平稳过程在正交变换下的能量密度效率

第一次计算出了宽平稳过程在三角变换和斜变换这样一些新正交变换下的能量密度效率。     

用液氮淬冷法进行花粉破壁的实验研究

通过正交设计实验，利用液氮将油菜花粉进行深低温超快速冷冻处理后，借助显微镜对解冻后的花粉进行显微观察，拍照和破壁率统计，同时采用苯酚-硫酸法进行胞外总糖含量测定，实验表明油菜花粉破壁优化条件为：外包紫铜，解冻温度95℃，反复冻结解冻3次，此时每克花粉中胞外总糖变化量最大值达59.588mg(以葡萄糖计），较未经冻结解冻处理的上升了31.25%，破壁率达94.97%.     

Projection techniques for nonlinear principal component analysis

Principal Components Analysis (PCA) is traditionally a linear technique for projecting multidimensional data onto lower dimensional subspaces with minimal loss of variance. However, there are several applications where the data lie in a lower dimensional subspace that is not linear; in these cases linear PCA is not the optimal method to recover this subspace and thus account for the largest proportion of variance in the data.Nonlinear PCA addresses the nonlinearity problem by relaxing the linear restrictions on standard PCA. We investigate both linear and nonlinear approaches to PCA both exclusively and in combination. In particular we introduce a combination of projection pursuit and nonlinear regression for nonlinear PCA. We compare the success of PCA techniques in variance recovery by applying linear, nonlinear and hybrid methods to some simulated and real data sets.We show that the best linear projection that captures the structure in the data (in the sense that the original data can be reconstructed from the projection) is not necessarily a (linear) principal component. We also show that the ability of certain nonlinear projections to capture data structure is affected by the choice of constraint in the eigendecomposition of a nonlinear transform of the data. Similar success in recovering data structure was observed for both linear and nonlinear projections.     

基于矩陣正交分解的自适应算法

自适应算法是各种自适应系统的核心.计算稳定性是衡量算法优良程度的重要指标之一.本文讨了论两类最小二乘算法的计算稳定性.其一是基于正则方程的递推求解方法,这是目前各种自适应算法的基础;另一是正交分解算法.后者的计算稳定性要比前者高.研究了一种基本的正交分解自适应算法,并指出,如果初始条件恰当,它将得到和批处理同样的结果.将这种方法用于空间谱估计,初步结果表明,用它能实现高分辨率精确测向.     

The Establishment of the Projections of Four to Seven-Dimensional Rectangular Coordinate Systems into the Three-Dimensional Space

Starting from the finite rotation group,the author makes a penetrating study of 4 to 7-dimensional hypercube so that we have acquired the projection models of 4 to 7-dimeneional spatial rectangular coordinate systems into the three-dimensional space to have the 4 to 7-dimensional geometric figures demonstrated correctly.     

3D图形平行投影的算法研究与实现

投影是３Ｄ图形显示中必不可少的步骤，本文给出了Ｓｕｎ平台上的图形软件包ＸＧＬ中的３Ｄ图形的平行投影的二种算法；即具广泛意义的算法及其改进算法，并在ＸＧＬ中实现它们；然后对两种方案进行了比较。     

Book Reviews

Books reviewed:
J.K. Lindsey, Introductory Statistics: A Modelling Approach
D.R. Brillinger, L.T. Fernholz & S. Morgenthaler (eds), The Practice of Data Analysis: Essays in Honor of John W. Tukey
Thomas P. Ryan, Modern Regression Methods
Samuel Kotz & Cynthia R. Lovelace, Process Capability Indices in Theory and Practice
David A. Harville, Matrix Algebra from a Statistician's Perspective
Steven G. Krantz, A Primer of Mathematical Writing
Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences     

句法-语义映射理论探微——兼谈理论在汉语中的运用问题

词库理论是语法研究的核心内容,汉语动词体系和英语动词体系存在明显的差别,需要对建立在英语语料上的理论做出适当调整,从而建立符合汉语事实的词汇语义-句法接口理论。     

混合HOGA-SVM财务风险预警模型实证研究

目前涉及遗传算法与支持向量机相结合的预测模型中,遗传算法基本上采用的是标准算法.但是在对全局函数的优化中,一般的遗传算法容易陷入局部最优,从而降低遗传算法收敛速度和搜索精度,进而影响财务风险预警模型的精度与速度.基于此,提出了基于混合全局优化正交遗传算法(HOGA)和支持向量机(SVM)的财务风险预警模型(HOGA-SVM),通过使用混合全局优化正交遗传算法连同支持向量机来改进支持向量机进行财务风险预警的效果.结果显示,提出的模型不仅提高了财务风险预警的准确率和速度,而且模型的两类分类错误率(尤其是第一类分类错误率)相对其他模型也有了明显下降.未来的工作可以把模型的应用扩大到多分类的财务风险预警问题中.     

Factor analysis as a tool for data analysis

The use of factor analysis in analyzing real data is influenced not only by mathematical models but also by the objectives of the research at hand, the amount of data to be analyzed and the departures of the data from the model. Factor analysis is a process performed in several steps, including data screening and assessment of assumptions necessary for the model as well as the actual computations—the new analyst may need assistance in deter-mining the initial method of extraction, how many factors to request, the method of rotation and how to interpret the factors— these steps are discussed with reference to figures containing computer output for a real problem. The importance of auxiliary information and graphical displays to aid the statistician during the factor analysis process is stressed.