一类积分不等式的推广

对一些基本的积分不等式进行了推广，给出了含有n个无关变元的更广泛的非线性积分不等式．利用所得的不等式讨论了某些非线性积分方程解的有界性．     

Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

中立型脉冲微分方程正解的存在性

本文利用Banach压缩映射原理，讨论了中立型时滞脉冲微分方程正解的存在性。     

Probability Interpretation of the Integral of Fractional Order

We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.     

Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions

This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.

     

四阶非线性边值问题解的存在性与上下解方法

该文讨论四阶常微分方程边值问题u^(4)(t)=f(t,u,u″), t∈［0,1］,u(0)=u(1)=u″(0)=u″(1)=0解的存在性, 其中f(t,u,v):［0,1］×R×R→R为Carathéodory函数. 在不限制f关于u,v的增长阶, 不假定f关于u,v的单调性的一般情形下, 用上下解方法获得了解的存在性结果,并讨论了单调迭代求解的有效性.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

甲基对硫磷的快速测定及电化学性质

研究了杀虫剂甲基对硫磷的电化学性质。在pH10．38的Bdtton—Robinson缓冲溶液中，采用微分脉冲溶出伏安法在悬汞电极上得到一个还原峰，峰电位为-0．5V(vs．Ag/AgCl)，本工作对实验条件进行了深入的研究，结合线性扫描伏安法等手段。研究了体系的电化学行为。实验表明，甲基对硫磷在汞电极上具有吸附性，电极反应具有不可逆性。该法用于水果及水样中甲基对硫磷残余量的测定，结果满意。