A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

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Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.     

高维系统周期解的共振分支

本文利用Liapunov－Schmidt方法获得了高维自治系统在共振情况下决定周期解个数的分支函数，并通过计算分支函数的主项，分析分支函数的零点，研究了具两对共轭特征根的四维系统多个周期解的共振分支问题．     

斜孔气膜冷却数值模拟分析

本文通过数值模拟分析圆柱孔和扩散孔的单斜孔气膜冷却特性,考察复合角、孔型和吹风比对流场和气膜冷却效果的影响。结果表明,复合角的引入使气膜侧向分布更宽,但冷却效果沿主流方向衰减更快。适中吹风比得到的气膜能更有效的保护壁面。在相同吹风比和复合角条件下,扩散孔的气膜冷却效率比圆柱孔更好,且冷却更为均匀持久。     

A computational study into the reactivity of epichlorohydrin and epibromohydrin under basic conditions in the gas phase and solution

Ab initio molecular orbital calculations were carried out on epibromohydrin (EBH) and epichlorohydrin (ECH) in an attempt to elucidate their reactivity with respect to a hard nucleophile, hydroxide. These systems were modeled in both the gas phase and a polar solvent under basic conditions. In the gas phase, it was determined that a direct displacement mechanism (nucleophilic attack at the C1 position) was operative for EBH, while an indirect pathway (nucleophilic attack at the C3 position and subsequent intramolecular displacement) was followed for ECH. In an acetone solution, only the indirect displacement mechanism was found to occur. An electrostatic argument is advanced to account for this behavior in polar solution. Copyright © 2007 John Wiley & Sons, Ltd.     

Continuity of the Solution Map in Parametric Affine Variational Inequalities

A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational inequalities is given in this paper. Several examples are constructed to analyze the results. This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program, and the KOSEF Brain Pool Program.     

Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.     

第三类Painlevé方程(δ=0或γ=0)解的渐近性态

对带有一般实参数第三类Painlevé方程,已有γ<0,δ>0时,解的有界性以及振荡渐近解的表达形式的结论.在本文中,我们给出当δ=0或γ=0时其振荡渐近解的表达形式.     

Insight into chain dimensions in PEO/water solutions

Small‐Angle Neutron Scattering has been performed from poly(ethylene oxide) in deuterated water at temperature ranging from 10 to 80 °C. A simple fitting model was used to obtain a correlation length and a Porod exponent. The correlation length L characterizes the average distance between entanglements in the semidilute region and is proportional to the individual coil sizes in the dilute region. L was found to increase with temperature in the semidilute region but it decreases with temperature in the dilute region. This decrease is the precursor to the single‐chain collapse which applies to very dilute polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2196–2200, 2007     

Numerical Computation of Figure-eight Solution for 3-body Problems

The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.