一种新的局部时间积分的区域分解波形松弛算法

提出一种新的区域分解波形松弛算法, 使得可以在不同的子域采用不同的时间步长来并行求解线性抛物方程的初边值问题. 与传统的区域分解波形松弛算法相比, 该算法可以通过预条件子来加快收敛速度, 并且对内存的需求大大降低. 给出了局部时间步长一种具体的实现方法, 证明了离散解的存在唯一性, 并在时间连续水平分析了预条件系统. 数值实验显示了新算法的有效性.     

广义KdV方程与广义Burgers方程的精确解

利用试探函数法和直接积分法构造广义KdV方程与广义Burgers方程的新的精确解.     

Bradyon-luxon symmetry

We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground of all physical processes is the union space. However, the physical processes in union space are differently projected on the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some consequences of this symmetry in the theory of elementary particles.     

流体的塔阱状态方程及其对迁移性质的推算

流体的塔阱状态方程及其对迁移性质的推算曾向东，严家（哈尔滨工业大学能源科学与工程学院哈尔滨１５０００６）牛文科，韩立中（哈尔滨船舶锅炉涡轮机研究所哈尔滨）关键词势能模型，配分函数，状态方程，平衡性质，迁移性质１流体的塔阱状态方程Ｐｒｉｇｏｇｉｎｅ认为...     

多缝衍射反演光谱学的稳定性理论研究── 一种第一类Fredholm积分方程数值解之稳定性分析

作者在前文￣（１，２）中通过计算机模拟实验给出了由多缝衍射反演光谱学的积分方程─一种第一类Ｆｒｅｄｈｏｌｍ积分方程─获得稳定线性方程组的条件，本文将进一步从数学上利用积分方程的本征值理论分析计算机的实验结果，阐明这些条件使线性方程组稳定的机制。     

Approximation, integration and differentiation of time functions using a set of orthogonal hybrid functions (HF) and their application to solution of first order differential equations

Differential equations of different types and orders are of utmost importance for mathematical modeling of control system problems. State variable method uses the concept of expressing n number of first order differential equations in vector matrix form to model and analyze/synthesize control systems.The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of sample-and-hold functions (SHF) and triangular functions (TF). This HF set is used to approximate a time function in a piecewise linear manner with the mean integral square error (MISE) much less than block pulse function based approximation which always provides staircase solutions.The operational matrices for integration and differentiation in HF domain are also derived and employed for solving non-homogeneous and homogeneous differential equations of the first order as well as state equations. The results are compared with exact solutions, the 4th order Runge-Kutta method and its further improved versions proposed by Simos [6]. The presented HF domain theory is well supported by a few illustrations.     

Application of rational expansion method for stochastic differential equations

By means of the Hermite transformation, a new general ansätz and the symbolic computation system Maple, we apply the Riccati equation rational expansion method [24] to uniformly construct a series of stochastic non-traveling wave solutions for stochastic differential equations. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions. The method can also be applied to solve other nonlinear stochastic differential equation or equations.     

The expected discounted penalty function under a renewal risk model with stochastic income

In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided.     

并行求解约束优化问题的QP-free型算法

针对约束块可分的最优化问题,引入序列线性方程组方法和有效集策略,提出了一个求解约束块可分优化问题的QP-free型并行变量分配（PVD）算法.算法中用三个系数具有对称结构的线性方程组来代替PVD算法中的二次规划问题以求解线搜索方向,避免了约束不相容,减小了计算量.并且算法不要求约束是凸的.最后证明了QP-free型PVD算法的全局收敛性.     

利用(G'/G)-展开法求广义的(2+1)维ZK-MEW方程的新精确解

结合齐次平衡法原理并利用(G'/G)-展开法,研究了广义的(2+1)维ZK-MEW方程的精确解,从而得到了广义的(2+1)维ZK-MEW方程的用双曲函数和三角函数表示的通解,当双曲函数通解中常数取特殊值时,便得到广义的(2+1)维ZK-MEW方程的孤立波解,获得了与现有文献不同的新精确解.