DISTRIBUTIONS OF LIMIT CYCLES FOR POLYNOMIAL VECTOR FIELDS (P_2, Q_3)

The distributions of limit cycles of cubic vector fields (P2, Q3) are considered in this paper, where P2 and Q3 are polynomials of x and y of order two and three, respectively. It is possibly seven different distributions of limit cycles given in [1]. We now prove that in which three kinds of distributions are impossible and other four kinds all can be realized by concrete vector fields of (P2,Q3). Some related results are also given.     

充实概率统计知识势在必行—对新高中数学教学大纲的一些认识

充实概率统计知识势在必行—对新高中数学教学大纲的一些认识饶汉昌（人民教育出版社１００００９）与《九年义务教育全日制初级中学数学教学大纲》（以下简称《义教大纲》）相衔接的《全日制普通高级中学数学教学大纲（供试验用）》（以下简称《新大纲》）已由国家教委颁...     

BIFURCATION DIAGRAMS OF SYSTEM =-y δx lx~2 ny~2,=x ax~2

Ｗｅｃｏｎｓｉｄｅｒｔｈｅｑｕａｄｒａｔｉｃｓｙｓｔｅｍｏｆｔｙｐｅ（Ｉ）ｍ＝０ａｃｏｒｄｉｎｇｔｏｔｈｅｃｌａｓｉｆｉｃａｔｉｏｎｏｆ［１］．Ｗｉｔｈｏｕｔｌｏｓｏｆｇｅｎｅｒａｌｉｔｙ，ｗｅｍａｙａｓｕｍｅｔｈａｔｔｈｅｓｙｓｔｅｍｉｓｔａｋｅｎ...     

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.     

关于自双反函数的性质之研究

阐述了双反函数、自双反函数和多数函数的定义,提出了自双反函数的性质.根据上述定义利用布尔代数中的基本概念、定理和公式证明了这些性质,展示了自双反函数在RM展开系数图(bj图)中的特点,讨论了自双反函数在函数分类中的应用.     

改进的本征态展开方法求解含时薛定谔方程

本改进了原有的本征态展开方法。通过从能量E到q=（2E）的平方根的表象变换，不仅准确地计算了在此方法中起重要作用的低能电子布居，而且大幅度地减少了计算时间。利用这个高效的方法，我们计算了在强激光作用下一个模型原子的高次谐波发射谱。     

怎样解动力学问题

动力学问题归根结底是既涉及力的作用，又涉及物体运动过程．解答这类问题，应抓住几个环节．１思路要正确，物理规律要掌握，并注意分析方法．动力学从三种角度研究力的作用效果，即力的瞬时效果，力的时间积累效果，力的空间（位移）积累效果．牛顿运动定律；动量定理和...     

Dynamic Mechanism of Sustainable Molecular Orientation Generated From Cyclic Rotational States

Recently, two papers presented by Ortigoso et al. [Phys. Rev. Lett. 93 （2004） 073001 and Phys. Rev. A 72 （2005） 053401] develop a novel strategy in which the best sustainable molecular alignment/orientation has been achieved. We intend to analyse the dynamic mechanisms, including those Ortigoso et al. have not clarified.