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Solving tri-criteria: total completion time, total late work, and maximum earliness by using exact, and heuristic methods on single machine scheduling problem
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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)  

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Publication Date
Thu Feb 01 2007
Journal Name
No
On Solvability of an Operator Equation-
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Publication Date
Wed Mar 01 2023
Journal Name
Baghdad Science Journal
Some New Results on Lucky Labeling
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Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph Kn, Complete bipartite graph Km,n and Complete tripartite graph Kl,m,n. It has also been studied how the lucky number changes whi

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Publication Date
Sat Mar 01 2008
Journal Name
Ibn Al– Haitham Journal For Pure And Applied Science
Some Results on Fiberewise Topological Spaces
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In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

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Publication Date
Fri Feb 08 2019
Journal Name
Journal Of The College Of Education For Women
Impact of Computer on Human Health
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As computers become part of our everyday life, more and more people are experiencing a
variety of ocular symptoms related to computer use. These include eyestrain, tired eyes, irritation,
redness, blurred vision, and double vision, collectively referred to as computer vision syndrome.
The effect of CVS to the body such as back and shoulder pain, wrist problem and neck pain.
Many risk factors are identified in this paper.
Primary prevention strategies have largely been confined to addressing environmental
exposure to ergonomic risk factors, since to date, no clear cause for this work-related neck pain
has been acknowledged. Today, millions of children use computers on a daily basis. Extensive
viewing of the compute

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Publication Date
Sun Jul 09 2023
Journal Name
Journal Of Engineering
Study on Safety Construction Management Plan
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After studying the reality of application to occupational safety in new Iraqi building projects and sampling the situation wilt that in developed and neighboring countries, researcher found that there is a big gap in the level of safety application conditions, this indicates the need fora quick and clear reference for local engineers to use it on site for safety conditions in their projects . As a case study the monitors work the researcher studied a huge project in the United Arab Emirates.This project considered for safety requirements to highest grades. This case study may be far away from the projects in Iraq, but we hope to rise the Iraqi work level in the near future. After seeing the way of administration work and how they were ra

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Publication Date
Sun Jan 01 2012
Journal Name
Journal Of The College Of Languages (jcl)
NEW PERSPECTIVES ON SHAKESPEAR'S "THE TEMPEST"
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         This paper is mainly concerned with the study of the moral aspects that prompts William Shakespeare to attempt a romance in which he has embedded the epitome of his thought, experience, and philosophy concerning certain significant aspects of human life whose absence or negligence may threaten human existence, peace, and stability. From the beginning of history man realizes the importance of prosperity on the many and various levels that touch and address his needs and desires—natural, material,  and spiritual. The Tempest, due to the dramatist's awareness of the aforementioned values, reflects the dramatist's duty as to projecting and unfolding these important aspects, rec

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Publication Date
Sun Sep 04 2016
Journal Name
Baghdad Science Journal
Some Results on Weak Essential Submodules
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Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
On Almost Quasi-Frobenius Fuzzy Rings
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In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.

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Publication Date
Sun Dec 07 2008
Journal Name
Baghdad Science Journal
ON CERTAIN SUB-SPACE OF X
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The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
On the Representations of M-Groups
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The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G? (G? is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).

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