证明性的

In chapter 5,we persue the ctiticality and complexity of thecritical sets.We describe carefully the Whitney's example in 1935.Meantime,we introduce some rsults about the critical sets and thecritical value sets,in particular,on W-sets and C-sets.And usingthe Lebesgue density theorem and the Vitali covering lemma weprove a rank zero theorem with Hausdorff measures.Finally wegive some examples to prove our results are sharp in the sense thatthe numbers k,m,n,s,〓,etc.,in the hypothesescan not be improved.

第五章研究临界点集的临界性和复杂性，并详细地描绘了Whit-ney在1935年的例子，同时也介绍了关于临界点集和临界值集的一些结果，尤其是W-集和C-集的一些结果，并利用Lebesgue密度定理和Vitali覆盖引理证明了一个与Hausdorff测度相关的秩零定理，最后举例证明我们的结果在定理的假设中的那些数字如k，m，n，s，a，r+/等不能被改进的情况下是最佳的。

In 1960's, the famous statist,named Moore, proved the asymptotic normality of one kind of linear order statistic. While Hajek gained the equational condition of the asymptotic normality of rank statistic.

早在二十世纪六十年代，Moore构造了一种较为一般的线性次序统计量，并证明了它的渐近正态性，而Hajek也得出了著名的Hajek基本定理，找出了线性秩统计量渐近性的一个充要条件。

It is proved that if a homeomorphism f on a compact metric space with the POTP is distal homeomorphism, then f does not have the average shadowing property.

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性，并给出了有平均跟踪性的同胚是极小的一个充分条件。

Finally, this paper proves the algorithm reliable in robustness, imperceptivity and safety by analyzing and comparing the datum from many attack experiments.

最后，本文通过对多个"攻击实验"的数据进行分析和对比，证明我们的方法在鲁棒性、不可见性和安全性等方面是可以信赖的。

The Diels-Alder cycloadditions of [60] fullerene for preparation of optical limitingmaterials are discussed in chapter 3 and 6. Soluble cycloaddition derivatives of 〓aresynthesized by the reaction of 〓 with indene,1,1'-biindene andcyclopentadiene derivatives.〓Particular, the Diels-Alder cycloaddition of 〓 with1,1'-biindene under controlled conditions affords the stable monoadduct 〓〓of novel structure, which was confirmed by HPLC, FTIR, FD-MS,〓NMR,〓 NMR, HMQC and HMBC spectra, Its two bridgehead cage carbons resonate at70.91ppm, The 〓 NMR spectra showed 38 lines consistent with the 〓 symmetryassociated with [6,6] addition. The 〓 shows similar optical limitingproperties to that of 〓 in toluene for 8ns laser at wave length 532nm. Moreover, thehigh solubility of this adduct in polar solvents such as THF, acetone enables itsincorporation into sol-gel glass matrix. The thin films prepared via the sol-gel methodshow improved OL behaviour compared to those of 〓. The langmuir-Blodgett filmformation and uv-visible absorption of 〓 are also investigated. LBmonolayer of this compound is prepared on the air-water interface at 〓 mol/l. In chapter 4, three water-soluble derivatives of [60] fullerene: fullerol(1), theaddition product (2)of fullerol (1)with polyvinylpyrrolidone and fumaric acidderivative of 〓(3) are synthesized and characterized.

通过Diels-Alder环加成反应，用茚〓和1，1'-联茚〓及取代茂合成了一系列可溶性的〓环加成衍生物，发现可控制反应条件，使1，1'-联茚与〓反应，并高产率地得到具有新颖结构的单加成物，用HPLC、FTIR、FD-MS 及〓、HMQC、HMBC等多种波谱技术对其结构进行表征，测得它的两个〓杂化的桥头碳的化学位移为〓ppm，证明生成的衍生物为6∶6闭式环加成，〓NMR谱中共给出38个信号，表明〓联茚衍生物分子具有〓对称性；在波长532nm，脉冲宽度8ns的激光下，〓联茚衍生物的甲苯溶液的光限幅性能与〓的甲苯溶液相近，由于〓联茚单加成衍生物熱稳定性好，在四氢呋喃，丙酮等极性溶剂中溶解性好，能分别均匀地掺入溶胶-凝胶中，已发现它的溶胶(so1)光限幅性能优于纯〓的光限幅性能；使用Langmuir-Blodgett技术将〓联茚衍生物在空气和水的界面进行了LB单层膜和多层膜实验以及UV-Vis吸收谱研究，通过等温压缩曲线测试，证明浓度为〓〓时，〓联茚衍生物能够形成单层膜。

The theory of scientific understanding is based on the intelligibility of world.

"世界的可理解性"是科学理解得以成立的前提和基础，而对这种可理解性的证明来自于"体用不二"这一本体论承诺。

Then we prove a nonsmooth minimax theorem by usingsome relative results about multi-valued maximal monotone mappings. Finally, we construct a nonsmooth minimax network to search for thesaddle points of the saddle functional. We have also proved that thetrajectory of the network is asymptotically convergent to thesaddle point of the saddle functional by usying Lyapunov function.

我们先介绍有关Clarke的广义梯度，次梯度及鞍泛函的有关结论；然后利用多值极大单调映象的满射性结果证明了一个非光滑的minimax定理；最后建立了一个非光滑的minimax神经网络来求解泛函的鞍点，并在一定的条件下构造出LYAPUNOV函数来证明网络的轨道渐近收敛于鞍泛函的鞍点。

Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type were proved.

该文给出了双调和型抛物方程初值问题解的Schauder估计，并且在适当的空间中证明了解的存在性与惟一性。

The stuff in between, including the internal Lemma, is there only to prove there exists an injective map from the group of rational points on an elliptic curve to the group of points over each finite field of prime order not dividing 2D where D is the discriminant.

证明中间的引理，主要是证明椭圆曲线上有限阶有理点到有限域上椭圆曲线的点之间的嵌入映射的存在性，其中点的阶不整除两倍的判别式2D。

In this paper, we propose an evaluating scheme for embedding security of NLW, define ideal undetectability, and design ways to construct an inter-proof system for undetectability against specific detector.

本文中，我们提出了一个自然语言水印嵌入安全性的评估方案，定义了理想不可检测性，并提出了构造针对特定检测器的不可检测性的交互证明系统。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。