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In this work, we consider a class of switched stochastic reaction-diffusion systems (SSRDSs, in short), where the discrete switching signal is a right continuous, piecewise function and the switching instants are stopping times or deterministic times. Criteria on finite-time stability in the probability of the trivial solution for SSRDSs are derived by means of Lyapunov functional methods. We propose an example to verify the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the practical stability in relation to a part of the variables of stochastic reaction–diffusion systems driven by G-Brownian motion (G-SRDSs, in short). With the aid of G-Lyapunov techniques and G-Itô's formula, the criteria of the global practical uniform kth moment exponential stability and the global practical uniform quasi surely exponential stability in relation to a part of variables of G-SRDSs are established. An example is given to illustrate the usefulness and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

As one of the most important topics in control theory, robust stability for the systems plays a key role in many areas of science and industry. This paper discusses the robust stochastic stability a class of multi-group coupled stochastic models with Markovian switching. Based on discrete-time observations in the diffusion part with time-delay, the robust stochastic exponential stability criterion in mean square sense is established in the forms of Lyapunov-type and coefficient-type. An application to the robust stochastic stability for a class of coupled oscillators is proposed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of Sobolev-type stochastic differential equations driven by G-Brownian motion (G-SSDEs, in short). We prove the existence and uniqueness of the mild solution for G-SSDEs. By means of two integral inequalities, the attracting and quasi-invariant sets of the equations are obtained. As a byproduct, the exponentially stability of the solution in mean-square sense is derived. An example is given to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs, in short). In particular, we study the exponentially and quasi sure exponential stability of the square-mean almost automorphic solutions of the IGSDEs. Specifically by employing the Lyapunov function method, a new set of sufficient conditions is derived for obtaining the required result. [ABSTRACT FROM AUTHOR]

CdWO4:Eu3+ nanocrystals were prepared by the hydrothermal method at different pH values (pH=4, 7.5, and 10) and annealed at different temperatures. Their structural and photoluminescence properties were systemically studied. The studies on electron spin resonance and Fourier-transfer infrared absorption spectra demonstrated that at least two kinds of surface defects were involved, the surface dangling bonds of transition metals and the surface adsorption of the OH- and CO32- groups. The surface adsorption in the pH=10 sample increased considerably, which led the surface dangling bonds to decrease and even to disappear. Due to the existence of surface defect states, especially the surface dangling bonds, tungstates at two symmetry sites were formed, the normal site and the perturbed site locating at/near the surface. The former tungstates located at high energy side (∼290 nm) in the excitation bands and emitted blue-green photons, while the latter located at low energy (∼340 nm) and emitted red photons. They can both effectively transfer the energies to Eu3+ ions, generating red 5D0-7FJ transitions. As the nanocrystalline powders were annealed, colorations appeared and evolved with temperature, while the surface dangling bonds and surface adsorption gradually disappeared. The defect states had great and complicated influence on luminescence efficiency, luminescent stability, and temperature-stability of tunstates and Eu3+ ions. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau-Yosida approximation method. Moreover, we give a probabilistic interpretation for the viscosity solutions of a kind of nonlinear variational inequalities. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of a solution for a class of multi-valued stochastic differential equations driven byG-Brownian motion (MSDEG) by means of the Yosida approximation method. Moreover, we set up an optimality principle of stochastic control problem and prove the value function of the control problem is the unique viscosity solution of a class of nonlinear partial differential variational inequalities. [ABSTRACT FROM AUTHOR]