特殊函数

The shape function of the meshless local radial point interpolation method has the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions.

无网格局部径向点插值方法的形状函数具有Kronecker delta函数的特性，便于施加位移边界条件，不需要进行特殊地处理。

In the first four sections of this paper, these basic knowledge and calculational methods for the study of potential energy function are simply introduced. 9-parameter Murrell-Sorbie analytical potential energy function that can accurately describe especial potential energy function of diatomic molecule is obtained through calculations and analysis for the first time.

本文前面部分在简单介绍与分子势能函数研究相关基础理论知识和计算方法的基础上，通过计算、分析比较，首次得到了能够正确描述双原子分子特殊势能曲线的九参数Murrell-Sorbie解析势能函数。

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

Based on specific requirement for the top-coal caving mining to the four-bar linkage ,a design method of the four-bar linkage is put forward in the paper in which the least difference function between the lemniscate locus and the power function curve is used as the main objective function.

基于综放工艺对支架四连杆机构的特殊要求，首次提出以双纽线与幂函数曲线之差值最小作为主要目标函数的数学模型，并在此基础上应用VisualBasic5 0编制了四连杆机构的优化设计程序，可以同时实现优化参数显示与优化结果的动态显

By introducing special stress functions, we find solutions of eighth order homogeneous linear equation set with complex functions method and approach of undetermined coefficients, deduce calculation formulas of bi-material elastic constants for two dissimilar orthotropic composite materials. The expressions of stress intensity factors near finite interface crack tip subjected to symmetric loadings are derived. A engineering application numerical example is given.

通过引入特殊的应力函数，采用复变函数方法和待定系数法求解了八阶齐次线性方程组，推出了两种相异正交异性复合材料板的双材料弹性常数的计算公式，得到了受对称载荷作用的界面裂纹尖端应力强度因子的计算公式，给出了一个工程应用算例。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

Special functions established in different reference frames served as the reference model and the adjustable model of MRAS, and the steady-state electric torque considering to be known and thereby employed to achieve on-line identification of the induction motor mutual inductance.

该方法采用一种特殊形式函数，将该函数同时建立在2种不同的参考坐标系下，分别作为MRAS的参考模型和可调模型，同时利用稳态电磁转矩并将其作为已知量，实现了对感应电机励磁互感的在线辨识。

And it is proved to be more efficient than Newton method from the theorectical of view.

另一方面，将Newton-PCG算法应用于求解单和函数优化问题，利用单和函数优化问题的特殊性，进一步开发Newton-PCG技术建立了更有效的特殊算法。

We developed an optimal perfectly matched layer method for scattering from cavity under both TM and TE polarizations by choosing a particular absorbing function with unbounded integral.

通过选取一类特殊的吸收函数，即在有界区域中其积分发散的函数，给出TM极化和TE极化情形下的洞穴电磁散射优化PML算法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。