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By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

But on the day we live in an America whose middle classis thriving and growing again, where all Americans, no matter wherethey live or where their ancestors came from, can earn a decent living,we will live in a stronger America and that is why we must elect BarackObama our President.

直到有一天，美国的中产阶级依然在奋斗并成长，每个人无论背景都能有尊严地活着，那将是一个更为强大的美国。这也是为什么我们要选择奥巴马做我们的总统的原因。

Aristotle said that in order to live and live better people live compactly in cities.

亚里斯多德说过，人们为了活着，聚集于城市；为了活得更好，居留于城市。

Go little coyote and live in mercy, live in peace and live in the grace of your creator.

小硐室和慈悲去住，生活在和平与住在你的造物主的恩典。

In order to reserve themselves the possibility to have a private life, some local celebrities prefer to live in a part of the world where they are rather unknown; thus, an entertainer who is well known in the German-speaking world could chose to live his private life in the US and fly into Germany to perform his shows (as Thomas Gottschalk actually does), and on the other hand, a US celebrity could decide to privately live in Europe.

为了保留自己的可能性，有一个私人生活中，一些当地名人喜欢生活在一个世界的一部分，他们是相当不明，因此，艺人谁是众所周知的在讲德语的世界可以选择住他私人生活在美国和飞入德国履行其显示（如托马斯哥特夏克实际上没有），而另一方面，美国名人可以决定私下生活在欧洲。

But we do choose how we shall live: to live richly and abundantly and eagerly or to live dully and meanly, that depends on ourselves.

但是我们可以选择怎样生活：是活的充实而丰富而热烈，还是沉闷而低贱地虚度光阴。这取决于我们自己。

If you live to be 100, I hope I live to be 100 minus 1 day, so I never have to live without you.

如果你活到100岁，我希望我每一天活100分钟，这样我就能永远陪伴着你。

"If you live to be 100, I hope I live to be 100 minus 1 day, so I never have to live without you."

如果你会活到100岁，我希望我能活到100岁零1天，这样我就永远不会离开你了。

They muddle along, live for money as mammonists, live for beer and skittles, live in defiance of conventions or even murder for property.

他们得过且过，或拜金主义为钱而活，或吃喝玩乐，或目无法纪甚至谋财害命。

The Prince Bo o k 5 Ho w C itie s o r Prin c ip a litie s Wh ic h Live d u n d e r Th e ir O w n La ws b e fo re Th e y We re O c c up ie d Sh o uld Be Ad m in iste re d When those states that are acquired, as has been said, are accustomed to living by their own laws and in liberty, there are three modes for those who want to hold them: first, ruin them; second, go there to live personally; third, let them live by their laws, taking tribute from them and creating within them an oligarchical state which keeps them friendly to you.

But in republics there is greater life， greater hatred， more desire for revenge； the memory of their 34 第五章 Book 5 第五章如何治理那些被占领之前有着自己法律的城邦和君主国如果被占领的国家如前所述，习惯于遵循自己的法律，而且是自由的，那么，想把它们掌握住，有三种办法：第一种是将它们夷为平地；第二种是您御驾亲临，驻扎在彼处；第三种办法是由着那儿的居民沿用他们的法律，对他们收取贡赋，建立一个对您友好的寡头政府统治他们。

Hanna: That's over now, isn't it?

都结束了，对吗

You must be ill. You look so pale.

你一定是病了，你的脸色苍白。