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For a long time, it is a main factor to hamper the real-time application of SHET. The research is carried on aiming to quickening convergence speed. The automatic-changing Homotopy algorithm is proposed in the dissertation. The algorithm, which can change the solving method based on fundamental component, has the advantages of large convergence domain, high convergence rate and high precision. Many trigonometric functions are contained in the mathematical model, during solving equation, the calculated speed and the precision are affected by the calculations of trigonometric functions.

特定谐波消除技术的数学模型是一组非线性方程组，长期以来，方程的求解一直是限制该技术实时应用的关键因素，本文针对特定消谐方程组的快速求解进行细致的研究，提出自动变同伦算法，该算法可根据基波幅值的取值范围来决定采用的求解方法，其对求解方法的可选择性使该算法与其它算法相比具有计算速度快、收敛域宽、计算精度高等优点。

Mathematical analysis is largely taken up with studying the conditions under which a given function will result in a convergent infinite series.

数学的分析常被当作研究形成收敛无穷级数的和的给定函数的条件。

Mathematical analysis is largely taken up with studying the conditions under which a given function will result in a convergent in finite series.

数学的分析常被当作研究形成收敛无穷级数的和的给定函数的条件。

Especially, its operation does not depend on packet dropping. In chapter 5, we have analyzed the relation between link rate and link price of the Newton-like algorithm, which is proposed by Low et al to solve the utility function. And then we reduce the convergence procedure of Newton-like algorithm to a simple recursive procedure along a convex curve after the reduction and mathematical derivation. Thus, we found the reason that leads to the severe fluctuation of the sending rate during its convergence procedure, and then proposed our improved algorithm.

在第五章，我们在对Low等人提出的用于解决效益函数的Newton-like算法的链路速率与链路价格之间关系的深入分析的基础上，经过简化和数学推导，我们将其收敛过程归结为沿着一个凸曲线的非常简单的收敛过程，由此找到了导致Newton-like算法收敛过程中信源速率振荡剧烈的原因，在此基础上，我们提出了一个改进的链路算法。

In the present paper,we first investigate the following initial-boundary valueproblem of parabolic Monge-Ampere equation〓 in 〓(1)〓 on 〓(2)where Ω is a bounded convex domain in 〓 denotes the parabolic boundaryof Q,and second give a preliminary probe into the initial value problem of aspecial kind of parabolic Monge-Ampere equation which comes from the theoryof optimal investment in mathematical finance.

本文首先讨论如下抛物型Mongc-Ampère方程的第一初边值问题〓（1）〓（2）其中〓为〓中的有界凸区域，〓为Q的抛物边界，然后针对一种在数学金融学的最优投资理论中导出的特殊形式的抛物型Monge-Ampère方程的初值问题进行了初步的探讨。

Convexity and convex function have extensive applications in functional analysis, optimal theory, and mathematical economy.

凸性和凸函数在不等式、泛函分析、最优理论、运筹学、控制论及数理经济学等应用数学领域都有很多应用。

The convex quadratic programming is an important branch of mathematical programming.

凸二次规划是数学规划中的一个重要分支，它在经济，市场均衡，管理，军事等各个领域均有重要应用。

Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming.

因此，对凸函数和广义凸函数的研究是数学规划中最重要的内容之一。

Convexity and generalized convexity play a central role in mathematical economics, engineering, management science, and optimization theory.

凸性和广义凸性在数理经济、工程、管理科学以及在最优化理论中起着非常重要的作用。

Based on the theory of heat and mass transfer for film type cooling, a mathematical model for the velocity distribution of a thin water film, the equations of mass and heat transfer, and evaporation cooling controlled by the latent heat transfer were established.

基于膜状冷却热、质传递机理，建立水膜薄层的速度分布，热、质传递方程和潜热蒸发冷却控制的数学模型。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。