给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l₁,l₂,…,l_m).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得最小覆盖成本和反向覆盖成本的顶点.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

基于流量测点的热网变动阻力系数优化辨识

随着供热计量系统的普及，系统可以根据负荷的变化进行调整，管网的阻力系数随即发生变化。对变动阻力系数进行优化辨识是了解供热管网实时运行状况的有效手段。提出一种基于流量监测数据的供热管网变动阻力系数优化辨识方法，并利用遗传算法进行求解。对洛阳市某小区供暖季管网实际运行数据进行验证，辨识结果的相对误差在5%以内。结果表明：该方法可以在只有流量观测数据时得到精度较高的供热管网变动阻力系数，为供热系统的运行调节提供指导。     

汽配件颜色喷涂顺序问题的TSP转化与建模

汽配件颜色喷涂顺序问题通常以生产线上相邻汽配件颜色切换次数少为最优目标,以进一步降低生产成本.该类问题具有所有汽配件都必须喷涂一次且只喷涂一次的特点,为此提出了TSP转化与建模的方法.将待喷涂汽配件定义为TSP顶点,任意两个待喷涂汽配件的颜色切换定义为顶点的距离,仿照TSP问题构建0-1规划模型;类似于顶点距离,将某些汽配件的颜色或类别不相邻要求定义为0-1矩阵,巧妙地构造了喷涂生产的约束条件.该建模方法简单快速,通用性高,适用于具有类似特点的各类生产实践问题.     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether $\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}$ takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range $0?\frac{\alpha (x)p(x)?n+\lambda (x)}{p(x)}?1$. We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.     

变刚度层叠梁的力学性能研究

为满足不同场景下的功能需求，变刚度结构得到越来越广泛的应用．以机器人手臂为例，在执行操作时，需要其手臂的结构刚度足够大，避免出现过大的扭曲和变形，而在与人交互时，又需要其结构足够柔软，以保证在此过程中与人交互的安全性．该类变刚度结构可根据需求通过外部激励在柔性和刚性状态之间自由切换．在该文章中，研究分析了层叠梁结构，通过理论推导和数值模拟，对其力学性能做出了很好的预测，同时为此类结构的研究提供了有效可靠的思路和方法．     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.