元函数

The new method is a combination of characteristic approximation to handle the convection part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller time truncation is gained at the same time, and a mixed finite elementspatial approximation to deal with the diffusion part, the sealer unknown and the adjoint vector function are approximated optimally and simultaneously.

此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的L~2逼近精度。

In order to enhance the difference of homogeneity measurement values between pixels, Cauchy distribution function was selected as the kernel function for proposed measurement method of the image homogeneity.

为增强图像中各像元的同质性测度值差异，以柯西分布函数作为核函数，提出一种图像同质性测度的新方法。

By using the group-chain, the wavefunctions of the 4f〓 configuration for RE ions are also expressed as linear combinations of group-chain basis functions in Butler's irreducible representation notation. The matrix elements of the CF Hamiltonian then are calculated by means of the Wigner-Eckart theorem and factorization lemma of the jm factors. Before the CF level fitting, a point-charge calculation of the conventional CF parameters B〓 has been performed by means of the lattice-sum technique from the known crystal structure data. The corresponding parameters in the group-chain are calculated by the conversion relationship between two schemes that proved identical in essence, which are usually used as initial values in the fit to the experimental levels. The ratios of the same k-value CF parameters are suggested as the constraint conditions in the fit, in order to utilize fully the symmetry distortion degree of the studied system.

利用群链理论，属稀土离子4f〓组态的波函数表示为以不可约表示标记的群链基波函数的线性组合；借助Wigner-Eckart定理和2jm和3jm因子的分解定律计算了晶场哈密顿的矩阵元；根据点电荷模型和已知晶体结构数据，利用点阵求和技术计算得到传统晶场参数B〓初值，相应的非传统形式的群链参数初值则由两种方案下的转换关系求得；这些初值通常作为非线性拟合晶场能级计算的初值，系统的对称性畸变信息则反映在以同阶晶场参数的比值作为能级拟合的约束条件。

Then after the author researches the interaction problem of the partial derivative operators with respect to the two points P and Q, analytical expressions as well as series expansions of the kernel function within disturbing gravity field elements are determined, and their explicit expressions which can be applied practically are given for the first time.

深入研究了关于 P 和 Q 两点局部导数算子的相互作用问题，得到了扰动场元之间核函数和协方差函数的解析与级数展开式，首次给出了较为实用的明晰表达式。

Utilizing plane sectorial domain Hamilton system function via variable substitutes and eigenfunction expansion method, an analytical element is proposed in this paper for the crack analysis of reinforced concrete structures combining the bridging model and Dugdale model. Combined with finite element, nolinear crack problems of reinforced concrete structure can be analyzed.

利用平面扇形域哈密顿体系方程，通过分离变量法及共轭辛本征函数向量展开法，结合Dugdale模型和桥联力模型，推导了钢筋混凝土结构裂纹尖端的解析元列式，将此解析元与普通有限元结合，可用于分析钢筋混凝土的非线性断裂问题。

The diffraction potential functions are obtained by using the eigenfunction expansion method, and expressions for reflection and transmission coefficients are defined.

首先利用特征函数展开法导出了绕射势函数的分析解并进一步得到透反射系数的计算公式，然后利用边界元方法验证了解析解。

Then a suitable statement of patch test for axisymmetric solid nonconforming element is presented.

导出了轴对称非协调元分片检验中检验函数的形式，其位移函数是一种不完全的线性函数。

In this paper, first we define a kind of transformation on the sequences of Boolean functions, and then analyze the changes of nonlinearity, algebraic degree and balancedness of Boolean functions under the transformation.

本文首先定义了对布尔函数的序列的一种变换，并分析了进行此种变换后布尔函数的非线性度、代数次数与平衡性的变化情况，最终在此基础上提出一种新的递归构造方法，可以构造出非线性度很高的n元m阶n-m-1次弹性函数。

According to the actual circumstance of performance evaluation for mechanical products, the general neural network is reformed. Therefore, we construct the fuzzy neural network. This paper expresses membership function in the network by trapezium formulae .The indicators are fuzzed using the membership function .

网络中采用梯形函数的四元组形式构造模糊隶属函数，并用隶属函数的端点值和中间值作为样本，用改进的反向传播算法训练网络，得到与待评价产品情况相符合的权重值。

From theoretical analyses and calculations, it has been confirmed that the local strains around Cr〓 in SrTiO〓: Cr〓 are about twice the bulk ones. It is found that the change of Dq〓 with pressure makes main contribution to PS of ground-state g factor of SrTiO〓: Cr〓. It is the admixtures of basic wave functions that cause the strain-induced splittings of t〓E and t〓A〓 levels of SrTiO〓: Cr〓. It is found that there are non-vanishing matrix elements of operators C , C and C between wave functions with positive M〓 and those with negative M〓 and the shortcomings in previous literature have been overcome.

通过微观理论分析与计算，证实了SrTiO〓：Cr〓中Cr〓周围的局域应变大约为整体应变的两倍；阐明了基态g因子随压力的变化主要来源于Dq〓的变化；发现波函数的混合对单轴压力导致的SrTiO〓：Cr〓t〓E和t〓A〓态的分裂是至关重要的；C、C和C算符在Ms为正的波函数与M〓为负的波函数之间的矩阵元不为零，纠正了过去文献对此的错误处理。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。