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)
T-cell activation and alteration of cytokine levels are involved in the pathogenesis of asthma. However, the profile of circulating T-lymphocyte subsets and related cytokines during asthmatic attacks is still unclear. We compared the serum concentrations of proinflammatory cytokines Interleukine-18( IL-18) and Interleukine-12(IL-12), T-helper 2 (Th2) cytokine Interleukine-13(IL-13 ) and Immunoglobuline-E ( IgE) in 27 asthmatic children and 21 sex and age matched healthy control subjects. Serum cytokines and IgE concentrations were measured by enzyme-linked immunosorbent assay. Serum IL-13 , IL-18 and IgE concentrations were significantly higher in asthmatic patients than normal control subjects ( IL-13: median 9.73 versus 4.43 pg/ml, P&l
... Show MoreThis study aimed to find relationship between thymidine kinase-1 (TK-1) as tumor marker and total antioxidant capacity (TAC) in Iraqi children patients with thrombocytopenia and with thrombocytosis. The present study conducted 60 children patients (30 patients with idiopathic thrombocytopenia purpura (ITP) and 30 patients with thrombocytosis caused by leukemia) attending the Children Fever Hospital in the Medical City / Baghdad, and 30 healthy children as a control group. All study groups were with range ages (1-15) years, and they were diagnosed by assay of platelet count, Prothrombin Time (PT), and partial Thromboplastin Time (PTT). The results shown elevation in plasma TK-1 and TAC values in children patients with thrombocytopenia and w
... Show MoreAs is known that the consumer price index (CPI) is one of the most important price indices because of its direct effect on the welfare of the individual and his living.
We have been address the problem of Strongly seasonal commodities in calculating (CPI) and identifying some of the solution.
We have used an actual data for a set of commodities (including strongly seasonal commodities) to calculate the index price by using (Annual Basket With Carry Forward Prices method) . Although this method can be successfully used in the context of seasonal&nbs
... Show MoreHR Ghanim, GA Abdulhassan, International Journal of Early Childhood Special Education, 2022
This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-
... Show MoreIn this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between t
... Show MoreIn this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using
In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using