对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

级数小于1的亚纯函数的Borel例外值

证明了当超越亚纯函数的级小于1时，其Norel例外值最多只有一个．由于存在任何级的整函数，因此一个例外值总可达到，故所得结果不能再改进。     

Effect of ion impinging on the microstructure and field emission of carbon nanotubes

Effects of ion impinging on the microstructure and field electron emission properties of screen-printed carbon nanotube films were investigated. We observed that the plasma treatment modified the microstructure of CNTs along with the remarkable increase of emission site density. With the prolongation of ion impinging time, the emission current falls down first, and then rises up to higher than that of the untreated films. It is proposed that the change of emission characteristics is due to the different emission mechanisms. After the treatment, electrons are emitted predominantly from the nano-nodes on the tube wall instead from the nanotube tips.     

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.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

线性泛函方程解的振动性的新结果

本文研究高阶泛函方程x(g(t))=P(t)x(t)+Q1(t)x(g2(t))+…+Qk(t)x(gk+1(t))解的振动性,得到了一些新的振动条件.改进和推广了已有结果.     

Highlights and Prospects of Hyperspherical Approach in Few-Body Quantum-Mechanical Systems

The binding energy of excitonium negative ion for ground ¹S-state in bulk conductors: Ge, Si, CdSe and for green and yellow lines of Cu₂O in hyperspherical coordinate method are found. Angular and radial correlations between electrons are taken into account by the channel functions, which are the eigen-functions of operator on the surface of sphere in six-dimensional sphere. The calculation of energies have been done using the adiabatic and Born-Oppenheimer approximations. In Born-Oppenheimer approximation is enough to give a binding energy with only 1.2% error, in adiabatic approximation this error drops to 0.7 %.     

Time Series Prediction Based on Chaotic Attractor

A new prediction technique is proposed for chaotic time series. The usefulness of the technique is thatit can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. Atime-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the timeevolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate thelocal dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is testedfor the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this predictiontechnique can improve the prediction of chaotic time series.