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)
Nanocrystalline copper sulphide (Cu2-xS) powders were synthesized by chemical precipitation from their aqueous solutions composed of different molar ratio of copper sulfate dehydrate (CuSO4.5H2O) and thiorea (NH2)2CS as source of Cu+2, S-2 ions respectively, and sodium ethylene diamine tetra acetic acid dehydrate (EDTA) as a complex agent. The compositions, morphological and structural properties of the nanopowders were characterized by energy dispersive spectroscopy (EDS), scanning electron microscope (SEM), and X-ray diffraction (XRD), respectively. The compositional results showed that the copper content was high and the Sulfur content was low for both CuS and Cu2S nanopowders. SEM images shows that all products consist of aggregate o
... Show MoreGrain size and shape are important yield indicators. A hint for reexamining the visual markers of grain weight can be found in the wheat grain width. A digital vernier caliper is used to measure length, width, and thickness. The data consisted of 1296 wheat grains, with measurements for each grain. In this data set, the average weight (We) of the twenty-four grains was measured and recorded. To determine measure of the length (L), width (W), thickness (T), weight (We), and volume(V). These features were manipulated to develop two mathematical models that were passed on to the multiple regression models. The results of the weight model demonstrated that the length and width of the grai
An R-module M is called rationally extending if each submodule of M is rational in a direct summand of M. In this paper we study this class of modules which is contained in the class of extending modules, Also we consider the class of strongly quasi-monoform modules, an R-module M is called strongly quasi-monoform if every nonzero proper submodule of M is quasi-invertible relative to some direct summand of M. Conditions are investigated to identify between these classes. Several properties are considered for such modules
Today’s world confronts various threats from different sources. Similar to deprivation of energy, economic facilities, or political deposition, educational poisoning is one of the dangerous phenomena that result from distorting and corrupting the ethical and educational components of teaching by various material and non – material means.This paper sheds light on the concept of the educational system which is not a mere process of teaching, but rather an endless process of socialization that begins in the family and develops into religious, ethical, scientific and mythological systems, all of which form the cognitive component. It also defines the necessary means by which it is transmitted from one generation into another. The educati
... Show MoreIn this paper we define and study new concepts of fibrwise totally topological spaces over B namely fibrewise totally compact and fibrwise locally totally compact spaces, which are generalization of well known concepts totally compact and locally totally compact topological spaces. Moreover, we study relationships between fibrewise totally compact (resp, fibrwise locally totally compact) spaces and some fibrewise totally separation axioms.
One of the most important problems in the statistical inference is estimating parameters and Reliability parameter and also interval estimation , and testing hypothesis . estimating two parameters of exponential distribution and also reliability parameter in a stress-strength model.
This parameter deals with estimating the scale parameter and the Location parameter µ , of two exponential distribution ,using moments estimator and maximum likelihood estimator , also we estimate the parameter R=pr(x>y), where x,y are two- parameter independent exponential random variables .
Statistical properties of this distribution and its properti
... Show MoreThe Civil Rights era has been an era of struggle for the African American in the
Unites states. Thus, many writers devoted their writing to reflect the racism and
discrimination that many have suffered from, among them is Ralph Ellison.
Ralph Ellison is a 20th century African-American writer and scholar best known for
his renowned, award-winning novel Invisible Man. He illustrates the powerful
social and political forces that conspire to keep black Americans in their place,
denying them the right to life, liberty, and the pursuit of happiness guaranteed to all
Americans. Invisible Man is a 1952 novel that addresses many of the social and intellectual
issues facing African-Americans in the twentieth century. It exa
Discourse markers are expressions used to connect sentences to what comes before or after and indicate a speaker's attitude to what he is saying.As linguistic items, they have important functions in discourses of various styles or registers. And being connective elements, discourse markers relate sentences, clauses and paragraphs to each other. "One of the most prominent function of discourse markers, however, is to signal the kinds of relations a speaker perceives between different parts of the discourse". (Lenk 1997: 2) Through political discourse, different types of discourse markers are used. This paper deals with the importance and functions of discourse markers and tries to shed light on the kinds of discourse markers used in polit
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