Krylov子空间投影法研究进展

Ｋｒｙｌｏｖ子空间投影法是一类非常有效的大型稀疏线性代数方程组解法，已被广泛应用于各种领域，随着左右空间Ｌｍ，Ｋｍ的不同取法可以得到许多人们熟知的方法．本文按矩阵Ｈｍ的不同类型，即为上Ｈｅｓｓｅｎｂｅｒｙ阵还是三对角阵将Ｋｒｙｌｏｖ子空间投影法分成两大类，从每步迭代是否具有最优性和方法的存储量、计算量等方面对Ｋｒｙｌｏｖ子空间法及其最新进展进行评述，指出Ｋｒｙｌｏｖ子空间法的局限及今后的研究方向．     

《光电技术》课程的教学改革与实践

对《光电技术》课程的教学内容和教学方法进行了改革，并提出了如将教学和科研有机结合起来开展实验教学改革，使教学能紧跟上高科技的飞速发展，充满活力和时代气息。实践证明，这些教学改革效果良好，不仅有助于激发学生学习兴趣，而且有利于培养学生分析问题和解决问题的能力。     

Samples Selection for Artificial Neural Network Training in Preliminary Structural Design

An artificial neural network (ANN) is applied in the preliminary structural design of reticulated shells. Major efforts are made to enhance the generalization ability of networks through well-selected training samples. Number-theoretic methods (NTMs) are adopted to generate samples with low discrepancy, i.e.uniformly scattered in the domain, where discrepancy is a quantitative measurement of the uniformity. The discrepancy of the NTM-based sample set is 1/6-1/7 that of samples with equal spacing. In a case study,networks trained by NTM-based samples are compared with those trained by equal-spaced samples in generalizing performance. The results show that both the computational precision and stability of the former ANNs are more satisfactory than those of the latter. It is concluded that the flexibility of ANNs in generalizing can be effectively increased by use of uniformly distributed training samples rather than simply piling data.More reliable uniformity should be obtained, however, through NTMs instead of equal-spaced samples.     

抛物型方程初值问题的概率数值解法

Ｆｒｉｅｄｍａｎ在［１］中给出了一般抛物型方程Ｃａｕｃｈｙ问题解的概率表达式。在此基础上，给出了它的概率数值及其误差估计。     

非线性自治系统不稳定性的一个判断方法

给出非线性自治系统不稳定性的一个简便的判据：从对应的特征方程的系数符号不尽相同，即可系统的零解是不稳定的。     

最小二乘解存在的充分必要条件

本文提出了当观测值的权矩阵为正定或半正定的前提下，其最小二乘解存在的充分必要条件为并以间接平差为例验证了该结论的正确性。     

修正的Navier—Stokes方程的再生性质和周期解

本文证明了由提出的修正的Navier-Stokes方程在小外力的条件下对t_1∈(0,T]存在唯一的初始速度分布使得相应的初边值问题的广义解具再生性质:(t_1)=(0)=.从而当外力还是时间t的周期函数时,是周期解.进而证明此周期解以指数方式吸引相应于同一外力但初值可任意的其它解.上述结论的证明基于对广义解v的导数v在空间L~∞(0,T;L~2(Ω))中估计.     

Forecasting recessions using the yield curve

We compare forecasts of recessions using four different specifications of the probit model: a time invariant conditionally independent version; a business cycle specific conditionally independent model; a time invariant probit with autocorrelated errors; and a business cycle specific probit with autocorrelated errors. The more sophisticated versions of the model take into account some of the potential underlying causes of the documented predictive instability of the yield curve. We find strong evidence in favour of the more sophisticated specification, which allows for multiple breakpoints across business cycles and autocorrelation. We also develop a new approach to the construction of real time forecasting of recession probabilities. Copyright © 2005 John Wiley & Sons, Ltd.     

复变函数论教学内容与教学方法的新探

随着高中数学教材内容的不断更新,高师院校复变函数论课程内容和教学方法的调整势在必行。本文在分析现状的前提下,就复变函数论课程内容和教学方法进行了一些有益的探索。     

银行系统网络运行现存的若干问题和解决建议

通过对银行系统网络现状的分析，从广域网和局域网两个不同的角度指出了银行现有的网络结构、体系存在的问题及其原因，并提出了较为可行的解决方法，对现在的大型网络系统有普遍的意义。