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Proof of a conjecture of Green and Liebeck on codes in symmetric groups 关于对称群中码的Green和Liebeck猜想的证明
IF 0.7 3区 数学 Q2 MATHEMATICS
Discrete Mathematics
Pub Date : 2026-01-15 DOI: 10.1016/j.disc.2026.114999
Teng Fang, Jinbao Li
<div><div>Let <em>A</em> and <em>B</em> be subsets of a finite group <em>G</em> and <em>r</em> a positive integer. If for every <span><math><mi>g</mi><mo>∈</mo><mi>G</mi></math></span>, there are precisely <em>r</em> pairs <span><math><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>∈</mo><mi>A</mi><mo>×</mo><mi>B</mi></math></span> such that <span><math><mi>g</mi><mo>=</mo><mi>a</mi><mi>b</mi></math></span>, then <em>B</em> is called a code in <em>G</em> with respect to <em>A</em> and we write <span><math><mi>r</mi><mi>G</mi><mo>=</mo><mi>A</mi><mo>⋅</mo><mi>B</mi></math></span>. If in addition <em>B</em> is a subgroup of <em>G</em>, then we say that <em>B</em> is a subgroup code in <em>G</em>. In this paper we resolve a conjecture by Green and Liebeck <span><span>[8, Conjecture 2.3]</span></span> on certain subgroup codes in the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Let <span><math><mi>n</mi><mo>></mo><mn>2</mn><mi>k</mi></math></span> and let <em>j</em> be such that <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>j</mi></mrow></msup><mo>⩽</mo><mi>k</mi><mo><</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>. Suppose that <em>X</em> is a conjugacy class in <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> containing <em>x</em>, and <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is the subgroup <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>×</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub></math></span> of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, where the factor <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> permutes the subset <span><math><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></math></span> and the factor <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub></math></span> permutes the subset <span><math><mo>{</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></math></span>. We prove that <span><math><mi>r</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>X</mi><mo>⋅</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> for some positive integer <em>r</em> if and only if the cycle type of <em>x</em> has exactly one cycle of length <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>i</mi></mrow></msup></math></span> for <span><math><mn>0</mn><mo>⩽</mo><mi>i</mi><mo>⩽</mo><mi>j</mi></math></span> and all other cycles have length at least <span><math><mi>k</mi><mo>+</mo><mn>1</mn></math></span>. We also propose several problems concerning the existence of certain subgroup codes in a finite group <em>G</em> with respect to a conjugation-closed subset i
设A和B是有限群G的子集，r是正整数。如果对于每一个g∈g，恰好有r对(a,b)∈A×B使得g=ab，那么b就被称为g中关于a的一个码，我们写成rG= a·b。如果另外B是G的子群，则我们说B是G中的子群码。本文解决了Green和Liebeck[8，猜想2.3]关于对称群Sn中某些子群码的一个猜想。设n>；2k和j满足2j≤k<；2j+1。设X是Sn中包含X的共轭类，Yk是Sn的子群Sk×Sn−k，其中因子Sk置换子集{1，…，k}，因子Sn−k置换子集{k+1，…，n}。证明对于正整数r， rSn=X⋅Yk当且仅当X的循环类型恰好有一个长度为2i的循环，且对于0≤i≤j，所有其他循环的长度至少为k+1。对于G中的共轭闭子集，给出了有限群G中某些子群码的存在性问题。
{"title":"Proof of a conjecture of Green and Liebeck on codes in symmetric groups","authors":"Teng Fang,&nbsp;Jinbao Li","doi":"10.1016/j.disc.2026.114999","DOIUrl":"10.1016/j.disc.2026.114999","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;em&gt;A&lt;/em&gt; and &lt;em&gt;B&lt;/em&gt; be subsets of a finite group &lt;em&gt;G&lt;/em&gt; and &lt;em&gt;r&lt;/em&gt; a positive integer. If for every &lt;span&gt;&lt;math&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, there are precisely &lt;em&gt;r&lt;/em&gt; pairs &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;em&gt;B&lt;/em&gt; is called a code in &lt;em&gt;G&lt;/em&gt; with respect to &lt;em&gt;A&lt;/em&gt; and we write &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. If in addition &lt;em&gt;B&lt;/em&gt; is a subgroup of &lt;em&gt;G&lt;/em&gt;, then we say that &lt;em&gt;B&lt;/em&gt; is a subgroup code in &lt;em&gt;G&lt;/em&gt;. In this paper we resolve a conjecture by Green and Liebeck &lt;span&gt;&lt;span&gt;[8, Conjecture 2.3]&lt;/span&gt;&lt;/span&gt; on certain subgroup codes in the symmetric group &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and let &lt;em&gt;j&lt;/em&gt; be such that &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. Suppose that &lt;em&gt;X&lt;/em&gt; is a conjugacy class in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; containing &lt;em&gt;x&lt;/em&gt;, and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the subgroup &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, where the factor &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; permutes the subset &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and the factor &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; permutes the subset &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We prove that &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for some positive integer &lt;em&gt;r&lt;/em&gt; if and only if the cycle type of &lt;em&gt;x&lt;/em&gt; has exactly one cycle of length &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;⩽&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and all other cycles have length at least &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. We also propose several problems concerning the existence of certain subgroup codes in a finite group &lt;em&gt;G&lt;/em&gt; with respect to a conjugation-closed subset i","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 5","pages":"Article 114999"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145977658","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
Fixed-time impulsive synchronization of heterogeneous complex networks 异构复杂网络的定时脉冲同步
IF 3.9 2区 数学 Q1 MATHEMATICS, APPLIED
Communications in Nonlinear Science and Numerical Simulation
Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109682
Yufei Ye, Wen Qin, Mouquan Shen, Zhihao Zhang, Hany M. Hasanien, Zheng H. Zhu
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引用次数: 0
Solving Variational Inequalities Using an Algorithm with Extrapolations from the Past and Relaxation 用过去外推法和松弛法求解变分不等式
IF 3.9 2区 数学 Q1 MATHEMATICS, APPLIED
Communications in Nonlinear Science and Numerical Simulation
Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109681
Yonghong Yao, Sani Salisu, Yekini Shehu
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引用次数: 0
Breaking the symmetry of social influence in information cascades 打破信息级联中社会影响的对称性
IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Chaos Solitons & Fractals
Pub Date : 2026-01-15 DOI: 10.1016/j.chaos.2026.117911
Hao Yu , Xingfu Ke , Junjie Fu , Fanyuan Meng
In modern interconnected societies, social influence often exhibits asymmetry, a crucial factor governing the dynamics of information cascades. Building upon the Watts threshold model, we propose a two-layer network framework to characterize this asymmetry: influence propagates via a primary layer with weight 1−α and a complementary layer with weight α, where α∈[0,0.5]. Overlapping edges, occurring with probability η∈[0,1], carry full influence weight 1. By systematically tuning η and α, we analyze how asymmetric social interaction shapes cascade dynamics on random networks. Our analysis shows that the cascade boundary in the (η,α) plane exhibits a step-like profile, with the critical overlap ηc displaying nonmonotonic dependence on α. Moreover, increasing η drives the cascade size from continuous growth to discontinuous transitions, even under strong asymmetry (small α). These results highlight the dual role of asymmetric influence: it can either facilitate or suppress large-scale cascades depending on the interplay between structural overlap and weight distribution. Our work provides actionable insights for designing influence strategies in multi-channel communication systems.
在现代相互联系的社会中，社会影响往往表现出不对称，这是控制信息级联动态的关键因素。在Watts阈值模型的基础上，我们提出了一个两层网络框架来表征这种不对称性：影响通过权重为1−α的初级层和权重为α的互补层传播，其中α∈[0,0.5]。重叠边的概率η∈[0,1]，其影响权值为1。通过系统地调整η和α，我们分析了不对称社会互动如何影响随机网络上的级联动力学。分析表明，（η,α）平面的叶栅边界呈阶梯状，临界重叠ηc与α呈非单调关系。此外，η的增大使叶栅尺寸从连续增长转变为不连续转变，即使在强不对称（小α）条件下也是如此。这些结果强调了不对称影响的双重作用：它可以促进或抑制大规模级联，这取决于结构重叠和重量分布之间的相互作用。我们的工作为设计多渠道通信系统中的影响策略提供了可行的见解。
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引用次数: 0
A class of flexible and efficient partitioned Runge-Kutta-Chebyshev methods for some time-dependent partial differential equations 一类灵活有效的时变偏微分方程的分块龙格-库塔-切比雪夫方法
IF 3.9 2区 数学 Q1 MATHEMATICS, APPLIED
Communications in Nonlinear Science and Numerical Simulation
Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109643
Xiao Tang, Junwei Huang
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引用次数: 0
The Myerson value for games with weighted signed networks 带有加权签名网络的博弈的Myerson值
IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Discrete Applied Mathematics
Pub Date : 2026-01-15 DOI: 10.1016/j.dam.2026.01.002
Yushuang Mou , Qiang Sun , Chao Zhang
Weighted signed networks capture both positive and negative relationships between individuals, with link weights representing the intensity of these relationships. We model cooperation in such networks as a cooperative game restricted by a weighted signed network. To address the distribution problem in these games, we introduce the weighted signed Myerson value (WS-Myerson value), which is grounded in structural balance theory and incorporates the minimum cost required to achieve balance within the network. We prove that the WS-Myerson value is uniquely determined by the axioms of component efficiency, fairness for conflict players, and marginality.
加权签名网络捕获了个体之间的积极和消极关系，链接权重代表了这些关系的强度。我们将这种网络中的合作建模为受加权签名网络约束的合作博弈。为了解决这些博弈中的分配问题，我们引入了加权签名Myerson值（WS-Myerson值），该值以结构平衡理论为基础，并结合了在网络内实现平衡所需的最小成本。我们证明了WS-Myerson值是由组件效率、冲突参与者公平和边际性公理唯一决定的。
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引用次数: 0
Fractionally Calabi–Yau lattices that tilt to higher Auslander algebras of type A 向A型高等Auslander代数倾斜的分数Calabi-Yau格
IF 1.5 1区 数学 Q1 MATHEMATICS
Advances in Mathematics
Pub Date : 2026-01-15 DOI: 10.1016/j.aim.2026.110785
Tal Gottesman
We prove that the bounded derived category of the lattice of order ideals of the product of two ordered chains is fractionally Calabi–Yau. We also show that these lattices are derived equivalent to higher Auslander algebras of type A. The proofs involve the study of intervals of the poset that have resolutions described with antichains having rigid properties. These two results combined corroborate a conjecture by Chapoton linking posets to Fukaya–Seidel Categories.
证明了两有序链积的有序理想格的有界派生范畴是分数Calabi-Yau。我们还证明了这些格的推导等价于a型的更高的Auslander代数。证明涉及到用具有刚性性质的反链描述分辨率的偏序集的区间的研究。这两个结果结合起来证实了Chapoton将偏置集与Fukaya-Seidel范畴联系起来的猜想。
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引用次数: 0
On a Theorem of Bohl Regarding Integrals of Quasi-Periodic Functions 关于拟周期函数积分的玻尔定理
IF 0.7 4区 数学 Q3 MATHEMATICS
Functional Analysis and Its Applications
Pub Date : 2026-01-15 DOI: 10.1134/S1234567825040020
Valery Kozlov

Bohl points of a conditionally periodic motion are defined as the phases such that the integral of a continuous function with zero mean value along the motion is always nonnegative (or nonpositive). Bohl points are known to always exist. This note is devoted to a generalization of this result to the case of uniquely ergodic dynamical systems as well as to almost periodic Bohr functions.

条件周期运动的波尔点被定义为使一个均值为零的连续函数沿运动方向的积分总是非负的（或非正的）相。众所周知，波尔点总是存在的。本文致力于将这一结果推广到唯一遍历动力系统和几乎周期玻尔函数的情况。
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引用次数: 0
On the Stability of Linear Elliptic Equations with (L^2)-Drifts of Negative Divergence and Singular Zero-Order Terms 具有(L^2) -负散度漂移和奇异零阶项的线性椭圆方程的稳定性
IF 0.7 4区 数学 Q3 MATHEMATICS
Functional Analysis and Its Applications
Pub Date : 2026-01-15 DOI: 10.1134/S1234567825040032
Haesung Lee

This paper first demonstrates the existence and uniqueness of solutions to homogeneous Dirichlet boundary value problems for second-order linear elliptic equations with (L^2)-drifts of negative divergence and positive (L^1)-zero-order terms, based on a functional analytic approach, including weak convergence methods and duality arguments. By improving the previous contraction properties, which may not be effective when the zero-order term is very small, this paper introduces a general (L^2)-“contraction” property for any positive zero-order term, leading to remarkable results regarding (L^2)-stability. These stability results are applicable to (L^2)-error analysis for physics-informed neural networks, and can also be applied to stationary Schrödinger operators with (L^2)-zero-order terms. We emphasize that all the constants arising in the estimates of this paper can be explicitly computed.

本文首先利用泛函解析方法，利用弱收敛方法和对偶性论证，证明了二阶线性椭圆方程具有(L^2) -负散度漂移和(L^1) -零阶项的齐次Dirichlet边值问题解的存在唯一性。通过改进以往在零阶项很小时可能不有效的收缩性质，本文引入了对于任何正零阶项的一般(L^2) -“收缩”性质，得到了关于(L^2) -稳定性的显著结果。这些稳定性结果适用于物理信息神经网络的(L^2) -误差分析，也可以应用于具有(L^2) -零阶项的平稳Schrödinger算子。我们强调，本文估计中出现的所有常数都可以显式计算。
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引用次数: 0
Zhang Neural Network Model and Algorithm with Inherent Properties for Tackling Temporally Dependent Generalized Sylvester’s Matrix Equation Problems with Applications 求解时变广义Sylvester矩阵方程问题的具有固有性质的张神经网络模型和算法及其应用
IF 3.9 2区 数学 Q1 MATHEMATICS, APPLIED
Communications in Nonlinear Science and Numerical Simulation
Pub Date : 2026-01-15 DOI: 10.1016/j.cnsns.2026.109703
Pengfei Guo, Yunong Zhang, Zheng-An Yao, Shuai Li
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引用次数: 0
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