随机动力系统的进展和问题

本文主要介绍随机动力系统的主要成果和进一步研究的问题。     

闭曲面上C0流有伪轨跟踪性质的条件

给出了闭曲面上奇点孤立的C⁰流有伪轨跟踪性质的充分必要条件     

Controllable Magnetic Focusing of Cold Atoms on a Chip

We propose a new lens scheme to focus cold atoms by using a controllable inhomogeneous magnetic field from a square current-carrying wire fabricated on a chip. The spatial distributions of the magnetic field are calculated, and the results show that the generated magnetic field is a two-dimensional （2D） quadrupole one and can be used to focus cold atoms or a cold atomic beam. The dynamic processes of cold atoms passing through our square wire layout and its focusing properties are studied by using Monte Carlo simulations. Our study shows that the atomic clouds can be focused effectively by our magnetic lens scheme, and the focal length of the atomic lens and its radius of focused spot can be continuously changed by adjusting the current in the wires.     

Compact Single-Stage Femtosecond Multipass Ti：Sapphire Amplifier at 1 kHz with High Beam Quality

A compact femtosecond Ti：sapphire amplifier system is reported using single-stage multipass configuration with high beam quality. A high dispersion glass stretcher and a pair of double prisms for compression are introduced based on broadband femtosecond seed pulses. The non-grating-based pulse stretcher and compressor are advantageous to increase high beam quality and to reduce the high-order dispersion. A Gaussian filter is used to reduce the gain narrowing effect in amplification. The compact femtosecond Ti：sapphire nine-pass amplifier delivers pulses with a duration of 26 fs and an energy of 800μJ at 7mJ pumping pulses energy at I kHz. The 1-kHz femtosecond amplifier with high beam quality and high stability is very suitable for ultrafast physics research applications, such as attosecond science, ultra-precision micromachining, and THz wave generation.     

一种基于预测分类的小波图像编码

对于小波较像编码，如何有效地组织小波域系数是提高图像压缩效果的关键。本文在研究小波域系数统计特性的基础上，提出一种用于图像压缩的预测分类模式，与基于零树结构的编码不同的是它充分利用了小波域中“重要”系数的各种相关性，并通过结合提出的种子膨胀算法实现系数的分类输出，实验结果表明该方法所取得的压缩效果要优于基于零树结构的图像编码，同时又具有较强的鲁棒性。     

二阶三点半正边值问题正解的存在性

利用锥的Krasnosel'skill不动点定理建立了二阶三点半正边值问题u″+λf(t,u)+δg(t,u)=0, t∈(0,1),u(0)=0, αu(η)=u(1).其中,λ,δ＞0, 0＜η＜1, 0＜αη＜1正解的存在性,这里,非线性项不需要是非负的.     

灰关联的表现形式与点、斜关联量化方法的探讨

灰关联的传统量化方法及其分析应用十分普遍，但是有时也出现其量化结 果与实际不相吻合，原因何在呢？笔者认为在进行灰关联分析时，先得搞清楚 灰关联的表现形式与灰关联思想，然后对症下药地去寻找其量化方法．为此， 本文提出了探讨性的意见──点、斜关联的量化方法．通过实例验证，得到较 为满意的结果．     

沿非线性界面传输的TM波传播常数的解析解

本文得到了沿一线性介质与非线性介质界面传输的ＴＭ波精确的色散关系和传播常数的解析计算公式，导出了计算非线性介质中传输功率流的积分公式。本文方法计算传播常数及功率流的优点是可不必先知道电场分布。     

带有势的Schrodinger方程解的点态收敛性

本文将考虑Schrodinger方程：iρ／ρtu(x,t)=△u(x,t) v(x)u(x,t)的解沿光滑曲线γ（x,t）的点态收敛性，从而部分改进了[3],[5]和[8]的结论。