证明

LIU Hui's Cyclotomic Method is one of the greatest achievements in the history of mathematics in China,even in the world,in which the special approach to understand the infinity and the method to solve it are presented.

有的著作认为在极限公式limx→0sinxx=1的证明中，要用到圆的面积公式S=21Lr，而对后者的证明中必须要用到重要极限limx→0sinxx=1，从而犯了循环论证的错误。魏晋刘徽的"割圆术"是对无限问题的独特认识和致用的处理方式，是为证明圆面积公式而设计出来的一种方法。

Provable Security is a formal method for proving the security of cryptographic schemes, in which the difficulty of breaking a particular scheme is formally related to that of solving a widely believed computational hard problem. Provable security has already become an important theme of theoretical researches in modern cryptography. This dissertation investigates the provable security of public-key encryptions and hybrid encryptions of asymmetric and symmetric encryptions. This includes the various formal security notions and the constructions can be proved to achieve them. Among the constructions, hybrid encryptions are themselves an important way to obtain public-key encryption schemes with chosen ciphertext security. The main results are as follows:(1) The one-wayness of the trapdoor one-way function in NTRU depends on the randomness of the session key, which is different from previous ones. Based on this observation, a new kind of trapdoor one-way function, trapdoor one-way functions with an auxiliary random variable is proposed.

可证明安全性是一种证明密码学方案安全性的形式化方法，它将密码学方案的安全性归约为公认的计算难题，已成为现代密码学领域中理论工作的主线，本文主要研究公钥加密与单双钥混合加密的可证明安全性，这包括它们的各种形式化安全性定义以及达到这些安全性定义的方案构造，而单双钥混合加密本身也是一种构造选择密文安全公钥加密的重要方法，本文得到的主要结果如下：(1)在研究NTRU公钥加密的特殊性基础上，对于公钥加密的陷门单向函数加密模型进行了扩展，提出了具有辅助陷门单向函数的概念，并将其扩展到多元的情况，讨论了可能的密码学用途。

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proofs on the subspace-lattice. Especially, one remarkable result is that a new q-analogue of the cube-sums identity is obtained with its combinatorial proof over the vector space.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从向量空间角度给出了一些恒等式的q-模拟及组合证明，其中突出的成果是给出了立方和恒等式的一个新的q-模拟及组合证明。

Its brand should be set up on perfect ecological economy, scientific -tech renovation, production standard for blackland green-food raw-material base and quality criterion as well as service. It establishes the safe-code product system, the Rule of Cold Zone Black Glebe Trademark Management and the Measure of Cold Zone Black Glebe Trademark Management, etc, editing the Name List of Cold Zone Black Glebe Specialties in brief introduction, nutritious index and edible instruction in Chinese -English version. It controls production in all aspects of base, farmer and enterprise to ensure the quality of named brand products.

寒地黑土品牌产品的内在品质源于建立健全了以生态经济为统领、生产技术标准、产品标准和服务标准体系，建立并推行了产品可追溯的产品安全码制度，制定了《寒地黑土证明商标使用管理规则》和《寒地黑土证明商标使用管理办法》、《寒地黑土证明商标使用权申请程序》等一系列的标准和执行制度，并编制了中英文对照，集产品简介、营养指标、食用方法于一体的《寒地黑土产品名录》，对生产基地、农户和相关加工企业的生产标准、产品质量进行"硬约束"，从而确保了寒地黑土绿色物产的产品质量和使用寒地黑土品牌的产品质量。

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。

The first part mainly focuses on the establishment purpose,theconcept and the basic content of burden of proof.

第一部分主要阐述了证明责任制度的设置目的、证明责任的概念和证明责任的基本内容。

Therefore,in order to simplify the proving process of these inequalities.Though reading a lot of relevant resource,we begin with the basic concept of math,and use an ingenious way――probabilistic method, which means that according to the main features of inequality theory,combining the basic concepts and formulas of probability,through creating one suitable probability model,giving some concrete meanings of random events or random variables,proving through probability theory,we discuss the Cauchy inequality,Class inequality,Jensen inequality,and several common inequality's proofs.

因此，为了简化这些不等式的证明过程，通过阅读大量的相关资料，本文从数学的基本概念入手，运用了1种巧妙的方法——概率方法，即根据不等式的主要特征，结合概率论的1些基本概念和公式，通过建立1个适当的概率模型，赋以1些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，讨论了柯西不等式，级数不等式，詹森不等式和几个1般不等式的证明。

On the basis of thorough introspectionof the popular viewpoints of "The claimer should give evidenceand"the shifting of burden of proof"among Chinese scholars,Iput forward my humble view of the standard of the share of burden ofproof,among which that"the civilcode enactment should consider theshare of burden of proof is alegislative proposal.

第十章是关于我国证明责任分配标准理论的反思与完善。在对我国学术界流行的"谁主张、谁举证"和"举证责任倒置"的观点进行全面反省的基础上，提出了建立与完善我国证明责任分配标准理论的拙见，其中"民法典的制定应考虑证明责任分配"属于立法建议。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了