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41.
    
Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.  相似文献   
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43.
The aim of this paper is to develop a new simple, fast and economical method for simultaneous quantitative determination of methylxanthine compounds based on TLC combined with image analysis. To obtain certain results, both extraction and chromatographic separation were optimized. The optimum extraction conditions were maceration in ethanol-water 8:2, v/v. The chromatographic separations were done on the silica gel F(254) TLC plates developed with chloroform-dichloromethane-isopropanol, 4:2:1 v/v/v. Detection was performed under UV lamp at 254?nm and the evaluation of the chromatographic plate was based on digital processing of chromatographic images. The developed TLC method was validated for parameters such as specificity, linearity and range, LOD and LOQ, precision, robustness and accuracy. This method was then applied for determination of caffeine, theobromine and theophylline in different types of tea, commercially available. Moreover, the content of methylxanthines detected and determined in commercial tea samples can be used as chemical marker in quality control.  相似文献   
44.
Polysulfone?silver composite nanoparticles have been prepared by combining polymer nanoprecipitation and redox synthesis of silver, in the presence of a glucose-modified cyclosiloxane as stabilizing agent. Based on previous kinetic investigations and on model reactions, we concluded that the reducing agent in this case is the tetrahydrofuran (THF) used as solvent for polysulfone. Dynamic light scattering measurements on the obtained polymer-silver composite particles indicated particle average diameter of 176 nm with a polydispersity index of 0.25. The UV–vis spectrum exhibited the silver plasmon resonance. By different microscopic methods (atomic force microscopy—AFM, high resolution transmission electron microscopy—HRTEM, and scanning electron microscopy—SEM), larger polymer particles coated with silver nanoprticles were observed. The Energy Dispersive X-Ray analysis—EDX; confirmed the presence of Ag on the surface of the particles, while the selected area electron diffraction showed single crystalline silver nanospheres with face-centered cubic structure.  相似文献   
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In this paper, we prove a local existence and uniqueness result for fuzzy delay differential equations driven by Liu process. We also establish continuous dependence of solution with respect to initial data.  相似文献   
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48.
We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)+-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.  相似文献   
49.
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.  相似文献   
50.
Following the Perron-Ta Li line of results, we give a characterization of the uniform exponential dichotomy property for the abstract continuous-time evolution families using a discrete-time approach.  相似文献   
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