WKB Wave Function of the General Time-Dependent Quadratic Hamiltonian System

We derived the WKB wave function for the general time-dependent quadratic Hamiltonian system using a unitary transformation method. We applied our research to sinusodially drived Caldirola–Kanai oscillator and confirmed that the time evolution of our approximated WKB wave function is similar to that of the exact one. This wave function can be used to analyze the interference between the probability amplitudes contributed by the area of overlap in phase space of quantum states.     

Line graphs of bipartite graphs with Hamiltonian paths

It is shown that, if t is an integer ≥3 and not equal to 7 or 8, then there is a unique maximal graph having the path P_t as a star complement for the eigenvalue ?2. The maximal graph is the line graph of K_m,m if t = 2m?1, and of K_m,m+1 if t = 2m. This result yields a characterization of L(G ) when G is a (t + 1)‐vertex bipartite graph with a Hamiltonian path. The graphs with star complement P_r ∪ P_s or P_r ∪ C_s for ?2 are also determined. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 137–149, 2003     

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.     

Effective stability for generalized Hamiltonian systems

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems, dimensions of action variables and angle variables might be distinct.     

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.     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.