Hadamard不等式的几种新证明

本利用几何算术不等式，矩阵的分解，行列式的性质给出Hadamard不等式几种新颖，简洁的证明。     

355nm Nd∶YAG激光在H_2中的高效一级斯托克斯转换

对脉冲Nd∶YAG激光(355 nm)在H2和H2∶He-Ar混合气体中的受激拉曼散射(SRS)进行了研究。在0.5 MPa的氢气中,同时测量到从二级反斯托克斯到三级斯托克斯的多波长输出,其总转化效率达88%;而高压下只剩下一级和二级斯托克斯输出,其中二级斯托克斯最大能量转化效率达44%(对应量子效率为63%)。由于高级斯托克斯的竞争,纯氢气中一级斯托克斯的最大能量转换效率不超过43%。通过向3 MPa氢气中掺入2 MPaAr气后,很好地抑制了二级斯托克斯的产生,从而获得了能量转换效率高达71%(对应量子效率为83%)的一级斯托克斯输出。对四波混频和级联受激拉曼散射在氢气多级斯托克斯产生中的作用以及惰性气体对它们的影响进行了讨论。     

《几何画板》教学实例

利用《几何画板》可以绘制动态直观的立体图形 ,通过图表的动静结合的交互演示 ,可以使枯燥生硬的图形变得生动形象 ,吸引学生的注意与兴趣 ,帮助学生实现从平面图形向立体图形 ,从二维平面向三维空间的过渡 ,培养学生的空间想象力 .本文通过用《几何画板》制作空间图形旋转时的直观图的教学实例 ,说明《几何画板》对优化教学环境 ,提高教学质量的促进作用 .1　旋转正棱柱的制作 (以正三棱柱为例) (如图 1 )1 )作一水平线段ＯＸ ,并在其上取一点Ｍ ,以图 1Ｏ为圆心 ,Ｍ、Ｘ分别为圆周上的点作小圆ｂ和大圆ａ ,过Ｏ作ＯＸ的垂线交大圆于点Ｐ …     

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota－Satsuma KdV system

In this paper,we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method.As a result,many explicit exact solutions,which contain new solitary wave solutions,periodic wave solutions,and the combined formal solitary wave solutions,and periodic wave solutions ,are obtained.     

Nonlinear Effects for Bose Einstein Condensates in Optical Lattices

Cold atoms and, more recently, Bose-Einstein condensates （BEC＇s） in optical lattices have attracted increasing interest since their first realization. In particular, the formal similarity between the wavefunction of a BEC inside the periodic potential of an optical lattice and of the electrons in a crystal lattice has triggered theoretical and experimental efforts alike. Many phenomena from condensed matter physics, such as Bloch oscillations and Landau-Zener tunneling have been shown to be observable also in optical lattices. An important difference between electrons in a crystal lattice and a BEC inside the periodic potential of an optical lattice is the strength of the self interaction and hence the magnitude of the nonlinearity of the system. Electrons in a metal are almost noninteracting, whereas atoms inside a BEC interact strongly. A＇ perturbation approach is appropriate in the former case while in the latter the full nonlinearity must be taken into account. From this feature new physics is expected. Most experiments to date have been carried out in the regime of shallow lattice depth, for which the system is well described by the mean field Gross-Pitaevskii equation with a periodic potential. Moreover, the nonlinearity induced by the mean-field of the condensate has been shown, both theoretically and experimentally, to give rise to instabilities in certain regions of the Brillouin zone. These instabilities are not present in the corresponding linear system, i.e. the electron system. Experimental and theoretical results on the subject of nonlinear Landau-Zener tunneling and nonlinearity-induced instabilities in a Bose-Einstein condensate interacting with an external periodic potential will be presented.     

一道解析几何题的多种解法

解析几何是用代数方法研究几何问题的数学分支，其中的题目可涉及到函数，三角，不等式等各种数学知识，这就决定了一个解析几何问题可能有多种不同的解法。解析几何的一题多解可以提高思维的灵活性，拓展人的思路，进而可以提高解决数学综合问题的能力。下面就以一道解析几何题给出几种不同的解法。     

二阶非线性椭圆型方程于无界域上的斜微商问题

在机械和物理中有许多问题的数学模型是一、二阶非线性椭圆型方程于包含无穷远点的多连通域上的某些边值问题,该文讨论了二阶非线性椭圆型方程于包含无穷远点的多连通域上的斜微商边值问题.     

从立方抛物线谈起(1)--余弦型振动,椭圆余弦型振动与双曲线型非周期运动

从立方抛物线的特性谈起 ,用较初浅的方法 ,借助于雅可比椭圆函数求椭圆方程的解来说明一大类一维保守系统的余弦振动、椭圆余弦型振动与双曲线型非周期运动 .并以杜芬振子、单摆、倒摆、转动圆环上的小环运动为典型实例作了详细讨论