离散

Restricted by the assumption of low-order linear displacement approximation in each block, Discrete Element Methods often have to mesh many continuum parts of the problem domain into small discrete blocks when simulating crack propagation problems, and the result is very sensitive to the very way that divides the domain.

一般离散单元计算方法受离散块体低阶线性位移近似的限制，在模拟开裂过程时，需要将大部分实际上连续的区域离散化，离散方式对分析结果有显著影响。

At and , we can get a univariate cubic equation in and its three roots . By the dependence of the roots and the coefficients of the equation, we can choose corresponding space points ( such that the distance is the shortest from to the point with parameters and . Thereby we can get all the data of discrete points on the cubic curve of blending surface at . Again we denote the maximum value and minimum value of planar parameter with which meets by and respectively.

利用根与系数的连续相依性，可以选相应的空间点使其距离的圆截线上对应值的点最近的两个根，从而得到处拼接曲面的截线的离散点的数据并确定出与相截的平面参数的最大最小值类似地由处拼接曲面截线的离散数据得到处的离散数据，这样可以依次计算出拼接曲面上对应所有参数点的离散点的坐标。

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。

The first, look like each detail picture of direction of picture and each layers to carry on DCT towards get of again, then will imbed to look like the son diagram DCT transformation through two value watermark pictures of the false random row preface behind of the part of the high part of frequency and the detail son diagram energy concentration.

本论文中提出的第一种算法是一种基于离散余弦变换和离散小波变换相结合的脆弱水印方法，即：先对图像进行离散小波变换，再对得到的近似图像和各层各方向的细节图像进行离散余弦变换，然后将经过伪随机排序的二值水印图像嵌入到近似子图DCT变换后的高频部分和细节子图能量集中的部分。

The stability and convergence of the fully discrete solutions are proved and the convergence order is also given.

从数值实验上也验证了该算法的可行性和高效性，对非定常N-S方程提出了一种新的全离散TGM：空间离散用标准FEM，时间离散用Crank-Nicolson格式，证明了全离散解的稳定性与收敛性。给出了收敛阶。

By analyzing the problem of hydrological 3D spatial dispersion in 3D finite differential numeric simulation of porous groundwater flow, as well as discontinuous spatial distribution and asymmetric thickness of porous aquiferous strata and partitive groundwater stratum, the paper presents the GIS-based technique of 3D spatial dispersion of porous aquiferous stratum system. Besides, the paper puts forward the 3D spatial dispersion method of irregular hexahedral unit based on GIS to guarantee to the greatest degree the uniqueness of the stratum types among the dispersed units and improve the precision of 3D spatial dispersion.

分析了目前孔隙地下水流三维有限差分数值模拟中对含水层系统三维空间离散存在的问题，针对自然界孔隙含水层与隔水层空间分布的不连续性与厚度的不均匀性，研究了基於GIS的孔隙含水层系统三维空间离散实现的技术路线，提出了基於GIS与不规则六面体元的孔隙含水层系统的三维空间离散方法，最大限度地保证了离散体元中含水层类型的单一性，提高了孔隙地下水流模拟模型三维空间离散的精度。

By analyzing the problem of hydrological 3D spatial dispersion in 3D finite differential numeric simulation of porous groundwater flow, as well as discontinuous spatial distribution and asymmetric thickness of porous aquiferous strata and partitive groundwater stratum, the paper presents the GIS-based technique of 3D spatial dispersion of porous aquiferous stratum system .

分析了目前孔隙地下水流三维有限差分数值模拟中对含水层系统三维空间离散存在的问题，针对自然界孔隙含水层与隔水层空间分布的不连续性与厚度的不均匀性，研究了基于GIS的孔隙含水层系统三维空间离散实现的技术路线，提出了基于GIS与不规则六面体元的孔隙含水层系统的三维空间离散方法，最大限度地保证了离散体元中含水层类型的单一性，提高了孔隙地下水流模拟模型三维空间离散的精度。

The Discrete Logarithm Problem was analyzed. Based on the discrete logarithm in the prime field, and combined with the elliptic curve DLP in the limited domain, a new digital signature was brought up.

分析了离散对数问题，以素数域上的离散对数为基础，同时结合有限域上的椭圆曲线离散对数问题，提出一种新的数字签名方案，其安全性建立在离散对数算法上。

In this theory, we firstly introduce the basic theory of discrete wavelet transform and lifting scheme. Secondly, we adopt a fully pipelining VLSI architecture for lifting-based DWT. Hence, we can operate on higher working frequency. Besides, we merge a QCB-based DWT method to achieve the higher parallelism for JPEG 2000 encoding system. By changing the output timing of the DWT process, the internal tile memory size can be reduced by a factor of 4. Moreover, the architecture can efficiently perform shape-adaptive DWT and solve boundary extension and subsampling problems. Finally, according to the comparison results with other architectures, the efficiency of proposed architecture is proven.

在这篇论文中，首先我们介绍离散小波转换和提升式架构的基本理论，接下来我们改良提升式架构采用全管线化的硬体架构，因此我们可以操作在较高的工作频率，并且我们合并了以四个编码方块为基础的方式来使得JPEG 2000编码系统具有更高的平行度，藉著改变离散小波转换的输出时序，内部的记体体需求可以减少为原本的四分之一，接著此架构也可以有效地支援可适应形状的离散小波转换，同时解决了边界延伸和子取样的问题，最后根据与其他架构比较的结果，来说明所提出之离散小波转换架构的贡献。

This course includes (1) Discrete time signal and systems,(2) Z transform,(3) Continuous-time signal sampling,(4) LTI system,(5) Discrete time systems,(6) Filter design,(7) DFT,(8) FFT.

课程内容包含：(1)离散时间信号和系统，(2) z转换，(3)连续时间信号的取样，(4)线性非时变系统的转换分析，(5)离散时间系统的结构，(6)滤波器设计技巧，(7)离散傅氏转换，(8)使用离散傅氏转换以对信号做傅氏分析。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。