离散问题

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

A novel hybrid algorithm, which combines predictor-corrector primal-dual interior point method and genetic algorithm, is presented for dynamic and static reactive optimization in this dissertation. The algorithm fully make use of the advantage of interior point method in solving successive optimization problem and the advantage of genetic algorithm in solving discrete optimization problem. The original problem is divided into three parts: total successive problem, discrete problem and successive problem.

结合内点法和遗传算法，本文提出了一种新颖的混合算法用于求解动、静态无功优化问题，算法充分利用了内点法易于求解连续优化问题和遗传算法易于求解离散优化问题的优势，将原优化问题分解为初步的连续优化问题、离散变量优化问题、连续变量优化问题这三个子问题分别求解。

In chapter three, the elliptic curve discrete logarithm problems on the elliptic curve finite group are discussed.

第3章在介绍有限域上的离散椭圆曲线的基础上，深入讨论了椭圆曲线有限群上的椭圆曲线离散对数问题，研究了目前已知的椭圆曲线离散对数问题的几类求解算法，分析了这些算法的特点和应用范围，并总结归纳出了一系列的安全椭圆曲线选取准则。

For reducing boundary distortion area, the elevations of grid DEM are viewed as a discrete sequence under a generalized coordinate, so that the boundary problem of two-dimensional discrete wavelet transform is turned into the boundary problem of one-dimensional discrete wavelet transform, which not only greatly reduces the boundary distortion area, improves the precision of reconstructed DEM data near the boundary, but also decreases the number of zeros adding on the boundary for wavelet transform, and boosts the compression ratio. On the basis of analyzing the distribution characteristics of coefficients in low and high frequency bands, a mixed entropy coding plan is applied, and a high efficient quantizator called"self-adaptive hard threshold"is established, which is helpful for improving the precision of the reconstructed DEM data and for enhancing compression ratio.

为了减小小波变换山区格网DEM数据压缩中边界失真区域，将山区格网DEM高程值视为广义坐标下的离散随机序列，把二维离散小波变换中的边界问题转换为一维离散小波变换中的边界问题，不仅大大减少了小波变换边界失真区域，提高了重构DEM数据边界点的精度，而且减少了边界补零个数，提高了压缩比；通过对山区格网DEM数据小波变换低频区和高频区变换系数分布特点的分析，采取了霍夫曼—游程混合熵编码方案，设计了高效、低失真的"自适应硬阈值"量化器，即对低频区变换系数不进行量化，直接进行霍夫曼编码；对高频区变换系数则先用"自适应硬阈值"方法量化处理，再进行游程编码。

The method ofsolution for linear discrete Hilbert boundary value problem on the unit circleis illustrated and it is proved that,in case of the index〓,the solutionsof the discrete Hilbert problems are stongly convergent to the solution of theoriginal problem.

我们给出了单位圆上线性离散Hilbert边值问题的解法，并且证明了当问题的指标k=0时离散Hilbert边值问题的解强收敛于原Hilbert边值问题的解。

To the discrete-time systems, we introduce a new discrete-time norm, the algorithm given is not depend upon the initial data. For a class of uncertain discrete-time systems, we also adopt the method of iterative learning control, we convert the problem of learning control into a global stability of trivial solution for lower triangular matrix dynamic systems, and obtain the result of tracking to desired state of the system.

对于一般非线性离散系统，引进了离散的范数，所给的算法不依赖于学习控制算法中的初始数据，对于一类不确定离散系统的状态跟踪问题，我们也采用迭代学习控制的方法，将相应的学习控制问题转化为一个下三角动力系统的平凡解全局稳定性问题，获得了对系统理想状态的跟踪结果，并对所给的算法的收敛性进行了分析。

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。

In order to improve the security, a signature scheme based on two hard problem assumptions is proposed. The security of the scheme is based on the difficulties of simultaneously solving the elliptic curve and quadratic residue. A attacker can't forge the signature of messages even if a attacker can solve theelliptic curve discrete logarithm problems or quadratic residue problem in the scheme.

为了提高签名的安全性，本文对Wang等人提出的签名方案进行改进，提出了一个基于椭圆曲线离散对数问题和二次剩余问题的数字签名方案，并对该方案的安全性进行分析，指出在椭圆曲线离散对数问题或二次剩余问题可解的情况下，攻击者也无法伪造消息的签名。

Considering the technical requirements,the stability andthe steady performance,the quantitative requirement for sampling frequency is present indiscrete control system.Considering that there is a step delay in discrete control in grid on inverter with a Lfilter,the quantitative relationship between critical FCCR and sampling frequency isanalyzed,and the steady performance is analyzed.Considering the technical requirements,the stability and the steady performance,the quantitative requirement for samplingfrequency is present in discrete control system with a step delay.

在L型并电加热管网中，考虑到离散化控制存在滞后一拍的问题时，本文分析并获得了离散PI控制系统稳定范围时闭环根临界频率fnmax和采样频率fs之间的定量关系；针对存在滞后一拍可能引起系统稳态特性下降的问题，分析了PI控制滞后一拍对频域特性造成的影响，综合考虑并网指标、稳定性要求和离散化对稳态特性影响三个主要因素，推导了存在滞后一拍的离散化PI控制对最低采样频率的量化要求。

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。