Set covering location models with stochastic critical distances

This paper formulates a new version of set covering models by introducing a customer-determined stochastic critical distance. In this model, all services are provided at the sites of facilities, and customers have to go to the facility sites to obtain the services. Due to the randomness of their critical distance, customers patronize a far or near facility with a probability. The objective is to find a minimum cost set of facilities so that every customer is covered by at least one facility with an average probability greater than a given level α. We consider an instance of the problem by embedding the exponential effect of distance into the model. An algorithm based on two searching paths is proposed for solutions to the instance. Experiments show that the algorithm performs well for problems with greater α, and the experimental results for smaller α are reported and analysed.     

非Lipschitz条件下的包含下微分算子的带跳倒向随机微分方程(英文)

本文在非Lipschitz系数下,考虑了一类多值的倒向随机微分方程.利用极大单调算子的Yosida估计和倒向随机微分方程在非Lipschitz条件下解的存在唯一性,获得了多值带跳的倒向随机微分方存在唯一解的结论.     

Hausdorff算子在Triebel-Lizorkin型空间上的有界性

证明了Hausdorff算子HΦ及HΦ,A在Triebel-Lizorkin型空间Fα,τp,q,上的有界性,并且求得HΦ相应的算子范数.     

ON GLOBAL ROBUST STABILITY FOR COMPETITIVE NEURAL NETWORKS WITH TIME DELAYS AND DIFFERENT TIME SCALES

In this paper, using the theory of topological degree and Liapunov functional methods, the authors study the competitive neural networks with time delays and different time scales and present some criteria of global robust stability for this neural network model.     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

一类具有连续变量的二阶非线性阻尼差分方程的振动准则

考虑了一类具有连续变量的二阶非线性阻尼差分方程,利用积分变换和广义R iccati变换,给出了此类方程的振动准则.     

Dynamics of an SIR epidemic model with limited medical resources revisited

The dynamics of an SIR epidemic model is explored in this paper in order to understand how the limited medical resources and their supply efficiency affect the transmission of infectious diseases. The study reveals that, with varying amount of medical resources and their supply efficiency, the target model admits both backward bifurcation and Hopf bifurcation. Sufficient criteria are established for the existence of backward bifurcation, the existence, the stability and the direction of Hopf bifurcation. The mechanism of backward bifurcation and its implication for the control of the infectious disease are also explored. Numerical simulations are presented to support and complement the theoretical findings.     

Equivalent Conditions for Local Error Bounds

In this paper we present two classes of equivalent conditions for local error bounds in finite dimensional spaces. We formulate conditions of the first class by using subderivatives, subdifferentials and strong slopes for nearby points outside the referenced set, and show that these conditions actually characterize a uniform version of the local error bound property. We demonstrate this uniformity for the max function of a finite collection of smooth functions, and as a consequence we show that quasinormality constraint qualifications guarantee the existence of local error bounds. We further present the second class of equivalent conditions for local error bounds by using the various limits defined on the boundary of the referenced set. In presenting these conditions, we exploit the variational geometry of the referenced set in a systematic way and unify some existing results in the literature.     

Weighted estimates for commutators of higher dimensional Hardy operators

得到了由加权Lipschitz函数(或加权CMO函数)和n维Hardy算子生成的交换子在一些函数空间的有界性,例如加权Lebesgue空间,加权Herz型空间.     

Oscillation criteria for second order linear matrix differential systems with damping

Using a generalization of Sturm’s comparison theorem, some new oscillation criteria are established for the matrix differential system with damping

(P(t)Y^′)^′+R(t)Y^′+Q(t)Y=0${\left(P\left(t\right)Y^{\prime }\right)}^{\prime }+R\left(t\right)Y^{\prime }+Q\left(t\right)Y=0$