转换函数

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 means of the dual of Said-Ball basis, the Marsden identity is got in terms of Said-Ball basis, and a degree reduction algorithm for Said-Ball curves is presented through the transform from Bezier curves to Said-Ball curves.

利用Said-Ball基函数的对偶基，得到幂基函数在Said-Ball基下的Marsden恒等式，及从Bézier曲线到Said-Ball曲线的转换。并给出Said-Ball曲线的降阶赋值算法。

Hence, reproducing kernel function has not only the advantage of calculation, e.g.it can transform the integration into the sum of finite function values, but also theadvantage of local characteristic of wavelet function.

所以再生核函数既具有计算优势，如能将积分计算准确地转换成有限个函数值的和来计算，又具有小波函数的局部刻画优势。

This function is an integral representing the Fourier transform of the line spread function.

此函数最后的型式是线扩散函数的傅立叶积分转换方程式。

It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function.

从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。

The redundant controller produces odd and even check code in setup time. After odd and even check code is calculated with Boolean function calculation, it is transformed into of Galois field. If the output of controller can satisfy odd and even check condition is checked with the function calculation to decide it exist fault or not.

该控制器在设定时间产生奇偶校验码，通过布尔函数逻辑运算转换成Galois域函数运算，检验其输出是否满足奇偶校验条件以判断是否存在故障。

In this dissertation, digital lock-in detection techniques under integer period sampling and non-integer period sampling are separately investigated (1) Under integer period sampling, digital signal sequence is acquired through sampling the measured signal, but digital reference sequence is acquired through mathematical operation, then digital lock-in detection can be realized by calculating crosscorrelation function of digital signal sequence and digital reference sequence Harmonic measure is also analyzed, and a method of measuring harmonic of a periodic signal under aliasing is put forward.

本文对使用采样ADC把模拟信号转换为数字信号并通过计算数字信号的相关函数来实现锁定检测的技术进行了研究，在此基础上设计了一个多功能的数字LIA并在一些科学实验中进行了应用。本文对整周期采样和非整周期采样时的数字锁定检测技术分别进行了研究。(1)在整周期采样时，对被测信号进行采样得到信号序列，而参考序列由数学运算得到，通过计算信号序列和参考序列的互相关函数就可实现锁定检测。

Based on second-order Laplace equation and boundary condition, obtains the integral equation after Green transformation.

基于二维Laplace方程和边界条件，经过Green转换得到以势函数及势函数法向导数为未知量的积分方程。

Using inverse function to generate exponential distribution random number, introduce new algorithm, namely Maclaurin Equation, which is easy to be implemented by Hardware, use Maclaurin Equation to extend the function of Logarithm, make it compose by addition, division and multiple.

对于反函数法产生指数分布的随机数，提出易于硬件实现的算法结构——麦克劳林展开法，先用麦克劳林展开式展开对数函数，把对数函数转换成一系列乘、加、除运算。

To prove that we can construct any boolean function using only NAND gates, we needonly show how to build an inverter, AND gate, and OR gate from a NAND (sincewe can create any boolean function using only AND, NOT, and OR).

为了证明使用NAND门我们能够构造任何布尔函数，我们只需要展示如何从一个NAND建立一个转换，与门，或门（因为我们可以用AND，OR，NOT建立任何布尔函数）。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。