This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended approach is applicable and accurate for solving such kinds of problems.
The goal of this investigation is to prepare zinc oxide (ZnO) nano-thin films by pulsed laser deposition (PLD) technique through Q-switching double frequency Nd:YAG laser (532 nm) wavelength, pulse frequency 6 Hz, and 300 mJ energy under vacuum conditions (10-3 torr) at room temperature. (ZnO) nano-thin films were deposited on glass substrates with different thickness of 300, 600 and 900 nm. ZnO films, were then annealed in air at a temperature of 500 °C for one hour. The results were compared with the researchers' previous theoretical study. The XRD analysis of ZnO nano-thin films indicated a hexagonal multi-crystalline wurtzite structure with preferential growth lines (100), (002), (101) for ZnO nano-thin films with different thi
... Show MoreThin films of (CdO)x (CuO)1-x (where x = 0.0, 0.2, 0.3, 0.4 and 0.5) were prepared by the pulsed laser deposition. The CuO addition caused an increase in diffraction peaks intensity at (111) and a decrease in diffraction peaks intensity at (200). As CuO content increases, the band gap increases to a maximum of 3.51 eV, maximum resistivity of 8.251x 104 Ω.cm with mobility of 199.5 cm2 / V.s, when x= 0.5. The results show that the conductivity is ntype when x value was changed in the range (0 to 0.4) but further addition of CuO converted the samples to p-type.
The presented study investigated the scheduling regarding jobs on a single machine. Each job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two
... Show MoreLead-acid batteries have been used increasingly in recent years in solar power systems, especially in homes and small businesses, due to their cheapness and advanced development in manufacturing them. However, these batteries have low voltages and low capacities, to increase voltage and capacities, they need to be connected in series and parallel. Whether they are connected in series or parallel, their voltages and capacities must be equal otherwise the quality of service will be degraded. The fact that these different voltages are inherent in their manufacturing, but these unbalanced voltages can be controlled. Using a switched capacitor is a method that was used in many methods for balancing voltages, but their respons
... Show MoreA method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.
A total of 258 voluntary blood donors (males 101; females 157) in the age range of 18-52 yr among males and 18-55 yr among females were examined for Toxoplasma gondii antibodies (IgG), and (IgM) by immunological technique (Enzyme linked Immunosorbant Assay) during the period from March 2009 to April 2010. This study covered a wide range of factors including immunological, age ,sex , place of residence and symptoms that may have a possible relationship with toxoplasmosis. Results presented in this study showed clearly that 38 (14.7%) of individuals participated in this study having IgG Toxoplasma Ab, among those 10 samples (9.9%) were males and 28 samples (17.8%) were females. Moreover, we found the prevalence of IgM seropositivity in th
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