System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

Algorithm for solving a class of general mixed variational inequalities and nonexpansive mappings in Hilbert spaces

This paper is devoted to study the convergence of a new class of generalized system for variational inequalities.The results presented in this paper modify and improve the recent result announced by Chang.[S.S.Chang,H.W.Joseph Lee,Generalzed system for relaxed cocoercive variational inequalities in Hilerbert space,doi:10.1016/j.aml.2006.04.017].

Iterative Methods for Solving a System of Variational Inclusions Involving （H, η）-Monotone Operators in Banach Spaces

In this paper, we introduce and study a new system of variational inclusions involving （H, η）-monotone operators in Banach space. Using the resolveut operator associated with （H, η）- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.

A study of the effective Hamiltonian method for decay dynamics

The decay dynamic of an excited quantum emitter(QE)is one of the most important contents in quantum optics.It has been widely applied in the field of quantum computing and quantum state manipulation.When the electromagnetic environment is described by several pseudomodes,the effective Hamiltonian method based on the multi-mode Jaynes-Cummings model provides a clear physical picture and a simple and convenient way to solve the decay dynamics.However,in previous studies,only the resonant modes are taken into account,while the non-resonant contributions are ignored.In this work,we study the applicability and accuracy of the effective Hamiltonian method for the decay dynamics.We consider different coupling strengths between a two-level QE and a gold nanosphere.The results for dynamics by the resolvent operator technique are used as a reference.Numerical results show that the effective Hamiltonian method provides accurate results when the two-level QE is resonant with the plasmon.However,when the detuning is large,the effective Hamiltonian method is not accurate.In addition,the effective Hamiltonian method cannot be applied when there is a bound state between the QE and the plasmon.These results are of great significance to the study of the decay dynamics in micro-nano structures described by quasi-normal modes.