Overlapping Schwarz and Spectral Element Methods for Linear Elasticity and Elastic Waves

The classical overlapping Schwarz algorithm is here extended to the spectral element discretization of linear elastic problems, for both homogeneous and heterogeneous compressible materials. The algorithm solves iteratively the resulting preconditioned system of linear equations by the conjugate gradient or GMRES methods. The overlapping Schwarz preconditioned technique is then applied to the numerical approximation of elastic waves with spectral elements methods in space and implicit Newmark time advancing schemes. The results of several numerical experiments, for both elastostatic and elastodynamic problems, show that the convergence rate of the proposed preconditioning algorithm is independent of the number of spectral elements (scalability), is independent of the spectral degree in case of generous overlap, otherwise it depends inversely on the overlap size. Some results on the convergence properties of the spectral element approximation combined with Newmark schemes for elastic waves are also presented.     

一类Feistel密码的线性分析

该文提出一种新的求取分组密码线性偏差上界的方法，特别适用于密钥线性作用的Feistel密码．该分析方法的思路是，首先对密码体制线性偏差进行严格的数学描述，分别给出密码线性偏差与轮函数F及S盒的线性偏差的数学关系；然后通过求取线性方程组最小重量解，确定密码线性偏差的上界．     

Boole函数的线性可分性(Ⅰ)——n-维超立方体的基本理论

Boole函数的线性可分性是前向人工神经网络理论中的一个比较困难的问题之一。目前仅对变量数n≤7的某些问题给予讨论。当n≥8时,尚无判别Boole函数线性可分的一般准则,更无线性可分Boole函数的计数公式。基于此,本文详细地研究了与Boole函数线性可分性有关的n-维超立方体的基本理论,包括n-维超立方体的基本性质、超立方体中的平行线、子超立方体的计数等,并给出了构造n-维超立方体图的一种新方法。     

插补法CAI研究

数字程序控制计算机辅助教学是将计算机技术用于数字程序控制的教学过程，它帮助学生学习并模拟教学实验．本文介绍了数字程序控制中直线插补和圆孤插补的ＣＡＩ实现方法．     

Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

COATES GRAPH APPROACH FOR GENERATING SYMBOLIC NETWORK FUNCTION

In this paper, symbolic code matrix ,constant matrix and count matrix are defined .The first twomatrices are used to describe the elemental expression of augmented matrix and the nede admittance equa-tion is thus obtained. The third matrix is used to obtain the incoming degree matrix, and according to thematrix all the 1- factors of the Coates graph are given. By using the data code, the determinant is expandedand the same items in the expansion are merged. Thus the symbolic network function in which no term can-cellation occurs is generated.     

切尔诺贝利事故释放的~(131)I所致牧草、奶类的污染水平及其变化规律

本文报道了苏联切尔诺贝利核电站事故释放的~(131)I对乌鲁木齐地区牧草、奶类的污染水平及动态变化规律。经估算,~(131)I经奶类所致成人(1.2μSv)和婴儿(120μSv)甲状腺最大待积剂量当量远低于我国放射卫生防护基本标准规定的年剂量限值,因此,对居民健康不会产生影响。     

一种在Kalman滤波中引入径向速度测量的新方法

研究在距离和径向速度测量噪声统计相关的情形下把径向速度测量引入Kalman滤波的新方法。分析了径向速度测量噪声与位置测量更新后状态滤波误差的统计相关性,根据Gauss-Markov定理导出了对应于径向速度测量的滤波方程由此而得到一种序贯滤波算法。两个不同的蒙特卡罗仿真表明,通过采用这一新算法引人径向速度测量,不仅可以大大提高状态估计的精度,而且其估计性能和计算效率优于传统的EKF。     

Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

Representation of shift-invariant operators onL 2 byH ∞ transfer functions: An elementary proof,a generalization toL p,and a counterexample forL ∞

We give an elementary proof of the well-known fact that shift-invariant operators onL ²[0, ∞) are represented by transfer functions which are bounded and analytic on the right open half-plane. We prove a generalization to Banach space-valuedL ^p -functions, where 1≤p<∞. We show that the result no longer holds forp=∞. This research was supported partially by the Weizmann Fellowship, and partially by the Air Force Office of Scientific Research under Contract F49620-86-C-0111.