Sharp oscillation and nonoscillation tests for delay dynamic equations

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp.     

Volterra积分方程和泛函微分方程的振动性

本文建立了Ｖｏｌｔｅｒａ积分方程和一阶泛函微分方程解的振动准则．     

非线性光子晶体中原子辐射光场的非经典性质

讨论了非线性光子晶体微腔中二能级原子在相干场驱动下腔场的频谱特性及光子的统计性质.研究结果表明,当光子晶体的态密度很大时,如果腔场模与原子共振荧光Mollow峰的中心峰共振,则腔场的涨落压缩到量子散弹噪声之下,且与线性光子晶体微腔的情况相比其谱线峰值变大.当驱动场频率较大时光子服从亚Poisson分布,且非常接近Poisson分布.     

一阶中立型时滞差分方程振动的充分必要条件

研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在01两种情况下该方程的一切解振动的充分必要条件.     

一类具有连续变量的二阶非线性阻尼差分方程的振动准则

考虑了一类具有连续变量的二阶非线性阻尼差分方程,利用积分变换和广义R iccati变换,给出了此类方程的振动准则.     

Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations

The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.     

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z of positive integers and for differential equations when the time scale is the set R of real numbers.     

Device research on GaAs-based InAlAs/InGaAs metamorphic high electron mobility transistors grown by metal organic chemical vapour deposition

This paper applies a novel quad-layer resist and e-beam lithography technique to fabricate a GaAs-based InAlAs/InGaAs metamorphic high electron mobility transistor (HEMT) grown by metal organic chemical vapour deposition (MOCVD). The gate length of the metamorphic HEMT was 150~nm, the maximum current density was 330~mA/mm, the maximum transconductance was 470~mS/mm, the threshold voltage was -0.6~V, and the maximum current gain cut-off frequency and maximum oscillation frequency were 102~GHz and 450~GHz, respectively. This is the first report on tri-termination devices whose frequency value is above 400~GHz in China. The excellent frequency performances promise the possibility of metamorphic HEMTs grown by MOCVD for millimetre-wave applications, and more outstanding device performances would be obtained after optimizing the material structure, the elaborate T-gate and other device processes further.     

中立型时滞差分方程解的渐近性

给出了中立型时滞差分方程△（ｘｎ＋ｐｘｎ－ｋ）＋ｑｎｆ（ｘｎ－ｍ）＝０一切非振动解趋于零（ｎ→∞）的充分条件，证明了方程（Ｅ）一切解振动的两个新的定理。     

华罗庚与爱因斯坦相对论及其扩展——纪念华罗庚诞辰一百周年

华罗庚先生运用矩阵几何与投影几何,研究并简化了爱因斯坦狭义相对论的基本原理,得到惯性运动的对称性,并促进了对德西特不变的狭义相对论的研究.他的深入考察至今仍引领着我们如何面对精确宇宙学的挑战.爱因斯坦相对论作为以宇宙常数Λ>0为特征的宇观物理学的基础面临疑难.相对性原理应该扩充到具有两个不变普适常数c和l,具有24个生成元的惯性运动对称性的相对性原理.于是,存在庞加莱、德西特和反德西特不变的3种相对论,伴随着对偶庞加莱运动学,它们构成相对论三位一体.取……,德西特相对论提供宇观尺度之新运动学,亦可避开相对性的宇宙佯谬.华老不仅是大数学家,而且是大思想家和大教育家,是一位为复兴中华民族而奉献终身的伟大代表.