数集

The main results, obtained in this dissertation, may be summarized as follows:1. In chapter 2, the differential property of the optimal value function with a non-compact set is studied. The expression of its lower-Hadamard directional derivative is obtained.

第2章研究了非紧致集上最优值函数的微分性质，首先给出了最优值函数的Hadamard下方向导数的表达式，其次在最优值函数的有效域为非空凸集的情况下刻画出了次微分的表达式。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

At the beginning of this paper we are devoted to studying the equicontinuity on the set of periodic points. Later we are researching on the property of the invariant set and measures dimension of the self-similiar IFS.

本文前面一部分主要着眼于连续映射在其周期点集上的等度连续性的研究，后面一部分主要涉及到相似迭代函数系统不变集性质和测度的维数的研究。

Complicated system ; fractal ; nonlinear dynamics ; Mandelbrot set ; Julia set ; extension factor ; ternary number ; period-checking algorithm ; volume rendering algorithm ; equivariant map ; chaotic dynamic system ; synthesis of mechanism

国家自然科学基金；国家重点基础研究发展计划(973计划)复杂系统；分形；非线性动力学；可视化； Mandelbrot集； Julia集；变形伸缩因子；三元数；周期检测法；体绘制算法；等变映射；混沌动力系统；机构综合

METHODS: Human umbilical cords were processes within 6 hours with explantation technique, collagenase digestion and enzymes combination digestion after harvested, and followed by counted colony numbers. A colony contains more than 50 cells.

脐带采集后在6 h内分别用植块法、胶原酶消化法、胶原酶与胰酶联合消化法进行分离培养，于培养第14天计数集落数，超过50个细胞计为集落。

In Chapter One,we find the relationship between strong open set condition , Hausdorff dimension,the positivity of the Hausdorff measure and β space of graph-directed self-similar sets in complete metric spaces.

在第一章中，我们讨论了在度量空间中，图定向自相似集的强开集条件、Hausdorff维数，正的Hausdorff测度和β空间之间的关系。

First image and inverse image of refinement of semi-topogenous order on L been defined by GOH.

并由此得到一维非退化扩散过程样本轨道的象集和逆象集的Hausdorff维数。

We researched the number problem of isomorphism classes of finite groups with given element orders.

研究了"元的阶之集"为某些给定数量集的有限群同构类的类数问题。

In other words,an affirmative answer are given for the question on the set of factorization indicesof completely positive realizations of a graph raised by N.

关于完全正矩阵：本文给出圈的双非负实现为完全正的一个充要条件，并确定其非负分解指数和非负分解；证明完全正图的非负分解指数集没有缺数，换句话说，给出了关于图的完全正矩阵实现的非负分解指数集的N。

The study showed that spectra information can be extracted thoroughly by the pretreatment method of first derivative combined with standard normal variate, with the SEC of 0.002 5, SEP of 0.006 6, and determination coefficients of 0.988 4 and 0.922 7 respectively.

分析表明采用一阶导数结合标准归一化处理能最有效地提取光谱信息，此时PLS模型校正集决定系数与检验集决定系数分别为0.988 4与0.922 7，校正标准误差与预测标准误差分别为0.002 5与

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。