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A polynomial system PS over the rational number field is constructed from the formula...,in a given many-valued logic system such that follows from ...,iff the algebraic variety defined by PS is empty, iff the idealenerated by PS is trivial.

由给定的多值逻辑系统中的一组公式，。。。，，出发，构造出了一组有理数域上的多项式PS，使得是，。。。，的逻辑结论，当且仅当PS定义的代数簇为空集，当且仅当PS生成的理想是平凡理想。

I picked up things, a pencil, an empty bottle, marveling at the beauty and aliveness of it all.

我拿起东西、一只铅笔、一只空罐子、惊叹于它的美丽和活泼。

Three envelopes, and when they're empty, I've spent my allotment.

当这三个信封一空，我就不再乱花钱。

But there's no reason to abandon your newfound allure in some empty hotel room.

但是没有理由放弃你在一个空空的旅馆房间里吸引你的新发现。

He's been by to visit their son. Alphonse, and he walks her through the now dark and empty courtyard to a cab.

他顺道去看他的儿子安丰斯，他和她走过黑暗空旷的庭院到出租车。

In the saint palace of the 帝 sand, believe many worship to hang to get empty in the half of work properly the coffin, two people see eyes certainly is foolish, the William is presumptuous to take off the precious stone on the altar, working properly the coffin to lose the buoyancy 堕 ground to smash immediately.

在帝沙的圣殿中，信众膜拜悬于半空的灵棺，二人看得目定口呆，William斗胆摘下祭坛上的宝石，灵棺立即失去浮力堕地粉碎。

You fill an empty sardine can with Cheerios and cross wire it to your alternator...

您填写一个空洞的沙丁鱼可以与cheerios和跨线到您的发电机。。。

It now appears that Amalthea's density is only about the same as water and since it is unlikely to be composed of ice it is most likely a loose rubble pile with a lot of empty spaces.

与木卫一类似，木卫五辐射出的热量比从太阳处收到的多（可能是因为木星磁场感应出的电流的关系）。

But to have good repute amidst such a world as this is an empty thing.

是为了在这样一个空洞的世界里有一个好名声。

You can only go in just one time, Perishable long and short life, if not to life many of the breeding to resort to emotional funeral music, life would become an empty skull.

你说在这仅仅只能走一回，漫长而又短暂易逝的生命中，如果不将生活中滋生的许多哀乐情感诉诸笔端，人生将变成空洞的骷髅。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。