解析

Since an analytic function can be arbitrary approximated by a polynomial, the provided methods can be applied to robust stability analysis of polynomial family with general non-linear perturbation parameters.

由于非线性解析函数可用多项式任意逼近，故该方法也可用于具有一般非线性参数摄动的多项式族的鲁棒稳定性分析。

Based on the analytic model of an eccentric slider crank mechanism with elastic effects at both joints of the coupler and four coupler Mathieu-typed equations of motion in terms of the generalized coordinates of the system,the extract solution is developed from the improved Hill method with accelerated convergence.

在所建立的连杆接头处具有弹性效应的曲柄滑块机构的动态解析模型以及在广义坐标下推导出的4个马修型运动方程的基础上，由具有加速收敛性的改进希尔法进行了精确求解。

The semi-analytic formula was taken as an interpolation function near crack tip notch and the degree of freedom near the notch tip were transformed into a set of generalized coordinates by means of series expansion formulas of displacement field.

该方法将半解析函数作为插值函数，将缺口尖端附近的自由度通过位移场的扩展公式转化为一组广义坐标。

In this paper, a kind of generalized Krylov function is defined and discussed.

河南省自然科学基金项目（984070700）资助摘要定义并讨论了一类广义克雷洛夫函数，给出了用该函数表示的弹性地基上铁摩辛柯梁的解析

In part one,because there is no long-range order in one-dimensional(1D)system,generalized second-order Green's function theory isused to 1D spin-1 antiferromagnetic spin chain.The Haldane gapin the excitation spectrum appears naturally in the analytical re-sult;When k is zero,there is a gap 2Δ.

第一部分中，在长程序为零的条件下，我们应用推广的二级格林函数理论，讨论了自旋为1的反铁磁一维链，Haldane能隙在解析结果中自然地得出，在k＝0时，能谱中存在一个2Δ能隙，Δ＝0.5J。

In summary, the current project successfully designs a user-friendly program which is powerful in data analysis in 40Ar/39Ar geochronology and is potentially useful to data analyses of other isotopes in compositional space.

换言之，本研究的方法在解释氩氩定年分析结果更加容易，因此，对於利用同位素分析、探讨历史复杂岩体的研究工作，提供一项有利的解析方法。

This paper gives a closed-form solution to Asian option with geometric average assets prices in a continuous situation.

采用几何平均法计算资产价格的平均值，并以连续时间的情形为例，得到了亚式期权的解析定价公式

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。

3We obtain the analytical price formulas for vanilla, forward-start and in-progress fixed-strike and floating-strike continuous geometric average Asian options and a put-call parity under generalized Black-Scholes with time-dependent parameters by risk neutral valuation and properties of stochastic integration.

在依赖时间参数的推广的Black-Scholes模型下，利用风险中性定价及随机积分的性质，得到平凡、远期开始和进展中的固定和浮动执行价格的连续几何平均欧式亚洲期权价格的解析公式和一个平价关系。

Compared with numerical method, analytic approach not only has clear geometric meaning, but improves the solving efficiency considerably.

本文提出的解析法丰富了装配约束求解理论，它不仅具有清晰的几何意义，而且便于计算机实现，能够大大提高求解效率。

We will see more and more activist government policies that distinguish economic activities according to the nationality of the actors.

我们将看到越来越多激进的政府政策，这些政策根据企业的国籍来区分经济活动。

If we can prove the independence of an axiomatic system, then we can guarantee the conciseness of this system, ie.

如果能够证明某个一阶谓词系统的独立性，那么就能够保证该系统的建立是精炼的，即没有任何一条公理或推理规则是多余的。