The fluorescence emission of Rhodamine 6G (R6G) and Acriflavine dyes in PMMA polymer have been studied by changing the irradiation and exposure time of laser light to know the effect of this parameter. It was found that the fluorescence intensity decreases in the polymer samples doped dyes as the exposure time increases and then reaches stabilization at long times, this behavior called photobleaching, which have been shown in liquid phase less than solid phase. Using 2nd harmonic with wavelength 530 nm laser, the photobleaching effect in the two dye-doped polymers different solvent but same was studied. It was observed that photobleaching of by different solution and by using dip spin coating the photobleaching seem in liquid phase

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc

In this paper, we study, in details the derivation of the variational formulation corresponding to functional with deviating arguments corresponding to movable boundaries. Natural or transversility conditions are also derived, as well as, the Eulers equation. Example has been taken to explain how to apply natural boundary conditions to find extremal of this functional.

In this paper, split-plate airlift electrochemical reactor as an apparatus with new configuration for wastewater treatment was provided. Two aluminum plates were fixed inside the reactor and present two functions; first it works as split plates for internal loop generation of the airlift system (the zone between the two plates acts as riser while the other two zones act as downcomer) and second it works as two electrodes for electrocoagulation process. Simulated wastewater contaminated with zinc ions was used to test the performance of this apparatus for zinc removal by studying the effect of different experimental variables such as initial concentration of zinc (50-800 ppm), electrical current density (2.67-21.4 mA/cm²), init

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT