Stability in a general oligopoly model

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.     

Research on simultaneous localization and mapping for AUV by an improved method: Variance reduction FastSLAM with simulated annealing

At present, simultaneous localization and mapping (SLAM) for an autonomous underwater vehicle (AUV) is a research hotspot. Aiming at the problem of non-linear model and non-Gaussian noise in AUV motion, an improved method of variance reduction fast simultaneous localization and mapping (FastSLAM) with simulated annealing is proposed to solve the problems of particle degradation, particle depletion and particle loss in traditional FastSLAM, which lead to the reduction of AUV location estimation accuracy. The adaptive exponential fading factor is generated by the anneal function of simulated annealing algorithm to improve the effective particle number and replace resampling. By increasing the weight of small particles and decreasing the weight of large particles, the variance of particle weight can be reduced, the number of effective particles can be increased, and the accuracy of AUV location and feature location estimation can be improved to some extent by retaining more information carried by particles. The experimental results based on trial data show that the proposed simulated annealing variance reduction FastSLAM method avoids particle degradation, maintains the diversity of particles, weakened the degeneracy and improves the accuracy and stability of AUV navigation and localization system.     

对几种不同维数据融合方法的仿真对比研究

在多雷达系统组网对空情报处理中，不同的数据融合方法在融合精度、求解时间及计算量方面都有较大差异。为了验证不同融合方法的融合效果及系统处理时间和性能，分析了多雷达系统组网对不同维数据融合处理的映射法、升维法、分维法的融合框架和融合算法，并分别进行了计算机仿真，得出并分析了对比数据。仿真结果表明了分维法在数据融合中的优势。     

作战模拟态势显示中的通用性技术研究

态势显示是基于HLA的作战模拟系统中观察战场态势、辅助决策的关键一环.目前已经应用的态势显示系统暴露了态势显示通用性问题和态势显示适应性问题.这两个问题制约了态势显示手段在作战模拟领域中的应用.针对这些问题,提出了利用军标映射实现通用和仿真态势数据预处理方法两项关键技术来改进态势显示方法.随后实现了一个应用了这些技术的态势显示系统.最后总结了这种态势显示新方法的优势和不足并展望了态势显示系统下一步发展的方向.     

一类非线性二阶多点边值问题多个正解的存在性研究

通过定义适当的锥,运用锥映射的不动点定理,结合上下解方法,给出了二阶多点边值问题多个正解存在性的判定方法.作为特例,获得了三点边值问题多个正解存在性的判定依据,从而推广了相关文献中关于二阶三点边值问题正解存在性的结果.     

关于Reich的公开问题

设E是具有一致G -可微范数的实Banach空间 ,D是E的非空闭凸子集 ,T :D→D是非扩张映象 ,F(T)非空。设 {αn} ,{ βn}是 [0 ,1]中满足一定条件的两个序列 ,定义压缩映象St:D→D为 :St(z) =(1-t)x tTz , x ,z∈D , n≥ 1,t∈ (0 ,1) .设zt 是St 的唯一不动点 ,若当t→ 1-时 ,{zt}强收敛于某点z∈F(T) .那么 ,Reich序列 {xn}强收敛于某点z∈F(T) .