查询词典 summation formula

In this paper, after taking over coupling effect between electronic spin and orbital angular momentum, to revise the formula of electronic angular momentum in Bohr's theory, and electronic speed formula is obtained in a single-electron system, and to correct the energy level formula of atomic orbit in Schr? dinger's method by relativistic effect, the theoretical improving formula is built for spectrum fine splitting calculation, the calculated values are in good agreement with experimental ones, and reflect changing law of spectrum fine splitting values.

本文在考虑了电子的自旋角动量与轨道角动量的耦合作用后，通过对Bohr理论中的电子运动角动量的修改，推导出单电子体系的电子速度公式，结合对Schrdinger的原子轨道能级表达式相对论效应修正，从而得出本文的氢及类氢离子光谱精细结构值的理论计算公式，应用此改进公式，所得的计算值与实验观测值符合得很好，计算结果也反映了氢及类氢离子光谱精细结构数据变化的规律性。

METHODS: C57BL/6J mice (15/group) were respectively received mash as AIN-93G formula, or 1% cholesterol supplemented AIN-93G formula, or 1% cholesterol and 14% long chain triglyceride rich in myristic acid supplemented AIN-93G formula, or 1%cholesterol and 14% MCT (caprylic acid/capric acid: 3/1) supplemented AIN-93G formula for 6 weeks.

分别用AIN-93G配方饲料，含1％胆固醇的AIN-93G配方饲料，含1％胆固醇和14%富含豆蔻酸的长链甘油三酯的AIN-93G配方饲料，含1％胆固醇和14％的中链甘油三酯的AIN-93G配方饲料喂养C57小鼠6周，每组15只。

By academic analyzing, it is concluded that two order discrete paraxial approximation formula of the paper, multiple transmitting formula and polynomial extrapolation formula are the different forms of continuous paraxial approximation formula, so they are with nearly equivalent precision and stability and with equivalent applicability and limitation.

据此文献[3]将傍轴近似公式归结为一类从特定的无限域模型导出的人工边界条件，并且提出了新的从一般无限域模型导出的具有普适性的、称为"多次透射公式"的局部人工边界条件。那么，是否也可以从一般无限域模型导出具有普适性的傍轴近似公式呢？

Combining Inclusion-Exclusion principle with Disjoint Sum of products formula,the new formula contains terms which correpond one by one to a class of special subnetworks. For a given newtork,terms of new formula are fewer than those of corresponding stryanarayna formula. Finally,an example illustrates our conclusion.

该公式本质上是将容斥原理公式和不交和公式融合在一起，公式中各项和网络的一类特殊子网络一一对应，与相应的Satyanarayanna公式比较，该公式包含更少的项和更少的算术运算，并给出一个算例验证上述这个结论。

Lagrange interpolation focus on the application of the formula .The comparison between the method of Transform and that of Lagrange's interpolation formula in square matrix form is made. Also the form of Lagrange's interpolation formula is generalized to include the double root case.The application of the generalized lagrange's interpolation formula in square matrix to solving state equations is found to be effective.

重点介绍了Lagrange插值公式在状态方程求解中的应用，用对角矩阵及相似矩阵的性质证明了，当状态转移矩阵中方阵的特征根相异时，拉格朗日插值公式与Laplace变换法对表达具有一致性，并用极限方法对方阵含二重根时拉格朗日插值公式的应用进行了推导。

Both upper bound formula and lower bound formula of the global truncation error of Euler method have been derived theoretically.After making certain approximat e processing,the derived upper formula changes into current upper bound formula.

从理论上推导出了欧拉方法的整体截断误差的上限公式和下限公式，作一定的近似后，得到的整体截断误差上限公式就变为现用的整体截断误差上限公式。

Though blocking computing matrix,it can decrease the calculation amount of matrix multiplication.Meanwhile,the different simplified formats are presented when computing Duhamel integration with Trapezium formula、Simpson formula、Cotes formula and Gauss formula.

通过分块计算矩阵，能够减小矩阵乘法的计算量，同时分别给出了利用梯形公式、Simpson公式、Cotes公式、高斯公式计算Duhamel积分时的不同简化格式。

4Based on a fact that the price formula of Asian options can be transformed into that of vanilla European option when the time to maturity is less than or equal to the length of average, we skillfully obtain the analytical price formula for the option on the minimum or the maximum of two geometric average prices and generalize it to obtain the price formula of several average prices for the first time. We also apply the method of [121], which approximates the arithmetic average by the geometric average, to the pricing of opitons on the minimum or the maximum of two arithmetic average prices to obtain Its approximated price formula. Numerical results show that the approximated price is relatively accurate when the riskless interest rate is large or the option is in the money and the volatility of two underlying assets are high and its accuracy is a little reduced but still good when the dividends are considered. However, it is hardly affected by the sampling number.

我们基于观察到的一个事实即当离到期时间小于或等于平均期间时亚洲期权的价格可变换成普通的欧式期权的价格，从而巧妙地得到了两个几何平均价格的最小或最大值期权价格的解析公式，通过简单地推广，首次得到了多个几何平均时的价格公式；将[121]用于算术平均亚洲期权的定价方法推广到两个算术平均价格的最小或最大值期权，从而得到它的渐进公式，数值结果表明：渐进价格的准确性在无风险利率较大或期权为实值且两标的资产的波动率较小时较好，抽样的个数对它没有影响，但考虑红利时它稍有下降但仍较好。

According to a given function, namely, composite trapezoidal formula using composite Simpson formula Romberg quadrature formula and the variable step-size integration quadrature formula results, and compare the accuracy of points.

详细说明：根据给定的函数，分别用复合梯形公式、复合辛普森公式、龙贝格求积公式和变步长的求积公式计算积分结果，并且比较积分的精确度。

In prime number distributed research process,and through established one kind of new sieve method and the stair theory,this article obtained about three group of prime number distribution recurrence formula: The 1st is not bigger than x the prime number integer recurrence formula;The 2nd is not bigger than x the twin prime integer recurrence formula;The(3rd Recurrence) formula.

在研究素数分布过程中，通过创立一种新的筛法与台阶理论，得到关于素数分布的三组递推公式：不大于x的素数个数与孪生素数对数量的递推公式；不大于x的孪生素数个数的递推公式；任意偶数x≥6表为两个奇素数之和与孪生素数对数量对数的递推公式。

" I' d like to get some rough idea about music in the baroque ear, please."

请简要介绍一下巴罗克时期的音乐，好吗？

The results showed that the peak latency and pattern of SEPs elicited by electrical needling in LI-l1 and MP were similar. The amplitude of SEPs elicited by electrical needling in LI-l1 was higher than that of MP. There was no obvious SEPs generation when MM was electrical needling.

结果显示，电针刺激曲池穴和其邻近桡侧伸腕长肌运动点诱发性脑电波的波形和波峰时间是类似的，只是穴位的诱发性脑电波波幅较大，而电针刺激非穴位点并没有明显的诱发性脑电位。