基本运算

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

The main content of this thesis includes six parts. First of all, it is a comprehensive systematic introduction about RSA algorithm including the present application situation and principle of RSA algorithm----producing big prime numbers and secret keys, the encryption arithmetic for information and the decryption for secret information, which establish the theory foundation for achieving concrete; secondly, it introduces some basic conception of RSA digital signature and theory of digital signature realizing process; thirdly, it introduces the basic principle of MD5 algorithm; fourthly, it states design and realization of RSA digital signature in detail. The main modules includes producing RSA secret keys, implementation of RSA encryption algorithm and decryption algorithm, producing message digest and realizing digital signature and verification by RSA; the fifth, it carries on testing entirely, analyzing and improving for this system;The sixth, it analyses the security of RSA digital signature and points out the development direction of RSA digital signature.

本文主要研究的内容包括：第一，对RSA算法进行了全面系统的介绍，包括RSA算法的应用现状和原理—大素数的产生、密钥对的产生、对明文的加密运算和密文的解密运算，为具体实现打下了理论基础；第二，介绍了RSA数字签名的一些基本概念和数字签名的理论实现过程；第三，对MD5算法基本原理的介绍；第四，详述了RSA数字签名的设计与实现，主要实现的模块包括RSA密钥的产生，RSA加密算法和解密算法的实现，消息摘要MD的生成以及利用RSA算法实现数字签名和签名的验证；第五，对该系统进行了整体的测试和分析改进；第六，分析了RSA数字签名的安全性，指出了RSA数字签名的发展方向。

When a truth-operation is applied to the results of truth-operations on elementary propositions, there is always a single operation on elementary propositions that has the same result.

对基本命题真值运算的结果再作一次真值运算，其结果总可等同于对基本命题施用某一单独的真值运算。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

On the basis of extending the concepts of the derived function, primitive function and integration of interval-valued function to complex interval-valued function and using the descomposition theorem of complex fuzzy set, the derived function, primitive function and integration of complex fuzzy set-valued function and some properties of them are proved.

2在国际上最先引入了复模糊集合与复模糊数的基本概念，证明了它们的基本代数运算的封闭性，并且其运算可通过α水平复集合的相应运算来进行

Sparse matrix of basic operations.

稀疏矩阵的基本运算。

We start by introducing some foundations of vector calculus to see how vectors apply on the field of Physics.

本课程从第一章的基础概念开始，先让同学认识向量的基本运算，并且以向量学在物理学上的简单应用，来吸引数学系的同学对於向量学领域的兴趣。

Firstly, based on the analysis of basic building blocks, the structure of IDEA is rearranged with eight pipelines.

首先，在分析IDEA算法的基本运算模块的基础上，重新安排了IDEA算法的各个子模块，采用8级流水线结构。

Questions in this content area are based on basic operations using whole numbers, decimals, fractions, and integers; place value; square roots and approximations; the concept of exponents; scientific notation; factors; ratio, proportion, and percent; linear equations in one variable; absolute value and ordering numbers by value; elementary counting techniques and simple probability; data collection, representation, and interpretation; and understanding simple descriptive statistics.

这方面的考试内容包括实数、小数、分数和整数的基本运算；位值；平方根和近似值；指数的概念；科学记数法；项；比率，比例以及百分比；只有一个未知数的线性方程；绝对值和数值的排列；初级的计数技巧和简单的概率；数据的收集、整理与说明；并理解简单的描述性统计数据。

The basic operations of mathematical morphology are computationally simple, so one of the main advantages of this technique is its high speed.

由于数学形态学的基本运算简单，因此这种方法的主要优点之一是它的快速有效。

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。