Input-to-state stability of impulsive systems with hybrid delayed impulse effects

The goal of this paper is to study properties of input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive systems with hybrid delayed impulses, and a set of Lyapunov-based sufficient conditions ensuring ISS/iISS properties are obtained. Those conditions reveal the effects of hybrid delayed impulses on ISS/iISS and establish the relationship between impulsive frequency and the time delay existing in hybrid impulses. When the continuous dynamics of the system are stabilizing, the ISS property can be retained under the impulse scheme even if there exist destabilizing impulses. Conversely, when the impulse dynamics are stabilizing, but the continuous dynamics are not, the ISS property can be obtained if the interval between impulses are not overly long. Two illustrative examples are presented, with their numerical simulations, to demonstrate the effectiveness of the main results.     

具有饱和反应率和阶段时滞结构的害虫生物防治模型

考虑了一个害虫和天敌都有阶段结构及具有饱和反应率的阶段时滞脉冲捕食者-食饵模型,利用人工周期定量地投放有病的害虫和天敌去治理害虫.借助脉冲时滞微分方程的相关理论和方法获得易感害虫根除周期解全局吸引的充分条件以及天敌与易感害虫可以共存且易感害虫的密度可以控制在经济危害水平之下的充分条件.我们的结论为现实的害虫管理提供了可靠的策略依据.     

随机环境中随机指标分枝过程矩的渐近性

引入了随机环境中随机指标分枝过程模型,证明了该模型矩的渐近性。     

具脉冲效应和Beddington-DeAnglis功能反应时滞周期捕食系统

研究一类具有脉冲效应和Beddington-DeAnglis功能反应的时滞周期捕食系统,给出系统持续生存和周期解存在的条件.证明了在无时滞情况下,周期解是全局稳定的.     

Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation

This paper deals with the approximation of the tail probability of randomly weighted sums of a sequence of pairwise quasi-asymptotically independent but non-identically distributed dominatedly-varying-tailed random variables. The weights are independent of the former sequence, satisfying some assumptions about the moments. But no requirements on the dependence structure of the weights are imposed.     

Cluster TOF‐SIMS imaging of human skin remains: analysis of a South‐Andean mummy sample

A skin sample from a South‐Andean mummy dating back from the XI^th century was analyzed using time‐of‐flight secondary ion mass spectrometry imaging using cluster primary ion beams (cluster‐TOF‐SIMS). For the first time on a mummy, skin dermis and epidermis could be chemically differentiated using mass spectrometry imaging. Differences in amino‐acid composition between keratin and collagen, the two major proteins of skin tissue, could indeed be exploited. A surprising lipid composition of hypodermis was also revealed and seems to result from fatty acids damage by bacteria. Using cluster‐TOF‐SIMS imaging skills, traces of bio‐mineralization could be identified at the micrometer scale, especially formation of calcium phosphate at the skin surface. Mineral deposits at the surface were characterized using both scanning electron microscopy (SEM) in combination with energy‐dispersive X‐ray spectroscopy and mass spectrometry imaging. The stratigraphy of such a sample was revealed for the first time using this technique. More precise molecular maps were also recorded at higher spatial resolution, below 1 µm. This was achieved using a non‐bunched mode of the primary ion source, while keeping intact the mass resolution thanks to a delayed extraction of the secondary ions. Details from biological structure as can be seen on SEM images are observable on chemical maps at this sub‐micrometer scale. Thus, this work illustrates the interesting possibilities of chemical imaging by cluster‐TOF‐SIMS concerning ancient biological tissues. Copyright © 2012 John Wiley & Sons, Ltd.     

Modulating the Electron-Donating Ability of Acridine Donor Units for Orange–Red Thermally Activated Delayed Fluorescence Emitters

The development of thermally activated delayed fluorescence (TADF) emitters with orange–red emission still lags behind that of their blue, green, and yellow counterparts. Recent research to address this problem mainly focused on developing new acceptor units. There were few donor units designed especially for orange–red emitters. Herein, with benzothiophene fused to a diphenylacridine donor unit, a new donor moiety, namely, 5,5-diphenyl-5,13-dihydrobenzo[4,5]thieno[3,2-c]acridine (BTDPAc), was designed and synthesized. Benefiting from the strong electron-donating ability of the new donor moiety, a new TADF emitter, 2-[4′-(tert-butyl)(1,1′-biphenyl)-4-yl]-6-[5,5-diphenylbenzo[4,5]thieno[3,2-c]acridin-13(5H)-yl]-1H-benzo[de]isoquinoline-1,3(2H)-dione (BTDPAc-PhNAI), shows an orange–red emission with a maximum at 610 nm in dilute toluene solution. Also, with the help of the diphenyl rings of the donor unit, high photoluminescence quantum yields were achieved for BTDPAc-PhNAI over a wide concentration range. Consequently, an orange–red organic light-emitting diode based on BTDPAc-PhNAI achieved a high external quantum efficiency of nearly 20 %, which was comparable to state-of-the-art device performances with similar emission spectra.     

A simple approach to the wave uniqueness problem

We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction–diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone (hence, slowly oscillating) semi-wavefronts to the KPP–Fisher equation with delay. Similarly, a broad family of the Mackey–Glass type diffusive equations is shown to possess a unique (up to translation) semi-wavefront for each admissible speed.     

Stability and Hopf bifurcation in a class of nonlocal delay differential equation with the zero‐flux boundary condition

The aim of this paper is to study the stability and Hopf bifurcation in a general class of differential equation with nonlocal delayed feedback that models the population dynamics of a two age structured spices. The existence of Hopf bifurcation is firstly established after delicately analyzing the eigenvalue problem of the linearized nonlocal equation. The direction of the Hopf bifurcation and stability of the bifurcated periodic solutions are then investigated by means of center manifold reduction. Subsequently, we apply our main results to explore the spatial‐temporal patterns of the nonlocal Mackey‐Glass equation. We obtain both spatially homogeneous and inhomogeneous periodic solutions and numerically show that the former is stable while the latter is unstable. We also show that the inhomogeneous periodic solutions will eventually tend to homogeneous periodic solutions after transient oscillations and increasing of the immature mobility constant will shorten the transient oscillation time.