预测我国钢铁工业发展趋势的递归模型

本文根据我国钢铁工业生产特点,建立了60多个变量、28个方程的递归模型,描述了钢铁工业生产的结构形式,确定了主要生产环节的生产函数,给出了各种经济变量间的相互关系,预测了我国矿、铁、钢、钢材、产值等28个主要的内生变量的未来值,分析了“七五”、“八五”、“九五”三个五年计划可达指标、发展速度及保证条件。经过1984年的实际检验,证明模型的预测效果良好。     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

块三对角矩阵方程的追赶法及其应用

导出了块三对角矩阵方程追赶法的一套递推关系式，并编制出相应的计算机Ｃｏｄｅ。该Ｃｏｄｅ具有良好的实用价值，可供在实际问题中使用。     

Dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps

In this paper, the dynamical behavior of a hybrid switching SIS epidemic model with vaccination and Lévy jumps is considered. Besides a standard geometric Brownian motion, another two driving processes are taken into account: a stationary Poisson point process and a continuous time finite-state Markov chain. Firstly, we establish sufficient conditions for persistence in the mean of the disease. Then we obtain sufficient conditions for extinction of the disease. In addition, we also establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.     

Network Dynamics in Elemental Assimilation and Metabolism

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element’s degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.     

On an Application of Newton's Method to Nonlinear Operators with w-Conditioned Second Derivative

We present a new approach to study the convergence of Newton's method in Banach spaces, which relax the conditions appearing in the usual studies. The approach is based on the bound required for the second derivative of the operator involved. An application to a nonlinear integral equation is presented.     

半直线上时间随机环境中随机游动的渐近性质

给出了半直线上时间随机环境下随机游动的模型, 并利用马氏链理论研究了该随机游动的常返暂留准则和依概率收敛的大数定律， 得到在非常返情形下的中心极限定理.     

显著边缘直接引导的动态模糊图像盲复原方法

针对主动视觉中运动载体和云台抖动导致图像模糊的问题,提出一种显著边缘直接引导的动态模糊图像盲复原方法。为了克服经典 Canny 算子只能对边缘进行标注的缺陷,设计了图像边缘搜索-增强算法,并基于此提出了仅依据图像中显著边缘邻域完成点扩散函数优化估计的方法;为解决传统残差图像方法不能适应预测图像错位的问题,提出图像解模糊的递归残差修正算法来抑制复原图像波动;设计了图像复原的分层迭代处理流程,保证模糊图像复原的可靠性和精度。理想光照条件下的仿真表明,算法能准确恢复模糊图像的边缘,同时抑制复原图像中的波动。非理想光照条件下的仿真也验证了算法对环境有良好的适应性,具有较高的实际应用价值。     

基于动态递归模糊神经网络的动态系统辨识

模糊系统和神经网络由于具有逼近任意连续非线性映射的特性而广泛应用于系统的辨识和控制,但是传统的模糊神经网络是一种静态映射,不适用于动态系统的辨识,而现实工程中的控制对象反映的是系统的动态行为.为了提高动态系统的辨识精度,提出了一种新型的动态递归模糊神经网络,并根据动态递归神经网络的数学模型推导其动态反向传播学习算法及其改进算法.仿真结果表明:由于动态模糊神经网络的辨识过程同时利用了系统的当前数据和历史数据,对动态系统的辨识,特别是对具有纯时间延迟动态系统的辨识,较传统模糊神经网络在辨识精度和稳定性方面具有更好的效果.同时,确定网络权值和隶属函数参数初始值的方法可使动态系统的辨识过程具有更快的收敛速度.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.