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For nonlinear harmonic oscillators, we close the flow equations and acquired an explicit expression of energy-level. For nonlinear-coupled harmonic oscillators, we close the flow equations and diagonalize the Hamiltonian by numerical analysis methods.

对非线性谐振子系统，计算出系统参数随流参数变化的一组方程及系统的能级；对耦合的非线性谐振子系统，得出系统参数随流参数变化的一组非线性方程，数值分析对角化了系统。

For nonlinear harmonic oscillators systems of coordinate coupling and momentum-coupling, one obtains a group differential equations for physical parameters about flow parameter by the numerical analysis method, one finds this method can diagonalize the Hamiltonian.

通过数值分析物理参数随流参数变化规律，给出了对角化的哈密顿量。

His main research direction is System of Hamiltonian, Table of Operator of Schrodinger, Differential operator and Small Wave Theory.

主要研究方向：Hamiltonian系统，Schrodinger算子的谱，微分算子、小波理论。

The fine structure Hamiltonian for Hydrogen-like atoms is derived using the nonrelativistic approximation of the Dirac equation for one electron moving in the Coulomb field.

从Coulomb场中运动的电子的Dirac方程出发，取其非相对论极限导出了类氢离子的精细结构哈密顿的表达式。

If d +d ≥n for every two strongly disjoint independent sets S and T with|S|=s and|T|=1, respectively, then G is hamiltonian.

设s，t是两个正整数，G是一个2-连通n阶图，若对任意两个强不交独立集S和T，其中|S|=s，|T|=t，有d+d≥n，则G是哈密尔顿图。

If d +d ≥n for every two strongly disjoint independent sets S and T with|S|=s and|T|=t, respectively, then G is hamiltonian.

若对任意两个强不交独立集S和T，其中|S|=s，|T|=t，有d+d≥n，则G是哈密尔顿图。

The fitted rms error based on the Hamiltonian with 9 parameters was 2.40 cm-1. The dissociation energy and force constant were also determined by the analytical potential energy surface.

结果表明，利用此代数Hamiltonian很好的实现了能级再现，它预测了振动总量子数达到20的全部振动能级，同时我们计算了分子的解离能与力常数。

In the second part, we have considered the polariton system described by the model effective Hamiltonian involving single mode photon field interacting with a transverse optical phonon in a more realistic form. On this basis, we have discussed the dynamical evolution of the wave function , the dynamical variables and the non-classical properties for the system in a analytic form for the first time.

第二部分将极化激元系统约化成模型单模光子—横向声子有效相互作用系统，在此基础上以解析形式首次讨论了系统的波函数、力学量和压缩态、亚泊松分布等非经典效应的动力学演化行为。

As an application, the completeness of the eigenfunction system of the infinite dimensional Hamiltonian operator corresponding to a wave equation is given.

作为应用，还给出了波动方程导出的无穷维Hamilton算子特征函数系的完备性。

Finally, to understand and reproduce the results of numerical simulations, we propose a phenomenological noise driven equations describing evolutions of macroscopic variables under the assumption of local energy equipartition and the fluctuation-dissipation theorem. The numerical results of the stochastic equations and those of numerical results from the original Hamiltonian dynamics coincide with each other very well.

最后，为了理解和重现数值模拟的结果，我们通过局域能量均分假设和涨落耗散定理，建立了一个由噪声驱动的宏观变量演化的唯象动力学方程。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。