Lyapunov stability of abstract nonlinear dynamic system in Banach space

The Lyapunov stability theory for nonlinear time-varying dynamic system in Banach space is given in this paper. The Lyapunov stable theorem and the Barbashin-Krasovskii-LaSalle invariant set principle in classical theory are extended to infinite-dimensional Banach space. Under the assumptions of the existence of solution and the additive property of motions, sufficient and necessary conditions for uniform stability and uniform asymptotic stability are obtained, and the Lyapunov functions are explicitly constructed. This extension can be used as a criterion of stability for continuous and discontinuous systems.postprin

Properties of a class of C0 semigroups on Banach spaces and their applications

In this paper we investigate some properties of a class of C0 semigroups on Banach spaces. Suppose that the spectrum of the infinitesimal generator is discrete and there are only finitely many eigenvalues in each vertical strip, we show that such semigroups can be expanded by their generalized eigenvectors under certain conditions. As a consequence, we assert that the semigroups with these conditions are eventually differentiable provided that the system of generalized eigenvectors is complete. As an example, we apply our results to a one-dimensional wave control system. © 2006 Elsevier Inc. All rights reserved.postprin

Riesz basis property of the generalized eigenvector system of a Timoshenko beam

The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in this paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C 0 semigroup, and its spectrum consists of two branches and has two asymptotes under some conditions. Furthermore it is proved that the sequence of all generalized eigenvectors of the system principal operator forms a Riesz basis for the state Hilbert space.postprin

Exponential stabilization of laminated beams with structural damping and boundary feedback controls

We study the boundary stabilization of laminated beams with structural damping which describes the slip occurring at the interface of two-layered objects. By using an invertible matrix function with an eigenvalue parameter and an asymptotic technique for the first order matrix differential equation, we find out an explicit asymptotic formula for the matrix fundamental solutions and then carry out the asymptotic analyses for the eigenpairs. Furthermore, we prove that there is a sequence of generalized eigenfunctions that forms a Riesz basis in the state Hilbert space, and hence the spectrum determined growth condition holds. Furthermore, exponential stability of the closed-loop system can be deduced from the eigenvalue expressions. In particular, the semigroup generated by the system operator is a Co-group due to the fact that the three asymptotes of the spectrum are parallel to the imaginary axis. © 2005 Society for Industrial and Applied Mathematics.published_or_final_versio

Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: A Riesz basis approach

In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a Riesz basis in the state Hilbert space. As a by-product, a conjecture in Guo (J. Optim. Theory Appl. 112(3) (2002) 529) is answered. © 2003 Elsevier B.V. All rights reserved.postprin

Mobility improvement of n-MOSFET's with nitrided gate oxide by backsurface Ar+ bombardment

Low-energy (550 eV) argon-ion beam was used to bombard directly, the backsurface of nitrided n-MOSFET's after the completion of all conventional nMOS processing steps. The interface characteristics and inversion layer mobility of the MOS devices were investigated. The results show that, as bombardment time increases, interface state density and fixed charge density decrease first, and then the change slows down or even turns around. Correspondingly, the carrier mobility and drain conductance of the MOS devices are found to enhance first, and then saturate or turn around. Therefore, this simple technique, which is readily compatible with existing IC processing, is effective for restoring some of the lost device performance associated with gate-oxide nitridation.published_or_final_versio

Iron-Catalyzed Nitrene Insertion Reaction for Facile Construction of Amide Compounds

A facile method for the construction of amide compounds from aldehydes by an iron-catalyzed nitrene insertion reaction has been developed. Both aryl and aliphatic aldehydes can directly afford the corresponding amides with an iron(II)-terpyridine (tpy) complex formed in situ as catalyst, and PhI=NTs as nitrogen source under mild reaction conditions. An ESI-MS study revealed the formation of [Fe(tpy)NTs)]+ as a reaction intermediate. © Georg Thieme Verlag Stuttgart - New York.postprin

Characterization and evaluation of Bacillus isolates for their potential plant growth and biocontrol activities against tomato bacterial wilt

About 200 Bacillus isolates were isolated from tomato and potato rhizosphere and examined for their antagonistic activities against Ralstonia solanacearum T-91, the causal agent of tomato bacterial wilt (TBW), in vitro and in vivo. Four strains, AM1, D16, D29 and H8, have shown high potential of antagonistic activity against the pathogen in laboratory and greenhouse experiments. In greenhouse, 81.1 to 89.0% reduction of disease incidence of TBW was recorded in treated tomato plants with 4 isolates, which also significantly (p > 0.05) increased plant height by 22.7 to 43.7% and dry weight by 47.93 to 91.55% compared with non-treated control. 16SrRNA gene sequence, the biochemical and physiological tests and fatty acid methyl esters analysis assigned strains AM1 and D29 as Bacillus amyloliquefaciens, while strains D16 and H8 as Bacillus subtilis and B. methylotrophicus, respectively. In addition, the 4 strains showed ability to inhibit growth of the three soil-borne fungi, produce indole-3- acetic acid, siderophores and also with exception of strain D16, the other 3 strains were capable of solubilizing phosphate. Therefore, these results suggest that out of 200 isolates, Bacillus stains AM1, D16, D29 and H8 support good antagonistic activity and could be applied as biocontrol agents against TBW under greenhouse conditions beside their potential to promote tomato plants growth.Key words: Tomato, Ralstonia solanacearum, Bacillus spp, biological control, plant growth promotion activitie