This curve here with the square shows you how many millions of vaccine doses were distributed across the U.S.

这个带方形的曲线图显示了,在美国数以百万计的,疫苗是如何使用的

耶鲁公开课 - 生物医学工程探索课程节选

At any instant, your motion, if it follows any curve, locally can be approximated as being part of some circle.

在任何时候,如果做曲线运动,都可以近似地认为是圆周的一部分

耶鲁公开课 - 基础物理课程节选

In my diagram, I said that the tangency portfolio-- I estimated that the tangency portfolio is 9% oil, 27% stocks, and 64% bonds.

在我的曲线图里我有提到切线资产组合-,我估算出切线资产组合是9%的石油，27%的股票和64%的债券。

耶鲁公开课 - 金融市场课程节选

So, what this lets us do now is directly compare, for example, the strength of a bond in terms of a hydrogen atom and hydrogen molecule, compared to any kind of molecule that we want to graph on top of it.

因此，这让我们现在可以做到直接进行比较，比如，将一个氢原子，和一个氢分子的键的强度，与任何其它类型的分子进行比较,我们只需要把它的曲线也画在这幅图上。

麻省理工公开课 - 化学原理课程节选

There's a pretty interesting and potentially important gender factor going on here where the women in the orange line, after about this point, start to diverge.

性别在该研究中是一个非常有趣的因素,并且是个潜在的重要因素,图中橙色曲线代表女性,在这个点之后,两条曲线开始分离

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

That's where the marginal cost and the demand thing, demand lines intersect.

应该是在边际成本,与需求曲线的交点上

耶鲁公开课 - 博弈论课程节选

Well, we say at the top of the loop, when it goes up and comes down the velocity is 0.

在曲线顶端,当物体上升,然后速度为0时候

耶鲁公开课 - 基础物理课程节选

So the velocity at any part of the curve is tangent to the curve at that point.

曲线上任意一点的速度,都在该点和曲线相切

耶鲁公开课 - 基础物理课程节选

You can see some of the points I've made along the blue line here.

你们可以看到我在蓝色曲线上标出了几个点。

耶鲁公开课 - 金融市场课程节选

You can see that it dominates the pink line.

可以看到这条蓝色曲线在粉色线之上。

耶鲁公开课 - 金融市场课程节选

As people's weights get high -I'm sorry let's go back here, got a little trigger happy here -as weights go high, from left to right you see the risk of Diabetes gets really very high.

随着体重的上升,抱歉,应该回到上一张幻灯片,刚才按多了,在曲线上从左到右,随着体重的上升,患糖尿病的风险在迅速上升

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

Now we're going to compare high glycemic index foods with low glycemic index foods, and so the curve of blood sugar with high glycemic index foods, those that create an exaggerated blood sugar response over a period of time might look like this.

现在我们要对高血糖指数的食物和,低血糖指数的食物进行对比,那些高血糖指数食物所形成的曲线,那些会在某段时间内产生过高血糖的食物,所形成的曲线看起来可能就是这样的

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.

在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度

耶鲁公开课 - 基础物理课程节选

So, let's, for example, look at nitrogen. So n 2, we can do the chart here in green, so it's the green dotted line, and what we see is that we have now defined this energy as where the 2 nitrogen atoms are separated.

那么，让我们举个例子，看一下氮，那么氮分子，我们可以把它用绿色曲线画在这，这是绿色的虚线，可以看到,我们已经定义为零点能，当两个氮原子分离时。

麻省理工公开课 - 化学原理课程节选

So, if we look at this graph where what we're charting is the internuclear distance, so the distance between these two hydrogen atoms, as a function of energy, -- what we are going to see is a curve that looks like this -- this is the general curve that you'll see for any covalent bond, and we'll explain where that comes from in a minute.

因此，如果我们来看一看这幅曲线图,这里我们画的横坐标是核间距，也就是这两个氢原子之间的距离，纵坐标是能量，我们看到的这是能量关于核间距的曲线-,这是一条普遍的曲线，在研究任何共价键时你都会遇到，我们马上就会解释一下它是怎么来的。

麻省理工公开课 - 化学原理课程节选

Now the two things to notice about this are the high spike that you have out here which occurs very rapidly and then the rapid decline in blood sugar, and insulin is involved in this whole reaction.

有两个需要注意的事情是,你们在这看到的急剧变化的曲线代表着,迅速上升和迅速下降的血糖,另外胰岛素也随之发生变化

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

If there were no credit markets, everyone would have to be on the production possibility frontier; there would be no other choice.

如果没有信贷市场,每个人的收入水平都会落在PPF曲线上,别无选择

耶鲁公开课 - 金融市场课程节选

for the most part, if stocks have done much better if you've bought them at a point that looks cheap on that graph than one that looks expensive.

如果你做得很糟糕的话-多半情况下，you've，done，poorly，if—,如果你通过市场曲线图,在看上去比另外一个时间点便宜的时候买进它们,而股票又表现得非常好。

耶鲁公开课 - 金融市场课程节选

Then, if n = 100--now I'm going to label this x differently, I'm now going to show the normal bell-shaped curve and I'm going to do this from 0 to .4.

如果n=100,现在我得重新标x值,我现在要画正态分布的钟形曲线了,在这儿用0到0.4

耶鲁公开课 - 金融市场课程节选

Let's create a graph here that on the x axis it's going to be time, so time zero will be when you first take in a food and then one hour later, two hours later will be shown as you go from left to right, and then we'll have blood glucose level up on the y axis.

我们在这建立一个曲线图,X轴代表的是时间,所以零时间点是你第一次进食的时间,然后一小时以后,两小时以后,是从左到右呈现在图表上的,在Y轴上是你的血糖值

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选