四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.     

Higher-order streamfunction-vorticity formulation of 2D steady-state Navier-Stokes equations

Based on regular boundary element method and a kind of linearity invariance under homotopy, a kind of numerical scheme of 2D steady-state Navier-Stokes equation in streamfunction-vorticity formulation is described. The flow inside a square cavity is used to illustrate this numerical scheme.     

OSCILLATION FOR A CLASS OF LOGISTIC EQUATIONS

The oscillation of a delay difference equationis studied and the necessary and sufficient condition for all positive solutions of (E) to oscillate about its positive equilibrium is obtained.     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

Resonance structure for 4s subshell in photoionization of Mn

It is shown that the 3d5(4X)4s(5X) of 4s satellites, except to the coupling between 3d54s(7,5S) and 3p→3d transition, plays a key role on the magnitude of photoionization of 4s cross section. The coupled equation method is improved to calculate this resonance by including these channels. The results of calculations are comp ared with the experimental data from 46 eV to 56 eV photon energies, which are in good agreement with the experiment.     

New Exact Solution to (3+1)-Dimensional Burgers Equation

In this Letter, using Backlund transformation and the new variable separation approach, we find a new general solution to the (3 1)-dimensional Burgers equation. The form of the universal formula obtained from many (2 1)-dimensional systems is extended. Abundant localized coherent structures can be found by seclecting corresponding functions appropriately.     

关于双特征Beltrami方程

该文研究空间Ｂｅｌｔｒａｍｉ方程的推广形式，即双特征Ｂｅｌｔｒａｍｉ方程．利用外微分形式与矩阵的外代数等工具，将双特征Ｂｅｌｔｒａｍｉ方程转化为一个非齐次的狆 调和方程，转化过程中只用到加于特征矩阵的一致椭圆型条件．然后验证了算子犃满足的条件：Ｌｉｐｓｃｈｉｔｚ型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件．并利用得到的狆 调和方程，给出了双特征Ｂｅｌｔｒａｍｉ方程广义解分量函数的弱单调性结果．     

水溶性高聚物聚丙烯酰胺的稀溶液性质(Ⅰ)

本工作利用光散射和粘度方法,使用辐射聚合聚丙烯酰胺(PAAM)的级分样品,研究了在较宽分子量范围(10~4-10~7)内PAAM的特性粘数,分子尺寸及第二维利系数对重均分子量的依赖性.从实验上得到了PAAM在0.2mol/lNaCl水溶液中的均方旋转半径与均方末端距之间的关系及高分子-溶剂相互作用参数.     

Limit Gaussian Behavior of the Solutions of the Multidimensional Burger'; Equation with Weak-Dependent Initial Conditions

Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved.