数集

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

The property of the invariant set and measures dimension of the IFS are main objects in the studying of fractal geometry.

完备度量空间上迭代函数系统的不变集性质及测度的维数是分形几何研究的主要对象。

We show that for any subshift of finite type determined by an irreducible and aperodic matrix, there is a finitely chaotic set with full Hausdorff dimension.

指出：对于由本原方阵所决定的符号空间有限型子转移而言，存在满Hausdorff维数的有限型混沌集。

This Hubble Space Telescope composite view of the gorgeous island universe was released at this week's meeting of the American Astronomical Society as one of the largest Hubble images ever made of a complete galaxy.

这张由哈伯太空望远镜拍摄的宇宙岛组合影像，是在这星期举行的美国天文学会年会中发布的，它也是哈伯望远镜完整星系影像集里最大的数张之一。

The paper proposes two new dimension reduction algorithms: The First is On the Expected Distortion Bound of Direct Random Projection. The second is Anchor points based Isometric Embedding under least square error criterion. On the Expected Distortion Bound of Direct Random Projection has a time complexity of O.

本文分别提出了两种新的维数约减算法：(1)基于期望扰动的直接随机映像算法On the Expected Distortion Bound of Direct Random Projection，简称DRP(2基于锚点集的最小平方误差等距嵌入算法(Anchor points based Isometric Embedding under least square error criterion，简称AIE)。

In sample data, we use the database of Taiwan Finance Database of Taiwan Economic Journal and collect 14,125 company's' finance data which include 153 default company's' data to study. We use these financial data to make Variance Inflation Factor test, and use the result of credit scoring model to make Kolmogorov–Smirnov test and Receiver Operating Characteristic check. Finally, the conclusions are listed as following

在样本资料中，主要是用台湾经济新报中，上市上柜与曾经上市上柜公司资料库，其最后，整理出来的资料结果，共有14125笔公司财务资料可以进行完整的实证分析，违约公司资料有153笔；并将这此公司的财务变数进行线性相关变异数影响因子检定，并将评分模型所得出的结果进行K–S检定与ROC验证，最后再将评分结果进行集区分析以及评等稳定度的检定，其结果所得出的结果包括下列几点

A SCNN approach is applied to solve linear and eigenvalue problem of the model. The scale of training set of the neural network in this approach is found only relates to the dimension of element stiffness matrix.

研究并提出了采用SCNN算法用于该问题的线性和特征值求解，且该算法中神经网络训练集的规模仅与单刚的维数相关。

The data in LLE are optimized using the small world algorithm, and the shortest path and the local neighbor set clustering coefficients are used as the local parameters. As a result, the problem of the embedding distortion using only local linear patch of the manifold to define neighborhood in Euclidean space is effectively solved. Three groups of standard data sets are selected to test and to compare the efficiency and robustness of SLLE and LLE.

将复杂网络算法引入到流形学习中，利用小世界算法对LLE算法进行数据优化，并以最短路径和局部集群系数作为局部优化参数，解决了数据点不规则时以欧氏空间作为邻域判别标准在构建局部超平面造成嵌入结果扭曲的难题。

The B-spline finite element Methodis becoming increasinglyimportant due to the derivative continuity and local support propertiesof its basis functions.

B样条有限元法以其基函数具有导数连续性和局部支集性而越来越受到人们的重视。

The Mixed-Potential Integration Equation based Partial Element Equivalent Circuit technique, which converts a circuit layout into a lumped RLC element coupled network, has been widely used in the modeling of integrated passives.

然而，通过部分等效电路算法产生的集总器件网络往往具有数量十分巨大的节点数和器件数目。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。