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)
In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved
Piroxicam is a non-steroidal anti-inflammatory drug (NSAID) used in the treatment of musculo-skeletal and joint disorders. The problem with this drug is its poor solubility in water and hence poor bioavailability after oral administration. In order to improve its solubility and dissolution behavior, hydrophilic additives such as starch, lactose, superdisintegrants including crospovidone (C.P), cross carmellose sodium (CCS), and sodium starch glycolate (SSG) were physically dry mixed with the drug by simple trituration. The improvement in the solubility in 0.1 N HCl was obtained as the amount of starch or lactose increased in the physical mixture, while for superdisintegrants, they further improve the solubility when they are present in s
... Show MoreIn this paper, a new class of non-convex functions called semi strongly (
The current study presents an experimental investigation of heat transfer and flow characteristic for subcooled flow boiling of deionized water in the microchannel heat sink. The test section consisted of a single microchannel having 300μm wide nominal dimensions and 300μm height (hydraulic diameter of 300μm). The test section formed of oxygen-free copper with 72mm length and 12mm width. Experimental operation conditions spanned the heat flux (78-800) kW/m2, mass flux (1700 and 2100) kg/m2.s at 31˚C subcooled inlet temperature. The boiling heat transfer coefficient is measured and compared with existing correlations. Also, the experimental pressure drop is measured and compared with microscale p
... Show MoreThe (NiTsPc) thin films operating by vacuum evaporation technique are high recital and good desirable for number of applications, were dumped on glass substrates at room temperature with (200±20nm) thickness and doped with Al at different percentage (0.01,0.03) besides annealing the sample with 200˚C for 1 hours . The stimuluses of aluminum dopant percentage on characterization of the dropped (Ni Ts Pc) thin films were studied through X-ray diffraction in addition from the attained results, were all the films have polycrystalline in nature, as well the fallouts of XRD aimed at film illustrations polycrystalline, depending on the Al ratio doping, the results, SEM exposed the surface is regularly homogeneous. Utilizing first-ideolog
... Show MoreThe study aimes to investigate the effects of leaves & fruits ethanolic extract of Duranta repens L. on biological performance for all stages of life cycle of the mosquito Culex pipiens piepiens L., For this purpose the mosquitoes were reared in the laboratory till the fourth generation .Different concentrations of leaves (800,1000,1200,1400ppm) and fruits (800,1000,1200ppm) were tested on (eggs,larval stages,pupal stages and the adult stages). The results revealed that the extracts gave highest mortality rate for the eggs at(100%) compared with control,fruits extract shown highest mortality rate of the four larval instars (100%)at 1200ppm compared with leave extract at(80,50,33.33,20%).Also the extract caused a high mortality rate for pupa
... Show MoreABSTRACT Background: According to Branemark’s protocol, the waiting period between tooth extraction and implant placement is 6–8 months; this is the late placement technique. Achieving and maintaining implant stability are prerequisites for a dental implant to be successful. Resonance Frequency Analysis (RFA) is a noninvasive diagnostic method that measures implant stability. The aim of this study was to investigate the influence of treatment protocol and implant dimensions on primary implant stability utilizing RFA. Materials and methods: This study included 63 Iraqi patients (37 male, 26 female; ranging 22-66 years). According to treatment protocol, the sample was divided into 2 groups; A (delayed) & B (immediate). Dental im
... Show MoreObjectives: The purpose of this in vitro study was to compare the effect of adding a poloxamer surfactant to the irrigant solutions on its cleaning efficiency. Design: In this study the roots of extracted permanent premolar teeth were used and evaluated by using Scanning Electronic Microscopy (SEM). Materials and Method: 72 human single tooth of permanent premolar (8 for each group) were used in this in vitro study. Roots after sectioning at cervical area to get 15 mm were embedded in a plastic container filled with impression silicon, then instrumented with ProTaper rotary instruments till size F4. Each group (8 root) were irrigated with one of the nine solutions used in study: three concentrations of NaOH [5% (A1), 2.5%(A2), 0.5%(A3)], th
... Show MoreThe seedlings of vegetables are exposed to stress states, especially through the first period, due to injuring their roots by transplanting or heavy rain , so it is necessary to provide an available nutrient to recover the growth and increase their early yield, which means more income for farmers. In this regard, an experiment was conducted in the College of Agricultural Engineering Sciences, Agriculture Faculty, University of Baghdad, Iraq to study the effect of different types and concentrations of mineral fertilizers as starter solutions by using high nitrogen (N), high phosphorus (P) and neutral fertilizers (Q) at three levels which were 4 g/l (S1), 8 g/l (S2) and 12 g/l (S3) on broccoli growth and yield. The results showed tha
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