证明

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

With a definite standard of proof, provided that the weight of proof met the standard, the factum probandum is to be proved and the burden of proof of parties is discharged, then the judge can regard the existence of the facts as the basis of judgment.

在一定的证明标准下，一旦证据的证明力达到这一标准，就认为待证事实得到了证明，即当事人卸除证明负担，法官可以该事实的存在作为裁判的依据。

A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs).

一个很好的例子，这是机器辅助证明了四色定理，这是非常具有争议的第一人数学证明基本上是无法核实由于人类的巨大规模，该项目的计算（如证明是所谓非surveyable证明）。

The first section introduces some basic concepts[9].The second section introduces Schmidt"s method of proving isoperimetric inequality [2].The third section introduces Hurwitz"s method [9].The fourth section takes from my tutors lecture notes.The method is due to REILLY [10].Finally,I make use of variational method to prove the circle among the curves of length L encloses the biggest area on the plane.

首先介绍了平面上的一些基本概念[9]，其次介绍了文献[2]中Schmidt证明等周不等式的方法，再次介绍了文献[9]中Hurwitz证明等周不等式的方法，然后介绍了导师吴发恩整理的文献[8]中REILLY的方法证明平面上的等周不等式[10]，最后我利用变分的方法证明了平面上等长的曲线围成的面积最大时为圆。

L,the SCHENECTADY COUNTY CLERK ,Clerk of the County of Schenectady ,and also Clerk of the Supreme and County Courts ,being Courts of Record held therein,do hereby certify that michoc'J Love whose name is subscribed to the Certificate of acknowledgment or proof of the annexed instrument ,and thereon written ,or whose name is subscribed to the annexed instrument ,and thereon written ,or whose name is subscribed to the annexed jurat,,was at the time of taking such acknowledgment,or proof,or of administering such oath oraffirmation ,a Notary Public –commissioner of Deeds in and for said County ,residing therein ,duly commis-sioned and sword and authorized by the laws of the State of Now York to take the acknowledgments an sworn and proofs of deeds of conveyances ,for land,tenements,or heredita-ments and to administer oaths or affirmations in said County ,And further,that I am well acquainted with the handwriting of said officer and verily believe that the signature to said jurat or certificate of acknowledgement or proof is genuine

l时， schenectady县秘书，秘书的县schenectady ，也是秘书的最高人民法院和县法院，法院的纪录，因此，特此证明michoc'j爱他的名字是订阅了该证书的确认或证明对所附文书，并就此写，或他的名字是认购所附文书，并就此写，或他的名字是认购所附朱拉特，，当时的考虑，如确认，或工作证明，或管理这类宣誓oraffirmation ，公证机构-专员的事迹，并表示，县，居住的地方，适当处长sioned和剑，并授权由该州的法律制定的，现在纽约采取认知，一种宣誓和实证的事迹运输工具，为土地，物业单位，或heredita 1912年和管理宣誓或誓词中说，县，并进一步，我熟悉的笔迹的表示，官に相信签字，以表示，朱拉特或证书的确认或证明是真实的

The existence of potential 〓、Ω is proved in linear functional space theories.

用线性函数空间理论证明了位函数〓、Ω的存在性；指出了现有文献在退化矢量位〓的唯一性证明中所存在的问题，并重新给予了证明；证明了位函数〓、Ω在导体与导体、导体与非导体界面上自然满足分界面条件；针对汽轮发机端部的轴对称涡流场，讨论了位函数〓、Ω的泛函及有限元代数方程组的形成。

One reason is that the model is an algebra method and it is based on the theory of minimal element. It can give more credible proof. Another reason is that the model tries to prove security of protocols, rather than check them. Thirdly, the model is simple and easy to use, and proof can be finished by manual. Moreover, graphic description makes its proof more comprehensible. Fourthly, there is much research work related to the model, which gives me a good springboard.

首先，该模型是一种代数方法，以极小元等理论为基础，可以给出可信度较高的证明；其次，该模型不是验证协议，而是试图证明协议的安全性；第三，该模型简单、易用，可以手工的方式完成证明，而且图形表示使其证明更加直观；第四，关于该模型有许多相关的研究工作，这为进一步工作打下了良好的基础。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

However,To prove Inequality with elementary method,we often create complex computational process. The second ,we will take full advantage of the knowledge of calculus Inquiry Testimony of inequality,and concluded the higher mathematics to prove Inequality several main method and its application conditions.Constructors in the context of the use of the monotone function,Calculus value theorem,function and the most extreme value,integral, it can be a very effective solution to the inequality problem proof. At last,we summed up several convenient and simple way to prove Inequality.It will be play a great role in our problem Solving.

但是用初等方法证明往往会造成复杂的运算过程，本文接着充分利用微积分的知识探究不等式的证明方法，并指出微分学和积分学在不等式的证明的具体应用，那就是在构造函数的背景下运用函数的单调性、微积分中值定理、函数的极值和最值、定积分，那么就可以十分有效地解决不等式中的证明问题，从而归纳出几种方便而又简捷的方法，这样对我们解题将会起到很大的作用。

Promote growth/understanding 211.in/out of proportion to 212.propose doing sth.

with a fine 241.make several purchases 242.on purpose 243.for…purpose 244.for purpose of 245.answer/ serve the purpose 246.pursue pleasure 247.push…aside 第 38 页共 50 页在进行中，在进展中禁止某人做某事许下/违背/遵守诺言履行诺言守约许诺某人某物答应做某事促进增长/了解和…相称，和…成比例建议…(比 suggest 正式)向某人求婚想要做某事勘探金矿探寻某人的新财富保护……免受环境保护向…提出抗议毫无怨言地为…而感到骄傲证明是，结果是证明某人，某事是证明某事证明…为某人提供某物为某人提供某物免费供给，为应付需要而提供如果心理测试青春期心理当众，公开地对公众进站/离站渡过难关推翻，摧毁穿上/脱掉靠边行驶因某事而惩罚某人处以罚金购买了几样东西故意地出于…的目的为了…起见达成目的寻欢作乐把…推到一旁高考词组汇编

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。