函数矩阵

Put the discrete algebraic equations of initial derivative conditions and algebraic equation system of governing differential equation together to form a new algebraic system.

采用重心Lagrange插值近似未知函数，推导了未知函数各阶导数微分矩阵的显式表达式，建立了求解二阶常微分方程初值问题的重心Lagrange插值配点法。

A control strategy using Mutual Mapping Neural Network to compute the solution of the backward and forward kinematics was presented in this paper. MMNN was consisted of two NN and one modify function, one NN was used for forward kinematics calculation, and another for Jacobi matrix calculation, the modify function was formed based on Lyapunov function.

双向映射神经元网络主要由两个神经网络和一个修正函数构成，其中一个神经网络用来进行正运动学求解，另一个神经网络用来计算雅可比矩阵，修正算法是根据李雅普诺夫函数来计算的。

To explain the time-resolved fluorescence depletion, we develop a dynamics theory of spectroscopy for a vibrational relaxation process, and a decay rate constant of the vibrational state on the excited electronic state is taken to be 〓〓 in which γ is vibrational relaxation rate constant of the transition 0→1 and k〓 is the Boltzmann constant.

电子激发态上的波函数可写作〓相比于以前密度矩阵理论的布居表象，本文所提出的波函数表象理论为在更本质的层次上揭示振动弛豫过程的物理图象，特别是研究超短脉冲激发下含有振动弛豫的动力学光谱创造了条件。

Based on censored data, a smoothing estimation method is proposed to estimate the parameter functions. Moreover, a consistent estimator for the asymptotic variance matrix of the estimators is provided. The limiting distribution of estimated functions and the estimator of variance matrix enable us to construct approximated regions.

根据截切资料，我们提供平滑估计法以便估计参数函数，接著，我们也对估计函数的变异矩阵提出一个估计式，利用估计式的常态分配逼近，其相对应的信赖区间建构法也被提出。

Secondly, by the P-L estimation of survivor function, this paper proposed the regression models of polynomial cumulative hazard function distribution models, respectively in the case of complete date and random right censoring date; meanwhile generalized least squares estimations of unknown parameters were proposed respectively using two steps algorithm and principal component analysis algorithm.

与已有的关于多项式危险函数模型的研究成果相比，首先本文在统计模型的构造上充分考虑了累积危险函数乘积限估计量的非独立性，给出了协方差矩阵的估计；其次在模型检验方面，本文利用非参数回归分析方法，充分利用了数据本身的信息，减少了对回归关系假定的主观因素，因而分析结果更为可靠。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

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。

By solving the Schrodinger equation and using the boundary conditions of delta function, We can get the Buttiker scattering Matrix.

通过解薛定谔方程求得自旋空间的波函数，再由边界条件确定波函数的振幅，进而求出散射矩阵。

In Chapter 4, using Newton series, we obtain a divided differences formula of composite functions, and give a matrix equivalent form of these composite functions. Moreover, we derive a divided differences for the reciprocal series.

第四章利用形式Newton级数得到了复合函数的差商公式，并给出复合函数的一个矩阵等价形式，从而得到一个反级数的差商公式。

By using the race matrix problem as an example, this paper gives a quick evaluation method of recursive functions.

本文以赛马矩阵为例，给出一种递归函数的快速计算方法，其要点是一个数组记录已算出的函数

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。