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We take sech form ansatz and solve the CNLS equations through variational approach. We obtain the analytical expression of nonlinear coupling term, which is in the lagrangian of CNLS. We apply a potential well model to analyze the interaction properties of self-trapping beams in detail, the results show that the interaction do not change the profile of the beams, two beams keep oscillating around their collective center periodically. The amplitude and period of this oscillation are both determined by initial separation of two beams.

我们采用Sech函数为试探函数，用变分法求解CNLS方程，（1）给出了CNLS方程所对应的拉格朗日中的非线性耦合项的解析表达，（2）利用势阱模型详细分析两自陷光束之间相互作用的特性，结果表明，相互作用没有改变孤子的形态，它们分别在与传播方向垂直的方向上绕它们的公共中心做往复振动，振动幅度及周期都取决于两光束的初始分隔。

On the basis of a unified definition of the dual operation and theself dual operation, the connection s of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity.

利用内外指标的对偶运算及自对偶运算的统一定义，将su(2 ，2 |1)主丛联络作为基本场变量来构建自对偶的共形超引力拉氏函数。

Sometimes traditional separation of variables is not work anymore if the problem is presented in a Lagrangian system.

本文针对弹性圆柱壳在热荷载、冲击荷载以及两种荷载耦合作用下的屈曲问题，通过引入原变量与对偶变量组成的全状态变量，建立了系统的哈密顿体系。

2The definition of relative robustness was taken as Lagrangian slack variable to incorporate in the robust model for an innovative product supply chain.

2把相对稳健性作为一种松弛变量纳入到创新产品供应链的稳健优化模型中。

Particles are tracked by computing the acceleration and motion equations of individual spherical particle within the computational domain in a Lagrangian way.

实验表明，圆湍射流切向不稳定性触发的蘑菇头状的二级流向涡将导致圆湍射流初级拟序涡环结构轴对称性质消失。

After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods,the quantum theory of scalar and spinor fields, and then of gauge fields,is developed The emphasis throughout is on functional methods,which have played a large part in modern field theory.

近来，一个新的主题正崭露头角，这第三个主题与分数化、拓扑／量子序、弦网凝聚有关，也和新的物质态以及其中显现的规范玻色子和费米子相关。

This paper using trajectory planning based on spline function,rigid robot Lagrangian kinetics set up system mathematical model.

论文运用了基于插值样条函数的轨迹规划法，机器人手臂拉格朗日动力学方程建立了系统数学模型，为自动包装机机器人手臂系统设计提供了新思路。

As an application, we develop the real-valued implicit Lagrangian and the corresponding smooth merit function for SCCP, and give a necessary and sufficient condition for the stationary point of the merit function to be a solution of SCCP.

在一致Ca(来源：ABC5fe9论文网www.abclunwen.com)rtesian-P性质下，证明此价值函数可为SCCP提供一个全局误差界。最后，给出了求解SCCP的一个混合牛顿算法。

Based on the total Lagrangian description, general stress and strain iensors corresponding to Kirchhoff siress tensor and Green strain tensor are used in the process of derivation.

推导过程基于完全的增量形式Lagrange描述法，采用与Kirchhoff应力张量和Green应变张量对应的广义应力和广义应变张量进行分析。

A lagrangian relaxation heuristic algorithm based on subgradient optimization is applicated to solving the practical scale problems. The solution algorithms solving sub-problems are also listed.

提出了求解实际规模问题的基于次梯度优化的拉格朗日松弛启发式算法，并给出了各子问题的求解算法。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。