The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains

ABSTRACT

We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure.     

基于几何光学法和惠更斯原理的微波暗室性能分析

微波暗室在导弹导引仿真中已广泛使用,针对导弹导引仿真试验中用到的微波暗室的静区性能评估问题,分别建立了基于几何光学法和惠更斯原理的评价分析模型.此模型考虑了暗室空间内各个壁面电磁辐射的相互影响,将壁面看作次级余弦辐射体,建立了描述壁面任一点垂直辐射强度的积分微分方程.通过离散方法将问题转化为求解线性方程组的数值问题.计算得到暗室壁面辐射强度分布以及性能指标γ.结果表明,垂直反射率为0.5时不满足要求,而0.05时满足要求.最后考察了模型的收敛性,随着离散度的增高,计算结果趋于稳定.     

具（口（t），P（t））-Laplacian项的二阶非自治系统周期解的存在性

本文用临界点理论中的能量最小原理得到了一类具（q（t）,P（t））-Laplacian项的二阶非自治系统存在周期解的充分条件．     

Optimal control of a vector borne disease with horizontal transmission

The paper presents the optimal control applied to a vector borne disease with direct transmission in host population. First, we show the existence of the control problem and then use both analytical and numerical techniques to investigate that there are cost effective control efforts for prevention of direct and indirect transmission of disease. In order to do this three control functions are used, one for vector-reduction strategies and the other two for personal (human) protection and blood screening, respectively. We completely characterize the optimal control and compute the numerical solution of the optimality system using an iterative method.     

Maximum principles for discrete-time nonlinear stochastic control systems

In this paper we treat discrete-time stochastic control systems. Using corresponding results for systems, which are linear with respect to the state variables, we derive under convexity assumptions optimality conditions in form of maximum principles     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Reconstruction of possibilistic behavior systems

Reconstructability analysis is viewed as a process of investigating the possibilities of reconstructing desirable properties of overall systems from the knowledge of the corresponding properties of their various subsystems. The reconstructability analysis consists of procedures for generating meaningful reconstruction hypotheses, procedures for the evaluation of the reconstruction hypotheses, and procedures for making various decisions regarding the acceptance of evaluated reconstruction hypotheses, generation of additional reconstruction hypotheses, termination of the analysis and the like.The paper discusses the evaluation of reconstruction hypotheses when the systems under consideration are possibilistic behavior systems. It is shown that a principle of maximum ambiguity, similar to the principle of maximum entropy for probabilistic systems, can be used for possibilistic systems. It is also shown that the unbiased (maximum ambiguity) reconstruction can be determined by a simple join procedure, in a similar fashion as for probabilistic systems. The join procedure for possibilistic systems turns out to be computationally simpler than the one for probabilistic systems. The paper also describes a general procedure for determining the reconstruction family.     

Whole-field digital measurement of principal stress directions in photoelasticity

A method that uses three light-field isoclinic images and the associated light-field unloaded model (or white) images for whole-field digital determination of the principal stress directions in photoelasticity is presented. Relevant theory is derived and explicit conditions for directly determining the directions to the range 0–π/2 are given. Tests of this method on a directly loaded two-dimensional disc and a stress frozen photoelastic slice are demonstrated. The results agree well with the values obtained from the manual method and/or the theory.     

Integral approximation sequences

Letn linear formsL _i onm variables be given, normalized so that all coefficients have absolute value at most unity. Letw ₁, ...,w _m be real numbers andx ₁, ...,x _m be integers. We sayE _i =L _i (w ₁, ...,w _m )-L _i (x ₁, ...,x _m ) is the error in approximating thew's by thex's with respect to formL _i It is shown that given anyw's there is an integral approximation ofx's so that the errorsE _i are small-roughly that simultaneously for alli.     

100例皮肤病患者发样微量元素的检测及多因素分析

对100例皮肤病患者发样中的Zn、Cu、Fe、Ca及Mg五种元素进行了检测，采用主成分分析及因子分析法对分析数据进行了统计学处理，探索皮肤病与该五种元素的关系，结果表明：Zn、Mg元素水平是皮肤病的重要样本特征，其中Mg元素是皮肤病的一个重要影响因子。其水平偏高及偏低者占病例数的92％；Cu、Fe元素水平基本正常；缺Zn影响则不是主要因素，低Zn者只占8％。可将皮肤病分为两大类：(1)Zn、Mg元素水平偏高类；占病例数的58％。(2)Ca、Mg元素水平偏低类，占病例数的32％。