查询词典 rational numbers

Taking operation of rational numbers as the carrier, this paper starts the research right from the study on multiplication of decimal, division of fraction and multiplication of rational numbers and studies the "understanding levels of operation of rational numbers and the teaching and learning strategies that matches them."

本论文以有理数运算作为载体，选取小数乘法、分数除法和有理数乘法作为研究的切入点，研究了&有理数运算的理解水平及其教与学的策略&，具体说来，研究了3个问题：(1)学生对有理数运算的理解达到怎样的水平；(2)学生达到某种理解水平的原因是什么；(3)基于学生的理解水平，有效的教与学的策略是什么。

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。

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。

There are natural numbers, negative numbers, rational numbers, irrational numbers, and many others

有自然数，负数，有理数，无理数和很多其他的数值。

Features - FSK and DTMF dual mode CLIP (Calling Line Identification Presentation)- Stores up to 50 calling numbers, up to 20 digits for each number*- Stores up to 3 last dialed numbers, up to 24 digits for each number*- Stores up to 50 PSTN Phone Book numbers, up to 12 characters for each name and 24 digits for each number (while the LCD displays the maximum of 12 digits)*- LCD displays calling and dialing number - Barring numbers setting (up to 5 numbers)*- Key lock setting - Hot call setting*- Call transfer of external calls*- Internal calls*- Three-way Conference Call*- Various ring melody (up to 9 for option)- Ring volume adjusting (up to 9 levels)- Handset earpiece volume setting (up to 9 levels)- Microphone mute - Delete single or all records in PSTN Phone Book*- Redialing and preparation dialing functions - Paging function to locate the handset easily from base station - Clicking key tone on or off - Supports GAP function - Speakerphon

特点－FSK和DTMF双模的CLIP－能存储多达50组来电，每组来电能够存储20个数字*－能够存储最近的3个已拨电话号码，每个号码能够存储24个数字*－能够存储50个PSTN电话簿号码，每个名字有12个字符，每个号码有24个数字（而LCD最多只能显示12个数字）*－LCD来电显示和去电号码－不包括号码设置（5个号码）*－键盘锁设置－热键设置*－外部来电转接*－内部呼叫*－三方电话会议*－多种铃声（一共有9种可供选择）－音量调节（一共有9个级别）－话机听筒音量设置（一共有9个级别）－静音－在PSTN电话簿内删除单个或者全部记录*－回拨和准备拨号功能－寻呼功能能够简单的从话机座定位话筒－开启或关闭滴答声－支持GAP功能－免提

If ris also irreducible in Z_nand f~n~κ≡fmodn,r(xfor all f∈Z_nthen we call n a Carmichael number of orderκmodulo r.Denote the set of all such numbers by C_κ,r(x.Define C_κ=∪_r(xC_κ,r(x,where rpasses through all monic irreducible polynomials over Z of degreeκ.We call elements of the set C_κCarmichael numbers of orderκ.ZHU and SUN[Journal of Sichuan University,42;1(2005), 47-51]first gave a necessary condition for Carmichael numbers of order 3.Then they gave a sufficient condition for Carmichael numbers of order 3,but did not find any such numbers less than 10~8 satisfying the sufficient condition.At last,they asked three questions;1.is the necessary condition also sufficient?

f∈Z_n，就称n是模r的κ阶Carmichael数，用C_κ，r(x表示所有这种数的集合，定义C_κ=∪_r(xC_κ，r(x，这里r跑遍Z中所有κ次首一不可约多项式，C_κ里面的元素就称为κ阶Carmichael数，C_κ称为κ阶Carmichael数集，朱文余和孙琦[四川大学学报，42；1(2005)，47-51]首先给出了3阶Carmichael数的一个必要条件；然后又给出了这种数的一个充分条件，并发现10~8内没有满足此充分条件的这种数；最后他们提出三个问题；一、问必要条件是否也是充分的？

Memorize numbers module — In this task, subjects must recall numbers that are given at baseline, then carry out an arithmetic "distractor" task, then reproduce the numbers given at the outset."If you have 2 numbers, it's easy, but if you have 10 numbers and then a distractor task, your working memory is working very hard to get this information," Dr. Penner notes.

记数模组—在这个任务中，受试者必须记住一开始给予的数字，之后进行算数诱答任务，接著再现一开始给予的数目；Penner博士指出，如果你有两个数字，那是简单的，但是如果有10个数字，然后进行诱答任务，你的操作记忆会难以得到此资讯。

By introducing the methods for transforming exact numbers and triangular fuzzy numbers trapezoidal fuzzy numbers, the ranking method is also practicable for ranking reciprocal judgment matrix with exact numbers and triangular fuzzy numbers.

同时给出精确值、三角模糊数的互补判断矩阵转化为梯形模糊数互补判断矩阵的方法，因此本文方法同样适合于处理精确值、三角模糊数的互补判断矩阵的排序问题。

Integers, rational numBers, and ir rational numBers are all real.

整数、有理数和无理数都是实数。

A historical region of southwest France between the Pyrenees and the Garonne River. The duchy of Aquitaine was joined with France after the marriage of Eleanor of Aquitaine to King Louis VII in1137, but its possession was disputed after her subsequent marriage to Henry II of England.

阿基坦法国西南部一个历史地区，位于比利牛斯山和加隆河之间，在1137年阿基坦的埃莉诺与国王路易斯七世结婚之后阿基坦公国加入法国，但当她再嫁英国亨利二世后，其归属权便受到争议

There are moments when I look at the smiling , happy faces of my expectant staff and wonder how they will cope when confronted by an outraged housemaster along with an unrepentant and recalcitrant bleached blond teenager in 18 years ' time .

有时候，我看着那些满怀期待的员工微笑，幸福的脸，想着当他们遇到一位愤怒的宿舍管理员和一位不知悔改，叛逆，而且将头发染成白色的18岁少年时，他们会如何处理。