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.     

Schrödinger invariance and strongly anisotropic critical systems

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent =z=2, the group of local scale transformation considered is the Schrödinger group, which can be obtained as the nonrelativistic limit of the conformal group. The requirement of Schrödinger invariance determines the two-point function in the bulk and reduces the three-point function to a scaling form of a single variable. Scaling forms are also derived for the two-point function close to a free surface which can be either spacelike or timelike. These results are reproduced in several exactly solvable statistical systems, namely the kinetic Ising model with Glauber dynamics, lattice diffusion, Lifshitz points in the spherical model, and critical dynamics of the spherical model with a nonconserved order parameter. For generic values of , evidence from higher-order Lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two-point function.     

Microwave-assisted Preparation of Temperature Sensitive Poly（N-isopropylacrylamide） Hydrogel with Improved Responsive Properties

Poly(N-isopropylacrylamide) (PNIPAM) hydrogel, which is insoluble but shrinkable or swellable in aqueous media when temperature rises or drops across 33oC1,2, has been extensively studied due to its potential applications in the fields of controlled drug …     

Study of process parameters for starch,gluten, and glycerol mixtures

This work involved a study of the effect of processing variables (temperature, water content, rotor speed, and time) on the mechanical properties of starch:gluten:glycerol mixtures in the weight ratio of 40:40:20. The properties of the materials were affected by the processing variables. The torque decreased with water content, indicating that water facilitates the plasticization of mixtures, whereas the increase in temperature accelerated the evaporation of water, thus increasing the torque. Ultimate tensile strength was achieved at the lowest temperature (110°C) and the highest water content (20%), whereas maximum elongation was achieved for the material processed at the highest temperature, 150°C, and the fastest rotor speed, 70 rpm. Copyright © 2007 John Wiley & Sons, Ltd.     

An Absence of Non-specific Immune Response towards para-Sulphonato-calix[n]arenes

The effects of para-Sulphonato-calix[4]arene, para-Sulphonato-calix[6]arene and para-Sulphonato-calix[8]arene on the activation of NADPH oxidase in neutrophils has been studied. All three molecules do not induce NADPH oxidase activation, and hence do not stimulate neutrophils. Measurement of cell viability demonstrates that these three water-soluble calix[n]arene derivatives are not cytotoxic.     

Potential response in the uncatalyzed bromate oscillatory system

The potential response of the platinum indicator electrode in the uncatalyzed bromate oscillator (UBO) with three different substrates, namely gallic acid (GA), pyrogallol (PG) and veratraldehyde (VA) has been analyzed. The large amplitude oscillations obtained with a Pt electrode are due to the sequential response of the indicator electrode to the varying concentration ratios of the redox couples present in the reaction mixture.     

All Solid‐State pH Electrode Based on Titanium Nitride Sensitive Film

Titanium nitride was used as pH‐sensitive material to fabricate all solid‐state pH electrode. The fabrication and the response performance of the pH electrode were described in the paper. The TiN film electrode showed a linear response in the pH range of 2–12 with a near‐Nenstian response (?55 mV/pH). The response time was within 1 min, and the electrode had good reproducibility, stability and low sensitivities for different species. Compared with the glass pH electrode, the electrode exhibited some advantages, for example, without activation, rapid response and high mechanical strength. In addition, the electrode performed excellently in a corrosion medium containing F^?(1 M). Electrochemical behaviors of TiN electrode in Britton‐Robinson buffers were studied with Electrochemical Impedance Spectroscopy (EIS).     

Electron capture detector performance parameters in view of the response presentation forms

Summary Four most frequently used presentation forms of the ECD response are described. Equations describing the dependence of the sensitivity, linearity and minimum detectable concentration of the ECD working under constant frequency mode of operation on the pulse period are derived from Wenthworth’s kinetic model for all four forms mentioned above. The forms presented are compared on the basis of equations derived. Results of the calculations are given and some predictions are experimentally tested for sulphur hexafluoride. Good agreement was found between the predicted and observed relationships. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

STUDIES ON PREPARATION OF INACTIVATED VACCINES FROM CELL CULTURES OF MINK ENTERITIS VIRUS (MEV) AND THEIR IMMUNITY

In this paper, superhigh reproductive rate strains of MEV with titre more than HA8192* or TCID50 log9.7 10 have been achieved both by cultivation in cell lines with different susceptibility to MEV and by isolating and identifying in field by the author. The systematic tests proved that S18 and L12 strains of MEV are the best strains for vaccine preparation. In this study, the best means for the tissue cultivation of MEV and the most advanced technological process for the production and detection of serum-free cell-cultured MEV fluids with super-high HA titre in batches in large quantities have been established for the first time. Optimum conditions for MEV inactivation were determined, and safe and effective inactivated vaccines with mineral oil or A1(OH)3 gel adjuvant were successfully prepared with serum-free cell-cultured MEV fluids. Both vaccines with different adjuvants can be manufactured in batches in large quantities and have been widely used all over China since 1986. The change laws of the imm     

Effect of enzyme concentration on the dynamic behavior of a membrane-bound enzyme system

The dynamic behavior of the reaction-diffusion system, composed of glucose oxidase (EC 1.1.3.4) immobilized at a uniform concentration in a membrane, used as a glucose electrode is represented by a diffusion equation with a nonlinear reaction-term in one-dimensional space. The mathematical model is analyzed by computer simulation, that is, numerical integration of the equation under various initial and boundary conditions, to examine the effect of enzyme concentration on the response characteristics (responsiveness and linearity in response) of the electrode. The analysis of the responses of the system to stepwise changes in the boundary value (glucose concentration in simple solution) infers that the enzyme concentration governs the patterns of the spatial distributions of the substrates (glucose and dissolved oxygen) in steady states and transient responses. It is also revealed that the response characteristics of the electrode are optimized with concentration of immobilized enzyme and that the system establishes the steady states at the same spatial distributions of the substrates, regardless of the boundary value. The diffusion of the substrates and the oxygen concentration also have significant effects on the response characteristics of the electrode.