The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.Comment: 18 page

On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page

Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page

Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical resultsComment: 2

Synthesis, electronic and optical properties of Si nanostructures

Silicon and silicon oxide nanostructures have been deposited on solid substrates, in an ultra high vacuum (UHV) chamber, by laser ablation or thermal vaporization. Laser ablation followed by substrate post annealing produced Si clusters with average size of a few nanometers, on highly oriented pyrolytic graphite (HOPG) surfaces. This technique, which is based on surface diffusion, is limited to the production of less than one layer of clusters on a given surface. The low coverage of Si clusters and the possibility of nonradiative decay of excitation in the Si cores to the HOPG substrates in these samples rendered them unsuitable for many optical measurements. Thermal vaporization of Si in an Ar buffer gas, on the contrary, yielded multilayer coverage of Si nanoclusters with a fairly narrow size distribution of about 2 nm, full width at half maximum (FWHM). As a result, further study was performed only on Si nanoclusters synthesized by thermal vaporization in a buffer gas. High resolution transmission electron microscopy (HRTEM) and X-ray diffraction (XRD) revealed that these nanoclusters were crystalline. However, during synthesis, if oxygen was the buffer gas, a network of amorphous Si oxide nanostructures (an-SiO{sub x}) with occasional embedded Si dots was formed. All samples showed strong infrared and/or visible photoluminescence (PL) with varying decay times from nanoseconds to microseconds depending on synthesis conditions. There were differences in PL spectra for hydrogen and oxygen passivated nc-Si, while many common PL properties between oxygen passivated nc-Si and an SiO{sub x} were observed. The observed experimental results can be best explained by a model involving absorption between quantum confined states in the Si cores and emission for which the decay times are very sensitive to surface and/or interface states

Some factors affecting the effectiveness of social work activities in supporting drug addicts concentrated in No. II drug addiction treatment facility in Hoa Binh province, Vietnam

The article deals with the current situation of factors affecting the effectiveness of social work activities in supporting drug addicts at the No. II Hoa Binh drug rehabilitation facility. To achieve this goal, we conducted a random survey of 110 students undergoing detoxification at the center. Factors such as the characteristics of drug addicts; responsiveness of drug addiction treatment establishments; performance quality of social workers; Care and support of drug addicts' families. From there, propose measures to improve the effectiveness of social work activities in supporting drug addicts concentrated at detoxification establishments

Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil

This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.Comment: 18 page

Dynamics of Electroweak Phase Transition in the 3-3-1-1 Model

The bubble nucleation in the framework of 3-3-1-1 model is studied. Previous studies show that first order electroweak phase transition occurs in two periods. In this paper we evaluate the bubble nucleation temperature throughout the parameter space. Using the stringent condition for bubble nucleation formation we find that in the first period, symmetry breaking from $SU(3)\rightarrow SU(2)$, the bubble is formed at the nucleation temperature $T=150$ GeV and the lower bound of the scalar mass is 600 GeV. In the second period, symmetry breaking from $(SU(2)\rightarrow U(1)$, only subcritical bubbles are formed. This constraint eliminates the electroweak baryon genesis in the second period of the model

Photoconductive UV Detectors Based on ZnO Films Prepared by R.F. Magnetron Sputtering Method

Highly c-axis oriented zinc oxide (ZnO) thin films were deposited on glass substrates by radio frequency (r.f.) sputtering. The photoconductor UV detector based on ZnO films, having a metal-semiconductor-metal (MSM) structure with interdigitation configuration, were fabricated by using aluminium (Al) as a contact metal. The characteristics of dark and photocurrent of the ultraviolet (UV) detector and the UV photo-response of the detector were investigated. The linear current-voltage (I-V) characteristics under both forward and reverse bias exhibit ohmic metal-semiconductor contacts. Under illumination by monochromatic light at a wavelength of 365~nm, the photo-generated current was measured to be 0.56 $\mu$A at a bias of 6 V. The photo-response decay in these devices is slow