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.     

基于压电力显微镜的铌酸锂电畴稳定性研究

研究了Z切700 nm厚的单晶铌酸锂(LiNbO₃)薄膜电畴的调控方法。利用X射线衍射仪(XRD)和原子力显微镜(AFM)对单晶LiNbO₃薄膜的晶向和形貌进行了表征,并通过外加电场对单晶LiNbO₃薄膜电畴进行调控。研究结果表明,该LiNbO₃薄膜具有单一的(006)衍射峰,表面光滑、粗糙度低(均方根粗糙度小于1 nm)。通过外加电场和预设电畴图案对LiNbO₃电畴进行精准调控,并测试了电畴稳定性。测试结果显示,调控后的电畴在温度为25~150℃内处于稳定状态,且在30 d内保持稳定,未发生弛豫现象。该研究为LiNbO₃电畴工程器件的研发和应用提供了重要的技术支撑。     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p _e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp _e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp _e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp _e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp _e are also discussed.     

Mechanical properties and molecular mobility in oriented polyolefines

The static modulus of elasticity (E) and the correlation time of rotation ( _c ) of 2,-2,6,6-tetramethylpiperidine-1-oxyl are studied as a function of the temperature (210<T <350°K) for oriented films of isotactic polypropylene and polyethylene of high and low density.E and _c change both upon heating and polymer orientation; this result indicates that sample properties are influenced by the microstructure of the amorphous phase where probes are localized.     

THE STRUCTURAL BASIS OF THE POOR FIBRIN SPECIFICITY OF UROKINASE(Ⅰ)——KNOWLEDGE-BASED PREDICTION OF KRINGLE STRUCTURES OF UROKINASE AND ITS RELATED PROTEINS

The Kringle-1 structure of plasminogen (PGK-1), the Kringle-2 structure of tissue plasminogen activator (PAK-2) and the Kringle structure of prourokinase (UKK) has been modeled on the basis of the three-dimensional structure of Kringle-1 of prothrombin (PTK-1) at 2.8 resolution. The predicted three-dimensional structure of these Kringles shows that the binding site of PGK-1 is characterized by an apparent dipolar site, the polar parts of which are separated by a hydrophobic region. PAK-2 possesses the anionic center but has not a cationic binding center which might be provided by a guanidinium group from Arg-69 located adjacent to the Arg-71 position. UKK possesses neither the anionic binding center nor the cationic center which are probably the main reason for the poor fibrin specificity of urokinase.     

一种液晶环氧树脂固化中扩散控制动力学研究

根据扩散控制反应的基本原理 ,建立了合适的反应模型 ,描述了 4 ,4′ 二 ( 2 ,3 环氧丙氧基 )偶氮苯(DGEAP) / 4,4′ 二氨基二苯甲烷 (DDM)环氧树脂的固化行为 .该模型认为 ,随着环氧基团反应程度的提高 ,基团的反应半径将受到影响 .当体系中出现了介晶基元的有序排列时 ,与之相连的反应基团的分布也受到影响 ,有序区内的局部浓度将变大 ,产生假浓度效应 ,并最终影响扩散控制反应动力学 .通过与普通环氧树脂固化动力学的比较 ,证实了这一效应 .     

In-gel deglycosylation of sodiumdodecyl sulfate polyacrylamide gel electrophoresis-separated glycoproteins for carbohydrate estimation by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Mass determination by mass spectrometric methods (electrospray ionization mass spectrometry (ESI-MS), matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS)) of sodiumdodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE)-separated proteins is a well known procedure and reliable protocols are available. In our efforts to use the established methods to determine the molecular mass of the disulfide bridged, heterodimeric glycoprotein GP3 and to determine the carbohydrate content of each protein subunit we developed an in-gel chemical deglycosylation method. For this purpose we established experimental conditions that allow maximum extraction of the high molecular mass protein subunits and developed a routine method to apply the HF-pyridine deglycosylation protocol to proteins isolated from polyacrylamide gel pieces. The novel protocol and extraction procedure described can be used to analyze O-glycosylated proteins up to 150 kDa after SDS-PAGE separation.     

Theoretical Study of Weakly Bound Dimers between Hydrogen Fluoride and Some Polar Molecules

Weakly bound linear and bent dimers, FH—X (where X = CO, OC, CNH, NCH, N₂O and ON₂), are investigated using the DFT B3LYP and ab initio MP2 methods with the same basis sets (6–311++G(3df,2pd)). The strengths of the H—C or H—N H‐bonds in dimers FH—CO, FH—CNH, and FH—N₂O are compared with those of the H—O or H—N H‐bonds in dimers FH—OC, FH—NCH, and FH—ON₂. The results obtained for the H‐bond distances, the elongation effect of the HF bond, the red shift of the HF stretching frequency, and the energy difference between the dimer and the charge transfer reveal that the H‐bonds of the first group of dimers are stronger than those of the second. The Gibbs energies calculated for the six dimer formations indicate that the weakly bound dimers are unstable at room temperature (T = 298 K) (FH—X's → FH + X's, ΔG < 0).     

The domain of partial attraction of a Poisson law

Groshev gave a characterization of the union of domains of partial attraction of all Poisson laws in 1941. His classical condition is expressed by the underlying distribution function and disguises the role of the mean of the attracting distribution. In the present paper we start out from results of the recent probabilistic approach and derive characterizations for any fixed >0 in terms of the underlying quantile function. The approach identifies the portion of the sample that contributes the limiting Poisson behavior of the sum, delineates the effect of extreme values, and leads to necessary and sufficient conditions all involving . It turns out that the limiting Poisson distributions arise in two qualitatively different ways depending upon whether >1 or <1. A concrete construction, illustrating all the results, also shows that in the boundary case when =1 both possibilities may occur.