结构函数

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统；然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理，建立符合能量准则的载荷函数，该函数不为零的最小值即为临界载荷，由此将稳定问题转化为无约束的多维优化问题；最后应用遗传算法求出相应于最优解的目标函数值。

Some conclusions are obtained:(1) The interval data concept can rationally settle the apart component's dependence problem of monitoring data;(2) The survey point's displacement which is the material parameter's increasing function or deducing function can be used to back-analyse the material parameter's up and down limit; and (3) Both the interval parameter perturbation back analysis method and the interval parameter monotony back analysis method can obtain satisfactory interval parameters.

通过分析得出结论：(1)可利用区间数概念合理解决监测资料中分离分量相关性的问题；(2)可利用工程结构中位移为待反分析材料参数的增函数或减函数的测点位移的上、下限，来反演得到不确定性材料参数的上、下限；(3)工程算例分析表明，区间参数摄动优化反分析法和区间参数单调性优化反分析法都能得到令人满意的参数区间。

In case of high input dimension system model, taking norm of input vector as the input of wavelet network instead of using tensor product method to construct wavelet network ,which could solve the problems of high computation and curse of dimensionality.

在模型结构方面，对于多维输入输出系统建模，本文放弃选用传统的标量积确定小波基函数的方法，将输入矢量的范数作为小波网络基函数的输入变量，从而避免了高维输入所带来的可用小波基数量巨大和计算复杂的缺点。

By both defining and quantifying of preference, four classes of preference functions and an aggregate preference function were constructed by using numerical method, and a mathematics model of physical programming was proposed.

通过定义偏好的概念及对偏好的数学量化，采用数值分析方法，构造了四种不同偏好结构的偏好函数，进而构造出综合偏好函数，并建立了物理规划数学模型。

Conventionally the electric load forecasting can hardly attain a result whose accuracy meets what's required. A short-term load forecasting model is therefore developed to solve the problem, based on the process neural network of which the input is the function of time and the high forecasting accuracy is available. Describes the structure of the model, discrete data fitting method by the expansion of function orthogonal basis and learning algorithm.

针对目前常用方法在解决负荷预测问题时，结果往往难以达到工程要求精度的现状，利用过程神经网络输入为时间函数以及预测精度高的特点，建立了基于过程神经网络的电力系统短期负荷预测模型；给出了模型的结构，基于函数正交基展开的离散数据拟合方法以及模型的学习算法。

When we use boundary element method to solve problems of fluid structure interaction, large amount of calculation of Green's function and its partial derivative is required.

Green函数及其偏导数的数值计算在水动力学中起着重要作用，当用边界元法求解流体结构相互作用问题时，需要大量的计算Green函数及其偏导数。

The contour is second-order continuous piecewise cubic but not a linear function, and a storage structure of contour information was also studied.

研究结果表明：内插结果是具有整体二阶连续的分段三次函数而不是线性函数；该内插方法与常规方法相比，存贮结构节省60%~70%的存贮空间，并且更适用于基于等高线的各种地学分析。

The cartoon component is described by piecewise smooth functions (Mumford-Shah model, or M-S model), while the texture is characterized by oscillating functions in G space.

其中结构成分用分段光滑的函数（即Mumford-Shah模型）刻画，纹理部分用振荡函数来描述。

Based on Lagrangion function in the form of a volume integration of liquid pressure superposed on the standard Lagrange function (kinetic energy minus potential energy), corresponding to liquid subsystem and structure subsystem respectively, the nonilnear coupled dynamic equations of the coupling system are established by means of variation principle and Lagrangion equation.

对液体子系统和结构子系统分别得到压力体积分形式的Lagrange函数和标准形式Lagrange函数，由变分方程和Lagrange方程可以建立系统的动力学方程。

The used SVM kernel function can not approach to any object function in regression.

针对目前使用的SVM核函数在回归中不能逼近任意目标函数的问题，在支持向量机的核方法和小波框架理论的基础上，提出了LS-WSVM结构模型。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷