Poincaré-Bendixson环域定理的推广

Poincare-Bendixson环域定理是平面动力系统最基本的结论之一,在应用上也极为重要.文献[3]指出,它基本上是由解的存在唯一性和Jordan定理这个简单的几何事实推得的.本文证明,当一个平面微分系统的解不满足唯一性时,Poincare-Bendixson环域定理的结论仍然成立.推广后的环域定理在应用上是方便的.在本文后半部分,我们考虑了Lienard方程的极限环的存在性问题,所得定理推广了著名的定理。     

某些微分差分方程的周期解

本文给出了微分差分方程及 x′(t)=-g(x(t))F(x(t),x(t-1))x′(t)=-g(x(t))F(x(t),x(t-1),…,x(t-n))存在非平凡周期解的充分条件。     

DYNAMIC SPECTRAL ANALYSIS OF INFRASONIC SIGNAL WITH HILBERT TRANSFORM

In the past we analyzde the dynamic spectrum of infrasonic waves with FFT,but that isnot suitable to this analysis in any case.In this paper another method is proposed to analyzeinfrasonic waves.This method is that,after digital filtering of the signal and Hilbert transform,this paper the computation of the envelope with Hilbert transform and 1/12-octave filter are dis-cussed.Then a synthetic infrasonic signal generated by a large nuclear explosion is analyzed withthe two methods,and their results are compared.It is shown that,in the dynamic spectrum,usingHilbert transform,not only higher resolution is obtained,the main frequency range of separatedmodes can be achieved,but also their waveform can be obtained preliminarily for some modes.Thus it seems that in some cases this method is more efficient for discovering the characteristicsof an infrasonic signal.     

从语言信号中提取基频的一种新方法

从语言信号中提取基频是语言声学中尚未满意解决的一个问题.近年来随着计算技术的发展,相继提出了多种方案,但在准确性和复杂性的矛盾上,仍有待进一步研究.本文提出了一种提取语言信号基频的新方法:用递归数字滤波器搜索和逻辑判决.经过在计算机上的模拟和硬件研制的实践证明,效果很好,合成语言有较好的自然度与可懂度,且硬件简单,适合于通信工程使用.     

具反馈控制和无穷时滞单种群模型周期正解

利用重合度理论和Liapunov泛函方法讨论了具反馈控制的无穷时滞单种群模型周期正解的存在性和全局吸引性，得到了周期正解存在和全局吸引的充分条件，推广并改进了某些已知相关结果。     

关于提高中学数学教学质量的几点措施

《中学数学教学大纲(试用草案)》中提出:“在中学阶段,数学是一门重要课程,必须进一步提高数学教学质量,给学生打好数学基础,以适应实现四个现代化的需要。” 多年来的教学实践,使我深深体会到:要想提高数学教学质量,教师必须深入钻研教材,熟悉教材。不仅需要通晓课本上的全部内容,而且必须注意教材     

无限时滞泛函微分方程周期解的存在性

J.K.Hale和J.Kato关于具无限时滞的滞后型泛函微分方程提出了很好的相空间理论,以这个理论为基础,本文把T.Yoshizawa的一个著名的关于有限时滞方程周期解的存在性定理推广到无限时滞的情况。     

CHARACTERISTICS OF A UNIFORM PIPE ARRAY AND ITS APPLICATION TO INFRASONIC RECEPTION

In this paper the acoustic behaviour of a uniform pipe array,one end of which is connected to aninfrasonic transducer and the other is terminated with an acoustic impedance,is discussed.Both theo-retical analysis and computation of the response of the pipe array are given.Influenes of the impedan-ces at the terminal and of the transducer on the response are shown.By using these results the frequen-cy and phase responses and the directivity can be calculated as a plane sound wave pass across thearray. The pipe array is used for detecting the infrasonic or gravity waves in wind noise.A model of windnoise is established and its average power spectrum density function and coherence can be computed.Based on the theoretical analysis of the pipe array,some imporvement in the signal-to-noise ratioof infrasonic waves in the wind noise back-ground can be got by calculation.Results of a numericalexample obtained by computer programme are given.It is found that there is a significant improve-ment in the period range     

Tm:K2YF5晶体的光谱参量计算

测量了Tm:K2YF5晶体的吸收光谱,根据Judd-Ofelt理论计算了Tm3+在K2YF5中的强度参数:Ω2=5.02×10-20cm2,Ω4=3.40×10-20cm2,Ω6=0.38×10-20cm2,以及Tm3+激发能级的自发辐射跃迁几率A,荧光分支比β,荧光寿命τ和积分发射截面∑等光谱参量.