文档介绍：一.
The expression of ... can be expanded as: ...
...的表达式可扩展为...
A is exponentially smaller than B,so it can be neglected.
A对B来说呈指数级减小,所以可以忽略不计。
Equation (1) is reduced to:
方程(1)化简为:
Substitute the values into equation (3), we get ...
把这些值代入方程3,我们得到...
According to our first assumption on Page 1,
根据我们第一页的第一个假设,
Thus we arrive at the conclusion:
因此我们得到结论:
From the model of ... ,we find that theoretically, it is almost true
that ...
由...模型,我们从理论上证明了... 是真实可信的。
That is the theoretical basis for ... in many application areas.
这是...在很多领域应用的理论基础。
To quantitatively analyze the different requirements of the two applications, we introduce two measures:
为了定量的分析这两种应用的不同要求,我们介绍来两个量度标准。
We give the criterion that...
我们给出了...的判别标准
According to the criterion of...
根据...的标准
So its expression can be derived from equation (3) with small change.
所以它的表达式可以由方程3做微小改动而推出。
Suppose that ...refers to ...
假设...指的是...
We can get the distribution of...
我们可以得到...的分布
along x and y axes
沿着x和y轴
For a further discussion of this model, please see Appendix A. 参见附录A
(detailed in Appendix I)
(详见附录一)
... is fitted to the normal distribution,with the mean at 0 and variance of σ=....
符合均值为0,。
shows ...
图4表明...
Thus, if ... is given, ...is determined.
因此,如果给定...,...就也确定了。
For a given r, we can calculate ...
对于给定的r, 我们可以算出...
The two distributions are independent.
这两个分布是相互独立的。
By calculation we obtain...
通过计算,我们得到...
So it is expressed as below:
所以它可以表示为:
... is ultimately determined by ...
... 最终由...决定
We fix A and examine the change of B with respect to C.
我们固定A然后观测B随C的变化。
the logarithm values of ...
...的对数值
That explains why the value of A decreases as B increases.
这就解释了为什么A的值随B的增加而减少。
二.
If r increases, p(r) increases accordingly.
如果r增长,p(r)也相应地增长。
due to
由于
A is the length of ... in unit of ...
A是...的长度,以...为单位。
We can see a "valley" between two curved faces which denoted the points where A=B.
我们可以看到在两个曲面之间有一个低谷,表示A