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Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对"中间点"的渐近性进行了研究，得出了一系列"中间点"的渐近性的结果，概括了有关文献对微分中值公式的"中间点"的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

In theory,based on the theory of actio libera in causa,we can conclude that the casual acts can not influence the hit-and-run behaviors;in practice,case review should be based on proofs,as well as dependence on the development of related judicial authentication.

在理论上以原因自由行为理论为基础，可以得出原因行为对逃逸行为已失去支配力；在实践方面，审查案件要以证据为基础，还要依赖于相关司法鉴定的发展。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis. This method overcomes the difficulties and limitations resulting from others. It shows that solving problems in analysis by probability theory has a bright future both in theory and practice.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

Chapter 2 is started from the basic theory of elastodynamics, the zero and the first order reflection and transmission coefficients of rough interface are derived in theory, and some numerical examples are given. Also dispersion characters of diffraction waves are discussed in the case of micro-rough interface in deep layers.

第二章从弹性动力学的基本理论出发，通过求解波动方程的定解问题，从理论上导出了地震波在粗糙界面上的零阶和一阶反射透射系数，并给出了数值算例；该章还讨论了深层微粗糙界面的绕射波的频散特征。

This paper not only in theory, but theory into practice, through the way of cases, the problem of common crime more detailed classification, through analysis of typical cases, and in different list for circumstance, common crime of general solution of this proposition, in order to make innovations.

本文并非单纯进行理论的阐述，而是理论融于实践，通过案例的方式，对加重犯的共同犯罪问题进行更为详细的分类，通过典型案例的列举与分析，在不同情况下，展开对加重犯的共同犯罪这个命题的一般解法，以期有所创新。

The results are identical with the variation of the factual size of particles. By the viable datum, the average size of particles in the cross section is calculated in the dilute phase area of Circulating Fluidized Beds riser.We successfully apply the two-fluid model and kinetic theory of granular flow studying the two dimensional dense gas-solid flow characteristics in the large scale circulating fluidized beds and the cold experimental system with PIV.

在对高浓度气固两相流的研究中，根据FLUENT软件现有的条件和解决工程实际问题的需要，采用单气固相双流体欧拉模型，采用模拟紊流固粒流中普遍接受的方法"颗粒流的运动理论(kinetic theory of granular flow)"，对大尺度循环流化床进行了二维数值模拟，与他人数值模拟结果和实验结果进行了对比，检验模型的准确性。

An integrated Hamiltonian theory was constituted in Classical Mechanics and applied to studying the form of Lagrange equation in theory of electromagnetic, the Schrodinger equation and the Liouville theorem in statistical Physics.

经典力学利用Hamilton系统建立了一套完整的Hamilton理论，用以研究电磁场理论的拉格朗日方程形式，薛定谔波方程，统计物理学中的Liouville定理等。

We give left and right prediction of jump detection on basis of orthonormal polynomial. In theory analysis, we first give some theorems, then to proof the approximation, which is in a jump point detection by nonlinear prediction, can arrive one to number of samples. This result is considerable well. In the meantime, we study the approximate theory of measurement of jump point.

在理论分析中，我们首先给出了几个引理，然后证明了非线性预测法在检测单个突变点的逼近程度达到样本数的分之一，这样的结果是比较好的。

This paper first analyses and summarizes the ststus quo and evolution trend of encryption, some common used cryptograph are introduced, including the algorithms used in symmetric cryptosystem and asymmetirc cryptosystem. We describe the theory of each algorithms and compare the elliptic curve cryptosystem with the other two asymmetric cryptosystems to show the advantages of this algorithm. Second, the principle of ECC is discussed, including the math foundation of ECC, basic conception of elliptic curves, constructiong idea of ECC, operation on the elliptic curve and so on. Third, the current attacks of ECC were analyzed deeply, and an algorithm based on limited prime number field was constructed. We analyzed its realizability in theory, and implement it by using certain function of MIRACL software package. Latter half in this paper, the implementation model of a simple elliptic curve encryption system which based on GF has been introduced. The paper also put a deep analysis on the algorithm of point addition and point multiplication.

本文首先对密码技术的发展现状及其发展趋势进行了分析和综述，详细的介绍了私钥密码系统和公钥密码系统的发展，说明各种算法的原理和优缺点，并给出了一些典型的密码体制的简要分析，重点将椭圆曲线算法与其它几种公钥密码算法比较，说明椭圆曲线算法的优势；其次，探讨了椭圆曲线密码体制的原理，包括椭圆曲线密码的数学基础、基本概念、椭圆曲线密码体制的构造思想等问题；第三作者对椭圆曲线的攻击现状作了详细的分析，针对所使用的大素数域F_p，设计了素数域上安全椭圆曲线产生的算法，从理论上做了可实施性分析，从软件上做了具体实现；在本文的后半部分，提出了一个简单的基于有限素数域上的椭圆曲线加密方按算实现模型，并对SECES中设计的点加和点乘运算进行了深入分析。

In theory, the artist in their optical theory of natural sciences as a guide, to color in painting the real picture with the intrinsic link between the analysis of rational, scientific reproduction; expression of "an instant impression" to pursue, but also more appropriate From painting to convey the inner feelings with visual impression, and this varies from person to person and is also a sensory impression of a certain subjective.

理论上，画家们以自然科学中的光学理论为指导，对色彩在绘画与实际景象之间的内在联系进行理性的分析，科学的表现；表达上，对"瞬间印象"的追求，又更加适宜于传达绘画者的内在感受与直观印象，并且这种感官印象也是因人而异而带有一定主观性的。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。