L² stability and arbitrary-order convergence of the method. Numerical experiments demonstrate that, compared to explicit Runge-Kutta methods, the proposed scheme improves computational efficiency. This method offers an efficient and accurate solution for applications with stringent precision.

提出了抛物型方程在时间复平面上的一种新的高阶时间离散格式。该方法的创新之处在于能够直接构建任意阶的时间离散化格式，同时获得与显式龙格-库塔方法相当的稳定性，同时在不影响稳定性的情况下提高计算效率。利用矩阵构造的方法，统一了常微分方程和偏微分方程稳定域的表征。证明了该方法的L2稳定性和任意阶收敛性。数值实验表明，与显式龙格-库塔方法相比，该方法提高了计算效率。该方法为精度要求高的应用提供了高效、准确的解决方案。

引用次数: 0

Lax functorialities of the comma construction for ω-categories ω-范畴的逗号结构的松弛功能

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-15 DOI: 10.1016/j.aim.2025.110762

Dimitri Ara , Léonard Guetta

Motivated by the Grothendieck construction, we study the functorialities of the comma construction for strict ω-categories. To state the most general functorialities, we use the language of Gray ω-categories, that is, categories enriched in the category of strict ω-categories endowed with the oplax Gray tensor product. Our main result is that the comma construction of strict ω-categories defines a Gray ω-functor, that is, a morphism of Gray ω-categories. To makes sense of this statement, we prove that slices of Gray ω-categories exist. Coming back to the Grothendieck construction, we propose a definition in terms of the comma construction and, as a consequence, we get that the Grothendieck construction of strict ω-categories defines a Gray ω-functor. Finally, as a by-product, we get a notion of Grothendieck construction for Gray ω-functors, which we plan to investigate in future work.

在Grothendieck结构的启发下，我们研究了严格ω-范畴的逗号结构的泛函性。为了描述最一般的功能，我们使用Gray ω-范畴的语言，即在赋予oplax Gray张量积的严格ω-范畴中丰富的范畴。我们的主要结果是严格ω-范畴的逗号构造定义了一个Gray ω-函子，即Gray ω-范畴的态射。为了使这句话有意义，我们证明了Gray ω-范畴片的存在。回到格罗滕狄克构造，我们提出了一个关于逗号构造的定义，作为结果，我们得到严格ω-范畴的格罗滕狄克构造定义了一个Gray ω-函子。最后，作为一个副产品，我们得到了Gray ω-函子的Grothendieck构造的概念，我们计划在未来的工作中对此进行研究。

引用次数: 0

De Bruijn tori without zeros: a field-theoretic perspective 没有零的德布鲁因托里：场理论视角

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications

Pub Date : 2026-01-15 DOI: 10.1016/j.ffa.2026.102790

Ming Hsuan Kang, Yu Hsuan Hsieh

We present an algebraic construction of trace-based De Bruijn tori over finite fields, focusing on the nonzero variant that omits the all-zero pattern. The construction arranges nonzero field elements on a toroidal grid using two multiplicatively independent generators, with values obtained by applying a fixed linear map, typically the field trace.

We characterize sampling patterns as subsets whose associated field elements form an

F_{p}

-basis, and show that column structures correspond to cyclic shifts of De Bruijn sequences determined by irreducible polynomials over subfields. Recursive update rules based on multiplicative translations enable efficient computation.

我们给出了有限域上基于迹的德布鲁因托里的代数构造，重点讨论了忽略全零模式的非零变体。该构造使用两个相乘独立的生成器在环面网格上排列非零场元素，其值通过应用固定的线性映射（通常是场迹）获得。我们将采样模式描述为子集，其相关的域元素形成一个fp基，并表明列结构对应于子域上由不可约多项式决定的De Bruijn序列的循环移位。基于乘法转换的递归更新规则实现了高效的计算。

引用次数: 0

Quasi-optimum distance flag codes 准最佳距离标志码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications

Pub Date : 2026-01-15 DOI: 10.1016/j.ffa.2026.102799

Clementa Alonso-González, Miguel Ángel Navarro-Pérez

A flag is a sequence of nested subspaces of a given ambient space

F_{q}^{n}

over a finite field

F_{q}

. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we investigate quasi-optimum distance flag codes, i.e., those attaining the second best possible distance value. We characterize them and present upper bounds for their cardinality. Moreover, we propose a systematic construction for every choice of the type vector by using partial spreads and sunflowers. For flag codes with lower minimum distance, we adapt the previous construction and provide some results towards their characterization, especially in the case of the third best possible distance value.

标志是给定环境空间Fqn在有限域Fq上的嵌套子空间序列。在网络编码中，标志码是一组标志，它们都具有相同的维数序列，即类型向量。在本文中，我们研究了准最优距离标志码，即那些达到次优可能距离值的标志码。我们对它们进行了表征，并给出了它们的基数的上界。此外，我们提出了一个系统的结构，为每一个选择的类型向量使用部分蔓延和向日葵。对于最小距离较低的标志码，我们调整了之前的结构，并对其表征提供了一些结果，特别是在第三最佳可能距离值的情况下。

引用次数: 0

Minimal Triangulations of Circle Bundles 圆束的最小三角剖分

IF 0.7 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications

Pub Date : 2026-01-15 DOI: 10.1134/S1234567825040056

Gaiane Panina, Maksim Turevskii

A triangulation of a circle bundle (E xrightarrow{pi} B) is a triangulation of the total space (E) and the base (B) such that the projection (pi) is a simplicial map. In the paper, we address the following questions. Which circle bundles can be triangulated over a given triangulation of the base? What are the minimal triangulations of a bundle? A complete solution for semisimplicial triangulations was given by N. Mnëv. Our results deal with classical triangulations, i.e., simplicial complexes. We give an exact answer for an infinite family of triangulated spheres (including the boundary of the (3)-simplex, the boundary of the octahedron, the suspension over an (n)-gon, the icosahedron). For the general case, we present a sufficient condition for the existence of a triangulation. Some minimality results follow straightforwadly.

圆束(E xrightarrow{pi} B)的三角剖分是总空间(E)和基底(B)的三角剖分，因此投影(pi)是一个简单的地图。在本文中，我们解决了以下问题。哪些圆束可以在给定的底边三角剖分上进行三角剖分？束的最小三角剖分是什么？N. Mnëv给出了半简单三角剖分的完全解。我们的结果处理经典三角剖分，即简单复合体。我们给出了无限族的三角球的精确答案（包括(3) -单纯形的边界，八面体的边界，悬浮在(n) -gon上，二十面体）。对于一般情况，给出了三角剖分存在的充分条件。一些最小化的结果紧随其后。

引用次数: 0

Sensor attack detection and identification for cyber-physical systems: A data-driven approach 网络物理系统的传感器攻击检测和识别：数据驱动的方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-01-15 DOI: 10.1016/j.amc.2026.129954

Kaiyu Wang , Dan Ye

This paper investigates the problem of sensor attack detection and identification in cyber-physical systems, leveraging the advantage of zonotopes in dealing with stochastic properties. Unlike previous research that relies on system dynamics knowledge to infer safety boundaries and monitoring schemes, the proposed approach is geared toward addressing the challenges posed by unknown system dynamics, attack strategies, and attack locations. Firstly, we analyze the feasibility of using zonotopes for attack detection and deduce the necessary information quantity and observation window length requirement for effective detection. Subsequently, a zonotopes-based algorithm is proposed for computing the over-approximated reachable set and measurement set from noisy data. Then, an attack detection and identification strategy based on the predicted measurement set is developed. To reduce the computational complexity of the presented detection method, a column truncation algorithm is proposed. The effectiveness of the proposed method is validated through numerical simulations.

本文研究了网络物理系统中传感器攻击的检测和识别问题，利用带拓扑在处理随机特性方面的优势。与以往依靠系统动力学知识推断安全边界和监测方案的研究不同，本文提出的方法旨在解决未知系统动力学、攻击策略和攻击位置带来的挑战。首先，我们分析了利用分区进行攻击检测的可行性，并推导出有效检测所需的信息量和观测窗口长度要求。随后，提出了一种基于分区拓扑的算法，用于计算噪声数据的过逼近可达集和测量集。然后，提出了一种基于预测测量集的攻击检测与识别策略。为了降低检测方法的计算复杂度，提出了一种列截断算法。通过数值仿真验证了该方法的有效性。

引用次数: 0

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