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The discrete curvature vector based method to fair mesh by modifying vertex positions We first low-pass filter the discrete curvature vector function to make it change more gradually and uniformly, and then modify the vertex positions according the resulted function to improve the fairness of mesh.

以此为基础，给出了两个算法：网格改点光顺的离散曲率向量法基本思想是先用低通滤波算子修匀曲率向量，并由此修改顶点的位置以改善网格的光顺性。具体算法吸取了优化问题中Zoutendijk可行方向法的基本思想。

The motion of a discrete curve in Minkowski space is first introduced. Then by identifying the spin vector of HF models with the unit vectors of discrete curve, respectively, we obtain the corresponding DNLS.

我们将主要考虑闵可夫斯基空间中离散曲线的运动情况，并利用离散曲线的单位矢量分别替代离散的MHF方程中的自旋矢量，给出相应的离散非线性薛定谔方程，从而建立了两者之间的几何等价性。

Firstly expound the structure of the OFDM system, then analysis the working principle of OFDM communication and research into the key technologies in OFDM system: string conversion, sub-carrier modulation and demodulation, inverse Discrete Fourier Transformation, Discrete Fourier Transformation, cyclic prefix Insert, etc.

该文首先阐述了OFDM系统的结构，分析了OFDM通信系统的工作原理，研究了OFDM系统实现过程中串并转换、子载波调制解调、离散逆傅里叶变换、离散傅里叶变换、循环前缀插入等关键技术。

In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not.

在离散算子差分方法中，无论单元位移函数是否协调，其位移函数均能在离散格式中得到十分好再现，说明了离散算子差分方法的离散格式是一种性能很优良的离散格式。

The concept of topology optimization of truss structures with discrete variables including two kinds of variables and the relative difference quotient algorithm for discrete optimization are extended to the topology optimization of plate and shell structures composed by plate and shell elements.

将包含两类变量的桁架结构拓扑优化设计的概念及求解离散优化的相对差商法进一步推广到由板壳单元组成的板壳结构的拓扑优化，建立了包含两类变量的板壳结构拓扑优化设计模型，并采用相对差商算法进行求解。

The derivation course and the discrete scheme of the first model-Perona-Malik model have been expatiated on emphasis. One item of the P-M model is omitted in the P-M's discrete scheme, and the gradient magnitude is replaced by the absolute value of difference quotient.

Perona-Malik给出的离散格式是一种显式离散格式，这一格式的连续形式省略了原模型中的一项，且用差商的绝对值代替了梯度模。

The main objective of this dissertation was to develop methodologies with capability of engineering application for simulating flow in fractured rock using discontinuum models. The study work includes three parts. In the first part, numerical methodology of three-dimensional discrete fracture network model casing on hybrid BEM-channel was presented, and the technique for improve the model's computing efficiency was also studied. Firstly in this part, computer simulation methodology based on the Baechermodel for generating network of discrete fractures was presented, which includes the follow details: probability distributions of fracture density,orientation, trace length, size, and aperture and estimation of their statistical parameters; stochastic models of fracture network; Monte-Carlo's simulation method; numerical simulation procedure and technicality.

给出了离散裂隙网络模型所依据的基本假定；发展了基于Baecher模型的离散裂隙网络计算机随机生成技术：详细地推导了单裂隙渗流和多裂隙相交网络渗流的边界单元法公式，发展了离散裂隙网络中稳态渗流的边界元数值技术，并且讨论了相关的具体数值技术细节，如角点的处理方法，单元的自动剖分等：描述了混合边界元—管流模拟方法及其数值实现；研究了裂隙网络的简化方法，并针对裂隙网络边界元法的特点提出了一种改进的分块三角分解法。

Study on design of the discrete state PI regulator and observers We extend the results of continuous system to discrete system in order to realize the state PI regulator by using computers.

离散状态PI调节器及估计器的设计研究将连续系统的有关结果推广到离散系统中，便于利用计算机进行计算和控制。

In response to signals and system simulation studies, MATLAB also demonstrated its strong role, with MATLAB simulation for the time signal convolution, discrete, continuous LIT system of time-domain analysis, synthesis and periodic signal of decomposition, the bi-frequency system Domain analysis, signal modulation and demodulation, discrete systems, the Z-domain analysis.

在信号与系统仿真响应的研究中，MATLAB也体现其强大的作用，用MATLAB仿真连续时间信号的卷积计算，离散、连续LIT系统的时域分析、周期信号的合成与分解、系统的复频域分析、信号的调制与解调，还有离散系统的Z域分析。

For the dynamic system of discrete coupled and nonlinear three phase voltage source PWM rectifier, the cycle switch average operator is introduced to transform the discrete system into continuous and the small signal perturbation method is used to transform the nonlinear system into linear, the small signal dynamic mathematical models are set up.

中文摘要：针对三相电压型PWM整流器这个离散的、耦合的、非线性的动态系统，引入开关周期平均算子将离散的系统变换为连续的系统，应用小信号扰动法将非线性的系统化解为线性的系统，进而分析系统的小信号动态数学模型。

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。