And when I am on the curve I am on the boundary of the surface, so there is a direction along the surface that is the curve and the other one is pointing into the surface.
当我在曲线上时，我是在曲面的边上的，所以一个是沿着曲面的边指，那个就是曲线的定向，另外一个就要指向曲面里面的那个方向。
"Why should we go another 20 years without knowing whether we're on high [warming] curve or the low curve?"
“为什么我们还要等20年才能知道我们是走高[升温]曲线还是走低曲线呢？”
Because, if you have a curve in space and say that you have wind or something like that, you cannot really ask how much air is flowing through the curve.
这是因为如果空间中有一条曲线，并假设存在风，或类似的流体，那么我们无法确定，空气通过曲线的量。
Flux, on the other hand, measures, when I go along the curve, roughly how much the field is going to across the curve.
从另一方面来看，“通量”度量的是，沿着曲线前进时，大致会有多少向量场通过曲线。
In general, events along a closed timelike curve cannot be compatible with an uninterrupted increase of entropy along the curve.
通常，沿着一个封闭的时间型曲线发生的事件不可能与沿着这个曲线不间断地增加的一致性相符合。
Both of these formulas basically relate work on a curve with what happens to the curl on the surface that is enclosed by this curve, that is bounded by this curve.
基本上，这两个公式把沿曲线的功，和被曲线包围的曲面上的旋度，联系起来了，曲面是以该曲线为边界的。
That is our convention to get a unit normal vector that points to the right of the curve as we move along the curve.
这是约定的得到单位法向量的方法，这种做法使得，当沿着曲线行进时，法向量始终指向右手方向。
You know it's automatically OK because if you have a closed curve, then the vector field is, I mean, if a vector field is defined on the curve it will also be defined inside.
它必然成立，因为如果给出一条闭合曲线，然后向量空间是…，我是指，向量空间在曲线上有定义，当然在区域内部也有定义。
That is the stuff that goes through my curve, in unit time,for a small portion of curve.
这就是在单位时间内，通过一小部分曲线的流体了。
And when we do that we can see this curve, this probability curve, where we have a maximum probability of finding the electron this far away from the nucleus.
当我们这样做时，我们可以看到这个曲线，这个概率分布曲线，这里有发现，电子的最大概率。
The shape of the curve when its falls is almost the same as the shape of the curve when its goin up into the air.
当炮弹在空气中运动的时候,其上升和下降的曲线形状几乎一样。
Don't look at that curve at just some dumb parabola, some dumb curve.
别老看那条曲线，别老看那些没用的抛物线、曲线。
To remind ourselves that we are doing it along a closed curve, very often we put just a circle for the integral to tell us this is a curve that closes on itself.
为了提醒我们是在封闭曲线上做积分，经常在积分符号上加个圆圈，告诉我们，这条曲线自我封闭。
A tangent is a straight line that just touches a curve, so the concept of "running the tangents" is to run the shortest distance possible by running straight from one curve to the next.
切线是一条直线，刚好接触到曲线，所以跑切线是从一个弯道跑到另一个最短的距离。
In the graph above, the cost curve would be flipped and aligned with the value curve.
在上图中，成本曲线就会与价值曲线趋于一致。
I get a curve, and I looked at the slope of that curve.
我得到了曲线，然后观察曲线的斜率。
And we didn't know whether we were going to be looking at history or not because when you look at a curve like that, an exponential curve going up can often just tilt over and crash back down again.
我们并不知道是否会鉴证历史，因为，在您看到那样的一个曲线时，那种上升的指数曲线往往会再次倾斜下滑。
And let's take my favorite curve and compute the line integral of that field, you know, the work done along the curve.
对我喜欢的曲线，计算其上的线积分，在这条线上所做的功。
Others claim that it is a mistake to see either learning curve effects or experience curve effects as a given.
还有人说把学习曲线效应和经验曲线效应看成给定的不对。
Figure 2: Risk reduction (pale curve) and value (purple curve) during the project lifecycle.
图2：项目生命周期过程中的风险减少(苍白色曲线)和价值(紫色曲线)。
In this example, if we say that this is the male curve and this is the female curve.
在图中，这条代表男性(视频中的深色曲线)，这条代表女性。
That means a vector that is at every point of the curve perpendicular to the curve and has length one.
也就是，曲线每一点上,垂直于曲线，模长为1的向量。
Figure 3: Risk reduction (red curve) and value creation (green curve) during the project lifecycle.
图3：项目生命周期期间的风险降低(红色曲线)和价值创造(绿色曲线)。
For your convenience, we provide an implementation for another space filling curve, the Hilbert curve (see the Resources section for information on the Hilbert curve) in the download section.
为了方便，我们在下载一节中提供了另一种空间填充曲线，即Hilbert曲线的实现(请参阅参考资料一节以了解关于Hilbert曲线的信息)。
The graph above shows that it is possible for someone with less luck to become successful faster than someone with more luck since the red curve is always above the blue curve.
下图是一个简单的示意图，这个图里面，红色的曲线对应的人和蓝色曲线对应的人相比，红线人的运气值是蓝线人的一半，但努力程度是其三倍。这个图中，红线是一直高于蓝线的，这表明了，有的人可能运气不是很好，但是通过非常刻苦的努力尝试，可能最后比那种经常撞大运的人更加成功。
So instead of putting this new curve on the same figure as the old curve, start a new one.
所以我们现在是，把这些拐点放在新图上，而不是在原来的老拐点的图上。
This blade has a gentle, sloping convex curve to the point versus the concave curve of the clip blade.
相对于回形刀刃的凹曲线而言，这种刀刃具有一条延伸到刀尖的、温和的凸斜率曲线。
On the basis of freeboard phenomenon in curve way and the improvement of curve flow velocity, this paper gets a useful calculating method of bed roughness.
本文基于弯道超高现象以及弯道流速计算的改进，得出了一种较为实用的泥石流沟床糙率计算方法。
Now if you add the blue curve and the red curve together, a straight line like you did before.
如果把蓝线和红线加一起，得到直线。
Now if you add the blue curve and the red curve together, a straight line like you did before.
如果把蓝线和红线加一起，得到直线。
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