离散问题

Analyzed some correlation problem of using elliptic curve construct cryptosystem.Make the correlation counterchange on the elliptic curve that suitable for constructing the cryptosystem and the op eration on it. Analyzed and researched discrete logarithm problems of elliptic c urve suitable for cryptosystem.

文中分析研究了利用有限域上的椭圆曲线构建密码体制的相关问题，对于适于建立密码体制的一类椭圆曲线进行了相应的仿射代换和其运算的映射变换，对椭圆曲线构建密码体制的椭圆离散对数问题进行了分析研究。

Z2Bn z$e0A0 Meshless method is a new numerical computation method that is developed rapidly in recent years. Without element mesh and based on the dispersed nodes to form approximate interpolative function dynamically, meshless method has distinct difference with traditional finite element method. Meshless method conquers the problems caused by mesh generation, mesh aberration and mesh move. With provides a new effective means to engineering problem, meshless method obtain highly recognition in international compute mechanics domain and engineering field.

6L！y6K1Q6h0k0 无网格方法是近年来迅速发展起来的一类新型数值计算方法，它们不借助单元网格而是基于离散结点动态构造近似插值函数，与传统的有限元方法有着显著的区别，克服了网格生成、网格畸变和网格移动引起的问题并为工程问题提供了一种新的有效分析方法，受到了国际计算力学界和工程界的高度重视。

In the process of this item, after the mainly uncertainties affecting the network planning are detailedly researched, some flexible planning models such as Blind Number Method and Scenario Method are proposed. Because power network planning is a nonlinear, discrete, multi-peak, multi-objective and nondifferentiable problem, it is very hard to be solved. Ant Colony Algorithm is an advanced metaheuristic method and has potential to deal with network planning problems.

本项目的研究过程中，针对影响电网规划的不确定性因素做了深入的定性和定量分析，采用盲数理论和多场景技术建立了多种具有良好适应性和灵活性的电网规划模型；同时，针对电网灵活规划模型非线性、离散性、多目标及目标函数不可微等特点，对多种优化算法在处理此类问题时的性质进行了分析和对比，并最终采用蚁群算法较好地解决了电网灵活规划问题。

DQRA can resolve the problems of delay and the bandwidth allocation parallelly in the networks.

智能蚂蚁算法已经成功地运用于TSP问题和一系列的离散优化问题，文中分析了智能蚂蚁算法的工作原理，并基于蚂蚁的自组织能力描述了一种新的分布式动态路由选择方法，QoS保证的分布式路由选择算法。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

In this paper,a quadratic programming method based on semidefinite programming is given to solve the design of FIR filters with discrete coefficients in the light of literature 6,which can give a better bound than a semidefinite programming relaxation method.Based on the model,the Branch-and-Bound algorithm is used to solve this problem.

基于离散系数滤波器设计问题已有的半定规划松弛模型，利用文献[6]的方法给出了该问题的二次规划松弛模型，该模型能给出比半定规划模型更好的界，然后运用分支定界方法求解该模型。

When a decision must be made in time, it will be unsignificative to solve it even if it's very precise. These LP models with large scales which one meets in practice, such as the ones for firms, economics, environment, traffic transport and so on, have serial decisions on discrete time points in them. The decision problems can be described with multiple simplex programming ones with special structures.

对于人们在实践中遇到的各种各样的大规模线性规划模型，如企业模型、经济模型，此外还有能源与环境模型、运输模型等等，它们都包含了在离散时间点上进行的系列决策，这些系列决策问题可以描述为具有特殊结构的多级线性规划问题，各级之间又有着一定的关联和影响，同时又相对独立。

Among them, one of the most promising seems to be Simulation Annealing that aims to reach the optimization of an objective function by physically analogizing to an annealing process of malerial at high temperature. This involves in a transformation of optimization of a function in continuous domain into a combinatorial optimization in discrete domain, as well as the proper choice of various control parameters such as temperature, iterative number etc.

为此，目前主要采用三种基于随机搜索策略的鲁棒技术，其中模拟退火算法是最有希望的一种，该算法的核心思想是随机模拟物理上的物质退火过程，它主要涉及将连续域优化问题转换为离散的组合优化问题，以及合理地选择各种控制参数、迭代时间等。

To eliminate the information of the surface model, thus improving the modeling speed and enhancing precision, an algorithm based on digital image processing for generating self-adaptive density mesh from measured dense scatted points is also introduced.

模型采用离散拓扑结构，无须进行曲面分片，因此不存在子曲面片之间的拼接问题；不采用解析函数表达曲面，因此不存在复杂组合曲面的参数域界定困难的问题；模型去噪能力强，特别适合大噪声场合。

We apply "points and normals" surface modeling technology to construct Coons surface of Correcting Lens.

校正透镜设计的本质是满足点及对应法矢这两个条件的光学曲面构造问题，不是单纯的离散点构造曲面问题。

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。