一个较精确加强型的半离散Hilbert型不等式

应用权函数的方法及Hermite Hadamard不等式, 建立一个较精确且加强型的半离散非齐次核Hilbert型不等式, 并给出该不等式具有最佳常数因子联系参数的一组等价性质及一些特殊参数不等式.      

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。     

微分中值定理的证明及应用中的辅助函数构造

微分中值定理是微分学的基础内容,也是用来研究函数性态的重要手段.因此,对微分中值定理的研究和再证明长期以来都是经久不衰的话题.通过对微分中值定理的再证明,不仅有利于初学者对定理的理解和掌握,也有利于其对定理的灵活运用,同时通过对微分中值定理的推广,还可以得到更加一般的情形.     

从一题多解看中值定理的应用

该文研究了高等数学中中值定理在解题中的应用,分别通过计算题和证明题的实例阐明了四个中值定理的有机联系及应用要点,以帮助学生更深刻地理解和掌握中值定理这一教学的重点和难点。     

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.     

洛伦兹函数均值和收入差距

分析了收入达不到洛伦兹函数均值的人口比例，以及这个比例和基尼系数的关系，探讨它所反映的贫富差距的信息，并通过模拟洛伦兹函数确定了参数取值与基尼系数在一定范围内的关系。     

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.     

齐次Poisson冲击模型中元件寿命递增的条件

证明元件寿命在齐次 Poisson 冲击模型中依期望序、反向失效率序、反向平均剩余寿命序、增凹序、Laplace 变换序等增加的充分条件,是促使元件失效的随机冲击次数也依相应的随机序增加.     

具有迷向S-曲率的指数度量

研究了Finsler几何中一类特殊(α,β)-度量-指数度量F=αeks的S-曲率性质.笔者通过把指数度量的S-曲率与其特殊S-曲率的表达式进行比较,采用代数方程公式运算的方法,分析方程因式指数的变化,得到了指数度量具有迷向S-曲率的充要条件:指数度量具有迷向S-曲率当且仅当它具有迷向平均Berwald曲率.此时,该度量的S-曲率为零,且是弱Berwald度量.结论表明:对于这类特殊的(α,β)-度量来说,它的曲率性质较简单,即它有迷向S-曲率等价于它有迷向平均Berwald曲率,等价于它具有为零的S-曲率.