风险谱函数的设计与选择

研究了风险谱函数的构造及谱风险度量在金融市场中的应用。根据风险厌恶系数和效用函数理论,提出了一种风险谱函数的设计构造方法,得到了指数风险谱函数和幂风险谱函数。实证分析表明,运用这两种谱函数所得到的谱风险度量的结果,差别并不大。最后,提出了以谱风险度量为目标函数的投资组合优化配置模型,并讨论了模型的求解结果。     

Al-12.7Si-0.7Mg合金超塑性变形行为及变形机理

对Al-12.7Si-0.7Mg合金在Instron5500电子万能材料试验机上进行超塑性拉伸实验.通过对该合金超塑性过程中延伸率δ,应变速率敏感性指数m值的计算,获得了不同变形温度、不同应变速率下δ和m值的变化规律.该合金在温度为793 K,应变速率为1.67×10-4s-1时,合金的应变速率敏感性指数和延伸率均达到最大值,分别为0.44,379%.分别构建了该合金的功率耗散率图以及铝合金RWS变形机理图.运用功率耗散率图预报该合金的超塑性变形区域;应用铝合金变形机理图并结合该合金超塑性拉伸前后显微组织变化规律,根据不同温度下Al-12.7Si-0.7Mg合金柏氏矢量补偿的晶粒尺寸值、模量补...     

气体热黏效应对干气密封性能影响的数值分析

基于气体多变过程理论和气体润滑理论,通过对雷诺方程的多变指数进行修正,建立了分析螺旋槽干气密封热黏效应的数学模型.采用有限元法对黏度对于干气密封性能的影响进行数值分析.结果表明：多变指数和黏度越大、压力和温度越高,则干气密封的端面气膜承载能力越强;在高速或中、高压工况下,需考虑气体热黏效应对干气密封性能的影响;当端面平均气膜厚度大于2 μm时,气体热黏效应对干气密封性能参数与气膜厚度关系的影响可以忽略不计.
     

Method for removing interference in chaotic signals based on the Lyapunov exponent

A new method based on the phenomenon of synchronization and the properties of chaos is proposed to reduce interference in the transferred chaotic signals of synchronized systems. The interference is considered as a series of small deviations from the original clean trajectory in the phase space. By means of our special design, these small deviations can be estimated using positive Lyapunov exponents, and removed from interfered chaotic signals. Application is illustrated for the Lorenz attractor, and numerical computing demonstrates that the method is effective in removing typical external interference.     

水分子振动体系动力学研究

在动力学群得到的水分子Hamiltonian的基础上,求解正则运动方程,计算固定键角近似下水分子振动体系的庞加莱截面、采用wolf重构法计算振动体系的最大Lyapunov指数．计算结果显示：对于四维振动体系,庞加莱截面只能反映体系局域的行为;非线性耦合和能量的局域化导致振动体系的混沌,强非线性耦合也导致体系的准周期运动．     

一类特殊双色有向图的本原指数

一个双色有向图D是本原的,如果存在非负整数h和k,且h＋k〉0,使得D中的每对顶点（i,j）,都存在从i到j的（h,k）途径．将k＋k的最小值定义为双色有向图D的本原指数．给出了一类双色有向图的本原条件和指数上界,并对极图进行了刻画．     

对称性与Sobolev嵌入

建立了一个Sobolev空间上部分对称函数到加权Lp空间的嵌入定理,并给出这一定理对具临界增长非线性椭圆边值问题的应用。过去这类结论主要是关于Holder函数的,笔者将这一结论推广到连续函数。     

变分方法及其在非线性偏微分方程应用方面的进展和未决问题

先介绍变分法发展的简单历史以及将来的发展趋势. 然后综述变分法应用于非线性偏微分方程的基本思想和最新成果. 通俗介绍环绕理论、变号临界点理论及应用,其中包括对称扰动方程和Rabinowitz公开问题、Brezis-Nirenberg临界指数方程、Li-Lin公开问题、Bose-Einstein凝聚、Berestycki-Caffarelli-Nirenberg猜测和Lane-Emden方程及猜想.     

Multifractal mass exponent spectrum of complex physiological time series

Physiological signal belongs to the kind of nonstationary and time-variant ones. Thus, the nonlinear analysis methods may be better to disclose its characteristics and mechanisms. There have been plenty of evidences that physiological signal generated by complex self-regulated system may have a fractal structure. In this work, we introduce a new measure to characterize multifractality, the mass exponent spectrum curvature, which can disclose the complexity of fractal structure from total bending degree of the spectrum. This parameter represents the nonlinear superpositions of the discrepancies of fractal dimension from all adjacent points in the curve and therefore solves the problem of original parameters for not fully reflecting the information of entire subsets in the fractal structure. The evaluations of deterministic fractal system Cantor measure validate that it is completely effective in exploring the complexity of chaotic series, and is also not affected by nonstability of the signal as well as disturbances of the noises. We then apply it to the analysis of human heart rate variability (HRV) signals and sleep electroencephalogram (EEG) signals. The experimental results show that this method can be better to discriminate cohorts under different physiological and pathological conditions. Compared with the indicator of singularity spectrum width, there are some improvements both on the computing efficiency and accuracy. Such conclusion may provide some valuable information for clinical diagnoses.     

甘肃省国内旅游客源市场分析

在论述旅游客源市场的内涵和客源市场分析有关理论的基础上,从时间特征、空间特征、旅游目的类型和人口特征4个方面对甘肃省国内客源市场进行了初步研究.结果表明,国内客流主要流向兰州、天水、酒泉和陇南,大多来自本省、临近省区和发达省区;客源市场淡旺季明显,旅游产品处于基础层次;以23～55岁游客为主,大部分具有本科以上学历,多为干部和学生;交通、食宿费用占旅游消费的主要部分.