嵌入定理

Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without conditions.

通过使用没有条件的极小极大定理，以及对最佳Sobolev嵌入常数的详细分析，得到了一些具临界Sobolev指数的半线性椭圆系统的真正非平凡解的存在性，并讨论了解的一些性质。

Debugging software is needed in the recognizing phase, it is used to watch the execution state, when all planted plane cubic tree structures are detected, they will be decoded into n natural numbers, and the original product of two prime numbers will be got through Chinese Remaining Theory.

水印的检测可以通过调试软件来实现，让调试软件监督嵌入水印的受维护程序的执行，当检测到全体n个PPCT构造后，将它们全体解码为n个天然数，最后应用中国剩余定理将这n个天然数还原出最初的两个大质数的乘积亦即最初的水印信息。

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我们讨论了具有自交数为+1的嵌入环面〓的4—流形的Donladson不变量，运用环面上欧拉数为-1的圆丛的单个不可约SU（2）表示给出了Donaldson不变量在环面表示的同调类上的一个粘合公式（定理2.4.1），这一结果补充了P。

The weight of an infinite continuous domain is equal to the of its Smyth power domain.

文献[5]、[6]提出了连续偏序集的定向完备化和嵌入基的概念，并且讨论了由此涉入的一些关系定理。

Channel capacity in information theory is used to analysis how many characters can be embedded in a certain size image on the base of zero error probability.

信息论中信道容量定理用于分析在零错误概率下一定尺度的图像中可以嵌入的字符数量。

It is shown that embedding reconstructions can be applied to time varying systems based on an observer approach.

摘 要：证实了在基于观察者途径的情况下， Takens的嵌入重构定理能扩展到时变混沌系统。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。