广义混合非线性Schr？dinger方程的拟谱方法

本文讨论了广义混合非线性Schrodinger方程的周期初值问题,构造了守恒的半离散Fourier拟谱格式,对其近似解进行了先验估计,并证明了格式的收敛性.证明了该方程存在孤立子解,并给出其孤立子解的精确表达式.研究了线性化方程的稳定性问题,即在初值有扰动的情况下,该方程只有振荡解和鞍点.最后,通过数值例子验证了格式的可信性,数值计算表明,本格式时间方向可取大步长且是长时间稳定的,我们还计算了孤立子解,并绘出了在初值有扰动的情况下,相空间的轨线图.     

Soliton Solutions,B/icklund Transformations and Lax Pair for a （3 ＋ 1）-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Fluids

Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.     

A block monotone iterative method for numerical solutions of nonlinear elliptic boundary value problems

The aim of this article is to develop a new block monotone iterative method for the numerical solutions of a nonlinear elliptic boundary value problem. The boundary value problem is discretized into a system of nonlinear algebraic equations, and a block monotone iterative method is established for the system using an upper solution or a lower solution as the initial iteration. The sequence of iterations can be computed in a parallel fashion and converge monotonically to a maximal solution or a minimal solution of the system. Three theoretical comparison results are given for the sequences from the proposed method and the block Jacobi monotone iterative method. The comparison results show that the sequence from the proposed method converges faster than the corresponding sequence given by the block Jacobi monotone iterative method. A simple and easily verified condition is obtained to guarantee a geometric convergence of the block monotone iterations. The numerical results demonstrate advantages of this new approach. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

色散方程的一类新的并行交替分段隐格式

本文给出了一组逼近色散方程的非对称差分格式，并用这组格式和对称的Crank-Nicolson型格式构造了求解色散方程的并行交替分段差分隐格式．这个格式是无条件稳定的，能直接在并行计算机上使用．数值试验表明，这个格式有很好的精度．     

K_（1，r）－free图的次限制树多项式算法

设Ｇ＝（Ｖ，Ｅ）为一连通图，ｄ＞０整数．Ｇ中存在生成树Ｔ，使得Δ（Ｔ）小于ｄ吗？这一问题已被证明是ＮＰ－完全的，故不太可能有多项式解法．本文证明了当Ｇ是Ｋ１，ｒ－ｆｒｅ时，则有Ｏ（ｎ２）的算法求出Ｇ的生成树Ｔ，使Δ（Ｔ）≤ｒ，并用一个例子显示了这一结果是最好可能的     

A maximum principle for fourth order ordinary differential equations

We present a maximum principle for fourth order ordinary differential equations, based on a new approach involving counting of inflection points. We use our results to compute solutions of nonlinear equations describing static displacements of a uniform beam     

三维混合沙输运数值模拟

采用计算流体力学和颗粒离散元耦合的方法模拟了三维混合沙输运过程。采用体平均的Navier-stokes方程来描述气相运动,考虑了气相和颗粒相的相互作用。颗粒运动通过求解牛顿运动方程来求解,采用硬球模型描述颗粒和颗粒及颗粒和壁面的碰撞。本模型中,颗粒运动是三维的而气相运动是二维的。计算结果表明:总输沙率沿高度方向在大于2cm以上按照指数衰减,在2 cm以下则偏大;各粒径颗粒具有不同的输沙率分布,粗粒径颗粒按指数规律衰减,其它粒径颗粒输沙率随高度先指数增加后减少;各粒径颗粒平均水平速度随高度对数函数增加且同高度时随粒径增大而减小,1 cm高度以下则相反;沙粒平均粒径沿高度线性递减,2 cm以下粒径偏大。     

非线性波方程准确孤立波解的符号计算

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.     

Computational Logic on Fock Space

Fock space may provide an important mathematical model for quantum computation. For this reason, it may be useful to generalize previous work on computational logic to the Fock space framework. The basic construction of this computational logic is the set D(H) of density operators on a Fock space H. We first define n-sector p _n() and total probabilities p() of elements D(H). We next discuss NOT, AND, and OR operations on D(H). Natural equivalence classes and Scotian elements are described. We also discuss minimal and maximal elements and quantum numbers for the equivalence classes. We finally treat the operation and the stronger equivalence classes associated with this operation.     

同心方槽电场的实验模拟和数值求解

对同心槽内静电场用稳恒电场进行实验模拟，并以有限差分法进行数值计算，由计算结果绘制出横截面内电势随场点变化的立体和等势经平在图，将实验模拟和数值计算进行比较。