中立型Volterra延迟积分微分方程块θ-方法的稳定性

研究了线性中立型V01terra延迟积分微分方程数值方法的稳定性，给出了块隐式θ-方法保持系统解析解不依赖于延迟的稳定性质的一个充分条件。最后，通过一些数值试验说明了这篇文章的主要结论。     

SERVICE VALUE NETWORKS： INTO PRACTICE

Modeling a business to match its customer perceived （and customer desired） outcomes, remains an on-going task. This paper considers shows how a service value networks （SVNs） approach may be engaged to model, and deliver, understanding of the front-end business and its direct engagement with its immediate （or front-end） customers. These front-end customers may be either： （1） its off-line, in-store customers - engaging directly with the business sales staff （or representative）, or-（2） its on-line, virtual customers - engaging with the business via internet or remote access. In this situation, both the business, and the customer draw upon their respective viewpoints, and both sides influence the interaction. External to these business and customer influences are additional factors that capture the immediate and broader global effects - termed environmental effects. These three business-customer engagement areas of influence are captured by a SVN SEM approach.
Without a business-customer encounter of some kind the likelihood of a services business, and a prospecting customer, successfully engaging in an exchange process is reduced. This exchange may be a physical, and/or services exchange, and/or an information and/or ideas exchange. To the business, this encounter is, in effect, a trade, and as a result, the business targets acquiring an economic exchange that will ultimately deliver a net positive economic outcome. To the customer, external and internal information feeds, servicing, perceived value, and satisfaction, are key encounter drivers. SVNs offers a new way to understand the business-customer encounter, and to then utilize this acquired knowledge to either： （1） build a strategic management model, or （2） reengineer its business networks, and to then create a re-positioned, more customer-aligned business operation - one that is capable of delivering win - win, competitive business-customer solutions.     

中国煤矿重大事故中故意违章行为影响因素结构方程模型研究

研究了中国煤矿重大事故中的煤矿工人故意违章行为的影响因素,以煤矿工人个体层面和煤矿组织层面的各类因素作为外源变量,行为效价和行为成本感知为中介变量,以煤矿工人高成本-高效价和高成本-低效价两类特征性故意违章行为作为内生变量,构建故意违章行为影响因素的结构方程模型,研究发现煤矿工人的传记特征对两类特征性故意违章行为具有直接的正向影响;煤矿生产条件对两类特征性故意违章行为没有显著影响;煤矿生产任务性质通过感知效价间接正向影响两类特征性故意违章行为;煤矿组织特征和关系特征变量均对两类特征性故意违章行为具有间接的负向影响.     

基于广义尤拉-沃克方程的白化滤波器

α-稳定分布可以更好地描述实际应用中所遇到的具有显著脉冲特性的随机信号和噪声,α稳定分布没有统一闭式的概率密度函数,其二阶及二阶以上统计量均不存在。描述了稳定分布的谱表示,提出了一种不同于二阶过程功率谱的共变谱密度概念,得到一种基于共变谱的稳定分布白噪声的概念及其判断标准,对传统意义上的白噪声进行了广义化,提出了一种新的预测反卷积广义尤拉-沃克方程及白化滤波器模型。计算机模拟表明,这种算法是一种具有良好韧性的白化滤波方法,是对传统的二阶统计量基础上的白化滤波方法的改造与推广。     

求解延迟微分方程块θ-方法的GPLm-稳定性

讨论了带有多个滞时量的延时微分方程的数值稳定性,分析了用块θ–方法求解多延迟微分方程GPm–稳定和GPLm–稳定的条件,基于Lagrange插值,证明了块θ–方法GPm–稳定的充分必要条件是方法是A-稳定的,块θ–方法GPLm–稳定的充分必要条件是θ=1。     

PEAK COVARIANCE STABILITY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.     

卡尔达诺关于三次方程的特殊法则

基于对卡尔达诺关于三次方程的一般法则和《大术》第6章的命题的分析,复原了卡尔达诺关于三次方程的17条特殊法则的构造过程,由此揭示出隐藏在这些法则背后的数学思想和方法,阐明了卡尔达诺对这些法则所作的模糊暗示的意义,并指出其综合叙述方式与这些法则的构造过程并不完全一致。另外,根据对这些特殊法则的适用范围的分类讨论,认为卡尔达诺构造这些特殊法则的目的并非专为解决三次方程的不可约情形。     

Jacobi符号在数论中的应用

Jacobi符号是数论中的重要工具.通过具体实例,讨论了利用Jacobi符号判断有理数是否是整数、求解不定方程、判断递归序列是否是平方数的基本方法.     

带强迫项的二阶脉冲时滞微分方程的振动性

研究带强迫项的二阶脉冲时滞微分方程的振动性,得到了若干判别此类方程振动的充分性条件,所得结果推广并改进了时滞微分方程的振动性理论中某些已知的相关结果.     

非线性Klein-Gordon方程的周期波解

利用构造新的辅助方程组,求出了两种形式的Klein-Gordon方程的大量的Jacobi椭圆函数形式的周期波解的精确表达式.同时,研究了解的极限情况,得到了方程的孤立波解.这种方法也可用于寻找其它非线性发展方程的新的精确解.