查询词典 rational number

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

The chapter, rational number, is the first chapter that students will learn after they go to the junior high school.

有理数》一章是学生进入初中的第一章学习内容，本文主要谈谈有理数学习中几种数学思想的体现及实施过程中要注意的问题。

Especially, the neumerical result would be accurate over the rational number field.

特别地，在有理数域上用计算机求得的结果是精确的。

Due to the rapid development of tertiary industry in the process contains a number of less rational factors (such as some local real estate consulting services to develop a non-rational), which would have the healthy development of the national economy and the government macro-control bring some negative effects.

由于快速发展的第三产业的过程中包含了一些不太合理的因素（如一些地方房地产咨询服务，以建立一个非理性），这将对健康发展的国民经济和政府宏观调控控制带来一些负面影响。

Provides a class that fully-encapsulates rational number operations.

提供的这个类完全封装了理性数字运算。

We show that there is a polynomial over the rational number field Q corresponding to a given porpositional formula in a given many-valued logic.

本文证明了对于给定的多值逻辑系统中的命题公式，存在有理数域上的多项式与之对应。

Show that we have the following special cases of the sinusoidal spiral,=acosn, where n is a rational number

试证明：我们有正弦螺线？＃？cosnθ的下列特殊情况。

After this, the values of m-th Gauss sums have been determined for small m(= 3,4,···, 12) by using arithmetic properties of cyclotomic fields Q- Recently the formulas of Gauss sums are determined in "self-conjugate" and "index 2" cases in which the Gauss sums belongs to the rational number field and certain imaginary quadratic field respectively.

继高斯之后，人们用代数数论对于m较小情形计算出m次高斯和。近年来，人们对于&自共轭&情形和&指数2&情形算出高斯和。对于这两种情形，高斯和的值分别属于有理数域和虚二次域。

This text considers that permeation teaching is the main way of mathematics method of thinking"s teaching,and analyzes permeation teaching of the different moment, particularizes two individual cases example: anatomizes mathematics method of thinking of the chapter cleping "rational number , and the project of its permeation teaching; anatomizes the teaching measure of making students fromfeeling numeral-form combination method of thinking, to agile using it.

本文指出渗透是数学思想和方法教学的主要方式，分析了不同阶段的渗透教学，并列举了两个案例：剖析有理数一章的数学思想和方法，及其渗透方案；分析学生从感悟数形结合的思想方法，到灵活运用的过程中的教学措施。

This study investigates the understanding situation of Middle School Students"in theterms of the following 3 dimensions: the definition of negative number, therelationship of negative number and life and the operation of rational numbers withpurpose of understanding the students"cognition of negative number"s essentialfeatures and finding the root cause which results in negative number concept"scognition difficult as well as raising teaching improvement measures.

本研究从负数的概念、负数与实际生活情境之间的联系以及有理数的运算三个纬度调查了初中生对负数概念的理解情况，目的是为了深入了解初中生对负数概念本质特征的认识，寻找引起概念认知困难的根本原因，并提出有针对性的教学改进措施。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。