Government aid could be withdrawn too soon, worries Alexis Garatti of Euler Hermes, a trade-credit insurer.

贸易信贷保险公司Euler HermesAlexis Garatti担心，政府可能会过早取消援助。

Oh, an Euler's Disk! Fun! Yeah, we're seeing if Raj can hold his breath longer than it.

欧拉盘! 好玩诶! 是啊，们在看拉杰憋气时间能不能比时间长。

We need to calculate all the Euler angles that would cause the sun to hit the liquid helium.

们需算出所有欧拉角避免太阳直射到液态氦。

Euler first dismissed the question as having nothing to do with math.

欧拉起初认为这个问题与数学无关。

In mathematics do you look upon Euler, Laplace, or Gauss as fools?

在数学上， 你把欧拉、拉拉斯或高斯看成傻瓜吗？

Just lingering on that one, Euler's Identity.

- 只是徘徊在欧拉恒等式上。

Euler was a German mathematician, I think in the 1700s.

欧拉是一位德国数学家，认为是在1700年代。

Fortunately, Euler himself invented a new method.

幸运是，欧拉自己发明了一种新方法。

But the proof that I'd like to show you is very different from the one that Euler had.

展示证明与欧拉那个非常不同。

In physics suggested between different Calabi-Yau, suggested that you couldn't actually compute the Euler characteristic of a Calabi-Yau.

在物理学中，不同卡拉比-丘空间之间似乎存在某种对称性，这暗示着实际上无法计算卡拉比-丘空间欧拉特征数。

Because the Euler-Bernoulli beam regards the shearing stiffness as an infinite value.

因为 Euler-Bernoulli 梁将剪切刚度视为无限值。

Euler used this proof to formulate a general theory that applies to all graphs with two or more nodes.

欧拉利用这一证明，制定了一个遍适用于包含两个或更多节点所有图形理论。

In honor of Euler, whose hometown was Basel, this infinite sum is often referred to as the Basel problem.

为了纪念欧拉， 他家乡是巴塞尔，这个无穷级数常被称为巴塞尔问题。

So I conjectured maybe for every Calabi-Yau with the Euler characteristics positive, there's one with negative.

因此，推测或许对于每一个欧拉特征数为正卡拉比-丘流形，都存在一个欧拉特征数为负对应流形。

Is it possible that for every Calabi-Yau, there's one with the opposite Euler characteristics?

是否每一个卡比-尤空间都有一个欧拉特征数相反对应空间？

And as Euler pointed out, the total energy must be conserved.

正如 Euler 指出那样，总能量必须守恒。

He said, well, we know more Calabi-Yaus with negative Euler characteristics than positive.

他说，好吧，们知道具有负欧拉特征卡法利-尤空间比正多。

Therefore, the Euler-Bernoulli beam model has an enormous limitation in reflecting the dislocation deformation between adjacent rings.

因此，Euler-Bernoulli 梁模型在反映相邻环之间位错变形方面存在巨大局限性。

But Euler changed this into an integral, so it's the integral of mass times velocity integrated over distance.

是欧拉将其变成了积分，因此是质量乘以速度对距离积分。

The segmental lining ring was considered as a Euler-Bernoulli model, yet the shearing dislocation of segmental ring was excluded.

将节段衬环视为 Euler-Bernoulli 模型，排除了节段环剪切位错。