刘维尔

通过研究完备的、Ricci曲率非负的黎曼流形上的次调和函数的性质，给出了Yau的关于黎曼流形上的刘维尔定理的另一证明。

The property of subharmonic function on any complete Riemannian manifold with nonnegative Ricci curvature was studied , another proof of Yau 's Liouville Theorem on Riemannian manifold can be obtained .

刘维尔积极扶持年轻人的高贵品质使然；

The nobility character of Liouville to support younger ;

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘维尔分数阶积分、微分的概念和相关定理。

The thesis introduces the concept and relative theories of fractal interpolation function and the Reimann-Liouville fractional integral of order v and fractional differential .

讨论由黎曼-刘维尔（Riemann-Liouville）分数导数描述的黏弹性体力学问题的数值方法。

The numerical method of mechanical problems for the viscoelastic solids with Riemann-Liouville fractional derivative model is presented in this paper .

关于线性微分方程的刘维尔公式组

On the Liouville Formulas of Linear Differential Equation

对线性微分方程中的刘维尔公式做了适当的补充和讨论。

In this paper , we discuss and replenish Liouville formula of linear differential equation .

弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。

This paper weakened the Liouville s theorem conditions , and gives the Liouville theorem of a promotion .

通过求解多能级布洛赫模型下的量子刘维尔方程，我们发现：分子定向值对太赫兹脉冲的载波相位和两个脉冲之间的延迟时间很敏感。

Numerical calculations are performed by solving the quantum Liouville equation based on multilevel Bloch model . The molecular orientation degree is sensitive to the carrier-envelope phase of the THz pulse and the delay time between the two pulses .

本文从粒子束的相空间表示法和刘维尔定理出发，介绍了发射度和亮度的物理概念，简单地讨论了束的发射度和相空间密度分布的测量方法。

, . Starting from the phase space representation of particle beam and Liouville 's theorem , this paper presented the physical concepts of emittance and brightness and simply discussed the determination of particle beam emittance and density distribution in the transverse phase space projection .