Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition

This paper discusses the semidiscrete finite element method for nonlinear hyperbolic equations with nonlinear boundary condition. The superclose property is derived through interpolation instead of the nonlinear H^1 projection and integral identity technique. Meanwhile, the global superconvergence is obtained based on the interpolated postprocessing techniques.     

Korn's inequality and Donati's theorem for the conformal Killing operator on pseudo-Euclidean space

We prove the Korn's inequality for the conformal Killing operator on pseudo-Euclidean space Rp,q, and an existence theorem for solutions to the non-homogeneous conformal Killing equation, which is a pseudo-Euclidean conformal generalization of Donati's theorem for Euclidean Killing operator.     

Numerical examination of the extended phase‐space volume‐preserving integrator by the Nosé‐Hoover molecular dynamics equations

This article illustrates practical applications to molecular dynamics simulations of the recently developed numerical integrators [Phys Rev E 2006, 73, 026703] for ordinary differential equations. This method consists of extending any set of ordinary differential equations in order to define a time invariant function, and then use the techniques of divergence‐free solvable decomposition and symmetric composition to obtain volume‐preserving integrators in the extended phase space. Here, we have developed the technique by constructing multiple extended‐variable formalism in order to enhance the handling in actual simulation, and by constituting higher order integrators to obtain further accuracies. Using these integrators, we perform constant temperature molecular dynamics simulations of liquid water, liquid argon and peptide in liquid water droplet. The temperature control is obtained through an extended version of the Nosé‐Hoover equations. Analyzing the effects of the simulation conditions including time step length, initial values, boundary conditions, and equation parameters, we investigate local accuracy, global accuracy, computational cost, and sensitivity along with the sampling validity. According to the results of these simulations, we show that the volume‐preserving integrators developed by the current method are more effective than traditional integrators that lack the volume‐preserving property. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

The Radon-Nikodým Property Does Not Imply the Separable Complementation Property

There is a Banach space X enjoying the Radon-Nikodým Property and a separable subspace Y which is not contained in any complemented separable subspace of X.     

递推与迭代在量子力学近似计算中的应用

综述了非简并微扰论和简并微扰论的递推形式，一维阶梯位势透射系数的递推计算及变化法的迭代形式，在给定的精度下，利用上述方法可以得到与精确解完全一致的效果。     

单晶SiNd：YAG激光连续退火的数值计算

应用固相外延模型来模拟单晶Si的连续Nd：YAG激光退火过程,在低功率密度连续激光退火下,用准静态模型模拟辐照区向非辐照区的径向传导散热。在数值计算中，应用部分线性法处理非线性非齐次热传导方程,得到相应的隐格式差分方程，再用追赶法求解隐格式差分方程,得出绝热边界条件下的温度的时间和空间分布，从而得出激光退火的再结晶厚度。当激光波长λ=1．06μm、功率密度io=700W／cm^2。预热温度T0=523K时，经过0．7秒，表面温度度升到1290K左右，再结晶厚度约为0．5μm。     

Some geometric and dynamical properties of the Urysohn space

This is a survey article about the geometry and dynamical properties of the Urysohn space. Most of the results presented here are part of the author's Ph.D. thesis and were published in the articles [J. Melleray, Stabilizers of closed sets in the Urysohn space, Fund. Math. 189 (1) (2006) 53-60; J. Melleray, Compact metrizable groups are isometry groups of compact metric spaces, Proc. Amer. Math. Soc. 136 (4) (2008) 1451; J. Melleray, On the geometry of Urysohn's universal metric space, Topology Appl. 154 (2007) 384-403]; a few results are new, most notably the fact that Iso(U) is not divisible.     

Convergence theorems for nonexpansive mappings and feasibility problems

In this paper, we introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and then prove weak convergence theorems which are connected with the problem of image recovery. Using the results, we consider the problem of finding a common fixed point of finite nonexpansive mappings.     

Frames of Periodic Shift-Invariant Spaces

This note studies Bessel sequences and frames of shift-invariant spaces generated by a countable set of periodic functions. We give characterizations under which the set of translations of the countable set is a Bessel sequence or a frame in terms of spectral decompositions of some self-adjoint operators.