Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

彩色透明微晶玻璃的吸收光谱

在Li2O-Al2O3-SiO2系统玻璃中掺入少量晶核剂TiO2,ZrO2,P2O5，再掺入稀土离子和过渡金属离子作为着色剂，在高温下溶制得到彩色透明玻璃，对上述玻璃进行微晶化处理，用差热分析（DTA）确定其晶化温度，测定与讨论了所获彩色透明微晶玻璃在紫外波段至近红外波段的吸收光谱特性，研究结果表明，玻璃微晶化后，由于基质玻璃对光的微弱散射，引起吸收的增强，但不改变稀土离子和过渡金属离子的本征吸收峰位。     

甜菜糖蜜酒精废液生产菌体蛋白饲料初探

甜菜糖蜜酒精废液含有大量的有机物，pH值低，BOD、CDO值高，直接排和会造成环境的严重污染，又损失了一些有机物，在此废液中可直接接入酵母菌，使其大量繁殖，生产出的菌体粗蛋白含量达41．7％，CDO值降低了20％以上，减轻了环境污染。     

A New theory for evaluating the number density of inclusions in films

A new formulation derived from thermal characters of inclusions and host films for estimating laser induced damage threshold has been deduced. This formulation is applicable for dielectric films when they are irradiated by laser beam with pulse width longer than tens picoseconds. This formulation can interpret the relationship between pulse-width and damage threshold energy density of laser pulse obtained experimentally. Using this formulation, we can analyze which kind of inclusion is the most harmful inclusion. Combining it with fractal distribution of inclusions, we have obtained an equation which describes relationship between number density of inclusions and damage probability. Using this equation, according to damage probability and corresponding laser energy density, we can evaluate the number density and distribution in size dimension of the most harmful inclusions.     

Autocorrelation Function of Hydrogen Atoms in Magnetic Fields

The autocorrelation function is an important quantity that can reflect the dynamical properties of the Rydberg wave packet and can be measured in experiments. Applying time-dependent perturbation theory and rotating wave approximation, we derive the autocorrelation function of the double-pulse laser describing the evolution of a Rydberg wave packet of hydrogen atoms in magnetic fields. The resulting expression is written as a sum of the modified Caussian terms. Each Caussian term comes from a parent semiclassical closed orbit. It provides a direct explanation and experimentally controllable measurement scheme, which allows us therefore to recognize the closed orbit and to determine its returning time in high precision.     

Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks

We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm. We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

紧矩阵量子群G的余表示与其对偶量子群(A)的关系

设 G=（A,△）为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过（A,△）的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C＊-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim（α）=dim（pα）.     

采用热处理方法提高MEH-PPV单层聚合物有机发光二极管发光性能的研究

对以MEH－PPV为发光层的单层聚合物有机发光二极管（OLED）器件在最佳条件下进行真空热处理，并用金相显微镜观察施加电压后器件的阴极表面形貌。发现处理后的器件阴极表面的气泡及黑斑明显减少。器件的发光性能显著提高。与未经处理的器件相比，最大相对发光强度提高了一个数量级、启亮电压降低了2．0V，半寿命提高了12．7倍。初步分析表明热处理方法提高器件发光性能的主要原因在于有效地减少了器件在工作过程中由于焦耳热产生的某些气体，从而减少阴极表面气泡及黑斑的出现，另一方面，热处理方法也增强了有机发光层与阴极接触界面的结合力，提高电子注入水平。