Photoluminescence properties of various CVD-grown ZnO nanostructures

We have studied systematically room-temperature photoluminescence (PL) properties of many nanostructured ZnO samples grown by chemical vapour deposition (CVD). Their PL spectra consist of two emissions peaked in the ultraviolet (UV) and green regions. The relative intensity of these emissions depends on the excitation energy density, size and morphology of ZnO nanostructures. Based on the excitation-density dependence of the integrated intensity ratio of UV-to-green emission, we could classify PL spectra of ZnO nanostructures into three groups characteristic of size and morphology. Our study also reveals that with increasing excitation density, the UV-peak position shifts slightly towards longer wavelengths while the green emission around 514-520 nm is almost unchanged. This green-luminescence emission is dominant when the nanostructure sizes range from 20 to 200 nm, which is related to a large surface-to-volume ratio.     

Weighted Calderón-Zygmund Estimates for Weak Solutions of Quasi-Linear Degenerate Elliptic Equations

Potential Analysis - This paper studies regularity estimates in Sobolev spaces for weak solutions of a class of degenerate and singular quasi-linear elliptic problems of the form...     

On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm Lebesgue Spaces

We establish local and global well-posedness of the 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces. The result demonstrates the persistence of the anisotropic behavior of the initial data under the evolution of the 2D dissipative quasi-geostrophic equation. The phenomenon is a priori nontrivial due to the nonlocal structure of the equation. Our approach is based on Kato's method using Picard's iteration, which can be adapted to the multi-dimensional case and other nonlinear non-local equations. We develop time decay estimates for solutions of fractional heat equation in mixed norm Lebesgue spaces that could be useful for other problems.     

Exponential attractor for Hindmarsh-Rose equations in neurodynamics

The existence of exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in the study of neurodynamics is proved through uniform estimates and a new theorem on the squeezing property of the abstract reaction-diffusion equation established in this paper. This result on the exponential attractor infers that the global attractor whose existence has been proved in [22] for the diffusive Hindmarsh-Rose semiflow has a finite fractal dimension.     

Global Attractor of Hindmarsh-Rose Equations in Neurodynamics

Global dynamics for a new mathematical model in neurodynamics of the diffusive Hindmarsh-Rose equations on a bounded domain is investigated in this paper. The existence of a global attractor and its regularity are proved through uniform estimates showing the dissipative properties and the asymptotically compact and smoothing characteristics.     

New Convolutions for Quadratic-Phase Fourier Integral Operators and their Applications

We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.     

On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities

We investigate the global exponential stability of equilibrium solutions of a projected dynamical system for variational inequalities. Under strong pseudomonotonicity and Lipschitz continuity assumptions, we prove that the dynamical system has a unique equilibrium solution. Moreover, this solution is globally exponentially stable. Some examples are given to analyze the effectiveness of the theoretical results. The numerical results confirm that the trajectory of the dynamical system globally exponentially converges to the unique solution of the considered variational inequality. The results established in this paper improve and extend some recent works.