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In the movies, hackers break into every system so easily in a few seconds.
在电影里，黑客用几秒钟的时间就能轻而易举地入侵各个系统。
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STUDENT: No. Not unless he wants to break the vase into little pieces and stuff it in the corners.
学生：【听不见】,教授：不，除非它想把花瓶打成碎片,然后把它们堆到角落里。
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We can break the book of Leviticus down into the units that are listed on that side of the board.
我们将整本《利未记》分成一个个单元来讲,单元表就在那边的板上。
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But it is a very handy way of thinking about, not just how to program, but how to break problems down into nice sized chunks.
但是它确实是一种很方便的思考方式，不仅仅限于编程序,在将程序分解为小部分时也很有用。
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When they do that they can actually engulf the bacteria in a process called phagocytosis and break them down into antigens.
免疫细胞确实是将细菌整个吞进了肚内,这一过程称为吞噬作用,并将细菌分解成小抗原
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As long as it's reversible, you know what the efficiency has to be, and in principle, you could break it down into a bunch of steps that you could formulate as isothermal and adiabatic.
只要这个循环过程是可逆的，你们知道效率是多少，从理论上说，可以将总过程,分解成一系列绝热,和等温的小过程。
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so, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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Now I am going to break this into elementary steps and look at the relative contributions.
我会把这整个变化过程化为几个基本的步骤,去考察每一步的变化量。
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Once a week you will break up into discussion sections.
每周有一次你们都将被分成讨论小组。
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Here is the five dollars, we're going to tear this into nine pieces, except I'd get arrested and deported if I did that, so we're going to find a way to break this into change later.
这是5美元,我要把它撕成9份,但我会为此被捕然后被驱逐出境的,所以待会儿我会想办法把它换成零钱
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and movies that are also trying to make break out into other festival circuits,
这些电影也正努力地打入其他电影节，
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What's the point of this? Again, now that I can think about things recursively, I can similarly break things down into simpler versions of the same problem. It could be one version.
这些的意思是什么呢？再一次我想说,我既然能够以递归的方式思考了,那么我就可以简单地把问题,转化为更简单的同类问题。
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Our goal is to take problems and break them down into these computational steps, these sequence of instructions that'll allow us to capture that process.
我们的目标是得到问题,然后将问题分解为这些计算步骤，这些指令集,可以让我们看到这个过程。
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For example, in terms of the atomic theory of matter, at the time at the turn of the Century, the understanding was that atoms were the most basic constituent of matter, meaning you couldn't break atoms up into anything smaller - that was it, you're done.
例如在原子理论中,在19，20世纪之交的时候,人们认为原子是,组成物质的最基本粒子,也就是说你不能,把原子再分割了,就这样了。
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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Well, break it down into pieces. Suppose x is positive. Does it terminate? Sure. All right?
好，分开来讨论，假设x是整数,程序会终结么？肯定会的对不对？
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And you know, you could have a reversible engine with lots and lots of steps, but you could always break them down into some sequence of adiabatic and isothermal steps.
你们知道，我们可以设计一个由，很多很多个,循环步骤的热机，但是总可以把它分割成,一系列的绝热,和等温过程。
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or at least one mechanism, I shouldn't say -- the only one-- one mechanism for doing that is going to be to add functions is that it's going to provide both of these things, so the first thing it's going to do is, it's going to let us break up into modules.
我们处理这些的机制--至少一种机制,我不会说只有一种,一种机制是在我们的语言中增加函数,函数的关键是它要提供分解和抽象,所以第一件要做的事，就是将代码分解为模块。
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So when we write that out, we just write sigma 1 s squared, or we can break it up into its individual parts, there's no reason we can't do that as well.
当我们把这个写出来时，我们写sigma1s的平方，或者我们可以把它拆分成每个部分，我们没有理由不能这么做。
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I have used divide and conquer, as we seen before, to recursively break it into smaller problems. But the smaller problem of fib of 4 and the smaller problem of fib of 3 overlap with each other.
正如我们之前看到的，我已经进行了划分,并且递归性的把它分解为更小的问题,但是fib的简化问题,和fib的简化问题会相互重叠。
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