线性随机桁架结构的平稳随机响应分析

研究了随机桁架结构的平稳随机响应问题。同时考虑结构的物理参数、几何尺寸的随机性，从结构平稳随机响应在频域上的表达式出发，利用求解随机变量函数矩的方法，导出了随机桁架结构在平稳随机激励下位移响应均方值的均值、均方差和变异系数的计算表达式。通过算例考察了随机荷载激励下结构物理参数、几何尺寸的随机性对结构随机响应的影响。     

Stochastic Hopf bifurcation in quasi-integrable-Hamiltonian systems

A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system‘s energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrable-Hamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system‘s parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions.     

依托于学科优势的物理实验教学改革研究

通过改革和实践,提高了学生的学习主动性和创新能力,促进了教学科研的良性互动,实现了教学科研协同育人。     

加筋土强度降低原因的理论分析

从理论上推导出了加筋土强度的数学表达式,分析了土的黏聚力与土筋界面参数变化对加筋土强度的影响,研究表明,当发生拉断型破坏时,黏聚力的减少比筋材提供的拉力占优势的情况下,加筋土的强度会低于素土的强度;当发生黏着型破坏时,黏聚力的减少比筋材提供的摩阻力占优势的情况下,加筋土的强度也会低于素土的强度。加筋土强度的降低程度与筋材在土中形成的夹层、土筋界面透水性、加筋间距有关。     

The MAP/PH/N retrial queue in a random environment

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.     

Method to accurate calibrate deposition rates of EUV multilayer coatings

Random thickness error is an important factor which effects the calibration accuracies of deposition rates for extreme ultraviolet （EUV） multilayer coatings fabricated by sputter deposition techniques. A least square fitting method is proposed to determine deposition rates and extract random thickness errors accurately. The validity of this method is shown by evaluating two deposition systems with control abilities of -0.1 nm and better than 0.01 nm respectively.     

具有变系数和时间延迟的随机SIV流行病模型

本文研究具有变系数和时间延迟的随机SIV流行病模型.首先证明模型存在唯一全局正解,然后利用半鞅收敛定理给出了疾病几乎处处灭绝的充分条件.     

不一致不完备直觉模糊信息系统的属性约简

利用广义优势关系,可完成不完备直觉模糊信息系统属性约简工作.若不完备直觉模糊信息系统属性约简不一致时,则可进一步利用广义优势关系定义此类信息系统的分布函数和最大分布函数,然后介绍分布约简和最大分布约简的概念,最后给出求分布约简和最大分布约简的有效方法.由此可成功解决不一致不完备直觉模糊信息系统属性约简问题.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.