A posteriori error estimates of mixed DG finite element methods for linear parabolic equations

In this article, we analyse a posteriori error estimates of mixed finite element discretizations for linear parabolic equations. The space discretization is done using the order λ?≥?1 Raviart–Thomas mixed finite elements, whereas the time discretization is based on discontinuous Galerkin (DG) methods (r?≥?1). Using the duality argument, we derive a posteriori l ^∞(L ²) error estimates for the scalar function, assuming that only the underlying mesh is static.     

Leonard Pairs and Leonard Triples of q-Racah Type from the Quantum Algebra U q (sl 2)

In this article, we describe the construction of Leonard pairs and Leonard triples that have q-Racah type from U _q (sl ₂)-modules by using equitable generators of U _q (sl ₂). Our result solves an open problem proposed by Terwilliger.     

Superconvergence and a posteriori error estimates of RT1 mixed methods for elliptic control problems with an integral constraint

In this paper, we investigate the superconvergence property and a posteriori error estimates of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Approximations of the optimal control of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order h ². Moreover, we derive a posteriori error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.     

Infinite horizon H_2/H_\infty optimal control for discrete-time Markov jump systems with (x,u,v)-dependent noise

In this paper, an infinite horizon $H_2/H_\infty $ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty $ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.     

Quadratic nonlinear response to 1.56-μm continuous wave laser in semi-insulating GaAs

The nonlinear photoresponse to a 1.56μm infrared continuous wave laser in semi-insulating （SI） galliu- marsenide （GaAs） is examined. The double-frequency absorption （DFA） is responsible for the nonlinear photoresponse based on the quadratic dependence of the photocurrent separately on the coupled optical power and bias voltage. The electric field-induced DFA remarkably affects the native DFA in SI GaAs. The surface electric field or the surface band-bending of SI GaAs significantly affects the magnitude variation of the Dhotocurrent and dark current     

Spin gapless armchair graphene nanoribbons under magnetic field and uniaxial strain

Using Green＇s function method, we investigate the spin transport properties of armchair graphene nanoribbons （AG- NRs） under magnetic field and uniaxial strain. Our results show that it is very difficult to transform narrow AGNRs directly from semiconductor to spin gapless semiconductors （SGS） by applying magnetic fields. However, as a uniaxial strain is exerted on the nanoribbons, the AGNRs can transform to SGS by a small magnetic field. The combination mode be- tween magnetic field and uniaxial strain displays a nonmonotonic arch-pattern relationship. In addition, we find that the combination mode is associated with the widths of nanoribbons, which exhibits group behaviors.     

Photoinduced charge injection in the metal/organic interface studied by transient photovoltage measurements with bias

Transient photovoltage of ITO/organic/Al cells is studied under different bias polarities and voltages.It is found that for an ITO/NPB/Al cell,light incidence on the Al side induces more bias-dependent transient photovoltage variation when the photovoltage is positive than when it is negative.However,for an ITO/C60 /Al cell,the variation characteristics of transient photovoltage is reversed.These results support the previously proposed mechanism that Al could inject charges into the organic layer upon photon excitation,indicating that the absorption of electrode can also contribute to photovoltaic effect.     

Permanence and periodic solutions for a class of delay Nicholson’s blowflies models

This paper covers the dynamic behaviors for a class of Nicholson’s blowflies models with a nonlinear density-dependent mortality term. By using inequality analyze technique and coincidence degree theory, some sufficient conditions are determined that guarantee the permanence of the model and the existence of positive periodic solutions. Moreover, we give an example to illustrate our main results.     

Distance unimodular equivalence of graphs

Let G be a connected graph and D(G) be its distance matrix. In this article, the Smith normal forms of the integer matrices D(G) are determined for trees, wheels, cycles, complements of cycles and are reduced for complete multipartite graphs.