黎曼

The duty of the drame and the music which was give by the subject was accomplished by three elements used in this dissertation as following:the musical theme"La Roi S'amuse"(from the opera"Rigoletto")was the center clue;the forming precess of the three main characters (Rigoletto、Duke and Gilda)was the major may to interprete the drama subject; meanwhile, their own Arias were used to rebuild the musical figures; and the chorus between each of them was the main means to put forward the plot of the drama.

本论文以歌剧《黎戈莱托》的主题"诅咒"作为主轴线，以歌剧中三个主人公(黎戈莱托、曼图阿公爵、黎戈莱托的女儿吉尔达)在歌剧中各自音乐形象的塑造过程作为对歌剧主题诠译的主要手段，同时又以他们各自在歌剧中的咏叹调作为塑造音乐形象的主要方式，以他们相互之间的合唱作为歌剧情节向前发展的重要方式，从而完成歌剧主题所赋予的戏剧任务和音乐任务。

One popular restriction is the use of "left-hand" and "right-hand" Riemann sums.

如果上的实函数是黎曼可积的，则它是勒贝格可积的。

We shall mainly study the existence and uniqueness of entropy solution to the associated Riemann Problem.

本文讨论了多条流入道路和流出道路的交汇处的交通流模型的数学理论，并重点研究了相应黎曼问题解的存在性和唯一性问题。

"It would be nice to work for Cambridge," he said."There are a few things I want to work on. I'd like to solve the Riemann Hypothesis."

他说，&能为剑桥工作是好事，能让我想要从事的事情不太多，我很愿意去解决一下黎曼猜想。&

"A geometer like Riemann might almost have foreseen the more important features of the actual world.

&，&一个像黎曼这样的几何学者几乎可以预见到现实世界的更重要的特徵。

Based upon studying its relationships with other subjects, this paper points out three origins of the idea of Riemann for geometry : mathematics, physics and philosophy.

在分析黎曼的几何思想和其他学科关系基础上，指出了其几何思想的三个来源：数学、物理和哲学。

They also pointed that the existence of an affine atlas is soley determined by the topology of the Riemann Surfaces.

同时也指出了样条函数的存在性与黎曼面的结构有着深刻的关系。

A new algorithm is presented to construct the Voronoi diagram in 2D Riemann manifolds.

本文提出了一种在二维黎曼流形中构造Voronoi图的新算法。

This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.

回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。

To compute the solution to the nonlinear equation of pressure in the Riemann problem for the pressure grdient equations, the Godunov scheme gives a reasonable approximate value for the exact solution. By using the Newton-Ruphson iteration method and some necessary computation, we get the inter-cell numerical flux directly.

为求压差方程黎曼问题中关于压力的非线性方程的解，Godunov格式给出一个合理的初始近似值，利用Newton迭代法和一些必要的计算得到格式中的数值流。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。