查询词典 imbedding theorem

The theorem seems to be so important and if we say that It has a very strong effect for almost 3-variable inequality, It's really incredible.

和definitally ，这是最大的关键，因为我们不需要使用任何中间阶段。上述两个例子可以证明了最小二乘分析方法，但在密闭的含义。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos theorem for convex bodies in higher dimensional Euclidean spaces,. Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos\' theorem for convex bodies in higher dimensional Euclidean spaces,.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

This Paper deals with problems of large number theorem in stochastic sense and obtains sufficient and necessary conditions,for weak law and strong law of large numbers in stochastic sense .

本文讨论随机大数定律，得到一个随机变量序列分别服从随机弱大数定律和随机强大数定律的充要条件。

The strong law of large numbers for the state frequency and the strong limit theorem of arbitrary function for the Markov chain field on the arbitrary Cayley tree are investigated.

主要研究任意Cayley树上马尔可夫链场的状态出现频率的强大数定律以及Cayley树上任意函数的一类强大数定律。

Thirdly, proper probabilistic model is built for the bilateral stop-and-go generator and the probability properties of its output sequence are studied. It is proved that the output sequence obey strong law of large numbers and central limit theorem and that, however, the distributions of 0 and 1 in the output sequence are imbalanced, which implies that this generator cannot be used as keystream generator directly. The rate of coincidence between the output sequence and corresponding LFSR sequences, together with their first derivatives are obtained, which reveal the existence of correlation between these sequences.

最后，建立了双侧停走生成器的概率模型，研究了双侧停走生成器输出序列的概率分布性质和大数性质，证明了生成器输出序列服从强大数定律和中心极限定理，得到了生成器输出序列中0，1分布是不平衡的结论，由此指出不能将这种生成器直接作为密钥流生成器；给出了双侧停走生成器输出序列和相应的线性移位寄存器序列之间的符合率以及一阶差分序列之间的符合率，得到了符合率的表达式，揭示了这些序列的对应比特和对应序列段之间存在相关性。

Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent; in addition, the output sequences of those combined generators are homogeneous Markov chains which are strictly stationary processes with ergodicity; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given.

我们的研究结论表明：虽然这些序列中随机变量之间不具有相互独立性，但它们的相关程度却比较低；证明了"停走"生成器，KM_1M_2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链；讨论了这些序列的概率极限性质，证明了它们均服从强大数定律和中心极限定理；还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次，分析了一般钟控停走组合生成器输出序列的概率分布性质，证明了生成器的输出序列是严平稳的，且服从强大数定律和中心极限定理；考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率，给出了符合率的具体计算公式；给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法，进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

By the Utev S.and Peligrad M.inequality of-mixing random variable sequence,we obtain the Hájeck-Rènyi inequality and three series theorem and Chung′s strong law of large numbers for-mixing random variable sequence,which extend and improve the corresponding results of Gan shixin and Wu Qunying,these resuls are consistent with that for independent random variable sequence.

不等式，得到了-混合随机变量序列的Hájeck-Rènyi不等式、三级数定理和Chung型强大数律，改进了甘师信与吴群英等人的结论，达到了与独立时一致的结果。

This thesis formulates a stable Control System based on Center air conditioning's structure and theorem.

本文就近年来出现的最为新型的远大户式燃气中央空调的控制系统进行了深入的研究，并且在实际中应用了模糊控制技术、集中控制技术、计算机网络控制技术、变频调速技术，实现了远程控制和与因特网的互联。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。