变分法

The quantum size effect of a very small thickness circular disclike GaAs quantum dot on exciton's ground state binding energy and the electron-hole distance are studied by using calculus of variations.

利用变分法研究了有很小厚度圆盘形GaAs量子点模型中激子的基态结合能，及电子-空穴间距随量子点尺寸变化的规律。

Within the framework of the effective-mass approximation, hydrogenic impurity states confined in a cylindrical zinc-blende GaN/AlxGa1-xN single quantum dot are investigated by means of a variational approach.

在有效质量近似下，用变分法研究了闪锌矿GaN/AlxGa1-xN单量子点中的类氢杂质态。

The scaling rule for hydrogenic impurity binding energy and the Virial theorem value in quantum wells and wires of rectangular cross section with three different section ratios are studied through the variational method.

利用变分法计算了矩形量子线和量子阱中类氢杂质束缚能的度规法则和维里定理值。

In order to know irradiant dynamic process we must have excitation crosssection of electron collision with molecule. Incident electron energy is inintermediate range. At low energy, there are several good methods thatcalculate electron collision with molecule for example Variation, R-matrix.

此时入射电子的能量已经达到中能，在低能范围内的电子与分子散射有许多好的方法如变分法、R-矩阵方法，在高能范围内利用Born近似等方法也能得到满意的结果，在中等能量范围的电子与分子碰撞则没有相应的成熟的方法，使用比较多的是密耦(Closing-Couple)方法，这种方法将相互作用势分为静态势、交换势、极化势，在耦合态的选取上比较自由，可以根据实际的问题及分子的特性选取耦合作用比较强的通道，这样既能保证精度又能减少计算量。

We use the methods of Rayleigh-Ritz variational and multiconfiguration-interaction to study the excited states of the lithium isoelectronic.

中文摘要：本文采用多组态相互作用方法和Rayleigh-Ritz变分法，以类锂等电子系列为研究对象，重点研究了(Z=2)He-的亲和能和束缚能，氦负离子是最简单的类锂离子，我们首先计算了氦负离子1s2s2p~4Po的能量，然后又计算了氦原子1s2s~3S的能量，由此可以得到氦负离子的亲和能。

Furthermore, we discussed and pointed out the exact distinction of the meanings of reactive current, irregular current, reactive power and irregular power, then we give them proper mathematic definition with uniformed conception respectively, we established new power system, which is helpful for people to understand about nonsinusoidal system and its energy conversion much more deeply and substantialy, especially to gain new ideas on depressing and eliminating harmonic waves, and some new design method for more satisfying correcting power function, and different kinds of compensation and eliminating harmonic wave systems.

本文分析了传统的正弦系统有关定义及其与非正弦系统的异同，指出了前者存在的缺点，结合所给特例，讨论并确定了时域中非正弦系统有功电流和有功功率的严格定义，阐明了畸变功率在非正弦系统能量转换过程中所起的作用，在上述基础上，进而讨论并严格区分子无功电流、畸变电流、无功功率、畸变功率等的含义，并利用变分法给出了与上述含义相一致的各个概念的严格的数学定义；提出了新的功率体系。

The optical soliton propagation in monomode optical fibres with third-order dispersion is reinvestigated by using variational method. The evolution equations for optical soliton parameters are found, and self-wave-peak shift phenomena is explained quantitatively.

用变分法重新研究了单模光纤中的三阶色散对光孤子传输的影响，找到了光孤子参数的演化方程组，定量地解释了光孤子的自波峰漂移现象。

The combination with the Calculus,physics,especially variational principles and geometry is one of the features of tiffs dissertation.

本文在查阅大量原始文献和相关研究文献的基础上，利用文献分析和比较研究方法，以&为什么数学&为切入点，结合微积分学、物理学以及几何学等背景，对变分法的起源和创立进行了系统分析和研究。

The mechanism of instability wrinkling in the process based on minimum energy principle is revealed, uniform mathematic description of the wrinkling wave on the strip of in-plane bending is established, the internal and external energy is deduced by energy method, and a uniform criteria of internal and external wrinkling is established; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper. The effects of the forming parameters on the deforming result are analyzed by the uniform predict criteria. The results show as follows: as the compress width increase, external wrinkling first come into being, then internal winkling do, and finally in-plane bend occur; the loading wedge angle increase, internal winkling first come into being, thenin-plane bend do, and finally external wrinkling occur; in-plane bend is possible to occur with a increase of the strain-hardening exponent and the strength coefficient; and the effect of the friction factor may be ignored.

2揭示了板带不均匀压下面内弯曲成形过程基于能量原理的失稳起皱机理，提出了统一的描述内外缘起皱波形的函数，采用变分法推导了服从该波形函数的内外缘起皱能，建立了统一的起皱预测准则；将新建立的统一的起皱预测准则引入到数值模拟系统IBS中，数值预测结果与实验结果的吻合较好；分析了成形过程各参数对起皱的影响规律：随着接触变形区宽度的逐渐增大，先是发生外缘起皱，然后发生内缘起皱，进而才出现稳定成形；随着实际加载楔角的增大，先是发生内缘起皱，然后发生稳定成形，进而出现外缘起皱；硬化指数和强化系数增大，易于稳定成形；摩擦因子对起皱的影响不明显；而且接触变形区宽度对起皱的影响最大。

Angular Momentum Algebra, Addition of Angular Momenta, Identical Particle Effect, One Dimensional Periodic Quantum Systems, Introduction to Quantum Statistical Mechanics, Time-independent Perturbation Theory, Fine Structure, WKB Approximation, Variational Principle, Aharonov-Bohm Effect, Quantum Transition.

量子力学( S0583)(0，3)角动量代数、角动量加成、等同粒子效应、一维周期性量子系统、量子统计简介、定态微扰理论、精细结构、 WKB 近似、变分法、 Aharonov-Bohm 效应、量子跃迁。

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。