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 exact methods are important; a Branch and Bound algorithm (BAB) and a complete enumeration (CEM) method are applied to solve the three proposed MSP criteria by finding a set of efficient solutions. The experimental results showed that CEM can solve problems for up to jobs. Two approaches of the BAB method were applied: the first approach was BAB without dominance rule (DR), and the BAB method used dominance rules to reduce the number of sequences that need to be considered. Also, this method can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. In addition, to find good approximate solutions, two heuristic methods for solving the problem are proposed, the first heuristic method can solve up to jobs, while the second heuristic method can solve up to jobs. Practical experiments prove the good performance regarding the two suggested approaches for the original problem. While for a sub-problem the experimental results showed that CEM can solve problems for up to jobs, the BAB without dominance rule (DR) can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. Finally, the heuristic method can solve up to jobs. Arithmetic results are calculated by coding (programming) algorithms using (MATLAB 2019a)
The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the exp
... Show MoreThe valley Dwiridj of drainage basins task that lies east of Iraq and thus we have in this study the application of tow models athletes on the three basins of the valley to get Mor e values accurate to Estimate the volume of runoff and peak discharge and time climax and through the use of Technology remote sensing (GIS),has been show through the application of both models, that the maximum value for the amount of Dwiridj valley of (1052/m3/s) According to Equation (SCS-CN) and about (1370.2/m3/s)by approach (GIUH) that difference is the amount of discharge to the Equation (SCS-CN) ar not accurate as(GIUH) approaches Equation ecalling the results of the Field ces Department of damand reservoirs that the volume of runoff to the valley wase
... Show MoreThis research is concerned with the re-analysis of optical data (the imaginary part of the dielectric function as a function of photon energy E) of a-Si:H films prepared by Jackson et al. and Ferlauto et al. through using nonlinear regression fitting we estimated the optical energy gap and the deviation from the Tauc model by considering the parameter of energy photon-dependence of the momentum matrix element of the p as a free parameter by assuming that density of states distribution to be a square root function. It is observed for films prepared by Jackson et al. that the value of the parameter p for the photon energy range is is close to the value assumed by the Cody model and the optical gap energy is which is also close to the value
... Show MoreThe increase globally fossil fuel consumption as it represents the main source of energy around the world, and the sources of heavy oil more than light, different techniques were used to reduce the viscosity and increase mobility of heavy crude oil. this study focusing on the experimental tests and modeling with Back Feed Forward Artificial Neural Network (BFF-ANN) of the dilution technique to reduce a heavy oil viscosity that was collected from the south- Iraq oil fields using organic solvents, organic diluents with different weight percentage (5, 10 and 20 wt.% ) of (n-heptane, toluene, and a mixture of different ratio
... Show MoreSpectrophotometric method was developed for the determination of copper(II) ion. Synthesized (2,2[O-Tolidine-4,4-bis azo]bis[4,5-diphenyl imidazole]) (MBBAI) was used as chromogenic reagent at pH=5. Various factors affecting complex formation, such as, pH effect, reagent concentration, time effect and temperature effect, have been considered and studied. Under optimum conditions concentration ranged from (5.00-80.00) µg/mL of copper(II) obeyed Beer`s Low. Maximum absorption of the complex was 409nm with molar absorpitivity 0.127x104 L mol-1 cm-1. Limit of detection(LOD) and Limit of quantification were 1.924 and 6.42 μg/mL, respectively.
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The nuclear structure of 28-40Si isotopes toward neutron dripline has been investigated in framework of shell model with Skyrme-Hrtree-Fock method using certain Skyrme parameterizations. Moreover, investigations of static properties such as nuclear densities for proton, neutron, mass, and, charge densities with their corresponding rms radii, neutron skin thicknesses, binding energies, separation energies, shell gap, and pairing gap have been performed using the most recent Skyrme parameterization. The calculated results have been compared with available experimental data to identify which of these parameterizations introduced equivalent results with the ex
... Show MoreThe techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of
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