两维的

The adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities. We give two methods to compute the normal form for the four dimensional nonlinear systems. The corresponding Maple programs are also given in the appendix. The results obtained in this dissertation have a completely agreement with the results obtained in other papers.

利用共轭算子法和规范形理论研究了含有三次非线性项的四维系统的规范形，给出了计算四维非线性规范形的两种算法，给出了相应的Maple符号推导程序，所得到的结果与其它文献所得结果完全一致。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

The boundary contour formulations of evaluatingstresses from the Somigliana stress identity are derived for 2-D problemswith quadratic boundary elements.The boundary contour method basedon the traction boundary integral equation is further discussed.Elasticproblems are first solved using the traction boundary contour method.Amixed collocation of the displacement boundary contour formulation andtraction boundary contour formulation is given.(4)The dual boundarycontour method is developed for the analysis of crack problems.

3建出了Somigliana应力积分式的二维和三维问题的边界轮廓法理论；给立了二维问题由Somigliana应力积分式计算应力的二次形函数的边界轮廓法方程，进而给出了基于面力边界积分方程的边界轮廓法；提出了一种以位移边界轮廓法方程与面力边界轮廓法方程混合配置的方案，首次实现了用两种积分方程相结合来求解弹性力学问题。

ERT is particularly suitable for the two-phase (or multi-phase) flow applications having a conductive continuous phase, and is able to provide 2D/3D visualization information of the parameters of a multi-phase mixture flowing inside a closed pipe or vessel.

电阻层析成像技术是近年来发展起来的一种基于电阻传感机理的过程层析成像技术，适用于两相流中以导电性介质为连续相的工业过程，可提供封闭的管道或过程容器设备内部多相组分物质参数的二维/三维可视化信息，具有非侵入、响应速度快、成本低、安全性能好、适应范围广等优点。

In the section of physical models, the paper presents a three-dimensional model called nine-equational model that treats the object as two phases and two components. The nine-equational model includesκ－εturbulence model and diffusibility model owing to the gradient of mass concentration.

在物理模型部分，本文对钢安全壳内部大空间提出了三维、两相、两组份、对气相引入κ－ε湍流计算模型和考虑由于气体浓度差引起的扩散效应的九方程模型。

And two models of single channel are also developed, one is formed by ruled-surface impeller, and the other is formed by enveloping surface impeller.

然后在专门的网格划分软件Gambit中对两个整体风机三维流场模型和两个单叶轮通道的流场模型进行网格划分及边界条件设置。

At first, it analyses the visibility processing of complex scene, including: spatial partition technology BSP, quadtree, octree and equational octree which can optimize scene, category of quick visibility estimation algorithm in the 3D scene, portal which can accelerate rendering, level of detail and mesh simplification based on quadric error metrics used to simply models in 3D scene.

首先分析了复杂场景的可视化处理，包括优化场景渲染的空间剖分技术：BSP树、四叉树、八叉树、均分八叉树；其次是三维场景快速可见性判断算法的分类，可加速渲染的入口技术；最后是用于三维场景中模型简化的两个算法：层次细节模型简化技术和基于视点的二次误差度量网格简化。

On one side sit the "modern" instruments: two violas and a cello, while on the other are the "old-fashioned" violas da gamba and violone.

一边是时兴的"现代"乐器：两把中提琴和大提琴，一边是旧式的维奥尔琴和低音提琴。两组之间形成对话。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

Captain?There are two ways to get to the island or chartered flight, it can be reached by ferry from Hervey Bay or Inskip Point north of Rainbow Beach .

到达岛上的方式有两种，坐飞机或是搭渡轮，渡轮则有两个点可以搭乘，赫维湾或是彩虹海滩北边的 Inskip Point 。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！