离散数学

This make it difficult to know the essence of fluidized beds. In order to viewthe motion behavior of a single particle in a fluidized bed in a reasonable cost, thegas-solid flow in a fluidized bed is modeled by a combined approach of discrete particlemethod and computational fluid dynamics, in which the motion ofindividual Particles is obtained by solving Newton\'s second law of motion and gas flowby the Navier-Stokes equation based on the concept of local average.

为了用数值模拟方法来弥补传统实验方法的不足，达到从单个颗粒的尺度上来研究流化床中颗粒的运动和气体流场的剧烈变化情况的目的，本论文建立了基于用Newton第二定律计算单个颗粒运动轨迹的离散颗粒法和基于区域平均值的计算流体动力学方法的数学模型的建立和求解过程；并依据Newton第三定律建立了DPM模型和CFD模型的耦合模型，编写和调试了DPM和CFD的耦合程序。

The quadratic optimal control problem of delay discrete-time linear system is proposed with quadratic performance index. It is transformed intoanother problem by using the Principle of Optimality. The direct expressions of theoptimal control sequence and performance index sequence are given by mathematicalinduction.

针对给定的二次型性能指标，提出了时滞离散系统线性二次最优控制问题，并利用最优性原理将该问题进行了转化，进而利用数学归纳法推出最优有记忆饱和控制序列及最优性能指标序列的直观表达式。

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

After rigorously mathematical deduction, some valuable conclusions are drawn: at the multiple times of symbol period, discrete peaks of the PACA function appear with 3 peaks in group, which includes a larger peak located in the middle and the other smaller two located symmetricly beside the larger one. The distance between small peaks is modulation offset of pulse position PPM.

经过严格数学推导，指出了TH-UWB信号的PACA函数不但在字符周期整数倍处出现离散峰值，而且按三个峰值(一大峰值左右对称出现小峰值)成对出现，大峰和小峰的间隔就是PPM调制时间偏移。

XEX ~ Arg min{FIy E ~2} where the upper level is about topological structure optimization(a~ is a topological structure varable), and the lower level is a constrained programming about continuous variable y. 2 Apply graph, the action of permutation group on a graph, equiva- lent class, orbit etc.

取得的主要成果有： 1 依点到集的映射、集值映射、二元映射和分离定理等理论首次建立了具有拓扑结构双层规划的数学模型 min F s.t.x∈X y∈Arg min｛F|y∈Ω｝其上层规划为关于离散变量x的拓扑结构优化，下层规划是关于连续变量的约束规划。

For the first time, from mathematics approach, the prior probability distribution of risk analysis was derived by the use of POME in two cases that were discrete and continuous information source.

首次分离散信源和连续信源两种情况，从数学途径阐述了POME在确定风险分析先验概率分布中的应用，以确定几种常用分布及估计其参数为例加以了解释。

For the first time, based on POME, two weighted generalized distances were defined to build up two fuzzy, which used relative membership degree, and optimal models for evaluation of water environment, considering both the randomness and the fuzziness.

首次分离散信源和连续信源两种情况，从数学途径阐述了POME在确定风险分析先验概率分布中的应用，以确定几种常用分布及估计其参数为例加以了解释。

Through the discussion on the calculating methods for failure probability of element section with the influence of one or more human errors ,a mathematic analytical formula under ideal known conditions is deduced.

通过对单个或任意多个人因差错影响下构件截面失效概率计算方法的分析讨论，推导出在理想已知条件下的数学解析求解公式；在考虑人因差错对结构参数影响程度的空间离散化后，得出了相应的简化计算方法；并以一个单筋梁的正截面为例进行了失效概率计算和人因差错影响程度分析。

The first kind of the digital signature schemes is based on the discrete logarithm problem and second kind of the digital signature scheme is based on discrete logarithm and factorization problem, the third kind of the digital signature schemes is based on quadratic residue problem.

本文第一章对数字签名方案进行分类，根据数字签名方案所基于的数学问题，将签名方案分为：基于离散对数问题的数字签名方案，基于素因子分解问题的数字签名方案和基于二次剩余问题的签名方案。

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。