正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测．本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测．     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

The Tolerance of All-Optical Switching Based on Cascaded Second-Order Nonlinearity in PPLN APE Waveguide

Based on solving the couple mode equation numerically, the characterization of the signal power on the gate power was analyzed. And the relationship of the tolerance of the grating period and the bulk temperature on the interaction length was analyzed.     

Dispersion and distribution of organically modified montmorillonite in nylon‐66 matrix

Nylon‐66 nanocomposites were prepared by melt‐compounding nylon‐66 with an alkyl ammonium surfactant pretreated montmorillonite (MMT). The thermal stability of the organic MMT powders was measured by thermogravimetric analysis. The decomposition of the surfactant on the MMT occurred from 200 to 500 °C. The low onset decomposition temperature of the organic MMT is one shortcoming when it is used to prepare polymer nanocomposites at high melt‐compounding temperatures. To provide greater property enhancement and better thermal stability of the polymer/MMT nanocomposites, it is necessary to develop MMT modified with more thermally stable surfactants. The dispersion and spatial distribution of the organic MMT layers in the nylon‐66 matrix were characterized by X‐ray diffraction. The organic MMT layers were exfoliated but not randomly dispersed in the nylon‐66 matrix. A model was proposed to describe the spatial distribution of the organic MMT layers in an injection‐molded rectangular bar of nylon‐66/organic MMT nanocomposites. Most organic MMT layers were oriented in the injection‐molding direction. Layers near the four surfaces of the bar were parallel to their corresponding surfaces; whereas those in the bulk differed from the near‐surface layers and rotated themselves about the injection‐molding direction. The influence of the spatial distribution of the organic MMT on crystallization of nylon‐66 was also investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1234–1243, 2003     

矩阵特征值的几个不等式

研究矩阵特征值的上、下界以及特征值的实部、虚部的不等式 ,给出了特征值一些新的上界和下界     

Hardy's inequality and the boundary size

We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

     

利用模式的对称性研究光子晶体光纤的色散

由光子晶体光纤的对称性可以得到模式分布的对称性，根据模式的对称性选择适当的展开函数，可以使计算量大大减少。计算了六角结构光子晶体光纤的色散特性，得到了波长在1．55pm处色散为零时，光子晶体光纤的结构参量所满足的方程。     

燃煤烟气中As、Se、Pb的形态分布及S、Cl元素对其形态分布的影响

基于化学热力学平衡分析方法，计算分析了燃煤烟气中重金属As、Se、Pb的形态分布规律，研究了S、Cl等元素对As、Se、Pb的形态分布规律的影响。结果表明，氧化性气氛下，As以As₂O₅、As₄O₆、AsO等氧化物的形式存在；Se主要以SeO₂形式存在；Pb在1000 K以下主要是固态PbSO₄，1200 K以上为气态PbO。还原性气氛下，As在较低温度时为固态As₂S₂，900-1400 K以As₂、AsS、AsN气体共存，2000 K以上全部转化为气态AsO。Se在1100 K以下主要以气态H₂Se存在，1100 K开始生成SeS和Se₂气体，1800 K时主要是气态Se和少量气态SeO；Pb在中低温时主要是PbS，1800 K以上气态Pb为主要存在形态。S在还原性气氛下增大了AsS（g）、PbS（g）、SeS（g）的比例，氧化性气氛下对As、Se、Pb形态分布基本无影响；Cl无论在氧化还是还原气氛下对As、Se影响均较小，但对Pb的形态分布影响较大。     

Dubrovin赋值斜群环

本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想.     

溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．