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Application of HHGL to lithium atom As a starting point for exactly solving schrodingerequation for lithium,the part has twofold purpose,one isto derive the coupled hyperradial differential equation,and discuss whether HHGL can be used or not,the other isto build the symmetric basis functionfor twodimensional irreducible representation of 〓 permutationgroup and estimate the ground-state eigenenergy.

首先根据Pauli原理的要求，将N电子原子的波函数向〓群不可约表示之基展开，积分掉角度部分，推导出N电子原子的超球径耦合微分方程，其形式与氦原子耦合微分方程相似，差别表现在矩阵元〓的计算上。

Data from Keck Observatory was used to derive the speed of the clusters along the line of sight, allowing the three-dimensional geometry and dynamics of MACS J0717 to be derived.

基于凯克天文台的数据用来测定星系团沿我们视线方向的速度，由此我们获得了MACS J0717的三维运动关系。

Through comparative studies, we consider that the core theme and basic plots derive all from the short heroic epic The Hero silin—galzuu—baatar in the khalkha tribe and the Barkh tribe in the 16th century.

通过比较研究，我们认为东蒙古英雄史诗的核心主题和基本情节题材共同起源于16世纪形。。。

To derive the continuity of solution for stochastic Volterra equation, the Kolmogorov continuity criterion will play a key role.

2为了在随机环境下得到Volterra型方程的连续性，Kolmogorov连续性准则将起到非常关键的作用。

In chapter 2 we make perturbation analysis for the two kinds of nonsingular systems AX=B and systems with multiple right hands involving Kronecker product, and derive normwise , mixed and componentwise condition numbers and their upper bounds respectively.

在第二章中我们对两类非奇异线性方程组AX=B和带Kronecker积的多右端系统进行了扰动分析，并应用矩阵导数得到范数型，混合型和分量型这三种条件数及其上界。

And we show the form of the reduced density matrix master equation and its solution at first .Then we derive the solutions of Ohmic spectrum and Laurent series spectra master equations. Finally, we make analysis of the solutions of stochastic process and their coefficients from the cumulants, late time uncertainty function and linear entropy

首先展示了有关约化密度矩阵主方程的形式和解的形式；接着推导出欧姆谱和分洛朗级数谱这两个随机过程主方程的解；最后从累积量，延时不确定关系和线性熵等方面来研究随机过程主方程的解及其系数特点。

In this paper, after introducing the meshless method simply, we derive the moving least squares approximation in detail.

本文首先阐述了无网格方法的一般理论，然后详细推导了移动最小二乘近似的构造过程。

The leftists derive their theory not from Confucius, but from Marx.

左派人士是从马克思而不是孔子那里获得他们的理论的。

The partial derivative of a multivariate normal integration, a extension case of Leibnitz's Rule, is derived in this study and used to derive the SCOs sensitivities.

一个多维度常态积分的偏微分关系，可以被视为莱布尼兹法则(Leibnitz's Rule)的推广，也在本研究里推导而得，并且被用来推导序列复合选择权的敏感度分析。

We derive the packet loss probability, average queueing delay and stable queue length distribution of any priority traffic.

我们分别导出了任意优先级业务的分组丢失率、排队的平均时延以及稳态的队列长度概率分布等特征参数。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。