A HYBRID METHOD OF FRACTIONAL STEPS WITH PREDICTOR-CORRECTOR DIFFERENCE-PSEUDOSPECTRUM FOR NUMERICAL-SOLUTION OF THE CONVECTION-DOMINATED FLOW PROBLEMS

A fractional-step method of predictor-corrector difference-pseudospectrum with unconditional L(2)-stability and exponential convergence is presented. The stability and convergence of this method is strictly proved mathematically for a nonlinear convection-dominated flow. The error estimation is given and the superiority of this method is verified by numerical test.

ω循环型预条件矩阵及其应用

In this paper, we apply the preconditioned conjugate gradient method to the solution of positive-definite Toeplitz systems, especially we introduce a new kind of co-circulant preconditioners Pn[ca] by the use of embedding method. We have also discussed the properties of these new preconditioners and proved that many of former preconditioners can be considered as some special cases of Pn[co\. Because of the introduction of co-circulant preconditioners pn[a>], we can greatly overcome the singularity caused by circulant preconditioners. We have discussed the oo-circulant series and functions. We compare the ordinary circularity with the co-circularity, showing that the latter one can be considered as the extended form of the former one; correspondingly, many methods and theorems of the ordinary circularity can be extended. Furthermore, we present the co-circulant decompositional method. By the use of this method, we can divide any co-circulant signal into a summation of many sub-signals; especially among those sub-signals, there are many subseries of which their period is just equal to 1, which are actually the frequency elements of the original co-circulant signal. In this way, we can establish the relationship between the signal and its frequency elements, that is, the frequency elements hi the frequency domain are actually signals with the period of 1 in the spatial domain. We have also proved that the co-circulant has already existed in the traditional Fourier theory. By the use of different criteria for constructing preconditioners, we can get many different preconditioned systems. From the preconditioned systems PN[

Total analytical method for Radix astragali extract using two-binary multi-segment gradient elution liquid chromatography

There is an urgent need for thorough analysis of Radix astragali, a widely used Chinese herb, for quality control purposes. This paper describes the development of a total analytical method for Radix astragali extract, a multi-component complex mixture. Twenty-four components were separated step by step from the extract using a series of isocratic isopropanol-methanol elutions, and then 42 components were separated similarly using methanol-water elutions. Based on the log k(w) and -S of the 66 components obtained from the above procedure and the optimization software developed in our laboratory, an optimum elution program consisting of seven methanol-water segments and four isopropanol-methanol segments was developed to finish the task of analyzing the total components in a single run. Under optimized gradient conditions, the sample of Radix astragali extract was analyzed. As expected, most of the components were well separated and the experimental chromatogram was in a good agreement with the predicted one.

Preparation of titania-based catalysts for formaldehyde photocatalytic oxidation from TiCl4 by the sol-gel method

Titania sols were prepared by acid hydrolysis of a TiCl4 precursor instead of titanium alkoxides. The effect of acid concentration on the particle size and stability of sol was investigated. Stable titania sols with mean particle size of 14 nm could be obtained when the H+/Ti molar ratio was 0.5. The titania sols were modified with Pt, SiO2, ZrO2, WO3 and MoO3 to prepare a series of modified catalysts, which were used for the photocatalytic oxidation of formaldehyde at 37 degreesC. They showed different photocatalytic activities due to the influence of the additives. Comparing with pure TiO2, the addition of silica or zirconia increased the photocatalytic activity, while the addition of Pt and MoO3 decreased the activity, and the addition Of WO3 had little effect on the activity. It is of great significance that the conversion of formaldehyde was increased up to 94% over the SiO2-TiO2 catalyst. The increased activity was partly due to higher surface area and porosity or smaller crystallite size. A comparison of our catalyst compositions with the literature in this field suggested that the difference in activity due to the addition of a second metal oxide maybe caused by the surface chemistry of the catalysts, particularly the acidity. (C) 2001 Elsevier Science B.V. All rights reserved.