查询词典 Numbers

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

The conjugates of an element are the roots of the irreducible polynormial of which the given element is a root. The conjugates of 根号（根号3+1） over the field of rational numbers are

a。题目中的'over the rational numbers'是不是指四次多项式的系数是有理数，怎么能这么表达呢，为什么要强调有理数，系数应是整理罢。

In iWork '09 New Features, instructor Garrick Chow focuses on the improvements to the new versions of Pages, Numbers, and Keynote.

教程中，讲师 Garrick Chow 将阐述 Pages， Numbers 和 Keynote 这三个组件在新版 iWork '09 中的全新功能。

Garrick demonstrates the improved thumbnail navigation in Pages, mixed charts types in Numbers, and the enhanced motion guides and new text transitions in Keynote.

Garrick Chow 展示了 Pages 增强的缩图导航，Numbers 的混合图表类型，Keynote 增强的轨迹运动和文字过渡。

The gyrfalcon,an Arctic bird of prey, has survived a close brush with extinction;its numbers are now five times greater than when the use of DDT was sharply restricted in the early 1970's.

我只知道numbers是表示总量概念，但是具体是怎么用的也不是很清楚。。贴上LDOCE里面的解释，绿底字部分

To the moduli with special forms (such as Mersenne numbers, pseudo-Mersenne numbers, generalized Mersenne numbers), we analysis and study modular arithmetic laws, and obtain the conclusions as follows: for Mersenne numbers and pseudo-Mersenne numbers, we get modular arithmetic formulas, and determine exact expressions of the number of modular addition to generalized Mersenne numbers generated by irreducible monic trinomials and pentanomials.

针对具有特殊形式的模数(如Mersenne数，伪Mersenne数，广义Mersenne数等)，深入分析了其取模运算规律，得到如下结果：对Mersenne数和伪Mersenne数，给出了取模运算转换为模加或模减运算的公式；对模数为任意首一三项式和五项式产生的广义Mersenne数，推导了相应取模运算的复杂度计算解析表达式。

If we rechange these two numbers: one number to two times as many as its original value, and the other to four times as many as its original value, the average of the five numbers will become 13. Which two numbers have been changed?I only know that the total sum of the original numbers is 45(5×9), the total sum of the 5 numbers after the first change is 40(5×8), and the total sum of the 5 numbers after the second change is 65(13×5). What can I do next? Please help me with the problem.Thank you!

这就要求琬婷一方面要用英语准确地把她想要问的问题清晰地表达出来，只有这样网上"数学博士"才能明白你要问的问题；另一方面琬婷还必须能够正确理解网上"数学博士"对她所提问题的英语答复，这两者是相互依赖的，否则就不能正确地帮助你理解和解决问题，这就要求琬婷必须用英语进行正确地表述和理解。

The second stage is a transformer which yield a frequency-domain spectral representation: Numbers of Selectively Synchronized Filters(NSSF:Numbers of Selectively Synchronized Filters).

第二部分是一个转换器，它产生一种频域表示：选择性同步滤波器数(Numbers of Se-lectively Synchronized Filters，NSSF)。

Find factorizations of cyclotomic numbers at Factorizations of Cyclotomic Numbers.

在Factorizations of Cyclotomic Numbers项目中寻找分圆数因子。

Find factorizations of cyclotomic numbers at Factorizations of Cyclotomic Numbers.

通过Factorizations of Cyclotomic Numbers项目寻找cyclotomic 数字的因士分解。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。