离散

The rational points of an elliptic curve forms an additive group. The discrete logarithm problem of this group is called elliptic curve discrete logarithm problem.

椭圆曲线上的有理点会形成一个加法群，此加法群上的离散对数问题称为椭圆曲线离散对数问题(elliptic curve discrete logarithm problem)。

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

The characteristic approximation is used to handle the convection part along the direc-tion of fluid namely characteristic direction to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion; The mixed finite element spatial approximation is employed to deal with diffusion part and approximate the scalar unknown and the adjoint vector function optimally and simultaneously; In order to preserve the integral conservation of the method, we introduce the modified characteristic method.

该方法对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性，消除数值弥散现象；对方程的扩散部分采用最低次混合有限元方法离散、同时以高精度逼近未知函数及未知函数的梯度；为保证方法的整体守恒性，在格式中引入修正项。

The admissible input of 2-D linear discrete singular general model is discussed more deeply, some very effective new criteria for the 2-D singular general model to accept all the input sequence have been developed, and a new algorithm that determines the admissible input sequence of the 2-D singular systems has been proposed.

在线性广义2-D系统可解性方面，首先研究了线性广义2-D连续—离散系统的可解性问题，给出了可解的条件，并给出了等价的判别条件；其次深入研究了线性广义2-D离散系统的允许输入序列问题，给出了系统接受所在区域上的所有输入的新的非常有效的判别方法以及确定系统允许输入序列的新的方法。

One of they is a cluster method based on rough entropy and orients to discrete attributes.

主要成果如下：（1）分析遥感影像分类特征的离散化方法及其对分类规则提取的影响，提出适用于遥感影像分类的基于改进粗糙熵的离散特征聚类方法和基于动态层次聚类的连续属性离散方法。

It indicates the distinct element method simulation model of charging of bell-less top blast furnace may replace the model experiment that takes very long time, and spends a great amount of both manpower and material resources to research the law of charging of bell-less top. The distinct element method simulation is made for opening furnace charging of reality bell-less top blast furnace. The result of simulation is also very identical with that of measuring.

本文在高炉无钟炉顶实验模型上进行了单环和多环布料实验研究，同时运用离散单元法模拟模型对实验进行了数值模拟，得到的炉料分布和料面形状的实验结果与模拟结果相当吻合，这证明了离散单元法在高炉无钟炉顶布料中的应用是可行的，并且表明运用高炉无钟炉顶布料离散单元法模拟模型可以替代费时、费钱、费力的物理模型实验，进行无钟炉顶布料规律研究。

A matrix method and a technique lased on minimax algebra are applied respectively to establish the discrete event state equation and the discrete event time-series equation which will benefit the performance evaluation of discrete event dynamic systems.

根据系统的网络表示，应用矩阵方法和极大代数方法分别建立了系统的离散事件状态方程和离散事件时序方程，为从现代控制理论的观点和体系来研究离散事件动态系统打下了基础。

Discrete system models in common use can be expressed in linear regression form and a complex system model can be expressed in combination of several simple system models.

根据离散系统模型结构的这些特点，我们用面向对象的程序设计思想，用&类&的概念来实现各种离散系统模型，从而形成离散系统模型类库，并可由此派生出其它更具针对性的模型类。

To increase the security of the watermark, a new binary image encryption algorithm based on TD-ERCS map is presented. The watermark is encrypted by a chaos sequence generated by TD-ERCS map; A novel color image watermarking algorithm is proposed based on discrete chaotic map and 2-dimensions discrete wavelet transform. The watermark is encrypted by the new binary image encryption algorithm, and the encrypted watermark is embed into four sub-bands of the most deep level of blue branch of host image by three-level wavelet transform, and the embedded positions are determined by general cat cha otic map; A novel color-image blind detection watermarking algorithm is proposed based on integer wavelet transform and subsampling. The scrambled watermark is encrypted and embed into the low sub-bands after four sub-images of the Y branch of host image is transformed by two-level wavelet transform, and the embedded positions are determined by Logistic chaotic map, this watermarking scheme can realize blind extraction.

为了提高水印图像的安全性，提出了一种基于TD-ERCS混沌映射的二值水印图像的加密算法，该算法利用TD-ERCS映射产生的混沌序列加密水印图像；将离散混沌映射和二维离散小波变换相结合，研究了彩色图像水印新算法，该算法先对混沌序列加密后的水印图像进行小波变换，再嵌入到宿主图像的蓝色分量的最深层的四个子带中，嵌入位置则由广义猫映射确定；将整数小波变换和图像子采样技术应用于数字水印，提出了一种彩色图像盲提取水印算法，水印嵌入时，先对宿主图像在YIQ色彩空间中的Y分量进行子采样，并对得到的四个子图像分别进行二级离散小波变换，然后将置乱并加密后的水印图像嵌入到小波变换后的低频子带中，其嵌入位置由Logistic混沌映射产生的混沌序列确定，实现了水印的盲提取。

This article based on net disperse method has first established the description arbitrary shape non-uniform face target mathematical model.

但是在计算其毁伤效果的时候，难以解决判断网格离散点是否属于目标离散点的问题，没有比较有效的算法对面目标进行离散化。

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。