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Chapter 3 discusses the algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the Bergman space, such as boundedness, compactness, spectral properties and so on.

第三章研究了多圆盘Bergman空间的正交补空间L_a~2(D~n~⊥上对偶Toeplitz算子的代数性质，比如：有界性、紧性和谱性质等。

The numerical techniques developed here, including the high accuracy method of using expansions in orthogonal functions in normal direction and the effective algebraic mapping to deal with the problem of infinite region, can raise the calculation precision and the convergence velocity greatly.

文中所发展的方法，如，在法向上采用高精度的高阶谱方法和对无限区域数值问题的更为有效的代数变换处理等，提高了计算精度和收敛速度；同时，通过预估校正迭代法，使抛物化稳定性方程中重要的正规化条件得到满足，保证了数值计算的稳定。

The material job and main conclusion are as follows:(1) A simple boundary orthogonalization procedure independence grids generation method is put forward on the base of algebraic grid generation method; Data structure and computational model on interface are established aiming at blocks of structured grids.

本文针对粘流场数值模拟技术的研究现状和发展动态作了比较全面的回顾与展望，重点研究了网格生成技术、数值求解技术、湍流模型技术和动边界模拟技术，在此基础上建立了模拟自由面湍流场的数学模型，并成功地应用到二维溢流坝和带闸墩的三维溢流坝过坝水流的数值计算。

The material job and main conclusion are as follows:(1)A simple boundary orthogonalization procedure independence grids generation method is put forward on the base of algebraic grid generation method; Data structure and computational model on interface are established aiming at blocks of structured grids.(2) SIMPLE procedure is established in nonorthogonal grids by use of the finite volume method and in-depth discusses on special topic such as boundary condition in nonorthogonal grids, deferred correction method and grads compute on calculational nodes, and so on.

本文完成的具体工作和主要结论如下： 1以代数网格生成方法为基础提出了一种简单的、可独立于网格生成方法之外的边界正交化技术；针对分区结构网格系统建立了分区交界面处的数据结构与计算模型； 2利用有限体积方法在非正交同位网格系统中建立了SIMPLE求解算法，对非正交网格系统中的边界条件、延迟修正技术及计算节点的梯度计算等专题进行了深入讨论。

On the basic of above job a mathematical model of simulation turbulent flow with free surface is established and triumphantly applied to numerical computation on 2D spillway and 3D spillway with frusta of brake.The material job and main conclusion are as follows:(1)A simple boundary orthogonalization procedure independence grids generation method is put forward on the base of algebraic grid generation method; Data structure and computational model on interface are established aiming at blocks of structured grids.

本文针对粘流场数值模拟技术的研究现状和发展动态作了比较全面的回顾与展望，重点研究了网格生成技术、数值求解技术、湍流模型技术和动边界模拟技术，在此基础上建立了模拟自由面湍流场的数学模型，并成功地应用到二维溢流坝和带闸墩的三维溢流坝过坝水流的数值计算。

Then the stability solution of the variable cross-section compression bar, that is discribed by a partial differential equation with variable coefficient is transformed into solving a set of algebraic equations established in the subspace.

首先以均匀梁的低阶纵向振动模態函数构成求解子空间，然后在此子空间中把变截面压桿稳定由变系数偏微分方程描述的求解问题转化为非线性代数方程组的求解，从而简化了计算过程。

Give a projecting plane,sign volume of pentahedron for each triangle in mesh,which is constructed by the triangle and it projection in projecting plane,is computed.Volume of the mesh is algebraic sum of all pentahedrons' signed volume.Triangles will be partition into several smaller triangles when necessary.

该方法通过指定投影平面，计算每个三角面片及其在投影平面上的投影所围成的凸五面体的带符号体积（必要时对三角面片进行细分），整个模型的体积为所有凸五面体带符号体积的代数和。

From the application it is found that there is a unique stable periodic solution to the differential-algebraic system.

在此基础上，给出了其周期解的存在性、唯一性和稳定性的保证性条件。

Utilizequadratic form and Perron value of bottleneck matrices, we study how the algebraic connectivityof a weighted tree changes under shifting its branches and changing its edge s weights and obtainmore entire information about algebrai.

利用代数连通度的二次型形式和瓶颈矩阵的Perron值，我们研究了当迁移或改变分支和变动一些边的权重时树的代数连通度的变化，得到了比过去更多的关于赋权树的代数连通度的结论。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。