基于多级微反射镜的傅里叶变换红外光谱仪中准直误差的分析

通过对基于多级微反射镜的空间调制傅里叶变换红外光谱仪准直误差的分析,模拟了准直误差的存在而导致的干涉图大光程差处对比度反转和光谱图边频噪声的产生。讨论了在不同的误差系数下复原光谱图的信噪比和分辨率,并且分析了干涉图大光程差处对比反转以及光谱图边频分量的产生原因。仿真结果表明,在误差系数α=0.15°.mm-1时,光谱的信噪比会下降到6 dB,同时光谱分辨率会退化到13.4cm-1。本文的结论将应用于微型光谱仪系统的光学设计与装调。     

Motion of a vortex filament with axial flow in the half space

We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of initial–boundary value problems as an attempt to analyze the motion of a tornado.     

On the dynamics of radially symmetric granulomas

A granuloma is a collection of macrophages that contains bacteria or other foreign substances that the body?s immune response is unable to eliminate. In this paper we present a simple mathematical model of radially symmetric granuloma dynamics. The model consists of a coupled system of two semi-linear parabolic equations for the macrophage density, and the bacterial density. The boundary of the granuloma is free. This simple framework makes it possible to conduct a mathematical analysis of the system dynamics. In particular, we show that the model system has a unique solution, and that, depending on the biological parameters; the bacterial load either disappears over time or persists. We use numerical methods to establish the existence of stationary solutions and examine how a stationary solution changes with the reproductive rate of the bacteria. These simulations show that the structure of the granuloma breaks down as the reproductive rate of the bacteria increases.     

Relaxation-time limit and initial layer in the isentropic hydrodynamic model for semiconductors

This work is concerned with the relaxation-time limit in the multidimensional isentropic hydrodynamic model for semiconductors in the critical Besov space. Firstly, we construct formal approximations of the initial layer solution to the nonlinear problem by the matched expansion method. Then, assuming some regularity of the solution to the reduced problem, and proves the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval.     

Design of solids for antigravity motion illusion

This paper presents a method for designing solid shapes containing slopes where orientation appears opposite to the actual orientation when observed from a unique vantage viewpoint. The resulting solids generate a new type of visual illusion, which we call “impossible motion”, in which balls placed on the slopes appear to roll uphill thereby defying the law of gravity. This is possible because a single retinal image lacks depth information and human visual perception tries to interpret images as the most familiar shape even though there are infinitely many possible interpretations. We specify the set of all possible solids represented by a single picture as the solution set of a system of equations and inequalities, and then relax the constraints in such a way that the antigravity slopes can be reconstructed. We present this design procedure with examples.     

On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.     

永泰县城峰镇旗山小区后山滑坡现场应急调查及处置分析

2010年5月20日,受连续降雨影响,福建省永泰县城峰镇旗山小区后山发现有滑坡地质灾害隐患,后山中下部产生多条35~80m长拉裂缝,坡脚崩塌不断,潜在滑坡规模约8×10⁴m³,存在继续下滑的危险,情况十分危急,威胁坡脚居民2565人的生命和约5.38亿元财产。本文在对灾害现场进行详细地质调查的基础上,结合现场测绘、监测等手段,对该滑坡体的基本特征进行了较深入的调查研究,对滑坡发生及成灾原因进行了初步分析。结果表明,滑坡区地形条件及岩土体特征是滑坡发生的基本条件,连续降雨的饱水加载作用以及雨水沿节理裂隙结构面的下渗软化作用是诱发滑坡发生的直接原因。同时,根据滑坡险情特征,提出了应处置建议及应急卸载措施。最后,根据监测结果信息化指导应急卸载工作,确保了施工安全及受灾群众的生命财产安全。本次成功排险,对指导福建海沿地区地质灾害应急处置工作提供了科学依据。     

An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

In this paper, we investigate the positivity property for a class of 2-stage explicit Runge-Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.     

The method of upper and lower solutions and impulsive fractional differential inclusions

In this paper the concept of lower and upper solutions combined with the fixed point theorem of Bohnnenblust–Karlin is used to investigate the existence of solutions for a class of the initial value problem for impulsive differential inclusions involving the Caputo fractional derivative.