导出

Chapter two proposes the unified form of Hojman"s conservation law and Lutzky"s conservation law. Firstly, the author introduces the general Lie group of transformations that the variations of both the time and the generalized coordinates are considered, derives the determining equation of Lie symmetry for the system, presents a new conservation law, which contains the Hojman"s and the Lutzky"s conservation law as two special cases, and obtains a condition to exclude trivial Hojmans conserved quantities.

第二章，Hojman定理和Lutzky定理的统一形式：首先，引入一般意义下的Lie变换群(即位型变量q_s和时间变量t同时变换)，给出系统的Lie对称性确定方程，提出一个新的守恒律，Hojman定理与Lutzky定理则分别是这个新守恒律在两个特殊情况下的推论，导出一个可排除平凡Hojman守恒量的定理，并分别讨论了Birkhoff系统和非完整系统的Lie对称性和Hojman守恒量，最后，讨论了Hamilton系统的梅对称性与Lie对称性的关系，给出了由梅对称性求Hojman守恒量的方法。

Concretely speaking, using the irreducible tensor theory, we deuced the formulism for fine-structure energies of boron-like atoms in the ground and first excited states, which involves spin-orbit, spin-spin and spin-other-orbit interactions; completing all the angular integrations and spin summations needed, we make the final expression for fine-structure energies of boron-like atoms in the ground and first excited states in a combination of radial integrations. Afterwards, employing the wave functions we got in Chapter Three, we accomplished all the radial integrations and so obtained the fine-structure energies.

具体地说，利用不可约张量理论导出了类硼离子基态以及第一激发态的精细结构的表达式，给出了自旋-轨道、自旋-自旋、自旋-其它轨道相互作用等所涉及的所有角向积分和自旋求和的解析计算方法，完成了角向积分、自旋求和的计算，使类硼离子基态以及第一激发态精细结构能级最终可以表示为径向积分之和；在此基础上利用以前所得到的非相对论性波函数，进一步完成了所有径向积分的计算，从而得到了对应能级的精细结构的理论计算值。

Under the information theory, more applications are provided to those back analysis methods. Based on the Duncan-Chang E-B model, which can simulate earth-rock dam's non-linear mechanics behavior well, the paper introduced the nature coordinate system to the stress space. In this way, hydrostatic stress and stress deviator were decomposed each other.

论文以能较好模拟土石坝非线性力学行为的Duncan-Chang E-B模型为基础，通过引入应力空间下的自然坐标系，分解应力球量与应力偏量，从而导出一个在有限元计算中，位移对参数偏导数的闭合形式公式。

With the aids of the angular momentum coupling theory, the diagonal sum rule and the irreducible tensor theory, a formulism for calculating the matrix elements of Boron-like atoms' non-relativistic Hamilton between the Racah wave functions have been derived. Based on this approach, the non-relativistic energies of Boron-like atoms in the ground and the first excited states have been obtained.

本论文借助角动量耦合理论、对角和法则和不可约张量理论，导出了类硼离子基态和第一激发态非相对论性哈密顿在拉卡基函数之间的矩阵元的表达式，给出了计算类硼离子基态和第一激发态非相对论性能量的方法，并应用此法计算了类硼离子基态和第一激发态非相对论性能量。

These formulas have been tested with several mediums and Langevin diamagnetic magnetic susceptibility of helium, and the results are in good agreement with the measured data.

应用电子云导体模型和能量守恒原理，导出介质折射率表达式，并用表达式计算了几种介质的折射率，计算结果与实测值符合很好。

The Murrell-Sorbie potential energy function curves of diatomic molecule of Au2 Cu2 Y2 AuY and AuCu have been obtained, then the spectral datum and force constants have been derived..

导出了Au_2、Cu_2、Y_2、AuY和AuCu双原子分子的Murrell-Sorbie势能函数，在此基础上推导出光谱项常数和力常数。

The relation of Murrell-Sorbie potential parameters and spectrum date for diatomic molecules is got.

摘 要：导出了Murrell-Sorbie势能参数与双原子分子光谱数据的关系。

So it has important meaning to factual work to have a thorough understanding of the interrelated concepts of dielectric constant.

首先介绍了介质和导体、半导体的区别，然后解释了介电常数的基本概念，并给出相对介电常数的另一种导出定义。

A leave-one-out error bound for SVR is derived in this paper. After the SVR model is obtained for a given set of hyperparameters, the bound can be computed with very little additional work. Considering the properties of the bound, an optimization method based on difference quotient is proposed.

本文针对当前SVR推广误差的估计大多需要较大计算费用的情况，推导出SVR的留一法误差的易于计算的界，这个界在得到学习算法的解后需要很少的额外工作量。

With the J/y anomalous suppression as a signal of QGP phase transition, on the basis of absorption of nucleons and comovers, the differential cross section of J/y production in high energy heavy ion collisions under the condition of the occurrence of phase transition is derived out, and the experimental data of NA50 collaboration in Pb-Pb collisions at 158A GeV/c is analysed.

以J/y反常抑制现象为夸克-胶子等离子体相变信号，在核与随动者吸收理论的基础上，导出了有相变产生时高能重离子碰撞中的J/y微分产生截面，并对NA50合作组给出的入射动量为158A GeV/c的Pb-Pb碰撞中的实验数据进行了分析，较好地解释了实验结果。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。