函数

A series of orthogonal finite element function is presented by group method and finite element method.

正交函数由于其相互正交使得计算量大大地减少，历来为人们所关注，在连续函数中有著名的调和函数，离散分析中有正弦变换和。。。

Any function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets. It plays an important role for numerical analysis of partial differential equations, signal processes, and other similar problems.

于是，任何有限区间上的函数皆可表示为该区间上的尺度函数和小波函数的有限和，即小波级数，这克服了用无穷区间上的小波进行有限信号处理时，在边界上误差较大的不足，同时将该小波用于偏微分方程具有同样重要的意义。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

Robust design objective is always structural response′s first derivative, constraint functions are nonlinear functi...

鲁棒设计目标函数为结构响应的一阶导数，约束函数也是非线性隐函数，因此是多变量的非线性优化问题。

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。

Second, a framework of finding invariant kernel space for any single parameter group is developed based on the fixed point theory of contractive mapping.

最后，对尺度不变核函数的初始函数及参数选择进行了深入研究，提出了基于微分方程组的初始函数求解方法及类似Fisher准则的参数选择依据。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

With the method, tendency of measured value was analyzed, harmonic mode was checked by using autocorrelation function, the relation between spectrum parameters was analyzed and Fourier coefficient was calculated based on the theory of Fourier series. Finally, the significance of every period was tested and dominant period determined so as to establish the prediction model.

首先对实测序列进行趋势项分析；其次用自相关函数进行谐波模式检验；然后根据函数的傅立叶级数展开理论，分析谱参数之间的函数关系，计算傅氏系数；最后采用F分布检验法对周期进行显著性检验，确定主要周期，从而建立预报模型。

Finally, we constructed a Laughlin-type wave function for the fractional quantum Hall states in presence of an in-plane magnetic field.

最后，在有平面内磁场的情况下，类比于Laughlin波函数，我们试图构造一种朗道规范下的分数量子霍耳态的变分基态波函数，这一波函数的有效性有待于进一步的精确对角化计算的验证。

The fractional structure of the objective function maximizing RAROC makes it difficult to be solved. We noticed that in real financial practice, the expected return function and risk function of the portfolio are often homogeneous with the amount of investment.

根据RAROC的分式结构，以及回报函数和风险函数通常是关于投资额的齐次函数，将分式优化问题转化为对其分母的最优化。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。