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FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

We give a brief proof of the existence theorem of Supremum and Infimum of a bounded set of fuzzy numbers given by Wu cong-xin and Wu chong in [30] . It is used to establish the monotone convergence theorem and the nest theorem of closed intervals on E〓,τ

给出了吴从忻、吴冲[30]得到的模糊数集的确界存在定理的一个简洁证明，并利用此定理在空间E〓，τ(l中建立了模糊数序列的单调收敛定理和闭区间套定理。

The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.

本文讨论了定义在上述非柱形区域中的半线性抛物方程零能控性，我们使用的方法主要是通过同胚映射将非柱形区域中的抛物方程转化为柱形区域中的抛物方程，再利用不动点方法得到半线性抛物方程的有关结果。

They provide the proof that you can only brag about.

他们可以为你只能自己吹嘘的事情提供证据。

Then, by way of supplementary proof, the apologist institutes an impartial comparison of Christianity with the various rival religious systems of the world -- Brahminism, Buddhism, Zoroastrianism, Confucianism, Taoism, Mohammedanism -- and shows how in the person of its founder, in its moral and religious ideal and influence, the Christian religion is immeasurably superior to all others, and alone has a claim to our assent as the absolute, divinely-revealed religion.

那么，透过补充证据，代言人院所一个公正的比较，基督教与各竞争对手的宗教系统中的世界-b rahminism，佛教， z oroastrianism，儒家，道家， m ohammedanism-表明了如何在人的，其创办人，在其道德和宗教理想和影响力，基督教宗教是不可估量优于所有其他国家，并单独有一个自称我们的赞同，因为绝对的，神圣的天启宗教。

No legal proof of this was obtainable , but Cowperwood was assumed to be a briber on a giant scale

关于这一点找不到任何合法的证据，但是柯帕乌确被认为是大规模行贿的人。

A briefer proof of Moshe and Hertz algorithm of DFT for the k-D case is given in this paper.

对于多维DFT的Moshe和Hertz算法，给出了一个更简短的证明。

Can you bring forward any proof of what you said.

对你所说的话，你能给出证据吗？

Can you bring forward any proof of what you said ?

你能为你所说的话提供证据吗？

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。