基于无约束非线性优化算法的光强自相关函数拟合

在光子相关光谱(PCS)颗粒测量技术中非线性累积反演方法是一种重要的算法。采用无约束非线性优化算法对反演过程中相关曲线的拟合问题进行了分析和研究, 实现了从任意初始值开始获取最优非线性拟合解, 并给出了算法的实现步骤。采用此方法对50 nm, 100 nm, 200 nm和500 nm的标准聚苯乙烯乳胶颗粒的实测光强自相关函数数据进行了拟合, 并反演了颗粒粒径, 与其他曲线拟合算法相比, 本算法不但对初始值的依赖性小, 而且得到的颗粒粒径更接近乳胶颗粒的标称直径, 测量误差更小。     

Exciplex emission in the blend of two blue luminescent materials

Organic light-emitting diodes (OLEDs) based on the blend of two blue luminescent materials N,N′-bis(1-naphthyl)-N,N′-diphenyl-1,1′-diphenyl-4,4′-diamine (NPB) and 2-(4-biphenylyl)-5(4-tert-butyl-phenyl)-1,3,4-oxadiazole (PBD) were fabricated. The electroluminescence (EL) spectra of this device showed a new emission that is different from their intrinsic exciton emission. Compared with the photoluminescence (PL) spectra of single layer NPB and PBD, respectively, there was an apparent red shift in that of their blend. Thus the exciplex formation in the blend can be concluded due to the similar emission in both PL and EL spectra. The exciplex formation process and the effect of applied voltage were analyzed by Gaussian fitting.     

20单元双压电片变形反射镜的影响函数有限元分析和实验测量

影响函数是分析双压电片变形反射镜像差校正能力的重要参量,通过建立有限元模型预测实际器件的影响函数,以有限元模型的不断优化替代实际器件的尝试性改进,可以减小构造的盲目性,从而节约研发成本,缩短双压电片变形镜的实用化进程.采用Veeco干涉仪测量了20单元双压电片变形反射镜的影响函数,同时建立有限元模型进行了相应计算,并将计算结果与实际器件的测量数据进行了对比分析.结果表明,相对于实测数据而言,有限元模型计算得出的影响函数在量值上略有偏小,但其形状和峰值位置与测量数据一致性好,两者对前35项泽尼克像差的拟合曲线也基本吻合,各项拟合误差系数之差皆小于0.1.这说明通过不断改进有限元模型实现对实际器件的优化设计是切实可行的.     

一种破译混沌直接序列扩频保密通信的方法

提出了一种新型的混沌保密通信破译方法,并破译了混沌直接序列扩频保密通信(简称混沌直扩).针对混沌直扩信号中只有一个混沌吸引子的特点,基于混沌系统广义同步的思想,提出了混沌拟合方法;针对混沌直扩中混沌实值序列和数字信号相乘的特点,充分利用混沌直扩的基本原理和信息码是慢变信号的特性,提出了用无先导卡尔曼滤波混沌拟合的方法估计信息码的破译方法;进一步针对无先导卡尔曼滤波的过程噪声和混沌拟合的拟合误差共同导致的跟踪误差,提出了跟踪误差控制因子的方法,从而将跟踪误差转变成有利因素并加以利用,根据跟踪误差的值域范围破     

法布里-珀罗气辉干涉成像仪的大气温度测量原理

讨论了法布里-珀罗干涉成像仪（FPI）对夜气辉的系统响应,更为明确地描述了建立该干涉系统数学模型的方法和结果。在此基础上阐述了利用FPI对热层大气温度进行测量的原理,并且通过分析稳频He-Ne激光器的干涉图对系统的传输函数进行了求解,对不同波长下系统传输函数的转换进行了讨论。干涉图的分析结果表明：该解析模型以及波长转换方法能够很好地表示干涉成像系统。另外对系统传输函数在实际气辉测量中的应用、系统的温度漂移以及误差估计也进行了简要讨论。     

The Chebyshev Hyperplane Optimization Problem

We consider the following problem. Given a finite set of pointsy ^j in we want to determine a hyperplane H such that the maximum Euclidean distance betweenH and the pointsy ^j is minimized. This problem(CHOP) is a non-convex optimization problem with a special structure. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments.     

On numerical methods for discrete least-squares approximation by trigonometric polynomials

Fast, efficient and reliable algorithms for discrete least-squares approximation of a real-valued function given at arbitrary distinct nodes in by trigonometric polynomials are presented. The algorithms are based on schemes for the solution of inverse unitary eigenproblems and require only arithmetic operations as compared to operations needed for algorithms that ignore the structure of the problem. An algorithm which solves this problem with real-valued data and real-valued solution using only real arithmetic is given. Numerical examples are presented that show that the proposed algorithms produce consistently accurate results that are often better than those obtained by general QR decomposition methods for the least-squares problem.

     

HELFIT: Helix fitting by a total least squares method

The problem of fitting a helix to data arises in analysis of protein structure, in nuclear physics, and in engineering. A continuous helix is described by five parameters: helix axis, helix radius, and helix pitch. One of these helix parameters is frequently predefined in the helix fitting. Other algorithms find only the helix axis or determine separately the helix axis, the helix radius, or the helix pitch. Here we describe a total least squares method, HELFIT, for helix fitting. HELFIT enables one to calculate simultaneously all five of the helix parameters with high accuracy. The minimum number of data points required for the analysis is only four. HELFIT is very insensitive to noise even in short helices. HELFIT also calculates a parameter, p = rmsd/(N − 1)^1/2, which estimates the regularity of helical structures independent of the number of data points, where rmsd is the root mean square distance from the best-fit helix to data points and N is the number of data points. It should become a basic tool of structural bioinformatics.     

Reference spectra of important adsorbed organic and inorganic phosphate binding forms for soil P speciation using synchrotron‐based K‐edge XANES spectroscopy

Direct speciation of soil phosphorus (P) by linear combination fitting (LCF) of P K‐edge XANES spectra requires a standard set of spectra representing all major P species supposed to be present in the investigated soil. Here, available spectra of free‐ and cation‐bound inositol hexakisphosphate (IHP), representing organic P, and of Fe, Al and Ca phosphate minerals are supplemented with spectra of adsorbed P binding forms. First, various soil constituents assumed to be potentially relevant for P sorption were compared with respect to their retention efficiency for orthophosphate and IHP at P levels typical for soils. Then, P K‐edge XANES spectra for orthophosphate and IHP retained by the most relevant constituents were acquired. The spectra were compared with each other as well as with spectra of Ca, Al or Fe orthophosphate and IHP precipitates. Orthophosphate and IHP were retained particularly efficiently by ferrihydrite, boehmite, Al‐saturated montmorillonite and Al‐saturated soil organic matter (SOM), but far less efficiently by hematite, Ca‐saturated montmorillonite and Ca‐saturated SOM. P retention by dolomite was negligible. Calcite retained a large portion of the applied IHP, but no orthophosphate. The respective P K‐edge XANES spectra of orthophosphate and IHP adsorbed to ferrihydrite, boehmite, Al‐saturated montmorillonite and Al‐saturated SOM differ from each other. They also are different from the spectra of amorphous FePO₄, amorphous or crystalline AlPO₄, Ca phosphates and free IHP. Inclusion of reference spectra of orthophosphate as well as IHP adsorbed to P‐retaining soil minerals in addition to spectra of free or cation‐bound IHP, AlPO₄, FePO₄ and Ca phosphate minerals in linear combination fitting exercises results in improved fit quality and a more realistic soil P speciation. A standard set of P K‐edge XANES spectra of the most relevant adsorbed P binding forms in soils is presented.