ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

链环的trip矩阵

ZULLI L首先构造了一个用于计算纽结Kauffman尖括号多项式的模2矩阵,纽结的trip矩阵.为了构造链环的trip矩阵,引入了一个带标识的穿有m个孔的圆盘来取代纽结情形下的圆盘,其中m为链环的分支数.主要结果为:定理若状态S是从状态AA…A经过i1,i2,…,ip位置上的标记替换(A换成B)而得的状态.设Ts是将trip矩阵T的左上角的n×n子块中ai1i1,ai2i2,…,aipip之值进行替换(0→1或1→0)所得的矩阵,则#(L|S)=n+m-秩(Ts).因此计算链环Kauffman尖括号多项式就归结为计算一组模2矩阵的秩.     

一类矩阵多项式的秩特征

给出了一类矩阵多项式的秩特征定理及它的多种证法.     

一种基于图论与熵的专家判断客观可信度的确定方法

本文给出一种群决策中确定专家判断可信度的方法，其主要思路是首先通过图论中最小生成树的方法提取专家判断矩阵的全部信息，其次，使用相对熵指标确定获得专家判断的最终结果，并同时衡量专家自身判断的统一程度，从而确定专家判断的相对客观可信度。最后，文章给出一个典型的算例以说明该方法的可行性和有效性。     

基于DS/AHP的供应商选择方法

供应商选择方法有很多种，在众多的方法中层次分析法以能够将定性指标定量化而被广泛应用于供应商选择决策中。考虑到供应商选择问题中包含有很多的不确定性而证据理论在处理不确定问题又有着独特的优点，因此本文采用了一种由层次分析法和证据理论结合而产生的DS／AHP决策方法，并将其应用于供应商选择决策问题中，该方法综合了层次分析法和证据理论的优点，可以更科学的进行供应商选择决策，最后通过一个例子说明这种方法在供应商选择中的应用。     

The polarization property and irradiance distribution of incoherent and coherent Gaussian beam combinations

Based on the beam coherence-polarization (BCP) matrix, the polarization property of coherent and incoherent Gaussian beam combinations is studied in detail. The general expressions for the degree of polarization P of the resulting beam in case of incoherent and coherent combinations are derived. It is shown that P is dependent on the incoherent or coherent combination, propagation distance, separation, azimuth of the polarization plane and numbers of beamlets in general. The irradiance distribution of the resulting beam for the coherent cases depends on the azimuth of the polarization plane of beamlets. However, for the incoherent case it does not.     

Measurements of Optical Signals and Their Spectra in the Femtosecond Range with Additional Phase Modulation

A solution to the phase problem in optics is considered within the context of the analysis of signals changing in time and of the effect of an object under investigation on the probing radiation. The solution is based on the use of a twin-wave interferometer with phase modulation in one of the channels and a spectrometer. The analysis is concerned, in particular, with signals and processes of ultrashort duration. To shift the frequency in the interferometer channel, an electrooptical crystal of ferroelectric perovskite is used as the modulator. Errors of amplitude and phase structures determined are analyzed.     

光线反射过程的矩阵表达方法

分析反射线交面方程的特点，引入了反射矩阵并分析其实质意义，导出描述反射过程的最简单的反射矩阵，为反射过程基于数学运算软件的自动运算及求取多反射平面连续反射时反射线交面方程的运算提供了依据和方法。     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.