Multigroup SIR epidemic model with stochastic perturbation

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R₀≤1, which means the disease will die out. On the other hand, when R₀>1, we derive the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. Furthermore, we prove the system is persistent in the mean which also reflects the disease will prevail. The key to our analysis is choosing appropriate Lyapunov functions. Finally, we illustrate the dynamic behavior of the model with n=2 and their approximations via a range of numerical experiments.     

基于光纤的三维可调胶体光子晶体

用改进的垂直沉积法在光纤端面制备了高质量的SiO₂胶体光子晶体,经过烧结、固化构成胶体光子晶体-光纤结构. 用扫描电子显微镜确定了样品为面心立方密排结构,其密排面平行于光纤基底表面. 利用全光纤传感网络测试了该胶体光子晶体,反射峰中心位于845 nm处,与Bragg理论计算值符合很好. 将该样品浸入不同折射率的液体中,反射光谱的峰值位置随着液体折射率的改变而发生偏移,近似呈线性关系,实现了峰位可调. 对于不同浓度引起的液体折射率的变化,基于光纤的胶体光子晶体结构也能够很好地分辨出来. 关键词： 可调胶体光子晶体 2微球')" href="#">SiO₂微球 Bragg反射 光纤     

A note on a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

In this paper, we show there is a stationary distribution of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation and it has ergodic property.     

A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM

In this paper, a novel method is proposed for solving nonlinear two-point boundary value problems (BVPs). This method is based on a combination of the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). A major advantage of this method over standard ADM is that it can avoid unnecessary computation in determining the unknown parameters. The proposed method can be applied to singular and nonsingular BVPs. Numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two-point boundary value problems.     

A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method

In this paper, a novel method is presented for solving a class of singularly perturbed boundary value problems. Firstly the original problem is reformulated as a new boundary value problem whose solution does not change rapidly via a proper transformation; then the reproducing kernel method is employed to solve the boundary value new problem. Numerical results show that the present method can provide very accurate analytical approximate solutions.     

Reproducing kernel method for singularly perturbed turning point problems having twin boundary layers

A numerical method is proposed for solving singularly perturbed turning point problems exhibiting twin boundary layers based on the reproducing kernel method (RKM). The original problem is reduced to two boundary layers problems and a regular domain problem. The regular domain problem is solved by using the RKM. Two boundary layers problems are treated by combining the method of stretching variable and the RKM. The boundary conditions at transition points are obtained by using the continuity of the approximate solution and its first derivatives at these points. Two numerical examples are provided to illustrate the effectiveness of the present method. The results compared with other methods show that the present method can provide very accurate approximate solutions.     

微喇曼和红外光谱法研究化学气相沉积金刚石多晶膜结晶质量特性

研究了化学气相沉积多晶膜的宏观性能（颜色和透光性）与微观性能（结晶质量、相纯度和氢杂质含量）之间的关系,喇曼谱与金刚石膜中氢杂质含量（红外光谱测得）的关联性.给出了根据颜色和透明度来区分样本膜质量的实验依据,颜色较深的膜的结晶质量差、相纯度低、氢杂质含量高,1 332 cm－1金刚石特征喇曼峰强度低,半峰宽大.由于多晶膜生长不均匀性、多晶以及粗糙度的影响,生长面的微喇曼光谱随采样点变化会产生较大的偏差,而光滑生长界面的喇曼光谱随采样点的变化偏差较小,因此生长界面的喇曼光谱更能反映化学气相沉积法制备金刚石膜的整体质量.     

Study on the structural characteristics of HgCdTe photodiodes using laser beam-induced current

The structural characteristics of typical n⁺-on-p HgCdTe photodiodes have been studied by laser beam-induced current (LBIC). The dependence of LBIC on laser wavelength, junction depth and localized leakage has been presented. The diffusion length of minority carrier of p-type region is extracted by the exponential decay fitting of the curve of LBIC. It is found that the peak magnitude of LBIC and junction depth approximate to a linear relationship for practical values of device fabrication. The diffusion length monotonously increases with the junction depth. A notable shift of LBIC profile is observed when localized leakage exists. This provides a useful explain for LBIC applying to characterize the structure and process uniformity of HgCdTe infrared detectors.     

Solvable complete lie algebras. I ∗

In this paper, we will discuss the properties of solvable complete Lie algebra, describe the structures of the root spaces of solvable complete Lie algebra, prove that solvable Lie algebras of maximal rank are com-plete, and construct some new complete Lie algebras from Kac-Moody algebras.     

Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

In this paper, we consider a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique positive solution to the system with positive initial value, and mainly investigate the long time behavior of the system. Condition for the system to be extinct is given and persistent condition is established. At last, numerical simulations are carried out to support our results.