推广

4Based on a fact that the price formula of Asian options can be transformed into that of vanilla European option when the time to maturity is less than or equal to the length of average, we skillfully obtain the analytical price formula for the option on the minimum or the maximum of two geometric average prices and generalize it to obtain the price formula of several average prices for the first time. We also apply the method of [121], which approximates the arithmetic average by the geometric average, to the pricing of opitons on the minimum or the maximum of two arithmetic average prices to obtain Its approximated price formula. Numerical results show that the approximated price is relatively accurate when the riskless interest rate is large or the option is in the money and the volatility of two underlying assets are high and its accuracy is a little reduced but still good when the dividends are considered. However, it is hardly affected by the sampling number.

我们基于观察到的一个事实即当离到期时间小于或等于平均期间时亚洲期权的价格可变换成普通的欧式期权的价格，从而巧妙地得到了两个几何平均价格的最小或最大值期权价格的解析公式，通过简单地推广，首次得到了多个几何平均时的价格公式；将[121]用于算术平均亚洲期权的定价方法推广到两个算术平均价格的最小或最大值期权，从而得到它的渐进公式，数值结果表明：渐进价格的准确性在无风险利率较大或期权为实值且两标的资产的波动率较小时较好，抽样的个数对它没有影响，但考虑红利时它稍有下降但仍较好。

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

In addition, attention to energy efficiency, environmental protection section of the building structural system extension, research and development, extension of the framework Kuangjian structural system, steel structural system, the CL system, heteromorphosis pillar framework GRG gypsum big board system.

此外，重视节能、环保型的建筑节结构体系的推广，研发、推广了框架框剪结构体系、钢结构体系、CL体系、异型柱框架GRG石膏大板体系等。

In the first part, the concepts of the completely normal spaces and strong completely normal spaces in L-topological spaces are defined, which are the generalization of the completely normal spaces in general topological spaces. They are some good properties such as hereditary, weakly homeomorphism invariant properties, good L-extension, but they arent producible in general.

第一部分的主要内容如下：第一部分这一部分是将一般拓扑学的完全正规分离性的概念推广到了L-拓扑空间，给出了L-拓扑空间的完全正规分离性和强完全正规分离性的定义并讨论了它们的若干性质，比如，它们都是可遗传的，弱同胚不变的，"Lowen意义下好的推广"等。

Extension Subtropical Horticulturist , Agricultural Extension Service , University of California , Riverside .

亚热带园艺推广专家，园艺推广中心，加州大学河滨校区

Thereby, it generalizes portfolio frontier curve from hyperbola to hyperboloid of two sheets. When there exists risk securities, it generalizes frontier from straight line to cone. Meanwhile it gives some corresponding conclusions.

从而把原模型中没有无风险证券时的前沿证券曲线从双曲线推广到双叶双曲面，把有无风险证券时的前沿证券曲线从直线推广到圆锥面，同时还得到了一系列相应结论。

Hyperelliptic curve cryptosystems is a natural generalization of elliptic curve cryptosystems.

摘要超椭圆曲线密码体制是椭圆曲线密码体制的自然推广，但不仅仅是一种简单的推广。

By using this method we obtain two gen-eralized transformation formulae of q-integral form,two identities of basic hypergeometric series,as well as formal extensions for q-Pfaff-Saalschütz formula,q-Chu-Vandermonde identity and a three-term transformation formula of _3φ_2-series.

我们推广了两个q-积分形式的变换公式和两个有关基本超几何级数的恒等式，还得到q-Pfaff-Saalschütz公式、q-Chu-Vandermonde恒等式和基本超几何级数中一个有关_3φ_(2~-)级数的三项变换公式等的形式推广。

In the area of registration and appraisal of trademark,brand hatching and extending ,we have professional knowledge and rich practice experience,so we can provide the customers brand plan and extending as well as the protection of immateriality assets.

在商标注册、商标评审、品牌策划与推广等方面拥有精湛的专业知识、丰富的实践经验，可以全方位地为客户提供品牌策划、推广以及无形资产的保护。

Firstly, the strict-feedback nonlinear systems with unknown virtual control coefficients bi have been studied and the problem of its inverse optimality has been solved, that isThe new solvable theorem of inverse optimal gain assignment problem has been proposed through the method of modular design for the original system.

本论文的内容安排如下：第一部分把上述严格反馈系统进一步推广为具有未知虚拟控制系数bi的严格反馈系非线性统并研究其逆最优问题，即第二部分对于推广之前的系统利用模块设计方法提出新的逆最优增益配置定理。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。