That’s called the kinetic energy density, and it’s the second term of Bernoulli’s equation.

这就是所谓的动能密度， 它是伯努利方程的第二项。

The first term in Bernoulli's equation takes that energy, and divides it by volume.

伯努利方程的第一项是 能量除以体积。

That's called the kinetic energy density, and it's the second term of Bernoulli's equation.

这称为动能密度， 它是伯努利方程的第二项。

We see some xi's from a Bernoulli distribution.

我们从伯努利看到了一些xi。

And then the variance of this Bernoulli distribution is going to be these two proportions multiplied.

然后这个伯努利的方差就是这两个样本比例的乘积。

The mean of this Bernoulli distribution is going to be P2.

这个伯努利的均值将是P2。

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

因为 Euler-Bernoulli 梁将剪切刚度为无限值。

The key is stability, and the essence is using aerodynamics, which is fundamentally based on Bernoulli's principle.

关键是稳定性， 而本质是使用空气动力，这从根本上是基于伯努利原理的。

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的位错变形方面存在巨大局限性。

Now with this definition of this-- and this is the most general definition of a Bernoulli Distribution.

现在有了这个定义——这是伯努利最一般的定义。

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

将节段衬环为 Euler-Bernoulli 模型，但排除了节段环的剪切位错。

The existing tunnel is equivalent to a continuous Euler–Bernoulli beam placed on a Pasternak foundation.

现有的隧道相当于放置在 Pasternak 基础上的连续 Euler-Bernoulli 梁。

The results showed that the Euler-Bernoulli model underestimates deformation but overestimates internal forces of tunnels.

结果表明，Euler-Bernoulli 模型低估了隧道的变形，但高估了隧道的内力。

The proper application of conservative Euler–Bernoulli beam theory can ensure the safety and stability of the tunnel to a large extent.

正确应用保守的 Euler-Bernoulli 梁理论可以在很大程度上保证隧道的安全性和稳定性。

A Euler–Bernoulli beam with a Pasternak foundation was used as a simplified model for tunnel stress analysis.

使用带有 Pasternak 基础的 Euler-Bernoulli 梁作为隧道应力析的简化模型。

In the method proposed in this paper, Euler–Bernoulli beams are used to simulate the bending deformation of existing tunnels.

在本文提出的方法，使用 Euler-Bernoulli 梁来模拟现有隧道的弯曲变形。

Nevertheless, scholars noticed that the Euler-Bernoulli model failed to indicate the dislocation between rings, while it widely occurred in in-service shield tunnels.

尽管如此，者们注意到 Euler-Bernoulli 模型未能指示环之间的位错，而它广泛发生在服役的盾构隧道。

A Euler–Bernoulli beam on a Pasternak foundation was used as a simplified model to analyze the stress of the existing tunnel.

使用 Pasternak 基础上的 Euler-Bernoulli 梁作为简化模型来析现有隧道的应力。

To figure out really the formulas for the mean and the variance of a Bernoulli Distribution if we don't have the actual numbers.

要推导出伯努利的均值和方差的公式，如果我们没有实际的数值。

And then we'll come up with general formulas for the mean and variance and standard deviation of this distribution, which is actually called the Bernoulli Distribution.

然后我们将推导出这个的平均值、方差和标准差的一般公式，这个实际上被称为贝努利。