.. I computed the efficient portfolio frontier for various-- it's the efficient portfolio frontier using the formula I just gave you.
我计算了来自不同组合有效边界-,这一条有效投资组合边界,就是用刚刚给出的公式算出来的。
Whatever the mortgage rate is quoted, you substitute it into this formula and you find out what the square bracket thing is.
如果知道利率,你把它带入公式,就能得出方括号的数值
This formula doesn't tell you which way it's pointing, because it's a scaler; it's not a vector equation.
这个式子没有说明方向,因为这是一个标量而非矢量方程
Lithium has three electrons. If it loses two one remains. What is this formula telling us?
锂原子有三个电子,如果它失去两个,剩下一个,那么这个式子告诉了我们什么?
It is a condition for Hobbes of maximum insecurity where in his famous formula " "life is solitary, poor, nasty, brutish, and short."
对霍布斯来说,这是一种使安全感最大化的状态,这种安全感在他有名的公式中被表述,“生命是孤独的,贫穷的,肮脏的,残忍的,短暂的“
They grew the virus in monkey cell cultures, they purified the virus because you got to get all the other stuff from the cells that you're growing it in a way, they inactivated it by treating it with formalin which is just a formula-- it's just a mixture of Formaldehyde; Formaldehyde cross links proteins.
研究人员将病毒种植在猴细胞内,进行培养,并提纯病毒,在某种程度上,通过这种方法,可以得到所有类型的病毒,研究人员用福尔马林,处理病毒,使其灭活,福尔马林就是甲醛的水溶液,甲醛可以使蛋白质发生交联反应
The formula is-- I could write it this way: price equals one hundred minus this.
公式是,可以这样写,价格等于100减去这些
To actually apply this it helps to go to something called the normal approximation to the binomial, because it's kind of difficult to compute this formula.
在实际应用这些公式的时候,需要运用二项分布的正态近似定理,因为二项分布公式的值很难计算
A peculiar property of this is that the mortgage balance falls slowly at first and then it gradually picks up; it's just a property of this formula.
其中一个特别的性质是,刚开始抵押贷款余额降得很慢,渐渐的,越降越快,这就是这个公式的性质
He quantified it by this formula.
就是这个公式。
So you cannot use the formula once it hits the ground because once it hits the ground, the fundamental premise that a was a constant of -9.8 or -10 is wrong.
当物体落地以后,该公式就不适用了,因为当物体落地后,公式的基本前提——,加速度为常数-9.8或-10——就不成立了
You guys probably know that too from your days at the daycare, but I want to derive the formula and put it up, then we'll see how to use it.
你们可能从幼儿园起就已经知道这个式子了,但是我想重新推导一遍,再来看如何进行运用
It seems like a logical extension of that formula to three assets and you can easily see how to extend it to four or more assets, it's just the logical extension of that.
这样就将前个公式推导为三个资产的情况,显而易见,你们可以将其运用到四个乃至更多资产的情况下,这只是对原始公式一个推导罢了。
I'm not going to expand on this because I can't get into-- This is not a course in probability theory but I'm hopeful that you can see the formula and you can apply it.
我不准备拓展这一部分,毕竟这节课不是概率论,但我希望你们能记住这个公式,并且学会应用
By doing it, I got this formula.
这样一来,我就得到了这个式子
Well, there's a formula that's been used by bond traders for hundreds of years and it's a traditional expression, which goes from the discount rate to the price.
这里有个债券交易商,用了上百年的公式,这是个传统表达式,它能用折扣率算得价格
The boy would go say, we're offering to pay a discount rate of 2.51-- that was the formula and then anyone could do these calculations; they knew what it meant.
小男孩跑去说,我们愿意以2.51%的折扣率买入,公式就是那样用的,每个人都能算出价格,他们知道是什么意思
They go back to this formula. If you sold it after five years, then there are twenty-five years left, so 25 x 12 is the number of months left; they plug that into this formula.
如果五年后卖掉房子,他们又搬出公式,此时剩余期限是20五年,所以剩余月份数是25乘以12,把月份数代入这个公式
They would pull out your entire life history of contributions-- they had it because you had filed it all at the post office and everything was bureaucratic and efficient-- and they calculated, according to a formula, what you would get.
政府会取出你这一生的交保记录-,这是由你自己在邮局填写的,所有的一切都行之有效-,然后他们根据公式计算你能得到养老金。
When you retire--you can actually get it now, electronically, your entire employment history, all your contributions-- when you retire, there will be a formula-- you can find it on the Social Security system website-- which resembles the formula that they did in 1889.
现在你退休之后可以自动得到,你这一生的工作情况,还有你全部的投保记录-,当你退休的时候-,你可在社会保障体系网站上找到一个公式-,类似于1889年使用的那个公式。
It's very important to understand that the mortgage balance is recomputed, according to this formula every month and they will send you a statement showing how your mortgage balance is falling.
根据这个公式 抵押贷款余额,每个月都要重新计算,理解这一点非常重要,他们会给你寄对账单,告诉你抵押贷款余额减少的情况
Your mortgage payment is constant through time but the fraction of it that goes to paying off principal versus interest changes through time and it just changes as dictated by this formula.
抵押贷款每月还款是固定的,但是其中本金和利息的比例关系,会随时间而改变,这是由这个公式所决定的
No, it's an exact formula.
不,这是精确等价的
Therefore, mathematically at a given time t, we can trade t for v and put it into this formula.
因此,从数学角度来说,在给定的时刻 t,我们可以用 v 来表示 t,并代入这个式子
Then you take that formula here and you put it here, that will see a times t, you put this expression.
你再拿这个式子,把它代到这里,这里就有at,带入表达式
It will typically look like this and the formula we say is F = - kx, where k is called "The force constant."
图像看上去一般就像这样,对应的式子是 F = - kx,k 叫做"弹性系数"
, r1, and r2 for those and I plugged it into that formula, which we just showed.
我计算了σ1,σ2,r1和r2,I,computed,the,σ1,,σ,代入我们刚刚展示的公式。
Once you've got that, one derivative will give you the velocity, then in a crunch you can eliminate t and put it into this formula.
一旦你得到了这个,求一阶导数就能得到速度,然后你可以消去t,把它代入这个式子
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