无理数

In 1869 Charles Meray, an apostle of the arithmetization of mathematics, gave a definition of the irrationals.

1869年查尔斯·梅雷作为数学算术化的革新者给出无理数的一个定义。

Physics majors learn the differential and integral calculus in the style of Cauchy and Weierstrass, with ε–δ definitions of continuity and differentiability.

这个定理还是非常有用的，下面就来演示一下。证明存在a，b两个无理数，使 a b 为有理数。是无理数，现在考察数X

In view of the coefficients of CDF9/7 wavelet filter are irrational number, we use the trigonometric function transform to factorize the perfect restruction and the biorthogonal conditions of biorthogonal wavelets filter banks, then optimize the coefficients of the original 9/7 wavelet filter banks, consequently a novel 9/7 wavelet filter banks with binary digit coefficients can be obtained.

2针对CDF9／7小波系数为无理数的缺点，对CDF9／7小波滤波器组的完全重构条件和双正交条件进行三角基函数变换和因式分解，并对求出的小波滤波器系数进行优化设计，得到一组滤波器系数都为二进制分数的9／7双正交小波滤波器组，大大降低了离散小波变换的算法复杂度。

However, taking into account the 16th and 17th centuries when European mathematicians still held the view that negative is "ridiculous number", Fibonacci's awareness of the negative undoubtedly is of great significance.4、Fibonacci's understanding of the irrational depends on the geometry, and the arithmetic of Fibonacci for square root was the tendency of algorithm.

虽他忽视二次方程之负数解，但考虑到16和17世纪，欧洲数学家仍认为负数是"荒谬的数"，斐波那契对负数的认识无疑具有重要的意义。4、斐波那契对无理数的认识有赖于几何图形，"开方法"趋于算法化。

The product of any irrational number and rational number is irrational.

命题：任何无理数和有理数的乘积都是无理数。

At last, a method on creation and calculation of a kind of irrational number is researched. The digit number of the extension of this irrational number is random on certain basis. Therefore, a stream cipher is designed, which uses the extension digit of the irrational number as the key stream.

最后本文在研究一种无理数的生成方法和计算方法的基础上，利用该类无理数在某基底的展开序列中各个位的数字具有良好的随机统计特性的特点，提出了一种以这类无理数的展开数字流作为密钥流的序列密码设计方法，并对生成的密钥流的统计特性进行了分析和测试。

Every Peak in the different groups is related to each other by means of an irrational number,the characteristic number of the two-component golden Fibonacci superlattice.

不同组中的峰值点彼此之间通过一个无理数关联，这个无理数是二组元金Fibonac

This paper analyzes irrational number series of square root of 2 and e in six aspects involving autocorrelation function,Power Spectral Density,phase space construction,correlation dimension,Principal Component Analysis and maximal Lyapunov exponent.

将已提出的π序列定义和分析方法推广到无理数领域，引出了无理数序列，并以常用的无理数根号2、e为例，对无理数序列的自相关、功率谱、相空间、关联维数、最大Lyapunov指数和主分量等6个方面进行深入分析。

For the case in a dc-bichromatic electric field (wB= 0), when one of the ratios is an irrational number, the other is a rational number, the dynamicallocalization always remains.

在直交流外场下，当其中一个比率是有理数，另一个是无理数时，总是保持动力学局域化；当两个比率都是有理数或无理数时，动力学局域化发生在准能带塌缩点。

This thesis analyze different cases where the sampling rate ratio is integer, r...

本文对于速率变换的整数倍、分数倍和无理数倍不同情况进行了详细的分析，其中无理数倍的速率变换是本文研究的重点。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。