一类带扰动的随机脉冲泛函微分方程解的渐近性北大核心CSCD

该文讨论了一类带扰动的随机脉冲泛函微分方程解的渐近性.通过比较扰动方程的解和原方程的解,得到了两者逼近的充分条件.首先,两者在有限的时间区间上相互逼近;其次,当扰动趋于零时,区间长度趋于无穷大,在这个区间上两个解仍然是相互逼近的.最后,举例说明了结果的有效性.     

Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model北大核心CSCD

A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on Ω ⊂ RN(N≥2). The global existence of the solution on Ω ⊂ R3 was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for N = 3 and N = 2. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

M-矩阵平方根的一类迭代法

矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.     

Schrödinger方程的连续时空有限元方法

本文讨论Schr?dinger方程的连续时空有限元方法,通过引入相应的时空投影算子,利用实部虚部分离技巧,得到了变量u在时间节点处的L²范数,以及u和u_t的全局L²(H¹)和L²(L²)范数意义下的最优误差估计结果.该文的结论对进一步探索和设计Schr?dinger方程的数值算法是有益的.     

基于不确定指数O-U过程带有浮动利率模型的亚式期权定价

不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。     

基于三阶段SBM模型的中国节能服务上市企业效率研究

节能服务企业效率对于推动节能服务产业发展和确保国家“双碳”目标实现具有重要意义。运用三阶段SBM模型,对2020年60家中国节能服务上市企业的综合效率进行实证研究,并分析效率的影响因素。研究结果表明,经济发展水平对综合效率具有双重影响,合适的产业结构和较高的投入资本回报率有利于综合效率提升,而政府补贴与企业存续时间制约了综合效率改进;剔除环境因素与随机误差影响后,多数企业综合效率下降,整体效率偏低;提高规模效率是提升综合效率的关键,且绝大部分企业处于规模收益递增状态。研究最后提出创新补贴方式、建立企业认证制度、开展综合能源服务和推动企业间兼并重组等可行建议,以提升节能服务企业的综合效率。     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Minimum energy configurations on a toric lattice as a quadratic assignment problem

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we prove that the SDP bound is stronger than the CQP bound. We then apply these to improve known bounds on a discrete energy minimization problem, reformulated as a QAP, which aims to minimize the potential energy between repulsive particles on a toric grid. Thus we are able to prove optimality for several configurations of particles and grid sizes, complementing earlier results by Bouman et al. (2013). The semidefinite programs in question are too large to solve without pre-processing, and we use a symmetry reduction method by Permenter and Parrilo (2020) to make computation of the SDP bounds possible.