一类具有多个偏差变元的高阶中立型微分方程的周期解

利用Mawhin重合度理论,获得了一类具有多个偏差变元的高阶中立型微分方程(x(t)-cx(t-r))~(l)+h(x(t))x′(t)+■α~i(t)f(x′(t-μ_i(t))+■β_j(t)g(x(t-τ_i(t)))=p(t)周期解存在性的新结果,推广和改进了已有文献的相关结果.     

Coupled common fixed point theorems for w-compatible mappings in ordered cone metric spaces

We establish coupled coincidence point results for mixed g-monotone mappings under general contractive conditions in partially ordered cone metric spaces over solid cones. We also present results on existence and uniqueness of coupled common fixed points. Our results generalize, extend and unify several well known comparable results in the literature. To illustrate our results and to distinguish them from the earlier ones, we equip the paper with examples.     

Raman spectroscopic studies of vibrational relaxation and non‐coincidence effect in substituted benzaldehyde binary mixtures

The molecular interaction in the binary mixture of 3‐phenoxybenzaldhyde (3Phbz) and 4‐ethoxybenzaldehyde (4Etob) was analysed in four different solvents. The concentration dependence of vibrational relaxation of the CO stretching band of 3Phbz in different solvents was investigated by varying the concentration of the solute molecule in the solvents by performing Raman spectroscopic measurements. The self‐associated nature and the formation of hydrogen‐bonded complexes in the solute molecule, 4Etob, were considered to analyse the wavenumber separation between the peaks of hydrogen‐bonded and free carbonyl groups. Copyright © 2009 John Wiley & Sons, Ltd.     

Many-electron effect in the Fe L3-M4,5M4,5 Auger electron spectrum of ultrathin Fe films grown on Cu(1 0 0)

D’Addato et al. [S. D’Addato, P. Luches, R. Gotter, L. Floreano, D. Cvetko, A. Morgante, A. Newton, D. Martin, P. Unsworth, P. Weightman, Surf. Rev. Lett. 9 (2002) 709] studied the variation with Fe coverages in the relative Fe L₃-M_4,5M_4,5 Auger electron spectroscopy (AES) spectral satellite intensity of ultrathin Fe films grown on Cu(1 0 0) by sweeping photon excitation energy through the Fe L₂-level ionization threshold. They interpreted that the M_4,5 hole in the L₃M_4,5 double-hole state created by the L₂-L₃M_4,5 Coster–Kronig (CK) decay remains localized for longer than the L₃-hole lifetime for the 0.3 and 10 ML coverages but has a lifetime comparable to the L₃-hole lifetime for the 1 ML coverages. The present many-body theory shows that when the M_4,5 hole created either by the CK decay or by the L₃M_4,5 shakeoff hops away from the ionized atomic site and becomes completely screened out prior to the L₃-hole decay, the Fe L₂-L₃M_4,5-L₃-M_4,5M_4,5 AES main line as well as the Fe L₃ M_4,5 (satellite)-L₃-M_4,5M_4,5 one, both of which are identical in line shape to the Fe L₃-M_4,5M_4,5 one, dominate in the Fe CK preceded AES spectrum. The present analysis shows that the delocalization time of the M_4,5 hole created in the 1 ML Fe/Cu(1 0 0) system by the L₂-L₃M_4,5 CK decay is much shorter than the L₃-hole lifetime so that the Fe L₃-M_4,5M_4,5 AES spectral line shape hardly changes, except for the presence of a very weak spectator L₂-L₃M_4,5-M_4,5M_4,5M_4,5 AES satellite, when the photon excitation energy is swept through the Fe L₂-level ionization threshold. For the 0.3 ML coverages the M_4,5-hole delocalization time is still shorter than the L₃-hole lifetime.     

时间测度上一类种群动力系统的周期解

在时间测度上研究一类具有时滞和Beddington-DeAngelis功能性反应的n种群食物链系统.利用Mawhin重合度理论建立了这一类系统的正周期解存在的充分性条件,从而使这一类系统的连续时间和离散时间情形即微分方程和差分方程得到了统一研究.     

共振条件下积分边值问题解的存在性

运用Mawhin重合度理论建立了二阶Stieltjes积分边值问题解的存在性定理,其所得结果推广了多点边值问题已有的一些结论。     

基于马赫-曾德尔干涉仪的单个光子操控

分别利用空间和光纤马赫—曾德尔干涉仪对空间和光纤传输中的单个光子的干涉现象进行了研究,干涉对比度可达到90％以上,实现了空间和光纤中的单个光子的路由操控。实验采用脉冲调制加衰减的方法产生单个光子,获得了每个脉冲中只包含0．1个光子的准单光子源。通过改变压电换能器的电压控制马赫—曾德尔干涉仪的单个光子在两个输出端的选择,实现了光子在节点上的路由。采用同步符合检测技术,利用重复频率为1kHz,脉冲宽度为100ns的同步信号对输出信号进行符合,实现了量子效率高于70％,暗计数小于0．2s^-1的单光子高灵敏度检测,观测到了单个光子在相位操控下出射到两个输出端的有序分配现象。验证了基于马赫—曾德尔干涉仪的单个光子路由操控实现的可能性。     

Periodic solutions for a type of neutral system with variable parameters

In this paper, we firstly analyze some properties of the linear difference operator $[Ax](t)=x(t)-C(t)x(t-\tau),$ where $C(t)$ is a $n\times n$ matrix function, and then using Mawhin''s continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments $\tau$ and $\mu$. Meanwhile, the approaches to estimate a $prior$ bounds of periodic solutions are different from the corresponding ones of the known literature.     

一类带有回馈控制的捕食-食饵模型正周期解的存在性(英文)

研究了一类具有Hassell-Varely功能性反应函数的食饵-捕食模型的回馈控制系统,利用比较连续定理和一致度定理,证明了系统正周期解的存在性,并通过构造Lyapunov函数给出了系统全局稳定性的充分条件和证明.