1. 为了弄清楚这种影响机制，通过分析基因池遗传算法的无限种群动力系统，刻画了双峰函数局部极值解的适值差与系统不动点之间的解析关系，进一步分析推广了理论结果的适用范围。

By analyzing the infinite population dynamical system using the gene pool GA and the BINEEDLE fitness function, we characterize the analytic relation between the fall of local optima and the fixed points in the infinite population dynamical system of the gene pool GA.

2. 研究表明：韦克比分布函数能够较好地拟合长江流域降水极值的概率分布。

It is proved that WAK can describe the probability distribution of precipitation extremes quite well calculated from observed and projected data.

3. 本文系统地论述了智能算法特别是粒子群优化算法的发展概况，并针对粒子群优化算法易于陷入局部极值陷阱问题，提出了改进措施；特别是针对极坐标模型的优化和多维多目标函数模型的优化问题提出了相应的基于极坐标的改进粒子群优化算法和多维多目标耦合的粒子群优化算法，以MATLAB软件实现了算法设计，并用典型的测试函数进行了仿真验证，最后应用所提出的算法对数控加工参数进行了优化。

We mainly carried some measures to solve the problems, which the particles of PSO are prone to drop into the Max. Trap. And feasible improved PSO algorithms, which are available to the Polar Coordination Question space and multi-dimensional multi-objective co-functioning optimization problems space, are brought forward respectively. these improving algorithms are programmed in the environment of MATLAB software, and some testing functions are chosen to illustrate their optimizing process. In the end, the latter improved algorithm was applied in parameters` optimization of numerical controlling cutting process, as an example of practical application.

4. 本文系统地论述了智能算法特别是粒子群优化算法的发展概况，并针对粒子群优化算法易于陷入局部极值陷阱问题，提出了改进措施；特别是针对极坐标模型的优化和多维多目标函数模型的优化问题提出了相应的基于极坐标的改进粒子群优化算法和多维多目标耦合的粒子群优化算法，以MATLAB软件实现了算法设计，并用典型的测试函数进行了仿真验证，最后应用所提出的算法对数控加工参数进行了优化。

The review of Intelligence Algorithms'development, especially that of Particle Swarm Optimizing algorithms, are introduced in the paper. We mainly carried some measures to solve the problems, which the particles of PSO are prone to drop into the Max. Trap. And feasible improved PSO algorithms, which are available to the Polar Coordination Question space and multi-dimensional multi-objective co-functioning optimization problems space, are brought forward respectively. these improving algorithms are programmed in the environment of MATLAB software, and some testing functions are chosen to illustrate their optimizing process. In the end, the latter improved algorithm was applied in parameters'optimization of numerical controlling cutting process, as an example of practical application.

5. 针对乌兰煤矿5342综放工作面的实际条件，采用立体网格状的测点布置，对该工作面瓦斯体积分数三维分布进行了测定，绘出了瓦斯分布等值线图，采用求函数极值点的方法，得出了工作面沿倾向瓦斯体积分数最低点分布曲线，提出了基于瓦斯体积分数最低点分布函数的瓦斯涌出分量比例计算方法。

Based on the actual conditions of the 5342 fully mechanized caving face of Wulan Coal Mine, the 3-D distribution of gas in the face is tested by measuring points arrangement in the stereo grid. The isograms of gas distribution of the face are drawn. Gas concentration nadir distribution curve along the working face incline direction is drawn by method of seeking function minimum points. The method of calculating gas emission components ratio of the face by means of the curve is brought forward.

6. 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。

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.

7. 利用测度变换以及布朗运动的一些重要性质，如反射原理，增量的独立性等，获得了两种极值分布函数的精确表达式，得到了首达时的分布函数。

By using measure change and some important properties, such as, reflection property and the independence of increment, we obtain the exact expression for the distributions of two kinds of extreme values and also get the distribution of the first passage time.

8. 其次，针对二元函数，在一种特殊情形下，运用多项式的惯性理论，得出了极值判别的一个漂亮结果。

And then, for binary function, by applying the inertia theory of polynomials, it has obtained an elegant result for extreme value discrimination in a special condition.

9. 多元函数微分学有着极其广泛的应用，其中条件极值在最优化问题中经常用到。

Multivariate Function Differential Calculus is widely used, so are the limits of conditions in optimization problems.

10. 一个用于求函数极值的遗传算法程序，使用VC++编程。

Seek function for a maximum of genetic algorithm, the use of VC.

11. 如果能找到被优化函数的全部极值点，就得到了全局最优点。

This algorithm is superior to other algorithms in the speed, accuration and globe of optimization.

12. 摘 要：判别函数极值的方法是数学分析中的重要组成部分。

Extreme function analysis of the mathematical method is the important component.

13. 依据极值原理，利用拉格朗日函数得到各个指标的权重值。

Based on maximum principles, Lagrangian function is adopted to obtain the weights of the indexes.

14. 本文采用分子动力学方法对NVT系综中水的密度极值问题以及分布函数和扩散系数等相关性质进行了模拟。

The density maximum of water and some related properties such as distribution function and diffusion coefficient were simulated in NVT ensemble by applying molecular dynamics method.

15. 本文根据边坡稳定性理论[2～ 4] ，分析了沙丘背风坡在重力作用下的稳定性问题，将其等价于一个双参变量函数的待定边界的泛函极值问题，并利用变分原理

lee slope of dune; stability analysis; variational method

16. 定理1 设函数在处可导，且在处取得极值，那么。

Theorem 1 If is differentiable at, and is a local extreme value of, then.

17. 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。

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.

18. 函数极值的翻译

18. 摘要求一元、二元函数的极值问题是数学分析中的基本内容，可应用于实践中求最大、最小的问题。

The calculations of extreme value for monadic and binary function are essential problem in mathematical analysis, which can apply to calculate maximum and minimum.

19. 本文对短程缺陷势深能级在能量趋向禁带边缘时波函数的行为作了研究。当深能级能量与禁带边能量差ε很小时，在一定的能量和对称性条件满足下，波函数在k空间向极值收缩而在实空间扩展。

The behavior of deep level wavefunctions induced by short range defect potential is investigated when the energy difference e between the defect state and the band edge is very small.

20. 它的应用表现在：利用导数求曲线的切线方程；利用导数求函数的单调区间；运用导数证明或求解不等式；利用导数求函数的极值和最值。

Its application shows: Utilize the derivative to ask the tangent line equation of the curve; Utilize the derivative to ask the dull block of the function; Use the derivative to prove or ask the inequality of solving; Utilize the derivative to ask the extreme value of the function and be most worth.