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Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min LiWang Guo-jun — 1997

Commentationes Mathematicae Universitatis Carolinae

In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

A modified quasi-boundary value method for the backward time-fractional diffusion problem

Ting WeiJun-Gang Wang — 2014

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an regularization parameter choice...

Stability analysis and absolute synchronization of a three-unit delayed neural network

Lin Jun WangYou Xiang XieZhou Chao WeiJian Peng — 2015

Kybernetika

In this paper, we consider a three-unit delayed neural network system, investigate the linear stability, and obtain some sufficient conditions ensuring the absolute synchronization of the system by the Lyapunov function. Numerical simulations show that the theoretically predicted results are in excellent agreement with the numerically observed behavior.

Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach

Jun-Min WangBao-Zhu GuoBoumediène Chentouf — 2006

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

Very true operators on MTL-algebras

Jun Tao WangXiao Long XinArsham Borumand Saeid — 2016

Open Mathematics

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...

On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback

Bao-Zhu GuoJun-Min WangCui-Lian Zhou — 2008

ESAIM: Control, Optimisation and Calculus of Variations

We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability...

Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach

Jun-Min WangBao-Zhu GuoBoumediène Chentouf — 2005

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

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