广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

一类广义的Kdv方程的显式差分解

本文考察一类具耗散的广义KdV方程组■ (gradφ(■))_x ■_(xxx)-α■_(xx) γ■ =■(x,t,■)的周期初值问题的显式差分格式．利用有界延拓法证明了该差分格式的收敛性与稳定性,并给出了算法和数值例子．     

Rheology of polystyrene solutions around the coil overlapping concentration: A phenomenological description of stresses in simple shear flow

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τ_RZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τ_L > τ_RZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ₁) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ²)^?1/2, where γ is the magnitude of shear. Contributions to η and Ψ₁ from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τ_st = τ + (τ_RZ ? τ)/(1 + 0.35τ_RZ γ˙) instead of τ_RZ. Here, γ˙ is the rate of shear, and τ is the τ_RZ value at the infinite dilution limit. η and Ψ₁ at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol^?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002     

The polysaccharide extracts from the fungi Coprinus comatus and Coprinellus truncorum do exhibit AChE inhibitory activity

The polysaccharide (PSH) extracts from the edible mushroom species Coprinus comatus and Coprinellus truncorum were screened in liquid for their acetylcholinesterase inhibitory (AChE) activity. Both extracts were found to display inhibition of the aforementioned enzyme reaching similar IC₅₀ values of 0.62 ± 0.07 and 0.61 ± 0.03 mg/mL, respectively. According to the means of FTIR spectroscopy, these PSH extracts mostly contained β-glucans. However, the presence of some proteins and polyphenolics as minor ingredients were also detected. Compared with existing literature data for anti-AChE activity of the sugar samples, the findings within this study may be treated as a profound bioactivity. Consequently, this study puts some light on the possible use of the screened macrofungi in the palliative treatment of Alzheimer’s disease.     

分子手性的温度效应：D-丙氨酸的变温X衍射和中子衍射研究

利用X衍射（300, 270, 250 K）和中子衍射（300, 260, 250, 240 K）研究D-氨酸单晶在静态的和动力学的变温过程中的结构特征以及考证Salam预言的由D到L构型转变的可能性. 实验发现丙氨酸晶体的空间群P212121对称性没有改变. 实验结果否定了构型相变的可能，但是发现在~250 K有一个微小的、连续的对称性破缺发生. 晶体分子振动产生的环电流模型可以用来解释D-和L-丙氨酸单晶直流磁化率和天然旋光角相反的现象， 与之相关的中子衍射数据进一步揭示了变温过程中αC－H(2), N－H(1), N－H(4), N－H(6) 键长的不同变化. 中子衍射还显示了质子移动所导致的动力学无序，来源于分子内氨基和羧基形成的氢键和分子间αC－H和氨基形成的氢键，从而产生的晶格扭曲和NH³⁺的扭转. 实验结果表明Salam预言相变不是传统意义的结构相变，而是由于温度效应导致了在相变点附近分子的宇称破缺能差（PVED）增大，然后通过氨基酸分子的隧道效应扩大了宇称破缺能差的影响，这一研究为生命现象中快速的均一手性形成提供了非线性机理的合理解释.     

A High-Order Finite Difference Scheme for 3D Unsteady Convection Diffusion Reaction Equations北大核心CSCD

针对三维非稳态对流扩散反应方程,构造了一种高精度紧致有限差分格式,对空间的离散采用四阶紧致差分方法,对时间的离散采用Taylor级数展开和余项修正技术,所提格式在时间上的精度为二阶、在空间上的精度为四阶。利用Fourier稳定性分析法证明了该格式是无条件稳定的。最后给出数值算例验证了理论结果。     

带五次项的非线性Schrödinger方程的守恒差分格式

本文研究带有五次项的非线性Schrödinger方程初边值问题的有限差分法,其中方程中二阶偏导数项的系数、五次项的系数及初值满足下面的条件（1.6）.针对此问题,我们研究了一个守恒差分格式,在条件（1.6）下,差分解的$L^{\infty}$模先验估计被得到.在此基础上,我们得到了差分解最优$L^2$模的误差估计.     

求解二维Fisher-KPP方程的一类保正保界差分格式及其Richardson外推法

本文研究求解二维Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP)方程的一类保正保界差分格式.运用能量分析法证明了当网格比满足$R_{x}+R_{y}+[b\tau (p-1)]/2\leq\frac{1}{2}$时差分解具有一系列数学性质,包括保正性、保界性和单调性,且在无穷范数意义下有$O (\tau+h_{x}^{2}+h_{y}^{2})$的收敛阶.然后通过发展Richardson外推法得到收敛阶为$O (\tau^{2}+h_{x}^{4}+h_{y}^{4})$的外推解.最后数值实验表明数值结果与理论结果相吻合.值得提及的是在运用本文构造的Richardson外推法时对时空网格比没有增加更严格的条件.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.