证明性的

Then, a self-certified anonymous proxy signature scheme based on the view of self-certified public key policy and the scheme of anonymous proxy signature are proposed. The proposed scheme not only lightens the burden of verifier, but also has characteristics such as anonymousness and trackability.

然后，结合自证明公钥体制和匿名代理签名，设计出一种自证明匿名代理签名方案，此方案不仅能减轻验证者的负担，还具有匿名性和可跟踪性的特点。

The details of proving the completeness theorem of formula system L~*, which is given by Prof. Wang, are reviewed, and the proving of strong completeness about L~* is analyzed and revised.

考察了形式系统*完备性的现有证明过程，并对其中所涉及的R0代数同构问题进行了研究，分析了关于*系统强完备性证明中的错误并给出了一个全新的修正证明。

Currently all the previous researches about deniability in group key establishment protocols were based on the Random Oracle assumption.

给出了一个标准模型下可证明安全和可证明可否认性的高效的群密钥协商协议，并基于DDH假设和伪随机函数集的存在性假设一同给出了其安全证明和可否认性证明。

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。

By introducing the generatingfunction method,the integrability of FDIHS is proved,which is thesimplest way we know so far.

通过引入母函数方法，较简洁地证明了系统的可积性，包括守恒积分族的对合性与独立性，其中关于对合性的证明是迄今为止最为简洁的证明。

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。

The payoff function v thus defined is proved to have supperadditivity,and the Shapley value so defined proved to satisfy axioms such as efficiency,symmetry,dummy and additivity.The fuzzy Shapley value method for profit allocation in enterprise coalitions was thus given by examples.

并证明了支付函数v具有超可加性，以及Shapley值满足有效性、对称性、哑元性与可加性的公理体系，实例证明了企业联盟收益分配的模糊Shapley值方法。

Tolksdorf [62] to prove the weak solutions of equation (2) are of C1,a if fand u are bounded with the help of some results in [40]. And by Morse iteration,we prove that the solutions are of C1,a even if f is of critical growth.

Tolksdor[62]的方法以及[40]中的一些定理证明了方程(1)弱解的C1，a的正则性；当f满足临界指数增长时，应用Morse迭代，我们首先证明了解的有界性，然后证明方程(1)的解也有C1，a的正则性。

Since the commutators of both sing-ular integral operators and fractional integral operator with BMO functions areone of the special cases of〓,so the discussion of the boundedness of〓notonly gives a new proof of the boundedness of the two commutators,but al-soweakens some of restrictions into discuss the problem,thus it impro-vessome of results inwith the method of complex analysis,show-ed boundedness of〓,then directly obtained boundedness of the commutato-rs of fractional integral operator with BMO functions.

既然奇异积分算子和分数次积分算子与BMO函数的交换子是其特殊情形，所以〓的有界性的讨论不仅给出了中关于这两类交换子有界性的一个新的证明，而且减弱了中讨论这一问题时对齐型空间所作的限制，从而改进了中的结果（利用复分析的方法，先证明〓的有界性，从而直接得到分数次积分算子与BMO函数的交换子〓的有界性。

This is the evidence to prove the four standards to be achieved, that is confirmed with each other, not contradictory, and closed the chain of evidence to prove the uniqueness of the conclusions.

足以证明是指这种证明要达到四项标准，即相互印证性、不矛盾性、证据锁链的闭合性及证明结论的唯一性。

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。