环面函数

In the present paper, we shall show that there are many elliptic invariant tori of the equation for a given analytic potential which is not necessary to be constant.

在这篇文章中，证明对于给定的解析势函数，不一定是常数，方程存在许多椭圆不变环面，与 Kuksin 和 Poschel 的文章不同的是，不变环面上承载的是高频的拟周期解。

In Kuksin's the monograph, assuming the potential depends on n-parameters, he showed that the Schrodinger equation with Dirichlet boundary condition possesses many invariant tori for "most"(in the sense of Lebesgue measure) parameters.

Kuksin 在他 1993 年的专著当中表明，对于依赖于参数的势函数来说，满足 Dirichlet 边值条件的非线性薛定谔方程，对于大多数(在 lebesgue 测度意义下)的参数，存在许多不变环面。

However, one does not know if there is any invariant torus of the schrodinger equation for a given potential.

然而对于某一给定的势函数，不变环面还是否存在并不清楚。

We also define two families of functions, named a torus height functionand an AdS-distance-squared function respectively, and use them to investigate thesingularities of the AdS-null surfaces and the torus Gauss images as applications ofsingularity theory of functions.

作为函数奇点理论的应用，利用这两个函数族来研究AdS-null曲面和环面高斯像的奇点。

In the transmission mechanism of optional drive ratio worm crank pin,the circular pitch of annulus worm changes from the function of optional drive ratio.When the annulus worm tums equably,the roll-pin crank brings shift tuming through joggling,and it can applly to dumping and turning mechanism of ladle.

变传动比蜗杆曲柄销式传动机构，其环面蜗杆的齿距是依变传动比的函数关系变化的，当环面蜗杆匀速转动时，通过啮合使滚销式曲柄产生预期的变速转动，可应用于铸造生产的铁水浇包的倾转机构。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。