This work deals with the study of a plane periodic multilayer structure in which the elementary stack consists of two plates in contact: one in aluminum (AL) and the other one in polyethylene (PE). These isotropic mat...This work deals with the study of a plane periodic multilayer structure in which the elementary stack consists of two plates in contact: one in aluminum (AL) and the other one in polyethylene (PE). These isotropic materials, present a high acoustic impedance contrast. The attenuation of the longitudinal and transverse waves is taken into account in the polyethylene but neglected in the aluminum plate. The effect of different defects is analyzed. Firstly, we focus on the effect of the presence of grease inclusion in the polyethylene plate (considering the two plates of the elementary stack in perfect contact). Secondly, the effect of disbond simulated by the insertion of a thin Teflon layer between the interfaces of the two layers constituting the elementary stack of the multilayer structure is investigated. Finally, the effect of the stacking sequences of the multilayer is analyzed. In order to obtain the effective acoustic parameters of polyethylene layer, allowing to evaluate the reflection and transmission coefficients using the stiffness matrix method developed by Rokhlin <em>et</em> <em>al</em>., four homogenization models are analyzed, then the best one to our configuration is chosen. The comparison of the simulation results is carried out.展开更多
This paper is devoted to problems stated by Z. Zhou and ELi in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topolo...This paper is devoted to problems stated by Z. Zhou and ELi in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The negative answer follows by our recent paper. But for continuous maps of the interval and other more general one-dimensional spaces we give more results; in some cases the answer is positive.展开更多
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient condit...In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient conditions are established. In particular, for the alm ost periodic system , the existence of strictly positive alm ostperiodic solutions is obtained. Som e previous results are im proved and generalized.展开更多
文摘This work deals with the study of a plane periodic multilayer structure in which the elementary stack consists of two plates in contact: one in aluminum (AL) and the other one in polyethylene (PE). These isotropic materials, present a high acoustic impedance contrast. The attenuation of the longitudinal and transverse waves is taken into account in the polyethylene but neglected in the aluminum plate. The effect of different defects is analyzed. Firstly, we focus on the effect of the presence of grease inclusion in the polyethylene plate (considering the two plates of the elementary stack in perfect contact). Secondly, the effect of disbond simulated by the insertion of a thin Teflon layer between the interfaces of the two layers constituting the elementary stack of the multilayer structure is investigated. Finally, the effect of the stacking sequences of the multilayer is analyzed. In order to obtain the effective acoustic parameters of polyethylene layer, allowing to evaluate the reflection and transmission coefficients using the stiffness matrix method developed by Rokhlin <em>et</em> <em>al</em>., four homogenization models are analyzed, then the best one to our configuration is chosen. The comparison of the simulation results is carried out.
基金Supported in part by the grant SGS/15/2010 from the Silesian University in Opava
文摘This paper is devoted to problems stated by Z. Zhou and ELi in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The negative answer follows by our recent paper. But for continuous maps of the interval and other more general one-dimensional spaces we give more results; in some cases the answer is positive.
文摘In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
文摘In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient conditions are established. In particular, for the alm ost periodic system , the existence of strictly positive alm ostperiodic solutions is obtained. Som e previous results are im proved and generalized.
