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By using the theories of conservation of momentum,conservation of energy and hydrokinetics,a mathematical model for describing the relationship among the fluid parameters,the formation parameters and the vibrant operation parameters was established.The analytic solutions of one-dimensional and radial transfusion equation for compressive and single-phase fluid flow through the compressive formation were obtained.The effects of each parameter on the vibrant operation were also gotten.On the basis of the above results,the computation models were established.

应用动量守恒、能量守恒、流体动力学等基本原理，建立了地层参数、流体参数和振动作业参数之间相互耦合的数学模型，求出了单相微可压缩流体在可压缩地层中的平面一维和平面径向渗流方程的解析解，得到了各项参数与振动作业效果之间的关系，为振动采油的数值模拟提供了初始压力分布表达式。

In this study, we adopt a Gauss-Markov hyetograph. We also propose a new approach for selecting regionalized representative design storm hyetograph in northern Taiwan. By combining the principal component analysis and cluster analysis techniques, we select five principal components and group design storm hyetograph into three categories in the study area. Finally, we employ the method of analytic hierarchy process to establish the regionalized representative hyetograph for northern Taiwan area.

本研究针对台湾北部地区提出一个新的方法来评估并建立区域代表雨型，首先选取各测站具尺度不变性之高斯马可夫雨型，其次利用主成份分析法萃取出雨型中的五个重要成份，并以群集分析法将研究区域内之设计暴雨雨型分为三个均匀群集，但同一群集内之雨型并非唯一，故研究中最后利用层级分析法进行评估，选取并建立出区域代表雨型。

By combining the principal component analysis and cluster analysis techniques, we select five factors and group design storm hyetograph into three categories in the study area. Finally, we employ the method of analytic hierarchy process to establish the regionalized representative hyetograph for Northern Taiwan area.

本研究针对台湾北部地区提出一个新的方法来评估并建立区域代表雨型，首先建立各测站具尺度不变性之高斯马尔柯夫雨型，其次利用主成份分析法萃取出雨型中的5个重要的控制因素，再就这些因素以聚类分析法将研究区域内之设计暴雨雨型分为3个均匀群集，但同一群集内之雨型并非唯一，故研究中最后利用层级分析法进行评估，选取并建立出区域代表雨型。

According to the relationship between hyperbola and its normal, the analytic equation is discussed.

根据双曲线与其法线的几何特征关系建立了求解法线的解析方程，分析了法线问题解析求解的繁杂性。

The third chapter discusses and proves Il"yashenko"s Theorem, that is, if every vertex on the polycycle of an analytic vector field in the real plane is hyperbolic, then limit cycles cannot accumulate on this polycycle.

第三章详细讨论和证明了Il'yashenko定理，即平面解析向量场的多边环上每一顶均为双曲奇点，则此多边环附近不能结集无限多个极限环。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

From theoretical viewpoint,Support Vector Machinesolution corresponds to the center of the lar- gest hypersphere inscribed in the version space,and Analytic Center Machinesolution corresponds to the ana- lytic center of the largest hypersphere inscribed in the version space.

1问题的提出支持向量机以其优越的泛化性能在机器学习和优化领域日益受到重视并得到广泛应用，其解对应于样本空间最大超球体的中心。

We also obtain the normal forms for a class of real analytic hypersurface in C^2, and the existence and uniqueness of the positive solutions of some quasilinear elliptic equations.

我们还研究了一类C^2上的实解析超曲面的规范型，以及一些拟线性椭圆型方程组正解的存在性和唯一性。

The analytic expression for such kind of hypersurfaces is given. Consequently, any umbilical Lorentzian isoparametric hypersurfaces of type Ⅱ with minimal polynomial^2 of A are the parallel hypersurface of M.

并且形算子A的最小多项式为(λ0a)^2的任何Ⅱ型全脐洛伦兹等参超曲面局部地与上述超曲面的平行超曲面叠合，从而完成了S(上标 n+1 下标 1)中的Ⅱ型全脐洛伦兹等参超曲面的分类。

Analytic personage says, the rhythm photograph that this and financial crisis affect to hypostatic economy is consistent.

分析人士说，这与金融危机对实体经济影响的节奏相一致。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。