有限维的

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.

然后，我们介绍环与模的(n，0)-投射维数，它可以衡量一个有限生成模与n-表现模的差距，以及衡量一个环与Noether环的差距。

In this paper,with the aid of the w~*- sequential compactness of bounded closed balls in the conjugate space of a separable space,we proved that the convex hull of a finite union of bounded closed balls in l~∞ is closed.

借助可分空间的共轭空间中有界闭球的弱星序列紧性，证明在无穷维数列空间l∞中有限个闭球之并的凸包仍为闭集

We will call the construction a crossed product. The results about the sufficient and necessary conditions for A#H, the smash product, to have finite global homological dimension have been discussed in ~WYZ. which will be extended to crossed prodcut A#a.

关于smash积有有限整体同调维数的充分必要条件这一结果在中已有了一定的讨论，本文主要是将关于smash积的这一结果推广到crossed积。

Cavity flows both with and without sound excitation are studied by solving the 2 D time dependent Reynolds averaged Navier Stokes equations using explicit predictor corrector difference algorithm of Mac Cormack.

采用显式MacCorma－ck二步预估校正有限差分格式，求解二维雷诺平均非定常Navier－Stokes方程；并用Cebeci－Smith代数紊流模型作适当修正来模拟紊流效应，对有、无前缘声激励两种情况的空腔流场作了数值模拟，计算的振荡频率及振荡幅值都与实验结果基本符合，并且较好地模拟出了声激励对流场的影响。

A three dimension mathematical model is developed which is used to calculate electric field of rare earth electrolytic cell with adjustable anode.

建立了可调极距式稀土电解槽电场计算的三维数学模型，通过有限差分方法对电解槽的电场进行了计算机模拟，并对结果进行分析与讨论，为电解槽的设计及改造提供了理论依

Three-dimension temperature field of flame tube is calculated by FDM, which may describe the actually working case of flame tube.

使用有限差分法分析火焰筒的三维温度场，该方法能真实地模拟燃烧室的实际工作情况。

In general, people are more interested in the photonic crystal with defect, because the defect in photonic crystal can localize and guide electromagnetic wave.

本文采用有限差分时域方法计算了二维光子晶体直波导的带结构和其中的局域模式。

In chapter 5, we present the third-order finite volume method for the Shallow Water Equations on unstructured meshes.

第五章利用最小二乘思想，通过一次扩张模板来提高数值方法的精度，发展了在非结构网格上解二维浅水波方程的高精度有限体积法。

1Finding out the principles of the two-dimensional finite element method for temperature field simulation of high power laserThe profile and boundary conditions of the chip and submount of the high power laser is simply, we adopt the right-angled triangle cell to divide the submount and chip of the laser into triangular elements.

1找到了适用于大功率半导体激光器温度场模拟的二维有限元规则大功率半导体激光器芯片与载体具有规整的外形和多个边界条件，所以我们对激光器载体和芯片都采用了直角三角形单元进行有限单元剖分。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。