可证明的

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

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。

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

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。

In section one, we introduce some background of the topic, in section two we review some basic and recent results about the structure and hierarchies of the computably enumerable degrees which are closely related to our topic- the algebraic structure of the plus cupping Turing degrees, in section three, we outline the basic principles of the priority tree argument, one of the main frameworks and tools of theorem proving in computability theory, and in section four, we prove a new result concerning the algebraic structure of the plus cupping Turing degrees that there exist two computably enumerable degrees a, b such that a, b ? PC, and the join a V b of a and b is high.

度结合为0′。本篇论文分为4个部分：第一部分介绍了这个领域的一些背景知识；第二部分主要回顾了前人在研究可计算枚举度的结构和层谱时所取得的一些基本和最新结果，这些结果与我们的主题—加杯图灵度的代数结构密切相关；在第三部分中，我们概要的描述了优先树方法的基本原理，此方法是可计算性理论中定理证明的一个重要框架和工具；第四部分证明了一个加杯图灵度代数结构的新结果：存在两个可计算枚举度a，b，满足a，b∈PC，而且a和b的并a∨b是一个高度。

This dissertation proves that the class of monotone increase functions is PAC solvable while the class of single peak functions is non-PAC solvable under a GA with reproduction and a mutation operator which mutate according to a pre-set order.

本文提出了概率意义上近似收敛可解的概念，并证明了随机行走和狄拉克δ函数都是非PAC可解的，证明了任何问题在只有杂交算符或变异算符的遗传算法下都是非PAC可解的。

In Chapter 2, we show that Xi 3 for all planar graphs of girth not less than 4 which contains no 5- and 6-circuits or contains no 7- and 8-circuits or contains no 8- and 9-circuits, we also show that Xi 3 for each planar graph of girth not less than 4 which contains no 6-, 7- and 9-circuits.

在第二章，论文证明了每个围长至少为4且不含5-圈和6-圈或7-圈和8-圈或8-圈和9-圈的平面图是3-可选色的。同时还证明了每个围长至少为4且不含6-圈，7-圈和9-圈的平面图是3-可选色的。

If you hope the certificate, when seeks for the Fermat's theorem with ten year the primary proof defeat to be possible to come back, you definitely may prove, from the Maxwell time, these smatters to mathematics the human in starts with more and more complex mark cover mathematics thought insufficiency, hides constructs the natural law in the studio, gains God's favor.

如果你希望证明，当用十年的时间寻找费马大定理的初等证明的失败可回来，你完全可证明，自麦克斯韦时代起，那些对数学一知半解的人就在开始用越来越复杂的符号掩盖数学思维的不足，躲在书房里构造自然规律，获取上帝的宠幸。

Factor's Act 1889）的第一条也对document of title to goods下了定义,并强调了货物的占有权和控制权,具体如下:"the expression of document of title shall include any bill of lading, dock warrant, warehouse-keeper's certificate, and warrant or order for the delivery of goods, and any other document used in the ordinary course of business as proof of the possession or control of goods, or authoring or purporting to authorize, either by endorsement or by delivery, the possessor of the document to transfer or receive goods thereby represented."

以此为立足点，该学说认为提单的持有和转让与货物所有权的拥有和转移在许多情况下是完全脱节的，提单的转让只是转让货物的推定占有，并不带来货物的所有权的必然转移；即使在国际贸易的运转程度中，提单也完全没有成为或强化为物权凭证的必要。因此，把提单说成是物权凭证是一场历史的误会。提单作为海上货物运输单证的一种，除了是海上货物运输合同以及货物已经由承运人接收或装船的证明外，它只能是一种可转让的权利凭证，即据以向承运人提取货物的凭证。

The change of pace might have gone but everything else is intact and, arguably, functioning better than ever – witness the deft right-footed pass that Rooney converted.

他的变速或许已经不复存在了，但其他的能力还都完好的保存着，当然还有一点，也是可证明的一点，那就是现在他在场上的作用比以往任何时候都要好——比如助攻鲁尼的那次右脚灵活的传球。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。