数值函数

The experimental data were trained by BP neural network, and the results were curve fitted to set up a fitting function which was used in the genetic algorithm process to reach the optimum.

首先利用BP神经网络来训练已有实验值，然后将训练后的神经网络作为知识源，通过曲线拟合与逼近求得设计变量与目标函数值的函数关系表达式，最后将这一函数表达式作为遗传算法的适应度函数进行遗传迭代寻找最优解。

It Newton iteration is used in the analysis of math value,and the simplicity formula is given to resolve(including original initial value formula and advanced approximation formula),which can be characterized by fast speed and easy remembering.

采用数值分析中的牛顿迭代法求反渐开线函数的根，并给出了符合精度要求的解算反渐开线函数的简单公式(包括原始初值公式和近似值精化公式)，具有迭代收敛速度快、简单易记的优点，它们适用于[0，π/2]的全区段，免除了分段计算的烦恼，并运用VB编写计算机程序，从而实现反渐开线函数快速求根的目的。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

Furthermore, buckling effect factors and their influence law are exploited. Finally, combining the character of piles foundation with high bridge piers with engineering practice, four optimal mathematic models are proposed and flow diagram of optimization analysis is fulfilled by the computer optimum program. A numerical example is analyzed to get optimal solution by using this program. Meanwhile based on the optimal model with buckling coefficient as the objective function, parameter variables are discussed about their effect rule toward the optimal value of objective function.

最后，针对高桥墩桩基础的特点，在基本优化模型的基础上，根据不同的目标函数建立了相应的优化模型，给出优化设计算法流程图，编制了相应的优化计算程序；并根据高桥墩桩基的工程实际设计了一个数值算例，采用本文编制的优化计算程序对该结构进行优化，得到了优化后的最优解；同时，采用高桥墩桩基屈曲系数作为目标函数的优化模型进行因素分析，初步探讨了参数变量对目标函数最优值的影响规律和程度。

Based on Monte Carlo method,four different weighted function moment methods for Pearson Ⅲ distribution which were developed in China are first compared by using the evaluation standard considering unbiasness and effectiveness of parameters and design values.

利用统计试验方法，以参数及设计值不偏性、有效性为评价标准，比较了现行几种权函数参数估计法，结果与以理想样本还原准则为标准所得的结论截然相反，以不偏性、有效性标准的结论是数值积分权函数法，并未对马秀峰权函数法作出改进，还从理论上比较分析以上两种评价标准，结论是理想样本还原为标准来评判估计方法的优劣存在较大缺陷，建议今后尽量不要使用该标

By constructing a different piecewise linear supply function, the existence of piecewise linear supply function equilibria in electricity market is proved. From the theoretical point of view, new results regarding existence of these equilibria are presented.

在这种电力市场环境下构造了一类分段线性供应函数，证明了分段线性供应函数纳什均衡解的存在性，从理论上获得了相关新结论，为电力市场供应函数均衡近似数值求解算法设计提供理论基础。

ChannelCaller: A function without a return value, in regular programming also known as 'void' This is the only function type you can use to create recursive functions.

通道调用：一个函数没有返回数值，在正常的程序都知道为空白点，只有此函数类型你可以用来创建循环函数。

First, for a given integer value of the objective function, the lower and upper bounds of the variables were determined by the optimum simplex tableau of the linear programming relaxation problem. Then the conditions on the bounds were added to the constraints as cuts to the associated objective function hyperplane. Finally, a branch procedure of the branch-and-bound algorithm was applied to finding a feasible solution on the objective function hyperplane.

对于给定的目标函数整数值，首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界，然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割，最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。

In this dissertation, many works have been done on the basis of the summarization of the merits of all kinds of meshless methods after a large number of relevant references are read and studied. The basic ideas, principles of meshless methods and their development in the recent years are introduced synoptically. Applications of Element-free Galerkin method in elastic foundation plate are studied deeply and some useful conclusions are obtained as follows:(1) Comparisons between numerical solutions and analytical solutions for several different styles of weight functions, including Gaussian weight function, spline weight function and singular weight function etc, are performed. The results show that Gaussian weight function is the best one.(2) Ranges of relevant parameters for Gaussian weight function are given.(3) Influences of nodal distribution schemes and the number of Gaussian integrated dots on computational results are discussed.

在本文中，作者在认真阅读和研究所搜集到的大量参考文献、综合各种无网格法优点的基础上，首先，对无网格法的基本思想、基本原理、发展现状作了概括性的介绍；其次，对无单元Galerkin法在弹性地基板计算中的应用进行了较为深入的探讨：(1)分别对高斯型、样条型、奇异型等不同形式的权函数进行比较分析，数值计算结果与级数解析解的比较表明，高斯型权函数效果较好：(2)对高斯型权函数进行参数研究，得到地基板计算中相关参数的选取范围；(3)对不同节点分布方案和不同高斯积分对计算结果的影响等作了有益的讨论。

For the first patern, elastic dynamics is adopted to study the steady state rolling contact, elastic dynamics incorporating with rigid dynamics is adopted to study the non-steady state. For the steady state, the analytical solution is obtained, and for the non-steady state, the variational formulation to solve the problem numerically is derived For the later patern, the function type friction coefficient is introduced. On the basis of the quasi-stastic theories of constant friction coefficients, both the exact theory and the simplified theory of the function type friction coefficient are established, the computer programms for both the theories are also made out. Using the function type friction coefficient, Shen-Hedrick-Elkins theory's application range is extended to large creepage .

对于速度对接触体力学特性的影响，本文采用弹性动力学方法和弹性动力学与刚体动力学相结合的方法分别对稳态和非稳态两种情况进行了研究，得到了稳态情况的解析解，给出了对非稳态情况进行数值求解的变分公式；对于速度对相关物理量的影响，本文主要讨论了速度对摩擦系数的影响，在滚动接触准静态理论的基础上引进了函数型摩擦系数，建立了函数型摩擦系数的滚动接触准静态精确理论和简化理论，并分别编制了相关的计算程序，还用函数型摩擦系数将简便的Shen-Hedrick-Elkins理论的适用范围扩展到大蠕滑区。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。