解析函数

Xml analytical procedures, through their own xml document written by the analytic function data acquisition format.

xml解析程序，对xml文件通过自己写的函数进行格式解析获取数据。

In this paper, Galerkin method is employed. First, test functions to satisfy natural boundary conditions are selected. Then the approximate analytic formulations of the system frequency are derived. Meanwhile the approximate analytic formulation of the limit velocity is got.

采用直接法，首先选取满足自然边界条件的试函数，而后求出了系统固有频率的近似解析公式，同时也得到了极限流速的近似解析公式。

The Paired Comparison and Constancy Graphical approaches for statistical analysis will be used for the psychological experiment.

因此，针对声源方向感受此一课题，以两反射音之模拟声场进行实验探讨，研究方法不仅以数理解析，并针对人们实验的心理感受进行调查分析，心理实验时采用配对比较法及恒常性图解法统计分析，试图藉由若干变因的控制进行量化，实验结果发现声源方向感度的变化，主要受制於双耳互函数级数及全反射音振幅的大小，双耳听觉互函数主要与反射到达测听者的方向和反射的幅度有关，证实声源方向感度与双耳互函数级数为正比之关系存在。

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。

Using the properties of the harmonic function and the theories of the expansion of the spherical harmonics,the equivalence between Moritz analytical continuation and Bjerhammar s virtual spherical solution is proved according to the power series expanded form of the real number field function,the differences in meaning between the two solutions are analyzed.

利用调和函数的性质以及球谐函数展开理论，并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性，同时分析了两种解的内在区别。

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。

Moreover, the proposed VIGA was applied to optimize two typical testing functions with multimodal and multivariate. From the comparison of different optimized solutions by conventional GA, simulated annealing algorithm with the analytical for the testing functions, the feasibility and validity of the VIGA was verified.

以2个典型测试函数为例，分别进行了多峰值、多变量测试函数寻优测试，通过将VIGA寻优结果与测试函数解析解、传统遗传算法(genetic algorithm，GA)以及模拟退火优化(simulated annealing algorithm，SA)策略所得优化结果进行对比分析，VIGA的可行性和有效性得到证实。

We defined two arithmetical functions and got mean value properties of the two functions by using elementary and analytic methods; we also studied the mean value property of Smarandache ceil function S_kn!

定义了两个新的算术函数，利用初等和解析方法研究了这两个函数的均值性质；研究了Smarandache ceil函数S_kn！

By usingthe dynamica l programming method, the optima l investment portfolio andconsumption policies for one kind of typica l utility function case areobtained,then we make numerica l simulation for it and get the numerica lsolution.

然后运用动态规划方法，对于一类特殊的效用函数情形，求出了最优投资组合及消费选择的显性解，并进行数值试验，得出了值函数的近似解，最后将值函数的解析解和数值解进行比较，得到了相对误差示意图。

The corresponding grain size distribution curve is very similar with those of available theoretical quasi-stationary grain size distributions in literature.

将该函数与Liu等提出的2种三维准稳态晶粒尺寸分布函数进行的对比表明：此3种函数的解析表达形式有所不同，但其曲线图在一定条件下相互吻合。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失