关于Mate-Nevai型非线性积分不等式

主要目的是将Mate-Nevai型积分不等式推广到非线性情形,得到了两个具有广泛意义的Mate-Nevai型非线性积分不等式,利用所得结论讨论某些积分方程解的有界性.     

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.     

具有服务水平的差异产品供应链网络均衡模型研究

顾客服务水平已成为当今企业获取较高市场占有率的重要手段。本文考虑了由多个供应商和多个零售商组成的供应链网络模型,通过制造商和零售商提供的服务水平,零售商的订货满足率以及零售价格等因素较为贴切的刻画消费者的选择偏好,利用变分不等式方法分析了制造商、零售商,需求市场以及整个供应链网络均衡条件,并给出了经济解释。最后,通过算例验证了模型的合理性。     

非紧超凸度量空间中的极大元定理及其对极大极小问题和鞍点问题的应用

在非紧超凸度量空间中的非紧次允许子集中建立了一个极大元定理．作为应用,研究了Fan-Browder型不动点定理、KyFan极大极小不等式和鞍点定理．     

n维欧氏空间En中Child不等式的推广

利用几何不等式理论与解析方法,研究了n维欧氏空间En中n维单形的内点到各顶点的距离与到各侧面距离之间的关系,获得相关的几个几何不等式,推广了Child不等式．     

两两PQD序列的完全收敛性和强大数定律

给出两两PQD序列部分和的几个不等式,研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

一个含参数的零齐次核的Hilbert型积分不等式

通过引入一个独立参数α及一对共轭指数,应用权函数的方法,建立了一个具有最佳常数因子的核为零齐次的Hilbert型积分不等式,作为应用,考虑了其等价式.     

Ergodicity of transition semigroups for stochastic fast diffusion equations

In this paper, we first show the uniqueness of invariant measures for the stochastic fast diffusion equation, which follows from an obtained new decay estimate. Then we establish the Harnack inequality for the stochastic fast diffusion equation with nonlinear perturbation in the drift and derive the heat kernel estimate and ultrabounded property for the associated transition semigroup. Moreover, the exponential ergodicity and the existence of a spectral gap are also investigated.     

A Noether type inequality

This paper gives a Noether type inequality of a minimal Gorenstein 3-fold of general type whose canonical map is generically finite.