Pad逼近求解抛物型偏微分方程的并行算法研究

一维抛物型偏微分方程可以用精细积分方法精确求解。当精细积分中的矩阵指数函数用Pad 逼近来代替时 ,可以得到一系列由简到繁、精度由低到高的差分格式 ,因而便于根据实际需要进行选取。常见的求解抛物型方程的差分格式如古典显式格式、隐式格式及六点差分格式为其中的特例。Pad 逼近格式主要包括矩阵运算和线性方程组求解。本文利用 Pad 逼近格式对应的方程组系数矩阵为带状矩阵的特点 ,把原来在整个区域上求解的问题转化为分区域求解 ,在 TRANSPUTER并行机上实现了该问题的并行算法 ,并对该并行算法的时间复杂度进行了分析。算例结果表明 Pad 逼近并行算法有很好的计算效果和并行效率。     

K-Li冷碰撞散射特性的理论研究

本文应用量子方法和半经典方法计算了表征锂(6Li,7Li)原子和钾(39K,40K,41K)原子间超冷碰撞特性的散射参数,如s波散射长度,有效力程,p波散射长度等.超冷温度下6Li-39K单重态和三重态原子间的弹性散射截面主要为s波贡献,随着碰撞能量的增加散射截面有丰富的形状共振出现,计算发现单重态和三重态散射截面均存在显著的i波形状共振.此外,本文应用简并内态近似获得了超精细态相互作用时的s波散射长度.     

水面舰船的数学船型

利用近似理论,提出船型曲线的带有形状因子的指数函数近似,进而利用设计要求中的排水量和浮心纵坐标,构造超越方程组.通过求解形状因子,得到船体型线的数学表达,获得满足静水性条件的初始船型,从而实现舰船的全参数化设计.技术利用舰船主尺度获得舰船初始船型,有助于舰船的概要设计和利用多学科设计优化技术.实例验证了方法的有效性.     

ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LEVY NOISES

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian α-stable Lévy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Lévy noises.     

《线性代数》新教材精彩案例(之二)

<正>李尚志为非数学专业编写的《线性代数》教材于2011年6月由高等教育出版社出版.本文介绍了书中一部分精彩案例.3内积的推广例1研究表明,某种材料在生产过程中的废品率y与某种化学成分的含量百分比x近似地成一次函数关系y=kx+b.试根据x,y的如下三组实测数据求待定常数k,b的值.     

一类新的拟Bernstein-Bézier曲线

构造了一类新的带双参数形状可调的拟Bernstein基函数,它是在三次Bernstein多项式的基础上扩展而成的一组n次拟Bernstein基.在此基础上,定义了带双形状参数的拟Bernstein-Bézier曲线,它保留了Bézier曲线的几何特征,并具有形状可调的特性.在控制点给定的情况下,可通过改变形状参数的值整体或局部地调控曲线的形状,同时给出参数控制及曲线拼接应用的实例.     

LIMIT CYCLES OF A GENERALIZED LINARD DIFFERENTIAL EQUATION VIA AVERAGING THEORY

We apply the averaging theory of first and second orders to a generalized Liénard differential equation to study the maximum number of limit cycles of the system.     

关于属性测度空间粗糙集模型的一个注记

文[1]关于属性粗糙集的定义中,上、下近似算子分别由等价类中元素属性测度的上、下确界来确定,没有充分反映等价类中其它元素的作用,在信息处理中不免造成元素信息的丢失。为此提出一种新的属性粗糙集近似算子的表示方法,给出了相应的性质,并实例说明了这一方法的合理性。     

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation method for the considered system.     

Modal acoustic impedance force on a spherical source near a rigid interface

The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.