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LIU Hui's Cyclotomic Method is one of the greatest achievements in the history of mathematics in China,even in the world,in which the special approach to understand the infinity and the method to solve it are presented.

有的著作认为在极限公式limx→0sinxx=1的证明中，要用到圆的面积公式S=21Lr，而对后者的证明中必须要用到重要极限limx→0sinxx=1，从而犯了循环论证的错误。魏晋刘徽的"割圆术"是对无限问题的独特认识和致用的处理方式，是为证明圆面积公式而设计出来的一种方法。

ChinaWang Yonghuidirected by Zhang ~Venpeng The main purpose of thesis is using the mean value theorem of the Dirichlet Lunctions to study the asymptotic property of the Dedekind sums and Hardy sums, and give two sharper asymptotic formulas.

关于Dedekind和的推广型均值公式及Hardy和的推广型均值公式本论文利用Dirichlet L-函数的均值定理研究了Dedekind和及Hardy和的一类均值估计问题，并给出了较为精确的渐近公式。

This paper uses field methods to calculate the winding loss and the modified Steinmetz experiential equation for core loss calculation.

本文所采用的铁心损耗公式是对正弦磁化波形下的Steinmetz经验公式进行修正和补充而得出的，该公式适用于任意磁化波形，并考虑了温度对铁心损耗的影响，从而提高了计算的精度。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

Multistep method is the first method applied to DAEs.Because of some reasonsin history,all algorighms for DAEs come from those for stiff ODEs,mainly thebackward difference formula.

多步法是最早用于直接求解微分代数方程的方法，由于历史上的原因，长期以来使用的公式都是由刚性常微分方程的求解公式导出的，主要是向后差分公式。

In this paper, a sort of recursive formulas of spherical harmonics integrals, which often appear in the gravitational gradient harmonic analysis, are deduced according to the recursive formulas between every other order of spherical harmonics and the trigonometric functions＇properties. And the calculated formulas on the recursive initialization also are brought forward.

本文根据球谐函数的跨次递推公式和三角函数的性质，详细推导了在重力梯度调和分析中出现的一类球楷函数积分的跨次递推公式和递推初始值的计算公式。

It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Takinginto account the riskneutral environment, we got a closedform analytical formula for deferred arithmetic asian options by the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simpleenough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives.

在标的价格服从几何布朗运动、收益服从对数正态分布的前提下，通过风险中性定价原理，对到期损益中的随机积分进行任意次Taylor近似，并由级数定义将此连续问题离散化，给出了延期算术平均亚式期权封闭形式的解析定价公式，并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验，结果表明，所得公式可以应用到金融实务中对此类衍生品定价中。

In chapter 2, the intensity and phase formulae of five photorefractive processes in intermediate regime are derived including the analytic expressions of codirectional parallel-or cross-polarization two-wave mixing in the depleted pump condition and the analytic expressions of contradirectional parallel-or cross-polarization two-wave mixing and degenerate four-wave mixing in the undepleted pump approximation.

给出了本文的结构和取得的主要结果。第二章推出了五种光折变过程的中间段强度与相位公式。既同向平行、交叉极化双光束耦合的大信号解析公式，异向平行、交叉极化双光束耦合以及简并四波混频的小信号解析公式。

Based on the prediction model for uncatalytic double base propellant burning rate the dissertation, carrys on the mathematical treatment to the hypothesis of polyemerization and disintegration, deduces the formula of catalytic double base propellant burning rate and pressure exponent; The results of experimental tests show that it can re-present quantitatively various stage of plateau combustion: super rate, plateau and mesa. The calculated results conform with the experimental results very well.

在非催化双基推进剂燃速预估理论的基础上，对聚合裂解的假设进行数学处理，导出催化双基推进剂的燃速公式和燃速压力指数公式；实验验证结果表明，模型中的公式可以定量地再现双基平台推进剂燃烧中的超速，平台和麦撒现象，而且计算值和实测值符合得较好。

Based on our formula of width equivalence of SIW and RW, the formula of length equivalence of SIW and RW has been derived, which is expected to find wide applications in the engineering design of SIW filter and resonance cavity.

根据已知的SIW和RW之间的宽度等效公式，通过对传播常数的分析，推导出SIW和等效的矩形波导之间的长度等效公式，这个公式在计算SIW短路结构和谐振腔时很实用。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！