离散数学

The segregation of the binary granular mixture in Brazil nut problem was simulated by using discrete element model. The influences of the frequency and the amplitude of the vibration on the segregation are discussed.

采用离散单元模型对巴西果问题进行了模拟研究，采用本数学模型可以准确地预测出垂直机械振动导致的不同大小颗粒的分离现象。

Other semirings arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, topology, graph theory, Euclidean geometry, probability theory, commutative and noncommutative ring theory, optimization theory, discrete event dynamical systems, automata theory, formal language theory and the mathematical modeling of quantum physics and parallel computation systems.

在许多不同的数学领域存在着其它形式的半环，比如组合学，泛函分析，拓扑学，图论，欧式几何，概率论，交换和非交换环，优化论，离散动力系统，自动化理论，形式语言理论，量子物理的数据模型和并行计算系统。

Formalization verification of service composition based on Process Algebra and Discrete Time Ambient-Calculus, as well as combinatorial optimization and the partition method based on QoS mathematic model are deeply studied. The service composition architecture supporting formalization verification and QoS-aware composition has been also implemented. Furthermore, the architecture is applied to digital cartoon cooperation manufacturing in the Internet.

为实现动态的跨企业业务协作与集成，本文围绕服务组合行为的正确性检验以及服务质量保证这二个正交的性质，深入研究了基于进程代数Pi演算及离散时间Ambient演算的服务组合形式化检验，以及基于QoS数学模型进行精确计算的服务组合优化与划分方法。

Thirdly, we should start with momentum equation and equation of continuity. They offer theory basement through equation dispersion, interpolation of disheveled datas and analysis of turbulence coefficient.

再者，从动量方程和连续方程入手，通过方程的离散、散乱数据的插值、紊动粘性系数等的分析，为数学模型的建立提供理论基础。

Nonstandard analysis ; nlargements of number systems ; transfer principle ; external producing principle ; comparative principle ; potential numbers ; measure ; continuum ; discontinuum ; cardinal number ; continuum hypothesis ; Hilbert's first problem Ner

非标准分析；数系的扩大；转移原则；外的生成原则；比较原则；潜在数；测度；连续统；离散统；基数；连续统假设； Hilbert第一问题；新的数学实体；不可分的连续体； Zeno的总格言； Aristotle的猜想；庄周；无厚不可积；万世不竭；测度论的基础

The discrete cosine transform is an important mathematical tool in digital image processing and many other fields.

摘 要：离散余弦变换是数字图像处理等许多领域的重要数学工具。

In a January, 1994 Mathematics of Computation article by Richard Crandall and Barry Fagin titled "Discrete Weighted Transforms and Large-Integer Arithmetic", the concept of using an irrational base FFT was introduced.

一节(译注：中文版第267页)。1994年1月，由理查德·克兰多尔和巴里·费金合著的题为"离散加权变换和大整数算术"的计算数学文章，引入了无理底数 FFT 的概念。

ECC system makes use of the finite group of elliptic curve on the finite field instead of finite cyclic group used in the discrete logarithm problem. The theory of ECC is being studied a lot and it is the focus of the cryptography and the industrial estate, especially the technique of the implementation of ECC.In this thesis, the meaning of the information technology is discussed firstly, then we analyze the classical cryptography algoritham. After that, the mathematics base of elliptic curve cryptosytems are introduced, especially the theory of the finite field. As for some algorithms, we also give out the program of reliazation.

随后，介绍了研究椭圆曲线密码系统所需要的数学理论基础，特别是有限域中的椭圆曲线理论，并对相关的方法给出相应的实例及其程序实现；论文第三章讨论给出了椭圆曲线密码体制的研究现状，综述了椭圆曲线与现有一些密码算法的结合，介绍了椭圆曲线的离散对数问题以及椭圆曲线面临的攻击，详细描述了椭圆曲线密码系统的实现细节及各个部分的实验数据。

In this paper,several continuous variables are introduced to replace the discrete decision variable s,most importantly the pipe .

在数学模型中，引入连续变量代替离散的决策变量，这些连续变量是管道的"分段长度"，将混合整数非线性规划问题转化成连续的非线性规划问题。

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current.

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。

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。