GLOBAL EXISTENCE FOR A CLASS OF SYSTEMSOF NONLINEAR WAVE EQUATIONS INTHREE SPACE DIMENSIONS

Consider a system of nonlinear wave equationsfor i = 1, … , m, where F, (i = 1, … , m) are smooth functions of degree 2 near the origin of their arguments, and u = (u1, … ,um), while u and x u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlineaxity for which the global existence of small solutions is ensured. For example, global existence of small solutions for arbitrary cubic terms,arbitrary cubic termswill be established, provided that c12 ≠ c22.     

A rigid graph for every set

A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002     

On operators and search space topology in multi-objective flow shop scheduling

Multi-objective optimization using evolutionary algorithms identifies Pareto-optimal alternatives or their close approximation by means of a sequence of successive local improvement moves. While several successful applications to combinatorial optimization problems are known, studies of underlying problem structures are still scarce.     

The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.     

用多焦点全息透镜实现多重谱分数傅里叶变换

提出用多焦点全息透镜实现多重谱分数傅里叶变换.利用全息方法通过一次曝光制作出多焦点的全息透镜,分析了用此全息元件实现这种变换的条件,并在实验上实现了多重谱分数傅里叶变换. 实验结果表明这种变换方法简便可行,可广泛应用于多通道光学信息处理系统及多目标图像识别系统中.     

晶体中离子质量差异与激活离子光谱线热加宽和热位移

证明了基质晶体离子的质量差异对其中的激活离子光谱线的热加宽和热位移有贡献，对于单声子吸收或发射机制产生的热加宽和热位移而言，其贡献可以用一个乘积因子D^2表示，对于喇曼散射机制引起的热加宽，其贡献可以用乘积因子D^4表示，文中分别给出两种离子组成的晶体和三种离子组成的晶体的D的表示式。     

各向异性材料中共线刚性线夹杂的纵向剪切问题

本文研究各向异性材料中共线刚性线夹杂，（有时称作“硬裂纹”或“反裂纹”问题）的纵向剪切问题。利用复变函数方法，提出了一般问题的公式和某些实际重要问题的封闭形式解，考察了刚性线端点附近的应力分布．从本文解答的特殊情形，可以直接导出各向同性材料相应问题的公式和结果，包括某些已有的结果￣［７］．     

Instability of Fabry-Perot interferometer with a multilayered paramagnetic filling

The results of the analysis of the stability of stationary solutions of wave equations discribing a behavior of the nonlinear Fabry-Perot interferometer with a saturated paramagnetic filling are presented in this paper. The cases when paramagnetic medium is characterized by a homogeneously and nonhomogeneously broadened line of the magnetic resonance have been considered. Areas of unstable behavior of these characteristics of the resonance structure have been found.     

Characterization of strongly interacted multiple cracks in an infinite plate

Based on the Kachanov method and the alternating iteration technique, a new method is proposed to deal with the problem of the strongly interacted multiple cracks in an infinite plate. Unlike the Kachanov method which neglects the interaction of the tractions of the non-uniform components, the tractions of the non-uniform components on the surfaces of cracks are considered through the alternating technique. The accuracy and efficiency of present method are validated by comparing the results of two collinear and two parallel overlapped open the cracks obtained by the present method with those of the exact solutions, the results of the Kachanov method and the alternating iteration technique. Applications of present method in solving sliding close crack problems and evaluating the plastic zones demonstrate the versatility of present method.     

Nonlinear multiple objective optimization: An algorithm and some theory

This paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using Zionts—Wallenius type of interaction. The Zionts—Wallenius method, as extended in this paper, can be used for solving multiple criteria problems with concave objective and (implicit) value functions and convex feasible regions. Modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed.This research was supported, in part, by a Faculty Research Development Award and by a Council of 100 Research Grant from Arizona State University (Roy), and by a grant from Y. Jahnsson Foundation, Finland (Wallenius). The research was performed while the second author was a Visiting Professor at Arizona State University.