The Grünwald–Letnikov Fractional-Order Derivative with Fixed Memory Length

Contrary to integer-order derivative, the fractional-order derivative of a non-constant periodic function is not a periodic function with the same period. As a consequence of this property, the time-invariant fractional-order systems do not have any non-constant periodic solution unless the lower terminal of the derivative is ±∞, which is not practical. This property limits the applicability of the fractional derivative and makes it unfavorable, for a wide range of periodic real phenomena. Therefore, enlarging the applicability of fractional systems to such periodic real phenomena is an important research topic. In this paper, we give a solution for the above problem by imposing a simple modification on the Grünwald–Letnikov definition of fractional derivative. This modification consists of fixing the memory length and varying the lower terminal of the derivative. It is shown that the new proposed definition of fractional derivative preserves the periodicity.     

Hopf bifurcation and chaos in fractional-order modified hybrid optical system

In this paper, a chaotic fractional-order modified hybrid optical system is presented. Some basic dynamical properties are further investigated by means of Poincaré mapping, parameter phase portraits, and the largest Lyapunov exponents. Fractional Hopf bifurcation conditions are proposed; it is found that Hopf bifurcation occurs on the proposed system when the fractional-order varies and passes a sequence of critical values. The chaotic motion is validated by the positive Lyapunov exponent. Finally, some numerical simulations are also carried out to illustrate our results.     

Photodegradation of Decabromo Diphenyl Ether Flame Retardant in Poly (Acrylonitrile Butadiene Styrene) (ABS)

Abstract

Decabromodiphenylether (DBDE) is a brominated flame retardant which belongs to the group of polybromodiphenylethers (PBDEs) often used as a fire resistant additive in various well known polymeric systems like polystyrene, poly(acrylonitrile-butadiene-styrene) (ABS), polypropylene, etc. This compound can be considered as a persistent organic pollutant and presents certain risks for the environment owing to the fact that it is bioaccumulable and not biodegradable. A detailed investigation, described here, was carried out on the effect of ultraviolet/visible radiation on DBDE in ABS with the aim to study the photolytic reactions of this molecule in the solid state, in order to improve the economic and ecological treatment of brominated plastic waste from waste electrical and electronic equipment (WEEE). This study presents new aspects of the photochemical degradation of DBDE/ABS systems in the solid state. The photodegradation of DBDE in ABS was followed by Fourier transform infrared spectroscopy (FTIR) as well as by thermogravimetrical analysis (TGA). Good agreement was obtained for the results of both analytical methods in terms of the overall photolysis of DBDE.     

Preparation of transparent conducting ZnO:Al films on glass substrates by ultrasonic spray technique

Transparent conductive Al doped ZnO thin films were deposited by ultrasonic spray technique.Conditions of preparation have been optimized to get good quality.A set of aluminum（Al） doped ZnO（between 0 and 5 wt%） thin films were grown on glass substrate at 350℃.Nanocrystalline films with a hexagonal wurtzite structure show a strong（002） preferred orientation.The maximum value of grain size G = 32.05 nm is attained of Al doped ZnO film with 3 wt%.All the films have low absorbance in the visible region,thus the films are transparent in the visible region;the band gap energy increased from 3.10 to 3.26 eV when Al concentration increased from 0 to 3 wt%.The electrical conductivity of the films increased from 7.5 to 15.2（Ω·cm）^-1.So the best results are achieved in Al doped ZnO film with 3 wt%.     

Nouvelles caracterisations des v-anneaux et des anneaux pseudo-frobeniusiens 1

A class of A-modules is socle-fine if for any A-modules M and N in this class, M and N are isomorphic if and only if socle of M and socle of N are isomorphic. A ring A is a left V-ring if and only if the class of indecomposable quasi-injective A-modules with large socle is socle-fine. A ring A is a left V-ring noetherian if and only if the class of quasi-injective /4-modules with large socle is socle-fine. A ring A is Pseudo-Frobenius if and only if A is a left, cogenerator and the class of projective A-modules is socle-fine.     

Analysis of the Linear GSIC Multiuser Detector Using a Matrix Iterative Approach

In this work, we use a new approach that relies on the theory of matrix iterative analysis to study the convergence behavior of the linear group-wise successive interference cancellation (GSIC) detector. Particularly, we show that the linear GSIC detector is in fact a realization of a modified block successive over-relaxation (BSOR) iterative method where the relaxation factor is a matrix instead of scalar. Consequently, to study the convergence behavior of the GSIC detector, we propose two new corollaries that extend the famous work of Kahan (Varga, Matrix iterative analysis, 2000) to the case where the relaxation factor is a matrix instead of a scalar. Using the two new corollaries we develop two new conditions of convergence for the linear GSIC detector. Simulation results are in excellent agreement with theory.

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.     

A new chip‐level linear SOR‐SIC multiuser detector for long‐code systems

In this work, we introduce a new chip‐level linear modified‐SIC multi‐user structure that is asymptotically equivalent to successive over‐relaxation (SOR) iteration, which is known to outperform the conventional Gauss–Seidel iteration by an order of magnitude in terms of convergence speed. The main advantage of this scheme is that it uses directly the spreading codes and not the cross‐correlation coefficients and thus reduces significantly the overall computational complexity. This is critical for the design of low‐complexity multiuser detectors for long‐code CDMA systems such as IS95 and UMTS. We use a matrix algebraic approach to show the equivalence of the proposed scheme to linear matrix filtering. This allows obtaining an analytical expression for both the bit‐error rate (BER) and the asymptotic multiuser efficiency (AME). Moreover, we study the convergence behavior of the proposed scheme and prove that it converges if the relaxation factor is within the interval ]0, 2[. Simulation results are in excellent agreement with theory. Copyright © 2008 John Wiley & Sons, Ltd.     

Low‐complexity linear group‐SIC detectors

In this paper, we consider a linear group polynomial expansion successive interference cancellation (GPE‐SIC) detector in a synchronous CDMA system. It is a hybrid detector, which combines parallel and successive cancellation techniques in order to extract the advantages of both schemes. We use the fact that even if the cross‐correlation matrix of the system is not diagonal dominant, the sub‐matrices corresponding to different groups can be forced to be diagonal dominant by suitable grouping of users to approximate the decorrelator/MMSE detector by a low‐complexity polynomial expansion detector. The latter is computationally very efficient if the cross‐correlation matrix of users within the same group is diagonal dominant. Simulation results showed that the (GPE‐SIC) detector has the same performance as the linear group decorrelator successive interference cancellation (GDEC‐SIC) detector but with low‐computational complexity. Copyright © 2006 John Wiley & Sons, Ltd.     

A combined chebyshev polynomials and sumudu transform for solving the neutron transport equation (Poster Presentation)

In the present paper we present a new approximation for the one dimensional transport equation, using Chebyshev polynomials [1] combined with the Sumudu transform. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)