φ-截曲率为常数的Sasaki统计流形中子流形的广义标准δ-Casorati曲率不等式

对φ-截曲率为常数的Sasaki统计流形中的子流形建立关于广义标准δ-Casorati曲率的不等式, 并给出不等式中等号成立的条件.     

基于可替换路径对的多用户均衡交通分配算法

针对多用户均衡交通分配问题，依据多用户均衡条件，给出了该问题的变分不等式模型和间隙函数。利用可替换路径对的概念，设计了基于可替换路径对的多用户均衡交通分配算法。在大规模交通网络上，对比分析了提出的交通分配算法、外梯度算法、基于用户的对角化算法和基于起点的对角化算法等的性能。数值结果表明，提出的基于可替换路径对的交通分配算法在求解精度、算法效率以及稳定性等方面都显著优于其他算法。     

模糊模式识别中隶属函数选取的探讨

通过数值实例,论证了利用最大隶属度原则对三角形类型模糊模式识别时隶属函数选取的优越性,并提出了一种给定阈值且以三角形内角和差关系作为底数变量和指数变量的指数型隶属函数.     

Ho∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system (NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller (S/C) and from controller to actuator (C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

Poisson方程各向异性一阶混合元格式

研究了Poisson方程在各向异性网格下的一阶混合元格式，在不引入传统投影算子的情况下，直接利用插值技巧得到了与以往文献相同的误差估计．     

关于垂足三角形的一个重要恒等式

给出了垂足三角形一个重要恒等式的证明,并给出这个恒等式的一些推论,其中包括与Ptolemy定理等价的“三弦定理”.最后,提出了有关垂足多边形的一个猜想.     

H_∞-based fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay

The fault detection problem for the nonlinear networked control system(NCS) with packet dropout and delay is investigated.A nonlinear stochastic system model is proposed to account for the NCS with random packet dropout and networkinduced non-uniformly distributed time-varying delay in both from sensor to controller(S/C) and from controller to actuator(C/A).Based on the obtained NCS model,employing an observer-based fault detection filter as the residual generator,the addressed fault detection problem is converted into an auxiliary nonlinear H∞ control problem.Then,with the help of Lyapunov functional approach,a sufficient condition for the desired fault detection filter is constructed in terms of certain linear matrix inequalities,which depend on not only the delay interval but also the delay interval occurrence rate and successful packet communication rate.Especially,a trade-off phenomenon between the maximum allowable delay bound and successful data packet transmission rate is found,which is typically resulted from the limited bandwidth of communication networks.The effectiveness of the proposed method is demonstrated by a simulation example.     

一类模式演化方程的全局吸引子及其维数估计

研究了一类源自模式演化问题的非线性发展方程所产生的动力系统,并考虑了其全局吸引子的存在性及维数估计问题.这类模式演化方程与化学反应和火焰燃烧有密切关系,因此具有重要的物理背景,而且因为它含有关于空间变量的四阶微分算子,还具有重要的理论价值.借助插值不等式以及sobolev嵌入定理,可以进行一系列精细的估计,最终根据一个经典的结果,证明了在维数不超过三维的空间中的有界集合上,系统的全局吸引子存在.进一步应用Sobolev-Lieb-Thirring不等式进行估计,可以得到全局吸引子的分形维数的界.     

On the Distribution of Prime-Triplets

A new approach to the research of the distribution of prime-triplets is developed．It differs from the usual methods（involving the sieve method）for this kind of research,and basing on Chebyshev inequality and on the computation of average concentration of all the related subset．It leads to the proofs of following Lemma ２and Theorem２（Lemma１and Theorem１in Reference１had been proved by means of this new method）： 　Lemma２　Among all the prime-triplet-subsets there exists at least one such subset which is an infinite set． 　Theorem２　All the prime-triplet-subsets or infinitely many such subsets are infinite sets． Formulas for estimating the amount of such infinite sets are provided in this paper．     

视景仿真系统中三维地形的实时生成方法

三维地形是虚拟自然环境中不可缺少的因素,也是虚拟仿真领域中视景系统的重要组成部分.三维地形的巨大数据量一直是视景仿真研究中的难点与热点.本文提出用函数曲面来保存地形顶点数据,在渲染开始前预先载入和计算生成地形数据,而在渲染阶段则利用视点相关LOD(Level of Detail)模型来简化渲染数据,实现大规模地形网格的绘制.实验结果表明,该方法能有效减少实时绘制时的计算量,提高绘制速度,较好地保证了大规模三维地形的实时生成效果.