极值函数

In fourth chapter of this paper,we mainly investigate the properties of a subclass S_p~* of starlike functions of orderα,including its coefficient estimate,distortion theorem,closure theorem and extreme points theorem.

在第四章中，我们主要研究了α次星形函数一类子族S_p~*的性质，包括系数估计，偏差定理，闭包定理，极值点定理。

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。

There are totally five chapters in the paper. Chapter 1 is the introduc-tion,and extreme value theory and methods and modelling for returns fat tails are introduced systematically in Chapter 2.This chapter also presents mean excess function and de Haan's moment estimate to decide on the reasonable exceedance threshold. Chapter 3 describes in detail non-linear time series mod-els such as GARCH models and the corresponding statistical inferences,and it also gives modelling and statistical analysis methods for returns series. Chap-ter 4 uses the models in Chapter 2 to analyzes the daily returns for Shanghai complex index and Shenzhen complex index in the Shanghai and Shenzhen stock markets. Chapter 5 applies the models in Chapter 3 to the volatility analysis of the two stock indices returns.

论文总共五章：第一章是引言部分；第二章系统介绍了极值理论方法和收益率厚尾的建模方法，给出了平均剩余函数法和de Haan矩估计相结合的方法确定合理的超越门限；第三章详细论述了非线性时间序列模型GARCH类模型及其统计推断，并且给出了收益率时间序列波动的建模和统计分析方法；第四章利用第二章的模型对国内沪深两市大盘指数上证综指和深证综指日收益率数据分布的厚尾进行了实证分析；第五章将第三章的模型应用到两个股指日收益率时间序列的波动分析。

The particle swarm optimization combined with the immune calculated extremal function optimization.

详细说明：将粒子群算法与免疫结合，计算函数的优化极值。

This article takes calibration data of assorted pressure gauge and jack of Qingfeng Bridge in Ningbo for example. According to that the quadratic sum of deviation in actual value and trend value has the minimum and extremal condition of the function,that is least square method.

本文以宁波市庆丰桥配套的千斤顶和压力表的标定数据为例，以实际值与趋势值的偏差的平方和最小为依据，根据函数存在的极值条件，求出线性方程，此为最小二乘法。

In this paper, the author estimated the module of quasiconformal mapping in curved fan, by the expression of local maximal dilatation function of quasiconformal mapping, Riemann′ s existence theorem and extremal length method, the author obtained a result of moduler deviation on curved fan.

本文对曲边扇形内的拟共形映照的模进行估计。借助拟共形映照的局部最大伸张函数来表达，利用黎曼存在定理和极值长度方法，得到关于曲边扇形的一个模偏差定理。

Defined object function can extract the extremal point s located accurately,form the stable extremal regions,and magnify the local intensity changes.

提出了一种基于不变区域提取算法，通过灰度指数变换，定义的目标函数不仅提取了定位准确的极值点，形成稳定的不变区域，而且突显了每个方向上灰度的变化。

Extremal optimization algorithm is a new heuristic method, whose principle is to select and update the worst variable, and improve the fitness of the whole problem.

极值优化算法是新开发的一种启发式算法，其基本思想是更新适值最差的变量，提高目标函数的适值。

Search Gaussian function to the extreme point.

用来搜索高斯函数的极值点。

In this paper, mathematical analysis, linear algebra is more material as the foundation, on the basis of previous studies, will solve a number of the function extreme value methods, such as distribution method, elimination method, the discriminant method, mean inequality method, the geometric method, vector method and derivative method, and so to summarize, and on this basis is given for each method the corresponding examples to illustrate for readers to reference and understanding.

本文以数学分析、线性代数更教材为基础，在前人研究的基础上，将求解函数极值的若干方法，如配方法、消元法、判别式法、均值不等式法、几何法、向量法和导数法等等进行归纳总结，并在此基础上针对每一种方法给出相应的例子加以说明，以便读者参考和理解。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。