A NEW DIFFERENCE SCHEME WITH MULTI-TIME LEVELS

In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p>3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally.     

Self-similar solutions for the anisotropic affine curve shortening problem

Similarity between the roles of the group on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group of on the Nirenberg problem for prescribed scalar curvature is explored. Sufficient conditions for the existence of affine self-similar curves are established. Received June 26, 1999 / Accepted January 28, 2000 / Published online December 8, 2000     

Studies on the Chemical Synthesis of Nanosized Nickel Powder and its Stability

The synthesis of nanosized nickel colloids is investigated by using nickel chloride as the precursor, hydrazine as the reducing agent and palladium as the nucleation agent. High purity nickel can be obtained when the reaction temperature is above 80^°C. At a lower reaction temperature, nickel hydroxide is also present in the precipitate form. Starting concentration of nickel ion is a dominant factor in affecting colloidal sizes, while other parameters such as reaction temperature and quantity of poly(vinyl pyrrolidone) (PVP) exhibit only minor effects. Although PVP has some dispersion power, it is not capable of preventing nickel colloids from gradual agglomeration. Our study shows that the subsequent addition of poly(acrylic acid) (PAA) after synthesis can help to stabilize the nickel suspension. This stabilized suspension can then be de-stabilized by changing pH to lower than 4 and vice versa. This reversible stabilization–de-stabilization process is likely due to the behaviour of PVP–PAA complex in the aqueous solutions.     

Collisional source of the second moment and pressure tensor for inhomogeneous rapid granular flows of highly inelastic spheres

By extending the constitutive theories for homogeneous granular flows of highly inelastic spheres by Richman (J. Rheol 33 (1989) 1293), Chou (J. CSME 16-6 (1995) 577), and Chou and Richman (Physica A 259 (1998) 430), the collisional source of the second moment of fluctuation velocity and pressure tensor were developed in this study for inhomogeneous rapid granular flows of identical smooth highly inelastic spheres. The important mean fields in this flow are the solid fraction, mean velocity, and full second moment of fluctuation velocity. The collisional source of second moment and the collisional flux of momentum are based upon an anisotropic Maxwellian velocity distribution function. The constitutive theory was combined with the experimental results measured by Hsiau and Jang (Exp. Thermal Fluid Sci. 17 (1998) 202) so as to determine the profiles of pressure tensor and collision source of second moment in the inhomogeneous rapid granular shear flows of inelastic spheres. The normal pressure discrepancies were also observed.     

Chaotic behaviour of the general symbolic dynamics

This paper extends symbolic dynamics to general cases. Some chaotic properties and applications of the general symbolic dynamics (∑(X),σ) and its special cases are discussed, where X is a separable metric space.     

Inf-dif-stability of oblique perturbation

Laurent and Rockafellar have studied certain problems of perturbation and of stability in convex minimization problems. Laurent has discussed inf-dif-stability conditions respectively for horizontal perturbation and for vertical perturbation. In this paper, we generalize some results of Laurent^[1] by giving several inf-dif-stability conditions of oblique perturbation.Project supported by the National Natural Science Foundation of China.     

Numerical-perturbation analysis of edge effect in bending laminated plate

In this paper, we consider a bending laminated plate. At first, the dimensionless variables are used to transform the equilibrium equations of any layer to perturbation differential equations. Secondly, the composite expansion is used and the solution domain is divided into interior and boundary layer regions and the mathematical models for the outer solution and the inner solution are yielded respectively. Then, the inner solution is expressed with the boundary intergral equation.Project Supported by the National Science Foundation of China.     

Direct Spectroscopic Evidence for 1ΔgO2 Production from the Photolysis of Vanadium(V)-Peroxo Complexes in Aqueous Solution

The chemiluminescence of ¹DL_gO₂ expelled from the UV photolysis of vanadium(V)-peroxo (VP) complexes in aqueous solution was observed for the first time. Using phenalenone photosensitization as a standard reference, the ¹O₂ quantum yields from the photolysis of 12 VP complexes were measured. No good correlation was found between the relative DNA-photocleavage activities and the ¹O₂ quantum yields of these complexes. This lack of correlation underscores the significant contribution of the complex-DNA binding interaction in determining the observed DNA-photocleavage activity of the complex. The small ¹O₂ quantum yields observed in these complexes were interpreted in terms of the minor ¹O₂ pho-toelimination channel relative to other more efficient relaxation processes.     

Alcalase-catalyzed Synthesis of Novel 2,6-Dimethoxyhydroquinone-3-mercaptoacetyl-peptide Conjugates

Seven dipeptide and one tripeptide conjugates of the cytotoxic drug 2,6-dimethoxyhydroquinone-3-mercaptoacetic acid (DMQ-MA) conjugates were prepared successfully by an alcalase-catalyzed reaction in alcohols, using DMQ-MA-X-OMe as the acyl donor and H₂N-Y-CONH₂ as the nucleophile (where X and Y are amino acids, and amino acid/dipeptides, respectively).     

C2, Symmetric Dibenzosuberanes as Templates for the Chirality Determination of Helicenes and Their Applications as Optically Switchable Memory Device

We have recently developed a new type of chiral templates, dibenzosuberanes. Thess C₂, symmetric diaryl modifiers have been successfully applied to the synthesis of chiral triarylcarbenium ions. They can serve as catalysts in the asymmetric Mukaiyama aldol reactions with moderate enantioselectivities of up to 50% [1]. We have subsequently found that one major side reaction between the catalyst and the substrate-silyl ketene acetal which releases extra silyl-X species is responsible for the erosion of asymmetric induction. The dibenzosuberane scaffold was found essential to prevent this type of side reaction. For the selection of carbenium counter ions, we have resorted to the chloride in order to completely suppress the undesired silyl catalysis [2].