Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic

This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control qua

The high and low water levels in Tigris River threaten the banks of the river. The study area is located on the main stream of Tigris River at Nu’maniyah City and the length of the considered reach is 5.4 km, especially the region from 400 m upstream Nu’maniyah Bridge and downstream of the bridge up to 1250 mwhich increased the risk ofthe problemthat itheading towardsthe streetand causingdanger tonearbyareas.

The aim of this research is to identify the reason of slope collapse and find proper treatments for erosion problem in the river banks with the least cost. The modeling approach consisted of several steps, the first of which  is by using “mini” JET (Jet Erosion Test) d

Machine scheduling problems (MSP) are     considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as  are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutio

The aim of this study is to compare the effects of three methods: problem-based learning (PBL), PBL with lecture method, and conventional teaching on self-directed learning skills among physics undergraduates. The actual sample size comprises of 122 students, who were selected randomly from the Physics Department, College of Education in Iraq. In this study, the pre- and post-test were done and the instruments were administered to the students for data collection. The data was analyzed and statistical results rejected null hypothesis of this study. This study revealed that there are no signifigant differences between PBL and PBL with lecture method, thus the PBL without or with lecture method enhances the self-directed learning skills bette

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

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Our creator has honored human beings and granted them a noble place, the provisions of the Islamic system are designed to strengthen and consolidate this dignity and respect. Since women are human beings, they have their respect, status and dignity. There are some prophetic sayings concerning women that may be understood as contrary to this value, the value of dignity and respect for human beings. One example is the Hadith of a woman cutting off a man’s prayer if she passed in front of his prayer. The study examines this topic and presents answers for it.

In dealing with the subject, the study followed the descriptive, analytical and deductive approach of mentioning legislative texts, analyzing them and deducing

Because the Coronavirus epidemic spread in Iraq, the COVID-19 epidemic of people quarantined due to infection is our application in this work. The numerical simulation methods used in this research are more suitable than other analytical and numerical methods because they solve random systems. Since the Covid-19 epidemic system has random variables coefficients, these methods are used. Suitable numerical simulation methods have been applied to solve the COVID-19 epidemic model in Iraq. The analytical results of the Variation iteration method (VIM) are executed to compare the results. One numerical method which is the Finite difference method (FD) has been used to solve the Coronavirus model and for comparison purposes. The numerical simulat