变分法

In chapter II, we calculate the binding energy of a quantum wire in the presence of a strong magnetic field along the wire axis by using the variational method and strong perturbation method.

在第二章中，我们用变分法和强相互作用方法计算了在一个沿着轴向的强磁场下的量子线的束缚能，讨论了束缚能随着量子线的半径，磁场和掺杂浓度的变化。

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

We cosider a class of semilinear elliptic systems with the Neumann boundary value condition by using variational methods, two existences theorem are proved for under critical exponents and critical exponents.

利用变分法讨论了一类带Neumann边界条件的半线性椭圆方程正解的存在性，并得到了在下临界指标时的两个存在性定理。

Matrices, Vector and Vector Calculus, Newtonian Mechanics-single Particle, Oscillations, Nonlinear Oscillations and Chaos, Gravitation, Some Methods in the Calculus of Variations, Hamilton's Principles Lagrangian and Hamiltonian Dynamics, Central-Force Motion, Dynamics of a System of Particles, Motion in a Noninertia Reference Frame, Dynamics of Rigid Body.

矩阵和向量的计算、单一质点的牛顿力学、线性与非线性的振动运动、重力、微积分上的变分法介绍、哈密顿原理、拉氏及哈氏力学、连心力下的运动、质点系的运动力学、在非惯性坐标中的运动、刚体的运动。

On this basis, anoptimization algorithm library named OPTLIB is formed. The study of dynamic optimization theory is followed. To solve the problem of thecoupling of the static and the dynamic parameters of the flying vehicle design, some auxiliaryvariables are introduced to deal with them together. Then the calculus of variation is adoptedand augment form of Pontryagin's Maximum Principle is derived.

研究了飞行器设计中的典型动态优化问题——轨迹优化问题及算法，针对飞行器设计中的静态参数和动态参数互相耦合的问题，引入辅助变量将静态参数和动态参数统一处理，在此基础上用变分法推导了极大值原理的增广形式，证明了单独的静态或动态最优并不等于总体最优。

The calculus of variations; Euler's equation; the principle of least action;δ-method; the multiplier rule

基础科学，数学，古典数学变分法；欧拉方程；最小作用原理；δ-方法；乘子法则

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。

The reduced Lagrange density of nonlocal nonlinear Schrodinger equation is obtained by expanding the real symmetric response function in Taylor's series in strongly nonlocal Kerr media.

在非局域非线性克尔介质中，通过对介质实对称响应函数的泰勒展开，简化了非局域非线性薛定谔方程所对应的 Lagrange密度，进而利用变分法对光束的传输问题进行了分析。

The ground-state binding energy of an exciton confined in quantum wires and quantum wells in the presence of a uniform electric field has been calculated under the effective-mass approximation using variational approach.

本文采用变分法研究了外加电场下无限深方形量子线中重空穴激子的束缚能，我们用平面波展开的方法求解在电场作用下无限深方形量子线中电子和空穴的基态能和基态波函数及低激发态的能量和波函数，并用所得到的波函数进一步计算激子的基态及低激发态的束缚能，最后计算了激子的Stark能移。

The study on the mean number of phonons of the strong-coupling bondage polarons in magnetic field;2. The first excitation energy and the mean number of phonon of the strong-coupling magetopolarons in the polyatomic semi-infinite polar crystals were studied through a linear-combination operator and unitary transformation.

采用线性组合算符和幺正变换，利用变分法计算了多原子半无限极性晶体中由电子和光学声子强耦合相互作用所产生的磁极化子的第一激发能量及平均声子数，并通过适当的数值计算图示了它们与磁场的关系。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。