1·After 10 years of research, they proved earlier this year that a curved shape called a hyperbolic paraboloid, which they and others had been folding for years, doesn't actually exist.
经过10年的研究，他们在今年年初证明了他们以及其他人已经折了好几年的一个叫双曲线抛物面的曲面实际上并不存在。
2·That is just going to be, if you look at this paraboloid from above, all you will see is the unit disk so it will be a double integral of the unit disk.
这就会变成…，如果俯视这个抛物面，所看到的就是单位圆盘，这就应该是单位圆上的二重积分了。
3·Let's say that what I wanted to know was not actually what I computed, namely, the volume below the paraboloid, but also the negative of some part that's now in the corner towards me.
我们想要的，并不是计算出来的结果，结果不只是抛物面底下的面积，也包含了，负值的部分。
4·Of course, I didn't tell you which way I am orienting my paraboloid.
当然这是因为没给出抛物面的的正方向。
5·Adopting paraboloid model of tip surface, presented the dynamics equation of negative ion flight in tip field and solve it with numerical method.
采用针尖的旋抛物面模型，给出了表面生成的负离子在针尖场中飞行的动力学方程，并用数值方法求解。