命令

最常用

man 帮助（按q退出man）
ls
pwd 输出工作目录
cd
mkdir
find 和 locate
cp
mv 改名、移动
more
kill 使用ps进程ID，kill进程
sudo
passwd 更改密码

sudo su

查看日志：tail -n 100 catalina.out

复制文件：
sudo cp kaopurServer.war /opt/apache-tomcat-8.0.24/webapps/

查看目录
ll

cat /etc/passwd

cat -n song.txt

给sh脚本增加执行权限：chmod +x yourshfile.sh

mkdir kaopurServer

cd kaopurServer

tar -zxvf ../kaopurServer.tar.gz

sudo \cp -rf kaopurServer/* /opt/apache-tomcat-8.0.24/webapps/kaopurServer

rm -f index.jsp

rm -rf WEB-INF/

如此才会覆盖：
sudo \cp -rf kaopurServer/* /opt/apache-tomcat-8.0.24/webapps/kaopurServer

sudo tar -zxf /home/hl/apache-activemq-5.9.1-bin.tar.gz

cat activemq.xml

linux下载文件：
curl -O http://mirrors.hust.edu.cn/apache/tomcat/tomcat-8/v8.0.28/bin/apache-tomcat-8.0.28.tar.gz

curl -O -L http://dev.mysql.com/get/Downloads/MySQL-5.6/mysql-5.6.27.tar.gz

xshell中文乱码：修改Terminal的字符集

$ ps -ef|grep tfs

curl -o emqttd-centos64-0.13.0-beta-20151108.zip -L http://emqtt.io/downloads/centos

cat /etc/redhat-release

linux常用命令
在 Linux 中用的是正斜杠 (/)，而不是您所熟悉的反斜杠 ()。反斜杠也用到了，但只是用来说明命令需要换行继续，这样可以提高比较长的命令的可读性。

ls -l 以长格式列出文件，包括文件大小、日期和时间、属性
ls -t 对文件以时间排序
ls -S 对文件以大小排序
ls -r 与一个排序开关组合起来使用，逆序排列。 ls -t 将最新的文件显示在列表的顶部。 ls -t 将最新的文件显示在底部。
ls -h 易读格式。使用 k、M、G 等来标识文件的大小，而不是以字节为单位。
ls -a 显示目录中所有的文件，包括隐藏文件

cp -R 递归地复制文件；当需要复制整个目录时会用到
cp -f 强制复制并覆盖已有的文件，不询问用户
cp -l 链接文件，而不是复制

使用 mv 命令来移动和重命名文件。这个命令的工作方式基本上与 DOS 中的 move 命令一样，不过它可以移动整个目录结构及所有文件。

cat
使用 cat 命令来查看文件的内容。它相当于 DOS 中的 type 命令。它将把文件的内容转储到另一个文件、屏幕或者其他命令。 cat 是concatenate 的简写，还可以将一系列的文件合并为一个大文件。

more
使用命令 more 可以以分页的方式查看文件。它基本上与 DOS 中的 more 命令相同。

less
less 命令也是用来查看文件，但是它支持上下滚屏以及在文档中进行文本搜索。

man
使用 man 命令来查看命令的文档。man 是 manual 的缩写。几乎每一个命令都有相应的文档。要深入了解 man ，请输入以下命令：

man man

info
info 命令与 man 命令类似，不过它提供了超链接文本，可以更方便地浏览文档。

curl -O -L http://dev.mysql.com/get/Downloads/MySQL-5.6/mysql-5.6.27.tar.gz

md5sum mysql-5.6.27.tar.gz

md5sum apache-tomcat-8.0.28.tar.gz

sudo tar -zxvf ~/apache-tomcat-8.0.28.tar.gz

sudo rm -r apache-tomcat-8.0.28/

/usr/apache-tomcat-8.0.28/webapps>sudo rm -r examples/

/usr>sudo rm -fr emqttd/

/home/hzg>sudo unzip emqttd-centos64-0.13.0-beta-20151108.zip -d /usr/

/usr/emqttd/bin>sudo ./emqttd console

/usr/emqttd/bin>./emqttd_ctl status

/opt/apache-tomcat-8.0.28/bin>ps -ef | grep tomcat

停止tomcat：
kill -9 2250

查看tomcat日志
/opt/apache-tomcat-8.0.28/logs>tail -n 50 catalina.out

curl -O -L http://download.redis.io/releases/redis-3.0.5.tar.gz

/home/hzg>sudo tar zxf redis-3.0.5.tar.gz -C /opt/

redis的java client
Jedis
lettuce
Redisson

/home/hzg>netstat -tnl | grep 3306

[root@instance-dqg4v0wr-3 ~]# du -sh
36K .

more /etc/passwd

lscpu

free -m

使用 su 或者 sudo -s 命令变为另一个用户
可以使用 whoami 命令来检查您当前有效的 id
可以使用 groups 命令找出您在什么组中

Linux 中的所有用户都存放于 /etc/passwd 文件中。您可以使用 more 命令来分页查看这个文件：
more /etc/passwd

who
功能：列出当前系统注册的用户
$who am i 列出当前系统使用者身份

ps
功能：显示后台进程的有关信息。单独使用ps将显示由
当前终端启动的后台进程的PID、终端号、进程已执行时间以及启动该进程的命令
语法：ps -options
参数说明：
-e：显示系统内当前运行的所有后台进程
-f：除ps所提供的信息外，还显示用户名、PPID（父进程ID）及启动时间
-l：除ps所提供的信息外，还显示 User ID, PPID 和进程优先级

kill
功能：杀死后台进程
语法：kill -num PID

find
功能：在一个或多个目录中查找符合指定条件的文件，
显示文件名或对这些文件进行特定的操作
语法：find path expression

find . –name ‘unix’ –print
find . –name ‘m*’ –exec ls –l {} ;
find . -perm 644 -mtime +4 –print

grep
功能：在文件或标准输入中搜索与指定格式相匹配的行
语法：grep [options] pattern [file1 file 2..]
grep –v mail .profile
grep “^a[0-9]z$” filename
grep a websm.log

vi

：w ：保存当前文件
：x：保存当前文件并退出
：q：退出vi
:q! 放弃所做修改直接退出到shell
:q 不退出
ZZ / :x 如果需要保存则保存，之后退出到shell
:w newfile / :w!
:wq 先保存文件，再退出到shell
回车后进行命令模式
在命令模式按a（光标之后）/ A（光标所在行的最后） / i（光标处）/I（光标所在行的开头） / o / O ，进入文本输入模式
在文本输入模式下，按Esc，回到命令模式
末行模式，Ex转义模式： 在命令模式下按:进行末行模式，末行命令执行后自动回到命令模式

插入文本类命令

i ：在光标前
I ：在当前行首
a：光标后
r：替换当前字符

删除命令

x或X：删除一个字符，x删除光标后的，而X删除光标前的
ndd：删除当前行及其后n-1行
dd 删除当前行

搜索及替换命令

/pattern：从光标开始处向文件尾搜索pattern
?pattern：从光标开始处向文件首搜索pattern
:g/p1/s//p2/g：将文件中所有p1均用p2替换

If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit (by car), how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily (given the methods I know) find a solution.

Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students, and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP-problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair taken from your coworker’s list also appears on the list from the Dean’s office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known universe! Thus no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.

1

Problem Statement. Does Ｐ = ＮＰ? 

Ｐ = {L | L = L(M) for some Turing machine M that runs in polynomial time}.

The notation ＮＰ stands for “Nondeterministic Polynomial time”, since originally ＮＰ was defined in terms of nondeterministic machines (that is, machines that have more than one possible move from a given configuration).

To put it more briefly, Ｐ is the set of easy decision problems. ＮＰ is the class of decision problems for which it is easy to check the correctness of a claimed answer, with the aid of a little extra information. So we aren’t asking for a way to find a solution, but only to verify that an alleged solution really is correct.

In Ｐ are the problems where it’s easy to find a solution, and in ＮＰ are the problems where it’s easy to check a solution that may have been very tedious to find.

\(\huge \mathbf{P} \subset \mathbf{NP} \tt{?}\)

The crucial question related to Ｐ and ＮＰ is whether the subset relation is proper?

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P ⊂ NP? 

很显然的是Ｐ类都属于ＮＰ类（P ⊆ NP），这样问题就变成：是否某些NP类问题（比如旅行推销员问题）不存在多项式时间过程算法? 问题难在如何证明这一点？如何从逻辑上排除旅行推销员问题存在多项式时间过程算法的可能性？这跟黎曼假设的严格数学证明要排除临界线外有复零点的可能性一样困难。

复杂性范畴之间的包含关系：

\(\mathrm{LOGSPACE} \subseteq \mathbf{P} \subseteq \mathbf{NP} \subseteq \mathrm{PSPACE} \)
\(\mathrm{LOGSPACE} \subset \mathrm{PSPACE} \)

LOGSPACE ⊆ P ⊆ NP ⊆ PSPACE，用简单的对角化论证法能够证明 LOGSPACE 是 PSPACE 的真子集，其余的包含关系是否为真包含关系？无人能够证明。

很多研究复杂性理论的专家都认为 Ｐ≠ＮＰ，Scott Aaronson 从哲学角度发表了他的看法：“如果P = NP，那么我们就会处于一个截然不同的世界中，创造性飞跃将失去其难能可贵的价值，解决一个问题和认识到问题有解没什么分别。任何一个能欣赏交响乐的人都能成为莫扎特，任何一个懂得数学证明的人都能成为高斯…”。（If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss…）。按 Stephen Cook 在白皮书中的说法，如果P = NP，那么机器就能给出克雷数学研究所七大难题的形式化证明，尽管证明会很繁琐很冗长。( If P = NP, …. For example, it would transform mathematics by allowing a computer to find a formal proof of any theorem that has a proof of reasonable length, since formal proofs can easily be recognized in polynomial time. Such theorems may well include all of the CMI prize problems. Although the formal proofs may not be initially intelligible to humans, the problem of finding intelligible proofs would be reduced to that of finding a recognition algorithm for intelligible proofs. Similar remarks apply to diverse creative human endeavors, such as designing airplane wings, creating physical theories, or even composing music. The question in each case is to what extent an efficient algorithm for recognizing a good result can be found. This is a fundamental problem in artificial intelligence, and one whose solution itself would be aided by the NP-solver by allowing easy testing of recognition theories. )

在克雷数学研究所的官方资料中，此问题由 Stephen Cook （创造性地提出 ＮＰ-complete 概念并证明The satisfiability problem是NP-完全问题）作出权威解读。

相关的经典论文

• Finite Automata and Their Decision Problems, Michael O. Rabin & Dana Scott, 1959
• The Complexity of Theorem-Proving Procedures, Stephen A. Cook, 1971
• Reducibility among combinatorial problems, Richard Karp, 1972

数学元素

• 图灵机（Turing Machine）
• 可计算性
• NP-完全：如果图论中的哈密顿回路有类似欧拉回路那样的多项式判定算法，则所有其它NP类问题也都能用多项式时间过程解决

ＮＰ-hard 问题

• 哈密顿回路判定 (Hamiltonian Circuit )
• 旅行推销员问题 (The Traveling Salesman problem)
• 背包问题 (The Bin Packing problem)
• 数独(Sudoku)

专家评论

• Richard Karp: (Berkeley, unsure, P!=NP) My intuitive belief is that P is unequal to NP,but the only supporting arguments I can offer are the failure of all efforts to place specific NP-complete problems in P by constructing polynomial-time algorithms.I believe that the traditional proof techniques will not suffice. Something entirely novel will be required. My hunch is that the problem will be solved by a young researcher who is not encumbered by too much conventional wisdom about how to attack the problem.
• Donald Knuth: (Retired from Stanford) It will be solved by either 2048 or 4096. I am currently somewhat pessimistic. The outcome will be the truly worst case scenario: namely that someone will prove “P=NP because there are only finitely many obstructions to the opposite hypothesis”; hence there will exists a polynomial time solution to SAT but we will never know its complexity!
• Alexander Razborov: (Institute for Advanced Study) Well, this problem is (at the moment) very unique since we seem to be missing even the most basic understanding of the nature of its difficulty. Neither we currently have any ideas of what approach might turn out to be viable and lead us to the solution (or at least to a better understanding of the problem). All approaches tried so far probably (in some cases, provably) have failed. In this sense P=NP is different from many other major mathematical problems on which a gradual progress was being constantly done (sometimes for centuries) whereupon they yielded, either completely or partially. Perhaps, although, the key word in this difference is “century”, and the P=NP problem has simply not aged enough yet (by mathematical standards).
• Bob Tarjan: (Princeton) In my view, there is no way to even make intelligent guesses about the answer to any of these questions. If I had to bet now, I would bet that P is not equal to NP. I estimate the half-life of this problem at 25 - 50 more years, but I wouldn’t bet on it being solved before 2100. Its solution will require unforeseen new techniques.
• Avi Wigderson: (Institute of Advanced Study) I think this project is a bit premature. I think we know too little of what is relevant to even guess answers to your questions, certainly if “we” is replaced by “I.”The only thing I can definitely say, is that it is one of the most important and interesting questions ever asked by humans, and more people and resources should participate in filling up the holes that would allow better guesses of answers to your questions.
• Andrew Yao（姚期智）: It’s hard to say when the question will be resolved. I don’t have even an educated guess. Probably the resolution is that P is not equal to NP. I think the mathematical techniques used will be beautiful.
• Scott Aaronson: Look, this question of whether P=NP, what can I say? People like to describe it as “probably the central unsolved problem of theoretical computer science.” That’s a comical understatement. P vs. NP is one of the deepest questions that human beings have ever asked. And not only that: it’s one of the seven million-dollar prize problems of the Clay Math Institute! What an honor! Imagine: our mathematician friends have decided that P vs. NP is as important as the Hodge Conjecture, or even Navier-Stokes existence and smoothness! (Apparently they weren’t going to include it, until they asked around to make sure it was important enough.) Dude. One way to measure P vs. NP’s importance is this. If NP problems were feasible, then mathematical creativity could be automated. The ability to check a proof would entail the ability to find one. Every Apple II, every Commodore, would have the reasoning power of Archimedes or Gauss. So by just programming your computer and letting it run, presumably you could immediately solve not only P vs. NP, but also the other six Clay problems. (Or five, now that Poincaré is down.) Well, we certainly believe P≠NP. Indeed, we don’t even believe there’s a general way to solve NP problems that’s dramatically better than brute-force search through every possibility. The central challenge any P≠NP proof will have to overcome is to separate the NP problems that really are hard from the ones that merely look hard.

观点

• P vs. NP 问题的解决可能有赖于大幅度创新的证明技术
  • Cantor’s diagonal argument: a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. Turing’s proof for the insolubility of the halting problem uses diagonal arguments as well.
  • Gödel numbering: Gödel’s incompleteness theorems
  • Forcing (mathematics): first used by Paul Cohen in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory.
• 堵丁柱 & 葛可一的《计算复杂性导论》前言：
  • 人们在七十年代开始对NP-完全问题的研究主要是横向发展，也就是以许多不同的计算模型来分析难解问题的本质。这些新的计算模型包括了平行计算模型、概率计算模型、布尔线路、判断树、平均复杂性、交互证明系统以及程式长度复杂性等等。对这些新的计算模型的研究一方面使我们对难解问题有了更深一层的认识，一方面也产生了一些预想不到的应用。最显著的一个例子就是计算密码学的革命性突破：基于 NP 问题的公钥密码体系。另一个有名的例子是线性规划的多项式时间解的发现。
  • 到了八十年代中，对NP-完全问题的研究有了纵向的突破，在许多表面看来并不相关的计算模型之间发现了深刻的刻划关系。这些刻划关系不但解决了几个令人困扰多年的未解问题，同时也刺激了其它相关领域的发展。其中之一是对线路复杂性的研究发现了一些问题在某种有限制的线路模型中必有指数下界。这些结果使用了组合数学与概率方法等新的数学工具，并且解决了一个有名的有关多项式分层的未解问题。另一个更重大的结果是以概率可验证明对 NP 类的刻划。由此得出了许多组合优化问题近似解的NP-完全性，从而刺激了算法界对近似算法研究的新热潮。这个结果来自于对交互证明系统这个概念的扩展，并且使用了线性代数与编码理论等数学证明技巧。
• 1993年 Razborov 和 Rudich 证明的一个结果表明，给定一个特定的可信的假设，在某种意义下「自然」的证明不能解决 P vs NP 问题。这表明一些现在似乎最有希望的方法不太可能成功。随着更多这类的定理得到证明，该定理的可能证明有越来越多的陷阱要规避。
• In 1994, Alexander Razborov and Steven Rudich discovered the natural proofs barrier, which explained why previous attempts to prove P ≠ NP had failed.
• Razborov and Rudich then proved their main result: A natural proof of P ≠ NP would require a very comprehensive understanding of how easy-to-compute and hard-to-compute functions differ, and that knowledge could also fuel a fast algorithm for spotting easy-to-compute functions even if they’re superficially complicated. If complexity theorists had succeeded in a natural proof of P ≠ NP, they would have discovered a nearly infallible way to glance at an arbitrary truth table and determine whether the corresponding function had high or low circuit complexity — a much stronger and more general result than they had set out to prove.

• Complexity Zoo
• Gödel's Lost Letter and P=NP | a personal view of the theory of computation
• Complexity Theory’s 50-Year Journey to the Limits of Knowledge
• A Short Guide to Hard Problems
• 阅微堂 - 理论计算机初步：P vs NP - 历史，现状和未来
• The Princeton Companion to Mathematics
• P vs NP — The Biggest Unsolved Problem in Computer Science
• Reasons to believe

• Substring : A pattern P is called a substring of Text T if the pattern appears in the Text in a continuous fashion.
• Subsequence : A pattern P is called a subsequence of Text T if the pattern preserves the relative ordering of characters within the text T and it might not appear in a continuous fashion. e.g., the prime numbers are a subsequence of the positive integers.

• Subsequence is a generalisation of substring, suffix, and prefix. Finding the longest string which is a subsequence of two or more strings is known as the longest common subsequence problem.

Example: The string “anna” is a subsequence of the string “banana”:

1
2
3

banana
 || ||
 an na

• Substring

A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix. If one string is a substring of another, it is also a subsequence, which is a more general concept.

Example: The string “ana” is a substring (and subsequence) of banana at two different offsets:

1
2
3
4
5

banana
 |||||
 ana||
   |||
   ana

• https://www.quora.com/What-is-difference-between-problems-related-to-substring-and-problems-related-to-sub-sequence-in-Strings-How-to-approach-both-kind-of-problems-e-g-Difference-between-Longest-Common-Sub-string-and-Longest-Common-Sub-sequence
• https://stackoverflow.com/questions/15505508/what-is-the-difference-between-string-substring-and-string-subsequence

書法家王羲之所作

永和九年，岁在癸(guǐ)丑。暮春之初，会于会(kuài)稽山阴之兰亭，修禊(xì)事也。群贤毕至，少长(zhǎng)咸集。此地有崇山峻岭，茂林修竹，又有清流激湍，映带左右，引以为流觞(shāng)曲水，列坐其次。虽无丝竹管弦之盛，一觞一咏，亦足以畅叙幽情。

是日也，天朗气清，惠风和畅。仰观宇宙之大，俯察品类之盛。所以游目骋(chěng)怀，足以极视听之娱，信可乐也。

夫(fú)人之相与，俯仰一世。或取诸怀抱，悟言一室之内; 或因寄所托，放浪形骸之外。虽趣(qǔ)舍万殊，静躁不同，当其欣于所遇，暂得于己，快然自足，不知老之将至; 及其所之既倦，情随事迁，感慨系之矣。向之所欣，俯仰之间，已为陈迹，犹不能不以之兴怀，况修短随化，终期于尽!古人云：“死生亦大矣”，岂不痛哉!

每览昔人兴感之由，若合一契，未尝不临文嗟悼，不能喻之于怀。固知一死生为虚诞，齐彭殇(shāng)为妄作。后之视今，亦犹今之视昔，悲夫!故列叙时人，录其所述，虽世殊事异，所以兴怀，其致一也。后之览者，亦将有感于斯文。

由林语堂翻译的英文版

Preface to the Poems Collected from the Orchid Pavilion

by Lin Yutang

It is the ninth year of Yonghe (A.C.353), also known as the year of Guichou in terms of the Chinese lunar calendar.

On one of those late spring days, we gather at the Orchid Pavilion, which is located in Shanyin County, Kuaiji Prefecture, for dispelling bad luck and praying for good fortune.

The attendees of the gathering are all virtuous intellectuals, varying from young to old.

Endowed with great mountains and lofty peaks, Orchid Pavilion has flourishing branches and high bamboo bushes all around, together with a clear winding brook engirdled, which can thereby serve the guests by floating the wine glasses on top for their drinking.

Seated by the bank of brook, people will still regale themselves right by poetizing their mixed feelings and emotions with wine and songs, never mind the absence of melody from string and wind instruments.

It is such a wonderful day, with fresh air and mild breeze. Facing upwards to the blue sky, we behold the vast immensity of the universe; when bowing our heads towards the ground, we again satisfy ourselves with the diversity of species.

Thereby we can refresh our views and let free our souls, with luxuriant satisfaction done to both ears and eyes. How infinite the cheer is!

People keep coming and going, and life soon rushes to its end. Some people prefer to share their proud aspiration and lofty goals with close friends indoors, while some others choose to follow their interest and free their minds wherever and whenever they like.

May characters vary from person to person, or some would rather stay peaceful while others like to live restlessly, they will all become delighted and satisfied once they meet something pleasant, so cheerful that they get unaware of their imminent old age.

However, when they get tired of their old fancies that they’ve already experienced, and sentiment correspondingly accompanies the change of situation, all sorts of complicated feelings will well up in the heart, too.

Isn’t it thought-provoking that the happiness we used to enjoy passes by without leaving a single trace, let alone that the length of life is subject to the fate, and death is inevitable for anybody in the end?

Just as some ancient man once put it, “Death also deserves our attention, like what life does.”, so how can we restrain ourselves from grieving?

Every time I ponder about the reasons why our predecessors would produce works with such inenarrable emotions, I find there seem some similarities between our minds.

Yet I cannot help lamenting their literary masterpieces while I am struggling for the very cause in my innermost world. Now I come to realize that it has been ridiculous for me to equate death with life, long life with short life.

The descendents view us just the way we look at our predecessors, and how woeful it is! Hence I write down all the names of the attendees and put their poetry into record.

Conditions may go with the changes of time, but people’s emotions shall stay the same. I believe the following readers will still have much to mediate about life and death when appreciating this poetry anthology.

• 蘭亭集序
• https://en.wikipedia.org/wiki/Lantingji_Xu

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1169. 72 threaten
1170. 72 depth
1171. 71 oppose
1172. 71 deliver
1173. 71 ancient
1174. 71 pray
1175. 71 adopt
1176. 71 birth
1177. 71 appearance
1178. 71 universe
1179. 71 busy
1180. 71 hurry
1181. 71 coast
1182. 71 forth
1183. 70 smell
1184. 70 furnish
1185. 70 female
1186. 70 hide
1187. 70 wire
1188. 70 proposal
1189. 70 ought
1190. 70 victory
1191. 69 quarter
1192. 69 engine
1193. 69 customer
1194. 69 waste
1195. 69 fool
1196. 69 intend
1197. 69 intention
1198. 69 desk
1199. 69 politics
1200. 69 passage
1201. 69 lawyer
1202. 68 root
1203. 68 climb
1204. 68 metal
1205. 68 gradual
1206. 68 hunt
1207. 68 protection
1208. 68 satisfy
1209. 68 roof
1210. 68 branch
1211. 68 pleasure
1212. 68 witness
1213. 68 loose
1214. 67 nose
1215. 67 mine
1216. 67 band
1217. 67 aside
1218. 67 risk
1219. 67 tomorrow
1220. 67 remind
1221. 67 ear
1222. 67 fish
1223. 67 shore
1224. 66 operator
1225. 66 civilize
1226. 66 being
1227. 66 silent
1228. 66 screen
1229. 66 bind
1230. 66 earn
1231. 66 pack
1232. 66 colony
1233. 66 besides
1234. 66 slip
1235. 66 cousin
1236. 66 scale
1237. 66 relief
1238. 66 explore
1239. 66 stem
1240. 65 brain
1241. 65 musician
1242. 65 defend
1243. 65 bend
1244. 65 somebody
1245. 65 shadow
1246. 64 mix
1247. 64 smoke
1248. 64 description
1249. 64 fruit
1250. 64 guilt
1251. 64 yield
1252. 64 sensitive
1253. 64 salt
1254. 64 pale
1255. 64 sweep
1256. 64 completion
1257. 64 throat
1258. 64 agriculture
1259. 64 admire
1260. 63 gentle
1261. 63 dozen
1262. 63 particle
1263. 63 pleasant
1264. 63 bay
1265. 63 cup
1266. 63 competition
1267. 63 moon
1268. 63 terrible
1269. 63 strip
1270. 63 mechanic
1271. 63 shock
1272. 63 conversation
1273. 63 angle
1274. 62 tall
1275. 62 plenty
1276. 62 star
1277. 62 yellow
1278. 62 sick
1279. 62 thorough
1280. 62 absolute
1281. 62 succeed
1282. 61 surround
1283. 61 proud
1284. 61 dear
1285. 61 card
1286. 61 lake
1287. 61 breath
1288. 61 afraid
1289. 61 silence
1290. 61 onto
1291. 60 shoe
1292. 60 somewhere
1293. 60 chain
1294. 60 slide
1295. 60 copy
1296. 60 machinery
1297. 60 wake
1298. 60 severe
1299. 60 pocket
1300. 60 bone
1301. 59 honest
1302. 59 freeze
1303. 59 dictionary
1304. 59 calm
1305. 59 swim
1306. 59 ice
1307. 59 male
1308. 59 skin
1309. 59 crack
1310. 59 rush
1311. 59 wet
1312. 58 meat
1313. 58 commerce
1314. 58 joint
1315. 58 gift
1316. 58 host
1317. 58 suspect
1318. 58 path
1319. 58 uncle
1320. 58 afford
1321. 58 instant
1322. 58 satisfactory
1323. 58 height
1324. 58 track
1325. 58 confidence
1326. 58 grass
1327. 57 suggestion
1328. 57 favorite
1329. 57 breakfast
1330. 57 apart
1331. 57 chest
1332. 57 entrance
1333. 57 march
1334. 57 sink
1335. 57 northern
1336. 57 iron
1337. 57 alive
1338. 57 ill
1339. 57 bag
1340. 57 disturb
1341. 57 native
1342. 57 bedroom
1343. 57 violent
1344. 57 beneath
1345. 57 pause
1346. 57 tough
1347. 56 substance
1348. 56 threat
1349. 56 charm
1350. 56 absence
1351. 56 factory
1352. 56 spite
1353. 56 meal
1354. 56 universal
1355. 56 accident
1356. 56 highway
1357. 56 sentence
1358. 56 liberty
1359. 55 wise
1360. 55 noise
1361. 55 discovery
1362. 55 tube
1363. 55 flash
1364. 55 twist
1365. 55 fence
1366. 55 childhood
1367. 55 joy
1368. 55 sister
1369. 54 sad
1370. 54 efficiency
1371. 54 disappear
1372. 54 defeat
1373. 54 extensive
1374. 54 rent
1375. 54 comparison
1376. 54 possess
1377. 54 grace
1378. 54 flesh
1379. 54 liquid
1380. 54 scientist
1381. 54 ease
1382. 53 heaven
1383. 53 milk
1384. 53 sympathy
1385. 53 rank
1386. 53 restaurant
1387. 53 frequency
1388. 53 angry
1389. 53 shade
1390. 53 accuse
1391. 53 necessity
1392. 53 knock
1393. 53 loud
1394. 53 permanent
1395. 53 row
1396. 53 lovely
1397. 53 confuse
1398. 52 gold
1399. 52 frighten
1400. 52 solve
1401. 52 grave
1402. 52 salary
1403. 52 photograph
1404. 52 advice
1405. 52 abroad
1406. 51 wound
1407. 51 virtue
1408. 51 dare
1409. 51 queen
1410. 51 extra
1411. 51 attract
1412. 50 numerous
1413. 50 pink
1414. 50 gate
1415. 50 expensive
1416. 50 shut
1417. 50 chicken
1418. 50 forgive
1419. 50 holy
1420. 50 wooden
1421. 49 prompt
1422. 49 crime
1423. 49 sorry
1424. 49 republic
1425. 49 anger
1426. 49 visitor
1427. 49 pile
1428. 49 violence
1429. 49 steel
1430. 49 wing
1431. 49 stair
1432. 49 partner
1433. 49 delay
1434. 49 gentleman
1435. 48 pour
1436. 48 confusion
1437. 48 damage
1438. 48 kick
1439. 48 safety
1440. 48 burst
1441. 48 network
1442. 48 resistance
1443. 48 screw
1444. 48 pride
1445. 48 till
1446. 47 hire
1447. 47 verb
1448. 47 preach
1449. 47 clerk
1450. 47 everywhere
1451. 47 anyway
1452. 47 fan
1453. 47 connect
1454. 47 egg
1455. 47 efficient
1456. 47 grain
1457. 46 calculate
1458. 46 drag
1459. 46 opposition
1460. 46 worship
1461. 46 arrest
1462. 46 discipline
1463. 46 string
1464. 46 harbor
1465. 46 camera
1466. 46 mechanism
1467. 46 cow
1468. 46 grand
1469. 46 funny
1470. 46 insurance
1471. 46 reduction
1472. 46 strict
1473. 46 lesson
1474. 46 tight
1475. 45 sand
1476. 45 plate
1477. 45 qualify
1478. 45 elsewhere
1479. 45 mad
1480. 45 interference
1481. 45 pupil
1482. 45 fold
1483. 45 royal
1484. 45 valuable
1485. 45 whisper
1486. 45 anybody
1487. 45 hurt
1488. 45 excess
1489. 44 quantity
1490. 44 fun
1491. 44 mud
1492. 44 extension
1493. 44 recognition
1494. 44 kiss
1495. 44 crop
1496. 44 sail
1497. 44 attractive
1498. 44 habit
1499. 44 relieve
1500. 44 wisdom
1501. 44 persuade
1502. 43 certainty
1503. 43 cloth
1504. 43 eager
1505. 43 deserve
1506. 43 sympathetic
1507. 43 cure
1508. 43 trap
1509. 43 puzzle
1510. 43 powder
1511. 43 raw
1512. 43 mankind
1513. 43 glad
1514. 43 blame
1515. 43 whenever
1516. 43 anxiety
1517. 42 bus
1518. 42 tremble
1519. 42 sacred
1520. 42 fortunate
1521. 42 glory
1522. 42 golden
1523. 42 neat
1524. 42 weekend
1525. 42 treasury
1526. 42 overcome
1527. 42 cat
1528. 42 sacrifice
1529. 42 complain
1530. 42 elect
1531. 41 roar
1532. 41 sake
1533. 41 temple
1534. 41 self
1535. 41 compete
1536. 41 nurse
1537. 41 stuff
1538. 41 stomach
1539. 41 peculiar
1540. 41 repair
1541. 41 storm
1542. 41 ton
1543. 41 desert
1544. 41 allowance
1545. 41 servant
1546. 41 hunger
1547. 41 conscience
1548. 41 bread
1549. 41 crash
1550. 40 tip
1551. 40 strengthen
1552. 40 proof
1553. 40 generous
1554. 40 sir
1555. 40 tonight
1556. 40 whip
1557. 40 tongue
1558. 40 mill
1559. 40 merchant
1560. 40 coal
1561. 40 ruin
1562. 40 introduction
1563. 40 courage
1564. 40 actor
1565. 40 belt
1566. 39 stir
1567. 39 package
1568. 39 punish
1569. 39 reflection
1570. 39 breathe
1571. 39 anywhere
1572. 39 amuse
1573. 39 dull
1574. 39 fate
1575. 39 net
1576. 39 fellowship
1577. 39 fault
1578. 39 furniture
1579. 39 beam
1580. 39 pencil
1581. 39 border
1582. 39 disappoint
1583. 38 flame
1584. 38 joke
1585. 38 bless
1586. 38 corn
1587. 38 shell
1588. 38 tempt
1589. 38 supper
1590. 38 destruction
1591. 38 dive
1592. 38 anxious
1593. 38 shine
1594. 38 cheap
1595. 38 dish
1596. 38 distant
1597. 38 greet
1598. 37 flood
1599. 37 excuse
1600. 37 insect
1601. 37 ocean
1602. 37 ceremony
1603. 37 decrease
1604. 37 prize
1605. 37 harm
1606. 37 insure
1607. 37 verse
1608. 37 pot
1609. 37 sincere
1610. 36 cotton
1611. 36 leaf
1612. 36 rub
1613. 36 medicine
1614. 36 stroke
1615. 36 bite
1616. 36 lung
1617. 36 lonely
1618. 36 admission
1619. 36 stupid
1620. 36 scratch
1621. 36 composition
1622. 36 broadcast
1623. 36 drum
1624. 36 resist
1625. 36 neglect
1626. 35 absent
1627. 35 passenger
1628. 35 adventure
1629. 35 beg
1630. 35 pipe
1631. 35 beard
1632. 35 bold
1633. 35 meanwhile
1634. 35 devil
1635. 35 cheer
1636. 35 nut
1637. 35 split
1638. 35 melt
1639. 35 swear
1640. 35 sugar
1641. 35 bury
1642. 35 wipe
1643. 35 faint
1644. 35 creature
1645. 35 tail
1646. 35 wealth
1647. 34 earnest
1648. 34 translate
1649. 34 suspicion
1650. 34 noble
1651. 34 inquiry
1652. 34 journey
1653. 34 hesitate
1654. 34 extraordinary
1655. 34 borrow
1656. 34 owe
1657. 34 funeral
1658. 34 ambition
1659. 34 mixture
1660. 34 slope
1661. 34 criminal
1662. 34 seldom
1663. 34 map
1664. 34 spin
1665. 34 praise
1666. 34 spare
1667. 33 plow
1668. 33 telegraph
1669. 33 barrel
1670. 33 straighten
1671. 33 scarce
1672. 33 lunch
1673. 33 slavery
1674. 33 creep
1675. 33 sweat
1676. 33 gay
1677. 33 stiff
1678. 33 brave
1679. 33 seize
1680. 33 convenient
1681. 33 horizon
1682. 33 moderate
1683. 33 complicate
1684. 33 dig
1685. 33 curse
1686. 33 weigh
1687. 33 priest
1688. 33 excessive
1689. 33 quarrel
1690. 32 widow
1691. 32 modest
1692. 32 dine
1693. 32 politician
1694. 32 custom
1695. 32 educate
1696. 32 salesman
1697. 32 nail
1698. 32 tap
1699. 32 eastern
1700. 32 possession
1701. 32 satisfaction
1702. 32 behave
1703. 32 mercy
1704. 31 scatter
1705. 31 objection
1706. 31 silver
1707. 31 tent
1708. 31 saddle
1709. 31 wrap
1710. 31 nest
1711. 31 grind
1712. 31 spell
1713. 31 plaster
1714. 31 arch
1715. 31 swell
1716. 31 friendship
1717. 31 bath
1718. 30 bundle
1719. 30 grateful
1720. 30 crown
1721. 30 boundary
1722. 30 nowhere
1723. 30 asleep
1724. 30 clock
1725. 30 boil
1726. 30 altogether
1727. 30 lend
1728. 30 holiday
1729. 30 precious
1730. 30 wander
1731. 30 ugly
1732. 30 reputation
1733. 30 ticket
1734. 30 pretend
1735. 30 dismiss
1736. 30 delicate
1737. 29 despair
1738. 29 awake
1739. 29 tea
1740. 29 FALSE
1741. 29 fortune
1742. 29 cap
1743. 29 thread
1744. 29 haste
1745. 29 bare
1746. 29 shirt
1747. 29 bargain
1748. 28 leather
1749. 28 rail
1750. 28 butter
1751. 28 dot
1752. 28 inquire
1753. 28 warmth
1754. 28 decisive
1755. 28 vessel
1756. 28 pity
1757. 28 steam
1758. 28 pin
1759. 28 bound
1760. 28 companion
1761. 28 toe
1762. 28 reward
1763. 28 forbid
1764. 28 wherever
1765. 28 tower
1766. 27 bathe
1767. 27 lodge
1768. 27 swallow
1769. 27 multiply
1770. 27 bow
1771. 27 kingdom
1772. 27 garage
1773. 27 permission
1774. 27 pump
1775. 27 prevention
1776. 27 urgent
1777. 27 aunt
1778. 27 zero
1779. 27 idle
1780. 27 fever
1781. 27 christmas
1782. 27 regret
1783. 26 jaw
1784. 26 soap
1785. 26 pronounce
1786. 26 empire
1787. 26 bowl
1788. 26 outline
1789. 26 organ
1790. 26 imitation
1791. 26 caution
1792. 26 mineral
1793. 26 disagree
1794. 26 blade
1795. 26 trick
1796. 26 treasure
1797. 26 immense
1798. 25 convenience
1799. 25 disapprove
1800. 25 destructive
1801. 25 fork
1802. 25 noon
1803. 25 ownership
1804. 25 tune
1805. 25 polish
1806. 25 poison
1807. 25 shame
1808. 25 loyalty
1809. 25 cottage
1810. 25 astonish
1811. 25 shave
1812. 25 feather
1813. 25 sauce
1814. 25 lid
1815. 25 debt
1816. 25 fade
1817. 25 confess
1818. 25 classification
1819. 24 descend
1820. 24 cape
1821. 24 mild
1822. 24 clever
1823. 24 envelope
1824. 24 invention
1825. 24 sheep
1826. 24 splendid
1827. 24 stamp
1828. 24 float
1829. 24 brick
1830. 24 rice
1831. 24 businessman
1832. 24 backward
1833. 24 qualification
1834. 24 artificial
1835. 24 attraction
1836. 24 lamp
1837. 24 curl
1838. 23 shower
1839. 23 elder
1840. 23 bunch
1841. 23 bell
1842. 23 steer
1843. 23 flavor
1844. 23 spit
1845. 23 rob
1846. 23 cream
1847. 23 interrupt
1848. 23 pen
1849. 23 weave
1850. 23 orange
1851. 23 rescue
1852. 23 crush
1853. 23 humble
1854. 23 fancy
1855. 23 decay
1856. 23 polite
1857. 23 tribe
1858. 22 bleed
1859. 22 coin
1860. 22 fond
1861. 22 autumn
1862. 22 classify
1863. 22 omit
1864. 22 loyal
1865. 22 needle
1866. 22 lessen
1867. 22 complaint
1868. 22 pad
1869. 22 steep
1870. 22 skirt
1871. 22 curtain
1872. 22 calculation
1873. 22 laughter
1874. 22 solemn
1875. 22 grease
1876. 22 interfere
1877. 22 explode
1878. 22 fasten
1879. 21 flag
1880. 21 resign
1881. 21 postpone
1882. 21 patience
1883. 21 boast
1884. 21 rope
1885. 21 envy
1886. 21 airplane
1887. 21 rid
1888. 21 shield
1889. 21 veil
1890. 21 kneel
1891. 21 tray
1892. 21 explosive
1893. 21 brass
1894. 21 taxi
1895. 21 wax
1896. 21 duck
1897. 21 button
1898. 21 invent
1899. 20 remedy
1900. 20 bush
1901. 20 thunder
1902. 20 weaken
1903. 20 poverty
1904. 20 scrape
1905. 20 arrow
1906. 20 tender
1907. 20 cruel
1908. 20 soften
1909. 20 mouse
1910. 20 hay
1911. 20 anyhow
1912. 20 alike
1913. 20 circular
1914. 20 juice
1915. 20 shelf
1916. 20 bake
1917. 20 hatred
1918. 20 cautious
1919. 19 basket
1920. 19 wreck
1921. 19 width
1922. 19 confident
1923. 19 log
1924. 19 heap
1925. 19 suck
1926. 19 ladder
1927. 19 gap
1928. 19 obey
1929. 19 hut
1930. 19 axe
1931. 19 translation
1932. 19 collar
1933. 19 delivery
1934. 19 reproduce
1935. 19 confession
1936. 19 pan
1937. 19 prejudice
1938. 19 voyage
1939. 19 tobacco
1940. 18 simplicity
1941. 18 paste
1942. 18 cake
1943. 18 elephant
1944. 18 ribbon
1945. 18 harvest
1946. 18 ashamed
1947. 18 cave
1948. 18 customary
1949. 18 thief
1950. 18 damp
1951. 18 sew
1952. 18 rust
1953. 18 separation
1954. 18 waiter
1955. 18 pet
1956. 18 straw
1957. 18 upset
1958. 18 towel
1959. 18 refresh
1960. 17 essence
1961. 17 fur
1962. 17 ambitious
1963. 17 defendant
1964. 17 daylight
1965. 17 dip
1966. 17 suspicious
1967. 17 imaginary
1968. 17 ash
1969. 17 carriage
1970. 17 educator
1971. 17 saw
1972. 17 stove
1973. 17 rubber
1974. 17 rug
1975. 17 misery
1976. 17 awkward
1977. 17 rival
1978. 16 roast
1979. 16 deed
1980. 16 preference
1981. 16 explosion
1982. 16 theatrical
1983. 16 cultivate
1984. 16 collector
1985. 16 miserable
1986. 16 wrist
1987. 16 rabbit
1988. 16 accustom
1989. 16 tide
1990. 16 insult
1991. 16 thumb
1992. 16 lump
1993. 16 annoy
1994. 16 toy
1995. 16 heal
1996. 16 shallow
1997. 16 repetition
1998. 16 soup
1999. 15 whistle
2000. 15 scenery
2001. 15 apple
2002. 15 offense
2003. 15 cork
2004. 15 ripe
2005. 15 temper
2006. 15 sore
2007. 15 pinch
2008. 15 diamond
2009. 15 razor
2010. 15 imaginative
2011. 15 hook
2012. 15 copper
2013. 15 landlord
2014. 14 influential
2015. 14 rot
2016. 14 hollow
2017. 14 enclose
2018. 14 harden
2019. 14 wicked
2020. 14 stiffen
2021. 14 silk
2022. 14 upright
2023. 14 selfish
2024. 14 stripe
2025. 14 pig
2026. 14 inward
2027. 14 excellence
2028. 14 rake
2029. 14 purple
2030. 14 hasten
2031. 14 shorten
2032. 14 applause
2033. 14 ache
2034. 14 apology
2035. 14 knot
2036. 14 nephew
2037. 14 cushion
2038. 14 drown
2039. 14 nursery
2040. 14 pint
2041. 14 fierce
2042. 13 imitate
2043. 13 aloud
2044. 13 gaiety
2045. 13 robbery
2046. 13 tighten
2047. 13 perfection
2048. 13 scorn
2049. 13 whoever
2050. 13 trunk
2051. 13 wool
2052. 13 sailor
2053. 13 competitor
2054. 13 moonlight
2055. 13 deer
2056. 13 bean
2057. 13 everyday
2058. 13 drawer
2059. 13 disregard
2060. 12 nowadays
2061. 12 patriotic
2062. 12 tin
2063. 12 penny
2064. 12 cage
2065. 12 pardon
2066. 12 lately
2067. 12 offend
2068. 12 coarse
2069. 12 spoil
2070. 12 horizontal
2071. 12 sting
2072. 12 ditch
2073. 12 librarian
2074. 12 meantime
2075. 12 cough
2076. 12 deaf
2077. 12 sword
2078. 12 messenger
2079. 12 vain
2080. 12 castle
2081. 12 elastic
2082. 12 comb
2083. 12 rod
2084. 11 widen
2085. 11 sorrow
2086. 11 inventor
2087. 11 cliff
2088. 11 umbrella
2089. 11 interruption
2090. 11 merry
2091. 11 gallon
2092. 11 conquest
2093. 11 headache
2094. 11 tailor
2095. 11 bucket
2096. 11 scent
2097. 11 signature
2098. 11 cart
2099. 11 darken
2100. 11 sometime
2101. 11 applaud
2102. 11 underneath
2103. 11 hello
2104. 11 pretense
2105. 11 descent
2106. 11 conquer
2107. 11 framework
2108. 11 confidential
2109. 11 adoption
2110. 11 disgust
2111. 11 waist
2112. 11 momentary
2113. 11 receipt
2114. 10 pearl
2115. 10 ray
2116. 10 lazy
2117. 10 limb
2118. 10 grammatical
2119. 10 beast
2120. 10 monkey
2121. 10 jewel
2122. 10 persuasion
2123. 10 obedience
2124. 10 sock
2125. 10 vowel
2126. 10 hammer
2127. 10 inn
2128. 10 chimney
2129. 10 dissatisfaction
2130. 10 annoyance
2131. 10 ornament
2132. 10 honesty
2133. 10 outward
2134. 10 sharpen
2135. 10 handkerchief
2136. 9 greed
2137. 9 heavenly
2138. 9 thirst
2139. 9 niece
2140. 9 spill
2141. 9 loaf
2142. 9 wheat
2143. 9 worm
2144. 9 secrecy
2145. 9 rude
2146. 9 heighten
2147. 9 flatten
2148. 9 loosen
2149. 9 cheese
2150. 9 rivalry
2151. 9 royalty
2152. 9 discontent
2153. 9 complication
2154. 9 fright
2155. 9 indoor
2156. 9 flour
2157. 9 actress
2158. 8 congratulation
2159. 8 ounce
2160. 8 fry
2161. 8 everlasting
2162. 8 goat
2163. 8 ink
2164. 8 disappearance
2165. 8 reproduction
2166. 8 thicken
2167. 8 avoidance
2168. 8 spoon
2169. 8 strap
2170. 8 deceive
2171. 7 lengthen
2172. 7 revenge
2173. 7 correction
2174. 7 descendant
2175. 7 hesitation
2176. 7 spade
2177. 7 basin
2178. 7 weed
2179. 7 omission
2180. 7 old-fashioned
2181. 7 bicycle
2182. 7 breadth
2183. 7 photography
2184. 7 coward
2185. 7 mat
2186. 7 rejoice
2187. 7 cheat
2188. 7 congratulate
2189. 7 discomfort
2190. 7 enclosure
2191. 7 attentive
2192. 7 paw
2193. 6 overflow
2194. 6 dissatisfy
2195. 6 multiplication
2196. 6 whichever
2197. 6 tidy
2198. 6 bribe
2199. 6 mend
2200. 6 stocking
2201. 6 feast
2202. 6 nuisance
2203. 6 thorn
2204. 6 tame
2205. 5 inclusive
2206. 5 homemade
2207. 5 handwriting
2208. 5 chalk
2209. 5 sour
2210. 5 slippery
2211. 5 procession
2212. 5 ripen
2213. 5 jealous
2214. 5 jealousy
2215. 5 liar
2216. 5 homecoming
2217. 5 barber
2218. 5 whiten
2219. 5 berry
2220. 5 lighten
2221. 5 pigeon
2222. 5 hinder
2223. 4 bravery
2224. 4 baggage
2225. 4 noun
2226. 4 amongst
2227. 4 grammar
2228. 4 cultivation
2229. 4 companionship
2230. 4 rubbish
2231. 4 modesty
2232. 4 woolen
2233. 4 deepen
2234. 4 pastry
2235. 4 cupboard
2236. 4 quart
2237. 4 canal
2238. 4 notebook
2239. 4 deceit
2240. 3 parcel
2241. 3 brighten
2242. 3 moderation
2243. 3 punctual
2244. 3 hurrah
2245. 3 lipstick
2246. 3 uppermost
2247. 3 fatten
2248. 3 conqueror
2249. 2 hindrance
2250. 2 cowardice
2251. 2 obedient
2252. 2 saucer
2253. 2 madden
2254. 2 scold
2255. 2 weekday
2256. 2 rotten
2257. 2 disrespect
2258. 1 widower
2259. 1 deafen
2260. 1 donkey
2261. 1 businesslike
2262. 1 motherhood
2263. 1 sadden
2264. 1 handshake
2265. 1 calculator
2266. 1 headdress
2267. 1 scissors
2268. 1 translator
2269. 1 possessor
2270. 1 shilling
2271. 1 redden
2272. 1 motherly
2273. 0 whose
2274. 0 cultivator
2275. 0 whom
2276. 0 homework
2277. 0 electrician
2278. 0 oar
2279. 0 bribery
2280. 0 sweeten
2281. 0 sow
2282. 0 pronunciation
2283. 0 beak
2284. 0 plural

• English Vocabulary - General Service List
• NEW GENERAL SERVICE LIST

Instead of waiting for stress or illness to come and then reacting to it, set goals and structure life in ways that are mostly likely to forge a healthy foundation. The following nine steps to greater happiness and better mental health are presented as guideline to encourage you to take a more active role in your own life and to create a more positive psychological environment for yourself and others. Think of the steps as year-round resolutions.

与其等压力或疾病自己找上门时再去应付，不如设定目标来健康地组织你的生活。下面9步可以带来更多的快乐和更好的精神健康，可以作为一种指导，鼓励你更加积极地生活，并为你自己和他人创建一个更加积极的心理环境。下面的步骤可以在一年内实施。

1. Never say bad things about yourself. Look for sources of your unhappiness in elements that can be modified by future actions. Give yourself and others only constructive criticism —— what can be done differently next time to get what you want?

永远不要说关于你的不好的事情。寻找那些你将来采取行动可以加以改变的不快乐的根源。只给你自己和他人建设性的批评－下次应该采取什么不同的做法来得到你想要的东西？

2. Compare your reactions, thoughts and feelings with those of friends, co-workers, family members and others so that you can gauge the appropriateness and relevance of your response against a suitable social norm.

将你的反应、想法和感受同你的朋友、同事、家庭成员以及其他人进行比较，从而使你可以估计出自己行为的适宜性以及你的反应和适宜的社会规范的关系。

3. Have several close friends with whom you can share feelings, joys and worries. Work at developing, maintaining and expanding your social support networks.

结交一些密友，你可以同他们分享感受、快乐和忧虑。致力于发展、保持和拓展你的社会支持网络。

4. Developing a sense of balanced time perspective in which you can flexibly focus on the demands of the task, the situation, and your needs; be future oriented when there is work to be done, present oriented when the goal is archieved and pleasure is at hand, and past orented to keey you in touch with your roots.

发展一种平衡时间的观点，从而可以灵活地对待你的工作、环境的要求和自身需求。有工作在手时请面向未来，目标达到、有快乐在握时请珍惜现在，和你的老友联系时请珍惜过去。

5. Always take full credit for your sucesses and happiness(and share positive feelings with other people). Keep an inventory of all the qualities that make you special and unique —— those qualities you can offer others. For example, a shy person can provide a talkative person with the gift of attentive listening. Know your sources of personal strength and available coping resources.

永远对你的成功和快乐充满信心（并且和他人分享你的积极感受）。清楚地了解你独特的、与众不同的品质－那些你可以提供给他人的品质。例如，一个害羞的人可以给一个善谈者提供专注的倾听。了解你的个人优势和可以有效进行应对的资源。

6. When you feel you are losing control over your emotions, distance youself from the situation by physically leaving it, role-playing the position of another person in the situation or conflict, projecting your imagination into the future to gain perspective on what seems an overwhelming problem now, or talking to a a sympathetic listener. Allow youself to feel and express your emotions.

当你感觉你就要对自己的情绪失去控制时，请用离开的办法避开使你不快的环境，或者站在另一个人的立场考虑一下，或者设想未来，使你看到问题得以克服的前景，或者向一个同情者加以倾诉。请允许你自己感受和表达自己的情绪。

7. Remember that failure and disappointment are sometimes blessing in disguise. They may tell you that your goals are not right for you or may save you from bigger letdowns later on. Learn from every failure. Acknowledge setbacks by saying, ‘I made a mistake’, and move on. Every accident, misfortune or violation of your expectations is potentially a wonderful oppportunity in disguise.

记住失败和失望有时是伪装下的祝福。它们可以告诉你目标可能并不适合你，或者救你于未来更大的失败之前。吃一堑，长一智。遭受挫折后说一句“我犯了个错误”，再继续前进。你所经历的每一次事故、不幸和挫折实际上都是一个潜在的美妙机会，只是它们未以真面目示人。

8. If you discover you cannot help yourself or another person in distress, seek the counsel of a trained specialist in your student health department or community. In some cases, a problem that appears to be psychological may really be physical and vice versa. Check out your student mental health services before you need them, and use them without concern about being stigmatised.

如果你发现你无法使自己或他人走出忧郁，那就向学校或社区的健康部门受过训练的专业人员寻求建议。在某些情况下，有些看上去的心理问题实际上是生理问题，有些则正好相反。在你需要它们之前就了解一下你的学生心理健康服务内容，而在运用它们时不必有任何被诬蔑的疑虑。

9. Cultivate healthy pleasures. Take time out to relax, to meditate, to get a message, to fly a kite and to enjoy hobbies and activities you can do alone and that help you get in touch with and better appreciate yourself.

培养健康的愉悦。花些时间去放松、去反省、去收集信息、去放风筝、去享受你的爱好、去进行一些可以独处的活动，以及那些你可以做到并得到更好的享受的活动。

Psychology and Life, Chapter 13 Emotion, stress and health, by Richard J Gerrig, Philip G Zimbardo, Andrew J Campbell, Steven R Cumming, Fiona J Wilkes

《心理学与生活》第16版

Rosetta Code

http://rosettacode.org/wiki/Rosetta_Code

用不同语言来演示各种算法。

Greatest common divisor

欧几里得算法
http://rosettacode.org/wiki/Greatest_common_divisor

Elliptic Curve Digital Signature Algorithm

https://rosettacode.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm

leetcode

practicer

https://leetcode.com/forestgump/

https://leetcode.com/i_am_the_senate/

The Number Mysteries: A Mathematical Odyssey through Everyday Life

du Sautoy, Marcus

One THE CURIOUS INCIDENT OF THE NEVER-ENDING PRIMES

p. 29

The Chinese were probably one of the first cultures to single out the primes as important numbers. They believed that each number had its own gender—even numbers were female, and odd numbers were male. They realized that some odd numbers were rather special. For example, if you have 15 stones, there is a way to arrange them into a nice-looking rectangle, in three rows of five. But if you have 17 stones, you can’t make a neat array: all you can do is line them up in a straight line. For the Chinese, the primes were therefore the really macho numbers. The odd numbers that aren’t prime, though they were male, were somehow rather effeminate. This ancient Chinese perspective homed in on the essential property of being prime, because the number of stones in a pile is prime if there is no way to arrange them into a nice rectangle.

Applied Combinatorics

Prelude

第6页
This book seeks to develop facility at combinatorial reasoning, which is the basis for analyzing a wide range of problems in computer science and discrete applied mathematics.

Preface

第1页
Combinatorial reasoning underlies all analysis of computer systems. It plays similar role in discrete operations research problems and in finite probability.

This book teaches students in the mathematical sciences how to reason and model combinatorially. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problems solving.

The three principal aspects of combinatorial reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem(e.g.,finding manageable sub pieces or first solving the problem with three objects instead of n), and ingenuity.

Becoming a Better Programmer

chapter 14 Software Development is

第131页
Too much modern software is like my Alphabetti custard: it’s the wrong thing, written the wrong way.

chapter 24 Live to Love to Learn

第221页
The Knowledge Portfolio

Be aware of the risk/reward balance of the items in your portfolio.

Purposefully manage your knowledge portfolio.

Complexity

第233页
What Is Network Thinking?

Network thinking means focusing on relationships between entities rather than the entities themselves.

Prime Numbers

prime number theorem and the prime counting function

第183页
De la Vallée Poussin also showed that Gauss’s estimate Li(x) is a better approximation to π (x) than x/(log x - a) no matter what value is assigned to the constant a (and also that the best value for a is 1).

第243页
And yet—Pythagoras claimed that the universe was made of numbers and Leopold Kronecker (1823–1891) claimed that “God made the integers and all the rest is the work of man.” Who knows? Perhaps the world is even more cunningly constructed out of the prime numbers!

当代数学大师-沃尔夫数学奖得主及其建树与见解-第四版

A.塞尔伯格( Selberg, Atle)

第1876页
当有人问他，如果作为非专业人士问你“黎曼假设告诉了我们关于素数的哪些东西？” 他明快地答道：“它告诉我们素数分布得相当好，以最大可能分布得均衡，分布得适宜。当然，我们不能期望一个完全均衡的分布。”

当有人问他，“你是否认为黎曼假设是正确的？” 他答道：“如果在我们的宇宙中还有什么东西是正确的，那必定就是黎曼假设，若找不出正确的理由，那纯粹的美学理由就够了。

谈谈方法

第三部分

第739页
一定要经过长期训练，反复思考，才能熟练地从这个角度去看万事万物。我相信，那些古代哲学家之所以能够摆脱命运的干扰，漠视痛苦和贫困，安乐赛过神仙，其秘密主要就在于此。因为他们不断地考察自然给他们划定的界限，终于大彻大悟，确信除了自己的思想之外，没有一样东西可以由他们做主，确信只要认清这一点就可以心无挂碍，不为外物所动；他们对自己的思想作出了绝对的支配，因此也就有理由认为自己又富又强，逍遥安乐，胜过所有的别人，别人不懂这种哲学，不管得到自然和命运多大优待，还是不能支配一切、事事如愿以偿的。

第734页
我的第三条准则是：永远只求克服自己，不求克服命运，只求改变自己的愿望，不求改变世间的秩序。总之，要始终相信：除了我们自己的思想以外，没有一样事情可以完全由我们做主。

七堂极简物理课

尾声 我们

第578页
我们的爱与真诚与生俱来，我们天生就渴望懂得更多，渴望不断学习。我们对世界的认知在不断增长。在知识的边界，我们的求知欲在燃烧。我们渴望探索空间纹理的细微之处，探索宇宙的起源，时间的本质，黑洞的现象，以及我们思维的运行。

现在，在人类已知事物的最前沿，我们将要航行于未知的海洋，世界的奥秘与美丽熠熠生辉，让我们目眩神迷。

第564页
诚如古罗马哲学家卢克莱修（Titus Lucretius Carus）所言：“我们对生命的胃口是贪得无厌的，我们对生命的渴求是永不满足的。”（《物性论》卷三，第1084行）

终极理论之梦

第一章 序幕

第1页
在我看来，好的科学哲学是对历史和科学发现的迷人解说。但是，我们不应指望靠它来指导今天的科学家如何去工作，或告诉他们将要发现什么。

从异教徒到基督徒

第五章 澄清佛教的迷雾

二、 罪与业

第1777页
如果宗教是意味着超脱凡世的，我反对它。如果宗教是意味着我们必须从这个现世、知觉的生活中走出，且有多快就多快地“逃避”它，像一只老鼠放弃快要下沉的船一样，我是和它对立的。我认为一个人必须有中国人的共有意识，勇敢地接受现世的生活，且像禅宗的信徒一样和它和平共处。而我强烈地觉得宗教（任何宗教）一天固执于一个来世，趋向于否定现世，且从上帝所赐给我们的这般丰富且有知觉的生命中逃避，我们将因此种做法而妨碍宗教（任何宗教）与近代青年的意识接触。我们将是上帝真正不知感恩的儿女，甚至不值得禅宗的信徒称我们为堂兄弟。

第六章 理性在宗教

二、现在的姿态

第1850页
在所谓宗教信仰与意见的繁茂丛林中，一切谬见，弗朗西斯·培根的“四个假象”，都被介绍了：一切偏见（种族的假象），例如上帝必然是一种人性的存在，一个神与人同性的上帝的观念；一切与个人的或国家的成见相符的信仰（洞穴的假象），例如做一个基督徒和做一个白人，事实上有同样意义的流行习惯；一切言辞的虚构及混乱（市场的假象）；一切以人造的哲学系统为根据的不合理的教条（舞台的假象），例如加尔文的“完全堕落”的教义。

三、可理解的止境

第1934页
柏拉图说得对，我们所能看见及知道的，只是一个影子的世界。我们感官的知觉，只能给我们一个现象世界的图，这是理性所能告诉我们的一切：在现象的背后是本性，是物体本身，而我们永远不能凭我们心的推理来知道绝对的真理。多么可怜！这是对人类缺陷的悲哀的宣判：它是以官觉的知识为根据，自然的东西的存在是知识而已，我们所认为存在的不过是知觉，且可能是一种幻觉，我们的体质注定我们要隔着一张幕来看东西，而且永远不能和绝对真理面对面。尽我们想做的来做，某些东西仍常留在后面，即那些可知世界的剩余区。这是对人类智力的侮辱，悲哀地宣判人的心智已至绝境。对此，人自觉无力反抗。佛曾宣讲它，柏拉图曾说明它，一群献身于对机械与攻击人类知识定律经历世纪之久的哲学家，伤心地承认它，而新近的科学也证实了它。

第1929页
把柏拉图洞穴的比喻放在现代科学中来看，是否适用和正确是超乎我们所能估计的。爱丁丝说：“真正了解到物质科学所谈及的是一个影子世界，是近代最有意义的进步之一。”而杰恩斯追求以太的量子及波长的时候说：“人们已开始觉得这个宇宙看来像一个伟大的思想，多过像一架伟大的机器。”量子的确成为物理学上的困惑。量子让我们首次看到物质与能力渡过不可见的边界的地方，使我们确认对于物质的老概念已不再适用。当我们对物质做进一步的探究，到了把次原子的极小量充以一百万伏特的电，我们简直是失去了它。这是今天舆论的客观趋势。

第1829页
其实人想及上帝时，必须把他抽离一切实在，而不将他想象为一个占据空间的形式，只是一种事物的秩序。上帝不是存在，纯是动力——一个形而上学世界秩序的元素。

现实不似你所见

11. 无穷的终结

第1950页
《数沙者》像是在开玩笑，但意义深远。凭借比启蒙运动早大约一千年的想象力，阿基米德对某种认识做出了反抗，这种认识坚持认为存在一些人类思想本质上无法触及的奥秘。他没有宣称确切地知道宇宙的维度，或者沙子的具体数目。他主张的不是知识的完备性，正好相反，他十分清楚他估算的近似性和暂时性。他谈到宇宙真实的大小有哪些可能，但没有做出明确的选择。重要的不是假设我们通晓一切，而是相反：意识到昨天的无知可能被今天阐明，今天的无知可以被明天照亮。

4. 量子

第1187页
在量子力学描述的世界中，实在只存在于物理系统之间的关联之中。并不是事物进入关联，而是关联是“事物”的基础。量子力学的世界不是物体的世界，它是事件的世界。事物通过基本事件的发生而建立，就像哲学家尼尔森·古德曼（Nelson Goodman）在20世纪50年代写出的美妙语句那样：“物体是一个不变的过程”。

黎曼猜想漫谈

未竟的探索

第183页
在所有高难度的数学猜想中，若以它们跟其他数学命题之间的关系，乃至与物理学那样的自然科学领域之间的关系（这些关系在很大程度上决定了一个数学猜想的重要性）而论，黎曼猜想可以说是无与伦比的。

与费马猜想或哥德巴赫猜想那种连中学生都能看懂题意的数学猜想不同，理解黎曼猜想是有一定“门槛”的，因为仅仅理解其表述就需要有一些复分析方面的知识。

《黎曼猜想漫谈》读后感（代序）

第10页

一旦这些RH解决了，人类就站在一个不知比现在高多少的数学平台上，看到更远得多的风景。— 王元

从存在到演化

第3章 量子力学

第918页
算符的引入从根本上改变了我们对自然的描述，因此把它说成“量子革命”是很恰当的。

一个算符的本征函数用来描述系统的状态，其中该算符所代表的物理量具有确定的值（即本征值）。因此用物理学的术语来说，不可对易性意味着，不可能存在这样的状态，在其中，比如说坐标q和动量p同时具有确定的值。这就是著名的海森伯测不准关系的内容。

第四章 热力学

第61页
总是和耗散结构相连的三个方面：用化学方程所表达的功能；不稳定性所产生的时空结构；以及触发这个不稳定性的涨落。

The Riemann Hypothesis

Prime Time

第13页

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. — Leonhard Euler

The Millennium Problems

The Riemann Hypothesis - Bernhard Riemann

第25页
While for many mathematicians “intuitive work” can be hit-or-miss, Riemann’s mathematical intuitions were incredibly acute, and his results generally turned out to be correct.

ZERO The Gauntlet is Thrown

第14页
Perhaps the best way to read this book is to think of the seven problems as the commonplace mathematics of the twenty-fifth century.

心理学与生活

chapter 12 Emotion, Stress, And Health — A toast to your health

第430页

1. Never say bad things about yourself.

在成年时期，社会关系和个人的成就占重要地位。

社会亲密感是成年期心理健康的先决条件，重要的不是社会交往的数量，而是质量。亲密感是一种对他人承担性爱、情感及道德承诺的能力。它要求坦率、勇气、伦理感，并且往往要牺牲一些个人偏好。

再生力的本质：良好的适应，依赖于成为一名“关注他人”的人－即成为一名关心他人、富有同情心并拥有良好的社会关系的人士。

编程珠玑(第二版)

第1章 开篇 – 1.7 进阶阅读

第9页
程序员的主要问题不一定是技术上的，更可能是心理上的；因为他试图解决一个错误的问题，所以他不能取得进步。通过打破概念上的障碍，转而解决一个更简单的问题，这样我们最终解决他的问题了。
James L.Adams所著的《Conceptual Blocking》研究了这种跳跃，通常它可以说是一种通向创造性思维的令人愉悦的激励。Adams将概念性障碍定义为“妨碍问题解决者正确认识问题或获得解答的心理屏障”。

第二版的尾声

第167页
Tom Duff：尽可能盗用别人的代码。
库非常伟大，任何时候都尽可能使用它们。

Thinking, Fast and Slow

Part 4. choices — 32 keeping score — Regret

第346页
Regret is one of the counterfactual emotions that are triggered by the availability of alternatives to reality.

素数论

第5章 重要的猜想

第105页
素数首先就是一些谜。

第2章 Riemann zeta函数

第41页
19世纪上半叶，Gauss根据当时已有的素数表，猜测对数积分li(x)给出了素数稀疏分布律的一个极好的近似，从而将Legendre的直觉精确化。

法文版前言

素数表显示了素数的混沌特性，而其表面的无序性最终却与一些，比如说源于物理现象的经典随机模型相吻合。…为什么像素数这样高度确定的序列能够包含着那样的随机性。

确定性的终结

引言 一种新的理性？

第3页
James Clerk Maxwell就谈到＂一种新型的知识＂会克服决定论的偏见。

问题解决心理学

第三章 问题表征：＂顿悟＂的案例

第63页
Reproductive thinking是问题的structurally blind,其表现是没有真正理解问题后面的结构。

与“众”不同的心理学

第十章 人类认知的死穴

第235页
很多人头脑里不具备概率推理的基本定律，或者即使有也不够用。

第一章 充满活力的心理学

第19页
公众更倾向于用哲学的思辩、神学的预言或是民间的常识来解释世界。

博大精深的素数

第四章 素数是如何分布的？

第162页
许多数学家都认为素数分布问题具有极大的美学动力。

机遇与混沌

11. 混沌：一个新的范式

第65页
物理学家杨振宁（C.N.Yang）邀请我去做了一个报告。之后，他取笑了我的＂有争议的湍流思想＂—在当时这是一个恰如其分的评价。

学会提问

第1章 提出正确问题的益处

第5页
如果一个读者始终依赖于海绵式思维，那么他将始终相信其最后接收到的信息。不管对个人还是社会，成为别人思想的傀儡都是一件可怕的事。
海绵式思维强调知识的获得，而淘金式思维强调与知识积极的互动。

认知心理学

第11章 问题解决与创造性

第312页
专家不仅仅拥有丰富的知识，而且知识的组织性更好，这样才使得他们能更有效地利用他们的知识。而且，专家的图式不仅包括更多某个问题领域的陈述性知识，而且与该领域相关的程序性策略也比新手更多。

薄伽梵歌论

附：薄伽梵歌 1957年海外初版序言

第465页
然舍是则无以立，不得已必落于言筌，则曰至真，即至善而尽美，曰太极，即全智而遍能；在印度教辄曰超上大梵，曰彼一，人格化而为薄伽梵，薄伽梵者，称谓之至尊，佛乘固尝以此尊称如来者也。欧西文字，辄译曰：天主，上帝，皆是也。

旁观者

第3章 怀恩师

第70页
不要从别人的错误中学习，看看别人是怎么做对的。

数学的语言

序曲 何谓数学

第3页
数学是研究模式的科学（science of patterns）。

我们内心的冲突

序言

第2页
神经症是由文化因素引起的。
神经症产生于人际关系的紊乱失调。

第1页
精神失调者…而是饱受内心冲突折磨的人。

第十章 人格衰竭

第111页
表明冲突存在的三种大的紊乱失调：其一是遇事都犹豫不决。精力被分散的第二个典型症状是一种普遍性的办事无效率，即一个人由于内心有冲突不能发挥最好的能力造成的。第三个典型的紊乱症状是普遍性怠惰，主动性和行动能力瘫痪，奋斗的方向不明确，对自我的严重疏离。

乔布斯产品圣经

179 发明比思想更能改变世界

第191页
那时我开始认为，也许爱迪生给世界带来的改变，比马克思和印度高僧尼姆•卡洛里•巴巴加起来的还要多。

项目百态

模式 33 扑克之夜

第80页
互相熟悉可以使彼此互相信任，也可以使彼此更有耐心。

除了在一起玩耍，我们从来没有在其他事情上面感觉到如此地有活力，如此放开地表现自己，以及如此地专注痴迷。—Charles E.Schaefer

混沌

第4章 生命的盛衰

第73页
在世界上压倒一切的是非线性。
如果有更多的人明白简单的非线性系统并不必然具有简单的动力学性质，那我们大家的日子都会好过得多。

数学的故事

第237页
Sophus Lie的新颖想法：Galois理论在微分方程上应该有一个相应的理论。

第352页
Jack Wisdom和Jacques Laskar：1、发现太阳系的动力学特性是混沌的。2、这俩位天文学家还证明了：月球潮汐能使地球保持稳定，否则的话，就会导致混沌运动，而致使天气迅速变化，从暖期一下子变到冰川时代，又从冰川时代迅速变回暖期。因此，混沌理论证明，如果没有月球，地球将会是一个非常不宜居的地方。

完美的证明

第110页
Everyone is a bastard, everyone is bad, with the possible exception of Jesus Christ. Einstein is bad too, because he did not leave America after the nuclear bomb was detonated over his objections.In the end, through the general interconnectedness of events, a person becomes, in some way or another, to a greater or lesser extent, party to everything that happens in the world, and if he can exert any influence whatsoever on any event, then he becomes responsible for it.

Alexandrov：
每个人都是混账、坏蛋，只有耶稣基督除外。爱因斯坦也是个坏蛋，因为在原子弹被引爆之后，他并没有离开美国，尽管他曾极力反对使用原子弹。
最终，通过事物之间的普遍联系，一个人会以这样或那样的方式，在深浅不等的程度上与世界上发生的所有事物都扯上干系。如果一个人可以对任何一个事件施加任何影响，那么他就要为此承担责任。

第二章 如何培养数学家

第17页
佩雷尔曼的母亲名叫Lubov，是犹太人，20世纪60年代的数学专业研究生，当了名数学老师。

The Music of the Primes

chapter one : who wants to be a millionaire?

第1页
Somebody allegedly asked Hilbert, ‘If you were to be received like Barbarossa, after five hundred years, what would you do?’ His reply:’I would ask, “Has someone proved the Riemann Hypothesis?”’

第10页
The dependence of so many results on Riemann’s challenge is why mathematicians refer to it as a hypothesis rather than a conjecture.

the atoms of arithmetic

第55页
As we shall see, Riemann’s Hypothesis can be interpreted as an example of a general philosophy among mathematicians that, given a choice between an ugly world and an aesthetic one, Nature always choose the latter.

Riemann’s Imaginary Mathematical Looking-Glass

第66页
His contemporaries were to see nothing of him while he waded through Cauchy’s output. Several weeks later Riemann resurfaced, declaring that ‘this is a new mathematics’. What had captured Cauchy and Riemann’s imagination was the emerging power of imaginary numbers.

chapter five The Mathematical RelayRace: Realising Riemann’s Revolution

第102页
Euclid in Alexandria. Euler in St. Petersburg. The Göttingen trio — Gauss, Dirichlet, Riemann. The problem of prime numbers had been passed on like a baton from one generation to another. The new perspectives of each generation provided impetus for a fresh surge along the track. Each wave of mathematicians left its characteristic mark on the primes, a reflection of their era’s particular cultural outlook on the mathematical world.

第106页
As Hilbert wrote in 1897, he wanted to implement ‘Riemann’s principle according to which proofs should be impelled by thought alone and not by computation’.

第128页
But Gauss had made a second conjecture: that his guess would always overestimate the number of primes…

But in 1912 Littlewood proved that as you counted higher you would eventually come to regions of numbers where Gauss’s guess switch from overestimating to underestimating the number of primes.

Littlewood also showed that Riemann’s refinement might look more accurate as we count through the first million numbers, but in the farther reaches of universe of numbers Gauss’s guess would sometimes give the better prediction.

Indeed, to this day no one has actually counted far enough to arrive at a region of numbers where Gauss’s guess underestimates the primes. It is only through Littlewood’s theoretical analysis and the power of mathematical proof that we can be sure that somewhere along the line Gauss’s original prediction is false.

第131页
From now on, proof was everything. Nothing could be trusted without conclusive evidence.

chapter six Ramanujan, the Mathematical Mystic

第136页
Mathematics seems to bring out the cranks.

chapter seven Mathematical Exodus: From Göttingen to Princeton

第159页
Selberg spoke about his view on the Riemann Hypothesis. Although he had made a major contribution on the way to a proof. he stressed that there was still very little to support its truth. ‘I think the reason that we were tempted to believe the Riemann Hypothesis then was essentially that it is the most beautiful and simple distribution that we can have. You have this symmetry down the line. It would lead also to the most natural distribution of primes. You think that at least something should be right in this universe.’

第160页
Some misinterpreted his comments, thinking that Selberg was casting doubt on the validity of the Riemann Hypothesis. Yet he was not as pessimistic as Littlewood who believed the lack of evidence meant the Hypothesis was false. ‘I have always been a strong believer in the Riemann Hypothesis. I would never bet against it. But at that stage I maintained that we didn’t really have any results either numerical or theoretical that pointed very strongly to its truth. What the results pointed to was that it was mostly true.’

第165页
Hardy once dismissively declared, ‘Probability is not a notion of pure mathematics but of philosophy or physics.’

第167页
Erdös liked this probabilistic interpretation of the Riemann Hypothesis.

chapter eight Machines of the Mind

第184页
Hilbert responded with a view shared by many mathematicians: ‘It is a completely misunderstanding of our science to construct differences according to peoples and races and the reasons for which this has been done are very shabby ones. Mathematics knows no races…for mathematics, the whole cultural world is a single country.’

第197页
Julia Robinson: ‘We can conceive of a chemistry that is different from ours, or a biology, but we cannot conceive a different mathematics of numbers. What is proved about numbers will be a fact in any universe.’

第202页
Cohen has been one of the few mathematicians to admit that he was actively working on this notoriously difficult problem. So far, though, it has held firm against his attack.

Chapter Nine The Computer Age: From the Mind to the Desktop

第222页
The Mertens Conjecture is very closely related to the Riemann Hypothesis, and its disproof showed mathematicians that if the Riemann Hypothesis were true, it was only just true.

chapter 10 - Cracking Numbers and Codes

第224页
If Gauss were alive today, he would be a hacker. — Peter Sarnak

Chapter 11 - From Orderly Zeros to Quantum Chaos

第257页
Gödel himself had voiced such concerns in relation to the Riemann Hypothesis: perhaps the axioms that formed the foundation of the mathematical edifice were not broad enough to carry the required proof, in which case you might continue building upwards and never find a connection to the Hypothesis.

第261页
As Littlewood had advised Montgomery during his time in Cambridge, ‘Don’t be afraid to work on hard problems because you might solve something interesting along the way.’
Atle Selberg had become something of a latter-day Gauss.

第263页
Chowla, who dragged Montgomery over and introduce to Dyson, is the only person ever to have bullied Selberg into writing a joint paper.

Chapter 12 - The Missing Piece of the Jigsaw

第291页
One epic in particular was to become a close companion throughout André Weil’s life: the Bhagavad-Gita, the song of God from the Mahabharata.

Chapter 12 - The Missing Piece of the Jigsaw

第311页
Many of the mathematicians who have contributed to our understanding of the primes have been rewarded with long lives. Having proved the prime number theorem in 1896, Jacques Hadamard and Charles de la Vallée-Poussin both lived into their nineties. People had begun to believe that their having proved the Prime Number Theorem had made them immortal. The belief in a connection between longevity and the primes has been further fulled by Atle Selberg and Paul Erdös, whose alternative elementary proof the Prime Number Theorem in the 1940s saw both of them live into their eighties. Mathematicians joke about a new conjecture: anyone who prove the Riemann Hypothesis will indeed become immortal.

Dr.Riemann’s Zeros

Proofs and refutations

There was a mathematician in the Soviet Union … called Nikolai Gavrilov, who in the early 1960s was a big Communist boss in one of the Ukrainian cities. He was an ameteur mathematician, and he got hold of the Riemann Hypothesis and thought he had a proof, and being a man of power he organized for his proof to be published. The fortunate thing is that the proof did get published. You should know that at that time the Soviets were competing, especially with the United States, in all fields - the cosmos, high technology, and so on - and they had fine number theorists and mathematicians in general. Especially one Gelfond and one Yuri Linnik. Now, when these men got hold of a false proof of the Riemann Hypothesis, it is said, Gelfond had a heart attack and Linnik was choking and gasping for breath. He almost died from shock. They were so frustrated because much damage had been done to Soviet mathematics by this false proof of the Riemann Hypothesis appearing.

The email address you use

As a general rule, firstname.lastname@emailprovider.com is a good format for your email address.

To/from field

From

It should simply be your first and last names, appropriately capitalised and spelt correctly, with no extra bits like hearts or exclamation marks.

To

your recipient’s email address

CC

“CC” field stands for “Carbon Copy”, and it means that they will see the email but will also see that it’s not directly addressed to them. Don’t use it unless there is a real need for this person to see the communication.

BCC

If you’re emailing several people, it’s bad form to include all their email addresses in the “To” field. In this instance, you should put your own email address in the “To” field and put those of your recipients into the “BCC” field. This stands for “Blind Carbon Copy”, and it means they’ll all see the email but won’t see who else you’ve sent it to.

Subject line

Write something descriptive in the subject line that summarises what the email is about. Don’t make it too long.

Salutation

However, go by how they address you; if their emails to you start “Dear”, you reply with “Dear”; if they start “Hi”, you can reply with “Hi”. An alternative email greeting that lies somewhere between formal and informal is “Good morning” or “Good afternoon”. This is perhaps a little friendlier and more personal than “Dear”, so if your style is not naturally very formal then this is an acceptable form of email greeting.

Signing off an email

These common conventions include:

• Best wishes,
• Kind regards,
• Best regards,
• All the best,
• Thanks,
• Thanks in advance,
• Many thanks,
• Sincerely,
• Yours truly,
• Thanks again,
• Appreciatively,
• Respectfully,

With all of these, make sure you have a comma at the end of the line, as in the examples above.

• How to Write Good Letters and Emails: a Guide for Those Who are New to the English Language
• 7 Useful Tips on How to Write a Perfect Professional Email in English
• HOW TO WRITE A PERFECT PROFESSIONAL EMAIL IN ENGLISH IN 5 STEPS

无线网络变得越来越普遍，大如蜂窝移动通信网络，小如无线局域网。大卫•奇斯纳尔试图效仿阿瑟•克拉克，对无线网络技术的发展前景进行预测。

新千年的元旦——一个历史性的日子。世界各地的电信公司将同时取消长途资费，所有的电话都将作为本地通话计费。这听起来异想天开，但这可是大约十年前阿瑟•克拉克_[1]曾经作出的预测。

事与愿违，现实总是不及愿望美好。电信运营商依旧按你拨打的被叫号码的程控交换距离来计费。然而，情况并非完全与阿瑟爵士的预言相反。这几年来我打国际长途电话付出的几乎只是宽带连接成本。但与公用电话交换网不同的是，IP电话的两端是连接在互联网上的设备。其实不管是固定电话还是IP电话，通话两端的物理链路经过的中继线缆一般都差不多。

全IP网络

英国的有线电话骨干网（由英国电信经营）和下一代无线电话网络都有一个共同点：他们本质上都是IP网络并把电话作为IP电话(VoIP)处理。我现在的手机支持UMTS _[2]（通用移动通讯系统），每当我使用它就会自动分配一个10/8的子网IP地址。这意味着它位于网络地址转换(NAT) 背后，因此就不能再接受入站连接。

10/8子网是最大的可分配私有网络。作为8位CIDR _[3]前缀，它容许224（等于16,777,216，将近1700万）个不同的IP地址。与连接到移动电话网络的庞大设备数量相比，这根本不算多，这也是为什么移动运营商很可能率先部署IPv6的原因。采用IPv6，一家公司（甚至个人）都能轻易获得64位网络前缀，意味着前64位可用来标识网络，后64位可用来标识设备。对此可以这么理解，这家公司拥有足够的地址空间使每个有效的IPv4地址都能扩张为互联网那么大的网络，或换言之每个人都可以在他（或她）的网络上接入30亿个IP独立的设备。更重要的是，它容许全世界每台设备都具有各自唯一的IP地址，路由表记录稀少，如此路由的代价大为降低。

IPv6带来与移动电话密切相关的另一个优点就是移动IPv6，其中设备可以改变其在网络中的位置而继续保持路由，其已有的连接不会被中断。在信号塔之间移动位置通常在协议栈的底层就已经做了处理，但这种新的构架允许手机在两个彼此独立的网络之间移动同时保持连接，只要两端都采用IPv6连接。

全IP网络强调提供接入和提供服务之间的区别——一个正在被移动运营商搞模糊的分别。每当你打电话，你就在使用他们的网络，当你在使用他们的路由系统的时候，同时也在使用移动运营商与其他电话网络之间的协议。

电话号码与联系人的对应关系已经不像过去那么重要。过去我打电话的过程很麻烦：首先，我会先在一个纸质的通讯录或本地缓存中寻找对方的电话号码——要么是个电话簿或是我的大脑记忆，然后拨这个号码（后来变成了按键）。相比之下，现在我只是从通讯录中选择这个人的名字，然后就按下拨号键。最近一项研究称人们的记忆力越来越糟，因为他们连朋友的电话号码都记不住了。对我而言，不仅仅是我不再记住我朋友的电话号码——我根本就没在意那个号码是什么。很多时候，一个朋友通过电子邮件或蓝牙把电子名片发送给我，而我从来都不会去看号码那一栏。打电话（而不是联系某人）的概念看来已经依稀有些过时了。

连接的移动性

802.11标准家族不太知名的一个标准是802.11r。这个标准着眼于在无线接入点之间进行快速切换。802.11接入点在户内通常只限于几个房间那么大的范围，户外则大约一百米左右。一个走动中的人几分钟之内就可能需要在六个左右的接入点之间跳转。802.11r标准针对这个需要提供了相应的机制。如果你坐在一个与两个无线接入点距离大致相等的位置上，你或许觉察到你的网络连接不时地停顿片刻，因为你的网络堆栈在接入点之间进行切换。802.11r标准改善了停顿时间，把切换时间降低到1秒以内。这样的改进使802.11对手机用户切实可行。在安装了.11r支持的无线接入区域，你可以边走边打电话，而不会察觉你的电话在接入点之间的跳转——就像现在当你的手机在信号塔之间跳转时你根本没注意到一样。（好吧，理论上你不会注意到；实际上，你可能会察觉到）

如果所有的接入点都在一个网段上，这种切换行之有效。然而，想象你走在一条布满了接入点的街道上，这些接入点都开放并且配置在一个网络上。你从其中一头往另一头走，你打的电话被第一家的网络连接路由。当你在这条街上继续走动时，你的电话被无缝地在接入点之间切换，直到你到达另外那头。在这点上，你的电话的数据包被一打接入点中继转发给被你呼叫的那方，这不是很有效率。理想的情况下，在这点之前你就会开始用新接入点上行数据。不幸的是，每个接入点都有不同的可路由的子网地址，这样如果你切换成新的接入点来上行数据，你就会突然切换IP地址，而这将中断你的连接。

这就是移动IPv6的用武之地。IPv4也有一个针对移动的变种，依赖于三角路由——简单来说，老的网络连接充当数据包的中继，每当你移动数据包就暗中增加。对IPv6，IPSec允许安全地更新路由表。目前，切换时间大约1秒，这对VoIP电话来说还不够快，但这个切换时间有望得到改善。

对移动IPv6来说，网络间的边界变得平滑。如果你坐在一个提供免费wifi的咖啡厅，你也许就想使用咖啡厅的网络，而不是使用需要花钱的移动运营商的网络。如果你边打电话边走进咖啡厅，你当然想自动切换到咖啡厅的免费wifi网络，而不是继续使用移动运营商那资源稀缺而费用昂贵的蜂窝网络。

提供接入

移动运营商很善于根据不同数据类型来收取不同的费用。他们的整个业务模式都基于此方案。如果每条文本信息你付10美分，算下来大约折合750美元/MB。许多人愿意为短信支付这些钱，但这样的话加载InformIT首页的费用就超过500美元，而我怀疑大多数人会愿意为浏览网页花那么多钱。

你可以在你的手机上运行一个即时通讯软件，即便是XMPP这样臃肿的协议算下来其成本也只是短信费用的一部分。不幸的是，你不能用它与手机上没有装IM客户端的用户沟通，这降低了它的可用性。你不只在为IM的带宽而付费，而且也需要为网络服务付费。

电话按与别的数据不同的方式计费。这样设计更合理。然而，由于电话的要求与浏览网页和电子邮件很不一样。GSM和相关的协议用于语音通话的传输速度大约为12Kb/秒。以这个速度，你打一个小时电话也只用了大约5MB的数据流量——这在现代网络中不值一提。

然而对语音通话来说带宽并非一切。如果延迟超过200毫秒左右，你很可能就会感觉到通话质量不好。更重要的是抖动，比起延迟都还要重要。如果延迟时间稍有增加，通话的双方就会产生说与听之间的脱节。如果延迟减缓，你只有以丢包的方式才能赶上，因为你不能以高于实时的速度回放音频而没有察觉。（你可以加快点速度，但很有限）。你可以通过在每个接收端进行缓冲来补偿抖动带来的损失，但这种方法增加了延迟，而这是你极力避免的事。

所以网络接入中你在为三件事买单：带宽、延迟和抖动。对于带宽来说，你想提高就得多掏钱；对延迟和抖动，你想降低就得多花钱。即时只是提供IP连接，移动网络仍旧能通过提供不同的QoS服务质量来收取不同档次的费用。如果你想打个电话，你或许会选择具有低延迟和低抖动而费用较高的连接，你更愿意在信号质量方面而不是带宽上花钱。

软件无线电: 工程师的梦想，监管者的梦魇

随着GNU Radio之类开源项目的出现，近几年来一个有趣的发展是软件无线电。当然，无线电系统不能完全是软件的，但其需要的硬件相对简单——差不多就是一架天线和一个数模转换/模数转换器。

过去，无线电设备的执法较容易。你检查硬件是否工作在限定频率和功率范围内；如果是，你就可以核准其批量生产。

对软件无线电来说，功率和频率都由软件控制。这对监管机构来说构成问题，尤其是与开源驱动一起使用的时候，因为这意味着终端用户能轻易地把合法设备换成不合法设备。（当然，总有人可能会通过增加放大器和天线做到这一点，但是如果你只需要下载固件的补丁，事情就变得更加容易了）

尽管令监管者不爽，软件无线电的确给通信带来一些有趣的变化。当你能够把同样一台硬件用于接收HDTV和WiFi两种信号时（同时，只要你有一个足够快的处理器），就带来了很多可能性。纯软件无线电是令人难以置信的处理器密集型应用，因此对移动设备意义不大（手机专用芯片计算能力不强），但它提供了一些启示。动态配置的信号处理单元能够集成到相同的包中，这样你现在就能得到能够运行许多不同无线协议的低功耗芯片。

未来几年里设备有可能会支持WiFi, WiMAX, HSPDA, GSM和其他流行的低功耗协议，以及在它们之间进行快速切换的能力。

尽管这种变化就其自身而言并非完全有用，当与移动IPv6相结合后就变得激动人心——给你的设备一种在各种各样的协议之间跳转的能力，可以针对你的需要选择最省钱的那种协议。

什么是频谱?

可悲的是，无线电频谱是一种稀缺资源。频率越低传输距离越远，但数据传输率越低。频率高则传输距离不远。这就是为什么WiFi比移动通信快得多的原因之一。另一个是信道竞争。信号传输距离越远，你需要的接入点越少（有利的一面），而同时有更多的人在共享这个信号（不利的一面）

一些较新的发展可能会缓解频谱稀缺面临的压力，尽管它们（总是）非常占用处理器计算能力。如果你在建筑物密集的地区或丘陵地区观看模拟电视，你或许会注意到重影。这是由于一个信号从发射机直接到达，而另一个信号从山上反弹过来，延迟到达。

在建筑物密集的地区，信号会被建筑物、树木反弹，某些频率甚至能被人反弹。对于大多数现有的协议，你必须计算反弹的均值以尝试找到你真正想要的那个信号。有了更精确的设备，你有另外更好的选择。你能用不同路径的信息来确定一个特定的端点。几个设备可以在同一地区以相同频率同时发射，提供了更多可用的频谱。

虽然并非完全相关，但这种缓兵之计表明一定宽度的频谱并不意味着等量的数字带宽。技术进步允许你在同等大小的信号空间中传输更多的信号。但就目前而言，这一事实并没有改变这样的现状，即频谱相对地还是稀缺。

目前我们有两种截然相反的供互联网接入的频谱分配方式：蜂窝网络和未管制的（WiFi及其邻接频谱区间）。前者被集中统一控制，网络覆盖面广。后者不受监管，任何人都能使用，但覆盖的范围有限。

我在前面提及的一些技术使这些界线有点模糊。有线电视公司可以部署一个很高效的城域网，给所有客户提供WiFi接入，使客户能通过Mesh多路径路由和移动IPv6的组合在二者之间按需跳转。

在美国，最近作出的一项决定允许一些以前用于电视的频谱（频道与频道之间那些所谓的“空白频谱”）也可以用于数据网络。这对城域网来说是个不错的频率范围，为其实现方式提供了另一种选择。

这里可用的频率范围甚至比用于蜂窝移动通信的频率还要低，因此信号传输距离更远（毫不奇怪，只要你想想移动通信基站比电视发射塔要密集得多）。这使它对提供覆盖面广的服务很有吸引力。由于FCC（联邦通讯委员会）决定将这一范围的频谱免授权开放使用，任何人都可以开展这种覆盖业务。一个城市可以拥有许多提供快速、覆盖范围小的接入方式的热点地区，同时还有一个更大的基站以较低的接入速率覆盖整个地区作为候选。当你走在两个热点之间时，你的手机转为使用空白频谱系统，而不影响你的覆盖范围（尽管你的可用带宽可能会减少）。

未来有望看到你的手持设备能透明地在由不同服务提供商控制的和不同服务质量的网络之间自由切换。提供统一的接入服务、不同级别的最低连接质量和其他多种选择将给创新型公司带来在诸多领域建立新的商业模式的机遇。

[1] 科幻小说作家，提出卫星通信地外中继的概念，作出的很多预测也大多应验

[2] 全球使用率最高的3G移动通信标准，采用WCDMA

[3] 无类别域间路由

以honest Translate的身份于2010年发表于 译言网 无线网络的未来，现在GitHub上留作备份，翻译不当之处欢迎指正

原文地址:The Future of Wireless Networking