A novel robust proportional-integral （PI） adaptive observer design for chaos synchronization

In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.     

WEIGHTED BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL HARDY OPERATORS WITH BESOV-LIPSCHITZ FUNCTIONS

In this paper,we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions.The main result is that this kind of commutator,denoted by Hb α,is bounded from L x γp (R +) to Lx δ q (R +) with the bound explicitly worked out.     

Aczel积分形的不等式推广

在文献［１］推广了有限和式的Ａｃｚｅｌ不等式，本文继续给出积分形式的Ａｃｚｅｌ不等式。     

分形集上广义凸函数的新Hermite-Hadamard型不等式及其应用

基于局部分数阶微积分理论,利用分形集上广义凸函数的定义,对Hermite-Hadamard型不等式进行一些有意义的推广,得到了几个分形集Rα(0α≤1)上涉及局部分数积分的新Hadamard型不等式.最后,给出了其在特殊均值和数值积分中的几个应用.     

H~1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley $g$ function and the Lusin area function for the Jacobi hypergroup and consider their $(H^1, L^1)$ boundedness. Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses better property than the classical $g$ operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the $(H^1, L^1)$ estimate for the Lusin area operator, a slight modification in its form is required.     

巧用斜坐标系解决一类二元一次线性规划问题

平面向量的基本定理里谈到:两个不共线的向量可以作为这个平面内所有向量的一组基底.而平时的数学问题中,也常建立平面直角坐标系来解决问题,但平面向量的这一组基底里的两个向量并不一定都是垂直关系.这种不统一性给我们解决某些问题带来了许多不便之处.例如下面的一个问题例题如图1,正六边形ABCDEF,P是△CDE内（包括边界）的动点,设AP=αAB+βAF（α,β∈R）,则α+β的取值范围是___     

彩色噪声驱动的分数阶随机热方程的传输不等式

本文研究了一类分数阶随机热方程的传输不等式.这类方程是由高斯噪声驱动的,其中关于时间是白的、关于空间是彩色的.利用Girsanov定理,我们在轨道空间上关于加权的L2范数得到了 Talagrand传输不等式.这在一定程度上推广了 Boufoussi和Hajji(2018)中的结果.     

核范数函数的广义变分不等式问题的稳定性

本文主要研究凸函数为线性矩阵映射核范数的广义变分不等式(generalized variational inequal-ity,GVI)问题的稳定性,提出GVI问题的严格Robinson约束规范和二阶充分最优性条件,并证明它们是KKT (Karush-Kuhn-Tucker)映射逆映射孤立平稳性的充分条件;还给出GVI...     

一类新的求解双边障碍问题的数值方法

针对双边障碍问题的离散互补形式,提出了一类新的格式将其等价转化为方程组的形式,并采用牛顿迭代法进行求解.实验结果显示所提算法能快速,有效地计算出数值解和接触集.     

分数次积分交换子的加权Hardy型估计

本文研究了分数次积分交换子的加权Hardy型估计.利用加权Hardy空间的原子分解理论,得到了分数次积分算子与加权Lipschitz函数生成的交换子在加权Hardy空间上的有界性质,推广了陆善镇等在2002年中国科学A上的结果.