Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Spreading of viscous droplets on a non viscous liquid

Some polymer melts (of high viscosity ) can wet completely the surface of a non miscible, simple liquid. We discuss here the laws of spreading for a macroscopic droplet of this type, when the internal friction of the droplet dominates. We predict a droplet radius increasing liket ^1/4 wheret is the spreading time, or equivalently a droplet curvature decreasing liket ^–1. The droplet should be surrounded by a precursor film, which is not discussed in the present note.     

飞行时间质谱仪中Ni^＋与酯分子束流的气相反应及机理

在一个石英反应室内，让激光解离的Ｎｉ＾＋与连续喷入的酯类化合物分子束流反应，生成的产物离子经飞行时间质谱仪检测，研究了Ｎｉ＾＋与乙酸乙酯、乙酸丙烯酯、乙酸乙烯酯、乙酸丁酯的气相反应。根据如下机理满意的解释了发生的反应：（１）Ｎｉ＾＋与酯形成激发态络合物；（２）β－Ｈ迁移至烃氧基的氧上形成Ｎｉ＾＋的双配体化合物离子；（３）失去一中性配体分子得Ｎｉ＾＋的单配体化合物离子。由酯的ΔＨ离和Ｄ（Ｎｉ＾＋－Ａ     

High-performance liquid chromatography with continuous gradient elution in screening for unknown metabolites of butoprozine directly in dog bile

This paper describes the screening for metabolites of butoprozine, a new anti-anginal drug, in dog bile by means of reverse-phase HPLC. Although it does involve a simple clean-up step to remove a substantial amount of endogenous bile compounds, this screening method nevertheless avoids extraction of metabolites and thus allows all metabolites to be introduced into the chromatographic system. A single run of 100 minutes from 100% water to 100% methanol in a linear gradient effects adequate separation of the great majority of metabolites without interference from remaining endogenous compounds. Two methods of differentiating between metabolite peaks and endogenous peaks have been worked out. The first one makes use of ¹⁴C-labeled butoprozine by measuring the amount of radioactivity in the column effluent while simultaneously recording the UV absorbance. The second method compares continuous gradient chromatograms of bile recorded before and after butoprozine administration under very similar conditions. The latter method can be applied to both radioactive and non-radioactive materials.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.     

Optimization of upper semidifferentiable functions

In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in ^m . The method generalizes Wolfe's algorithm for convex functions and Mifflin's algorithm for semismooth functions to a broader class of functions, so-called upper semidifferentiable. With this objective, we define a new enlargement of Clarke's generalized gradient that recovers, in special cases, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.The author would like to thank J. B. Hiriart-Urruty (Toulouse) for having provided him with Definition 2.1 and the referees for their constructive remarks about a first version of the paper.     

Multifold curdlan gel formation by dialysis into aqueous solutions of metal salts

We have found that the dialysis of curdlan dissolved in alkaline solution into aqueous solutions of metal salts yielded multifold gel structures. Aqueous sodium chloride and potassium chloride as well as pure water induced isotropic gels. Aqueous calcium salts induced liquid crystalline gel with refractive index gradient/amorphous gel alternative structure. Aqueous salts of trivalent aluminum and ferric cations induced a rigid liquid crystalline gel, which shrank above a threshold concentration of each salt. On the other hand, Liesegang ring-like pattern was observed with aqueous solutions of mixed salts of calcium chloride and magnesium chloride. The patterns have been classified to discuss the mechanism of forming the variety of structures.     

A quantitative method for dual‐pass electrostatic force microscopy phase measurements

Electrostatic force microscopy (EFM) has become a powerful tool for investigating charges on surfaces. The use of phase measurement in EFM is a direct and fast way to detect electrostatic force gradients, but only qualitatively. With the dual‐pass scheme, the phase signal at lifted height is often assumed to exclude any influences from the topography, but it does not. We report the collection of both topography and phase data by EFM on charged, micron‐sized metal wires. In order to quantify the electrostatic force, a cone model and finite element analysis are provided to integrate the force gradient from the phase signal. Copyright © 2007 John Wiley & Sons, Ltd.     

新型无泵阀毛细管等速电泳仪的研制——Ⅰ.积木式分离管路结构及电位梯度检测器

本文介绍本实验室研制的新型无泵阀毛细管等速电泳仪的积木式分离管路结构及电位梯度检测器,该管路结构及检测器构造均较现有的仪器简单、合理,拆卸和组接方便,造价低廉,用其构成的无泵阀毛细管等速电泳仪分离分析阴、阳离子样品,结果表明该仪器的检测灵敏度及重现性等均良好。