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Global Stein theorem on Hardy spaces 哈代空间上的全局斯坦因定理
IF 0.7 3区 数学 Q3 Mathematics Pub Date : 2024-09-05 DOI: 10.1007/s10476-024-00003-2
A. Bonami, S. Grellier, B. F. Sehba

Let (f) be an integrable function which has integral (0) on (mathbb{R}^n ).What is the largest condition on (|f|) that guarantees that (f) is in the Hardy space(mathcal{H}^1(mathbb{R}^n))? When (f) is compactly supported, it is well-known that the largest conditionon (|f|) is the fact that (|f|in L log L(mathbb{R}^n) ). We consider the same kind ofproblem here, but without any condition on the support. We do so for (mathcal{H}^1(mathbb{R}^n)),as well as for the Hardy space (mathcal{H}_{log}(mathbb{R}^n)) which appears in the study of pointwiseproducts of functions in (mathcal{H}^1(mathbb{R}^n)) and in its dual BMO.

让 (f) 是一个可积分函数,它在(mathbb{R}^n )上有积分 (0),那么保证 (f) 在 Hardy 空间(mathcal{H}^1(mathbb{R}^n))中的(|f|)的最大条件是什么?当 (f) 紧凑支撑时,众所周知,对 (|f|) 最大的条件就是 (|f|in L log L(mathbb{R}^n) )。我们在这里考虑的是同类问题,但不需要任何支持条件。我们对 (mathcal{H}^1(mathbb{R}^n)) 以及 Hardy 空间 (mathcal{H}_{log}(mathbb{R}^n))这样做,后者出现在 (mathcal{H}^1(mathbb{R}^n)) 及其对偶 BMO 中函数的点异积研究中。
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引用次数: 0
On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems 关于偏斜对称和移位偏斜对称线性系统的克雷洛夫子空间方法
IF 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-07-19 DOI: 10.1007/s10444-024-10178-9
Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang

Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in Greif et al. [SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1071–1087]. In this work, we extend the results of Greif et al. to singular skew-symmetric linear systems. In addition, we systematically study three Krylov subspace methods (called S(^3)CG, S(^3)MR, and S(^3)LQ) for solving shifted skew-symmetric linear systems. They all are based on Lanczos triangularization for skew-symmetric matrices and correspond to CG, MINRES, and SYMMLQ for solving symmetric linear systems, respectively. To the best of our knowledge, this is the first work that studies S(^3)LQ. We give some new theoretical results on S(^3)CG, S(^3)MR, and S(^3)LQ. We also provide relations among the three methods and those based on Golub–Kahan bidiagonalization and Saunders–Simon–Yip tridiagonalization. Numerical examples are given to illustrate our theoretical findings.

用于求解涉及偏斜对称矩阵的线性方程组的 Krylov 子空间方法近年来备受关注。Greif 等人[SIAM J. Matrix Anal. Appl., 37 (2016), pp.]在这项工作中,我们将 Greif 等人的结果扩展到奇异偏斜对称线性系统。此外,我们还系统地研究了三种克雷洛夫子空间方法(称为 S(^3)CG, S(^3)MR 和 S(^3)LQ ),用于求解移位偏斜对称线性系统。它们都是基于偏斜对称矩阵的 Lanczos 三角化,分别对应于求解对称线性系统的 CG、MINRES 和 SYMMLQ。据我们所知,这是第一部研究 S(^3)LQ 的著作。我们给出了关于 S(^3)CG, S(^3)MR 和 S(^3)LQ 的一些新的理论结果。我们还提供了这三种方法与基于 Golub-Kahan 二对角化和 Saunders-Simon-Yip 三对角化的方法之间的关系。我们还给出了数值实例来说明我们的理论发现。
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引用次数: 0
The number of string C-groups of high rank 高阶弦 C 群的数量
IF 1.5 1区 数学 Q1 MATHEMATICS Pub Date : 2024-07-18 DOI: 10.1016/j.aim.2024.109832

If G is a transitive group of degree n having a string C-group of rank r(n+3)/2, then G is necessarily the symmetric group Sn. We prove that if n is large enough, up to isomorphism and duality, the number of string C-groups of rank r for Sn (with r(n+3)/2) is the same as the number of string C-groups of rank r+1 for Sn+1. This result and the tools used in its proof, in particular the rank and degree extension, imply that if one knows the string C-groups of rank (n+3)/2 for Sn with n odd, one can construct from them all string C-groups of rank (n+3)/2+k for Sn+k for any positive integer k. The classification of the string C-groups of rank r(n+3)/2 for Sn is thus reduced to classifying string C-groups of rank r for S2r3. A consequence of this result is the complete classification of all string C-groups of Sn with rank nκ for κ{1,,7}, when n2κ+3, which extends previously known results. The number of string C-groups of rank nκ, with n2κ+3, of this classification gives the following sequence of integers indexed by κ and starting at κ=1:(1,1,7,9,35,<
如果 G 是一个阶数为 n 的传递群,它有一个秩为 r≥(n+3)/2 的弦 C 群,那么 G 必然是对称群 Sn。我们证明,如果 n 足够大,在同构和对偶性的前提下,Sn(r≥(n+3)/2)的秩为 r 的弦 C 群的数目与 Sn+1 的秩为 r+1 的弦 C 群的数目相同。这一结果及其证明中使用的工具,特别是秩和度的扩展,意味着如果知道 Sn 的秩为 (n+3)/2 的弦 C 群(n 为奇数),那么对于任何正整数 k,都可以从中构造出 Sn+k 的所有秩为 (n+3)/2+k 的弦 C 群。这一结果的一个结果是,当 n≥2κ+3 时,对 Sn 的所有秩为 n-κ 的弦 C 群进行了完整的分类,即 κ∈{1,...,7},这扩展了之前已知的结果。秩为 n-κ 的弦 C 群的数量,当 n≥2κ+3 时,这种分类给出了以下以 κ 为索引、从 κ=1 开始的整数序列:(1,1,7,9,35,48,135) 根据《在线整数序列百科全书》(On-Line Encyclopedia of Integer Sequences),这个整数序列是新的。它的序列号为 A359367。
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引用次数: 0
On the nonlinear Schrödinger-Poisson systems with positron-electron interaction 关于具有正电子相互作用的非线性薛定谔-泊松系统
IF 2.4 2区 数学 Q1 MATHEMATICS Pub Date : 2024-07-18 DOI: 10.1016/j.jde.2024.06.038

We study the Schrödinger-Poisson type system:{Δu+λu+(μ11ϕuμ12ϕv)u=12π02π|u+eiθv|p1(u+eiθv)dθ in R3,Δv+λv+(μ22ϕvμ12ϕu)v=12π02π|v+eiθu|p1(v+eiθu)dθ in R3,where 1<p<3 with parameters λ,μij>0. Novel approaches are employed to prove the existence of a positive solution for 1<p<3 including, particularly, the finding of a ground state solution for 2p<3 using established linear algebra techniques and demonstrating the existence of two distinct positive solutions for 1<p<2. The analysis here, by employing alternative techniques, yields a

我们研究的是薛定谔-泊松型系统:{-Δu+λu+(μ11ju-μ12jv)u=12π∫02π|u+eiθv|p-1(u+eiθv)dθ在R3中,-Δv+λv+(μ22jv-μ12ju)v=12π∫02π|v+eiθu|p-1(v+eiθu)dθ在R3中,其中1<p<3的参数为λ,μij>0。本文采用了新颖的方法来证明 1<p<3 正解的存在,特别是利用成熟的线性代数技术找到了 2≤p<3 的基态解,并证明了 1<p<2 存在两个不同的正解。本文的分析采用了其他技术,与 Jin 和 Seok (2023) [14] 的研究相比,获得了更多改进的结果。
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引用次数: 0
New quadratic and cubic polynomial enrichments of the Crouzeix–Raviart finite element Crouzeix-Raviart 有限元的新二次多项式和三次多项式富集
IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-07-18 DOI: 10.1016/j.camwa.2024.06.019

In this paper, we introduce quadratic and cubic polynomial enrichments of the classical Crouzeix–Raviart finite element, with the aim of constructing accurate approximations in such enriched elements. To achieve this goal, we respectively add three and seven weighted line integrals as enriched degrees of freedom. For each case, we present a necessary and sufficient condition under which these augmented elements are well-defined. For illustration purposes, we then use a general approach to define two-parameter families of admissible degrees of freedom. Additionally, we provide explicit expressions for the associated basis functions and subsequently introduce new quadratic and cubic approximation operators based on the proposed admissible elements. The efficiency of the enriched methods is compared with that of the triangular Crouzeix–Raviart element. As expected, the numerical results exhibit a significant improvement, confirming the effectiveness of the developed enrichment strategy.

在本文中,我们引入了经典 Crouzeix-Raviart 有限元的二次多项式和三次多项式富集,目的是在这种富集元素中构建精确的近似值。为实现这一目标,我们分别添加了三个和七个加权线积分作为丰富自由度。针对每种情况,我们都提出了这些增强元素定义明确的必要条件和充分条件。为了说明问题,我们随后使用一般方法定义了可容许自由度的双参数族。此外,我们还提供了相关基函数的明确表达式,并随后根据所提出的可容许元素引入了新的二次方和三次方近似算子。我们将丰富方法的效率与三角 Crouzeix-Raviart 元素的效率进行了比较。正如预期的那样,数值结果显示出显著的改进,证实了所开发的丰富策略的有效性。
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引用次数: 0
Exponential stability, T-controllability and optimal controllability of higher-order fractional neutral stochastic differential equation via integral contractor 通过积分承包商实现高阶分数中性随机微分方程的指数稳定性、T 可控性和最优可控性
IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-18 DOI: 10.1016/j.chaos.2024.115278

The existence, uniqueness, exponential stability with the trajectory (T-)controllability and optimal control results for mild solutions to the fractional neutral stochastic differential system (FNSDSs) are presented in this article. To demonstrate the results, the concept of bounded integral contractors combined with the regularity, a weaker notion of Lipschitz continuity, with stochastic approach and sequencing techniques are used. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the stability results, and the relevant nonlinear function does not have to meet the Lipschitz condition. Furthermore, exponential stability result for FNSDSs with Poisson jump via impulsive integral inequality is established following the trajectory (T-) controllability for higher-order FNSDSs via integral contractors with the help of Gronwall’s inequality and the optimal control problem for higher-order FNSDSs via Balder’s theorem. A numerical example is discussed to justify the theory. Finally, a filtration model and the real life stochastic Kelvin–Voigt and Maxwell models with the numerical simulation are demonstrated to satisfy the acquired results. This paper extends all previous works having the nonlinear Lipschitz continuous operators.

本文提出了分数中性随机微分系统(FNSDSs)温和解的存在性、唯一性、指数稳定性、轨迹(T-)可控性和最优控制结果。为了证明这些结果,我们使用了与正则性相结合的有界积分契约概念、较弱的 Lipschitz 连续性概念、随机方法和排序技术。与以往出版物不同的是,我们无需指定可控性算子的诱导逆来证明稳定性结果,相关非线性函数也不必满足 Lipschitz 条件。此外,在借助 Gronwall 不等式和 Balder 定理解决高阶 FNSDS 的轨迹(T-)可控性问题之后,通过脉冲积分不等式建立了具有泊松跳跃的 FNSDS 的指数稳定性结果。讨论了一个数值实例,以证明该理论的正确性。最后,通过数值模拟展示了过滤模型和现实生活中的随机开尔文-沃伊特和麦克斯韦模型,以满足所获得的结果。本文扩展了之前所有关于非线性 Lipschitz 连续算子的研究。
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引用次数: 0
Non-canonical maximum cliques without a design structure in the block graphs of 2-designs 2-设计块图中无设计结构的非正则最大簇
IF 1.6 2区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-07-18 DOI: 10.1007/s10623-024-01459-x
Sergey Goryainov, Elena V. Konstantinova

In this note we answer positively a question of Chris Godsil and Karen Meagher on the existence of a 2-design whose block graph has a non-canonical maximum clique without a design structure.

在本论文中,我们正面回答了克里斯-戈德希尔(Chris Godsil)和凯伦-米格尔(Karen Meagher)提出的一个问题,即是否存在一个块图具有非经典最大簇而没有设计结构的 2 设计。
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引用次数: 0
Numerical analysis of time filter method for the stabilized incompressible diffusive Peterlin viscoelastic fluid model 稳定的不可压缩扩散性彼得林粘弹性流体模型的时间滤波法数值分析
IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2024-07-18 DOI: 10.1016/j.camwa.2024.07.002

The Diffusion Peterlin Viscoelastic Fluid (DPVF) model describes the movement of specific incompressible polymeric fluids. In this paper, we introduce and evaluate a new low-complexity linear-time filter finite element (FE) method for the DPVF model. In order to avoid the value at time t=Δt, the proposed time filter method consists of three steps, including a post-processing step. Firstly, a first-order Euler backward nonlinear fully discrete mixed FE scheme is employed to compute the numerical solutions at time t1=Δt. For n1, we obtain the intermediate values (u˜hn+1,p˜hn+1,d˜hn+1) in Step II using a fully implicit backward Euler scheme. At the same time level, we proceed with these intermediate values (u˜hn+1,p˜hn+1,d˜hn+1) using the linear time filters. The linear time filters step does not significantly increase computational complexity. However, it can enhance temporal convergence accuracy from first order to second order for backward Euler time filter (BE time filter), and from second order to three order for BDF2 time filter. We demonstrate the almost unconditional stability of the scheme. Error estimates for the time filter method are derived and presented. Several numerical experiments are conducted to validate the theoretical findings and showcase the efficiency of the proposed method.

扩散彼得林粘弹性流体(DPVF)模型描述了特定不可压缩聚合物流体的运动。本文针对 DPVF 模型介绍并评估了一种新的低复杂度线性时间滤波有限元(FE)方法。为了避免时间 t=-Δt 时的数值,所提出的时间滤波法由三个步骤组成,包括一个后处理步骤。首先,采用一阶欧拉后向非线性全离散混合 FE 方案计算时间 t1=Δt 时的数值解。对于 n≥1,我们在步骤 II 中采用全隐式后向欧拉方案获得中间值(u˜hn+1,p˜hn+1,d˜hn+1)。同时,我们使用线性时间滤波器对这些中间值(u˜hn+1,p˜hn+1,d˜hn+1)进行处理。线性时间滤波器步骤不会显著增加计算复杂度。但是,它可以提高时间收敛精度,对于后向欧拉时间滤波器(BE 时间滤波器),收敛精度从一阶提高到二阶;对于 BDF2 时间滤波器,收敛精度从二阶提高到三阶。我们证明了该方案几乎无条件的稳定性。推导并给出了时间滤波方法的误差估计值。我们还进行了一些数值实验来验证理论结论,并展示了所提方法的效率。
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引用次数: 0
Heterogeneity-induced competitive firing dynamics in balanced excitatory-inhibitory spiking neuron networks 平衡兴奋-抑制尖峰神经元网络中异质性诱导的竞争性点燃动力学
IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-18 DOI: 10.1016/j.chaos.2024.115282

Excitatory–inhibitory (E-I) balance is important to maintain normal working and functioning of neuron networks. Parameter heterogeneity exists ubiquitously in neuron systems and plays significant roles in modulating neuron functions. This work concentrates on competitive and collective spiking behaviors of E-I neuron networks by considering heterogeneities in intra-network, inter-network couplings, and excitability currents. Macroscopic order-parameter dynamics is analytically derived in terms of the Lorentz-ansatz (LA) approach for a large population of quadratic integrate-and-fire (QIF) neurons, which is proved to accurately demonstrate various collective firing behaviors. Collaborated firing bifurcations of both independent excitatory/inhibitory networks and the coupled E-I networks are explored, and a wealth of collaborative firing behaviors are unveiled in the presence of parameter disorders, such as the steady state, the limit-cycle oscillations, the quasi-periodicity, and the chaotic firing. The emergence of fast and slow oscillatory modes due to the competition between the excitatory and inhibitory neuron populations is revealed. This mechanism is successfully applied to analysis of the fast-slow mode transitions and complicated collective firing behaviors. These studies are expected to well facilitate the understandings of working principles of coupling disorder in E-I balanced neuron networks.

兴奋-抑制(E-I)平衡对于维持神经元网络的正常工作和功能非常重要。参数异质性普遍存在于神经元系统中,并在调节神经元功能方面发挥着重要作用。本研究通过考虑网络内、网络间耦合和兴奋电流的异质性,集中研究 E-I 神经元网络的竞争和集体尖峰行为。研究采用洛伦兹-安萨(Lorentz-ansatz,LA)方法,分析推导了大量二次积分-发射(QIF)神经元的宏观阶参数动力学,并证明该方法能准确展示各种集体发射行为。探讨了独立兴奋/抑制网络和耦合 E-I 网络的协同发射分岔,揭示了在参数紊乱情况下的丰富协同发射行为,如稳态、极限周期振荡、准周期性和混沌发射。研究揭示了由于兴奋神经元群和抑制神经元群之间的竞争而产生的快慢振荡模式。这一机制被成功应用于分析快慢模式转换和复杂的集体发射行为。这些研究有望很好地促进对 E-I 平衡神经元网络耦合失调工作原理的理解。
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引用次数: 0
Linear and superlinear spreading speeds of monostable equations with nonlocal delayed effects 具有非局部延迟效应的单稳方程的线性和超线性扩展速度
IF 2.4 2区 数学 Q1 MATHEMATICS Pub Date : 2024-07-18 DOI: 10.1016/j.jde.2024.07.018

This paper is concerned with the propagation phenomena for the nonlocal reaction-diffusion monostable equation with delay of the formu(t,x)t=dΔu(t,x)+f(u(t,x),RJ(xy)u(tτ,y)dy),t>0,xR. It is well-known that if we take J(x)=δ(x) and τ=0, there exists a minimal wave speed c>0, such that this equation has no traveling wave front for 0<c<c and a traveling wave front for each cc, which is unique up to translation and is globally asymptotically stable. Furthermore, when J is symmetry and exponentially bounded and τ>0, Wang et al. (2008) [27] considered the effects of delay and nonlocality on the spreading speed and proved that (i) if 2f(0,0)>0, then the delay can slow the spreading speed of the wave fronts and the nonlocality can increase the spreading speed; and (ii) if 2f(0,0)=0, then the delay and nonlocality do not affect the spreading speed. However, when J is asymmetry or exponentially unbounded, the question was left open. In this paper we obtain a rather complete answer to this question. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed. We also investigate the case of exponentially unbounded kernels where we prove the non-existence of traveling wave solutions and obtain upper and lower bounds for the position of any level set of the solutions. These bounds allow us

本文主要研究形式为∂u(t,x)∂t=dΔu(t,x)+f(u(t,x),∫RJ(x-y)u(t-τ,y)dy),t>0,x∈R 的非局部反应-扩散单稳态延迟方程的传播现象。众所周知,如果取 J(x)=δ(x),τ=0,则存在一个最小波速 c⁎>0,使得该方程在 0<c<c⁎ 时没有行进波前,而在每个 c≥c⁎ 时都有行进波前,该波速在平移之前是唯一的,并且全局渐近稳定。此外,当 J 是对称的、指数有界且 τ>0 时,Wang 等人(2008)[27] 考虑了 J 的对称性。(Wang 等(2008)[27] 考虑了延迟和非位置性对传播速度的影响,并证明:(i) 若 ∂2f(0,0)>0,则延迟可减慢波阵面的传播速度,而非位置性可增加传播速度;(ii) 若 ∂2f(0,0)=0,则延迟和非位置性不影响传播速度。然而,当 J 为非对称或指数无界时,问题就悬而未决了。在本文中,我们得到了这个问题的一个相当完整的答案。更准确地说,我们证明了对于指数有界的内核,行波的最小速度是存在的,并且与传播速度相吻合。我们还研究了指数无界核的情况,在这种情况下,我们证明了行波解的不存在,并获得了解的任意水平集位置的上界和下界。通过这些界限,我们可以估计解是如何扩散的,这取决于内核。
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