Stable Rank One and Real Rank Zero for Crossed Products by Finite Group Actions with the Tracial Rokhlin Property

The authors prove that the crossed product of an infinite dimensional simple separable unital C＊-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C＊-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.     

（2＋1）维色散长波方程的扩展椭圆函数有理展开解法

在一个新的更一般的假设下,借助于符号计算,提出了一个椭圆函数有理展开法,并用它统一地求出许多非线性发展方程新的双周期精确解.本文选择(2+1)维色散长波方程作为此方法的应用来加以说明.得到了Yan方法所得的所有解,并且得到更多的一般形式的解.在m取它的极限时,可得到许多冲击波解和孤立波解.     

THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.     

一类非线性非紧算子不动点定理的推广及其应用

本文研究了一类非线性非紧算子不动点定理.利用锥理论,在不需要非线性项满足连续性和紧性条件下,获得无穷区间上Frodholm型积分方程解的存在唯一性,并给出逼近解迭代序列的误差估计.     

(2+1)维色散长波方程新的类孤子解

通过一个简单的变换,将(2+1)维色散长波方程简化为人们熟知的带强迫项Burgers方程,借助Mathematica软件,利用齐次平衡原则和变系数投影Riccati方程法,求出了(2+1)维色散长波方程新的精确解.     

高维无穷时滞脉冲积分微分方程概周期解的存在唯一性

研究一类高维无穷时滞的非线性脉冲积分微分方程x′(t)=A(t)x(t)+∫-t∞C(t,s)g(s,x(s))ds+f(t,x(t-τ))+b(t),t≠tkΔx(t)=Bkx(t)+Ik(x(t))+γk,t=tk,k∈Z概周期解的存在性、唯一性问题.利用不动点原理和线性系统的指数二分性理论,建立了保证其概周期解存在性、唯一性的充分条件,得到了一些新的结果.     

Z[3]上无限维矩阵广义逆

研究整环Z[3]上无限维矩阵V关于无限维矩阵构造下的逆、M-P逆和群逆,给出V的不同的逆、M-P逆等,推广了Saranya和Sivakumar的结果,并且得到Z[3]上无限维矩阵广义逆更广泛的性质.     

无穷维Hamilton算子的二次数值域

研究了一类无界无穷维Hamilton算子的二次数值域的性质,进而,应用二次数值域来刻画了无穷维Hamilton算子谱的分布范围,并给出了二次数值域的闭包包含谱集的结论.     

基于机场货运预测的GM(1,1)建模过程问题分析

运用灰色系统GM(1,1)模型进行预测时,模拟精度和预测精度是关注的焦点.对原始数据构造缓冲算子和进行完整的前期检验,运用等维灰数递补的动态建模方法,针对误差建立残差修正模型,都可以提高预测的可信度.通过归纳建模各阶段可能出现的典型问题以及解决方法,以期对建立优化模型有所帮助.最后建立GM(1,1)模型预测天津滨海机场货邮吞吐量.     

A PML Method for Electromagnetic Scattering from Two-dimensional Overfilled Cavities

In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer （PML） is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.