This study presents the multi criteria single-machine model. The machine scheduling problem (MSP) for ntasks on a single machine involves minimizing a function of three criteria: total completion time (C_j),maximum earliest (E_max), and tardiness (〖ΣT〗_j), This is an NP-hard issue. Within this work's theoretical section, we present the mathematical formulation of The presented topic thenhighlights the usefulness of the dominance rule (DR), which may be used to develop effective solutions. Whilein the practical part, one of the important exact methods; The proposed MSP tricriteria are solved by applyingthe Branch and Bound (BAB) method, which finds a set of efficient solutions for 1//F(ΣC_j ,ΣT_j ,E_max) upto n=100 jobs. The BAB appro

Each phenomenon contains several variables. Studying these variables, we find mathematical formula to get the joint distribution and the copula that are a useful and good tool to find the amount of correlation, where the survival function was used to measure the relationship of age with the level of cretonne in the remaining blood of the person. The Spss program was also used to extract the influencing variables from a group of variables using factor analysis and then using the Clayton copula function that is used to find the shared binary distributions using multivariate distributions, where the bivariate distribution was calculated, and then the survival function value was calculated for a sample size (50) drawn from Yarmouk Ho

    The weak and strong forms are so called because it is not their lexical content that primary matter, but the role they have in the sentence. The problematic confusion, our students encounter, in recognizing and producing the correct pronunciation of weak and strong forms of the English function words is the main incentive behind conducting  this study. In order to gather the data, this paper used two types of tests: a recognition test and a production test. The general results reached  through the analysis of the students' answers seem to conform to the researcher's assumption: students face a critical problem in recognizing and producing correct pronunciation of the weak and strong forms of the English funct

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

The problem of this study lies in that NATO was formed in the first place to protect Europe from Warsaw Pact. The geographical and military strategy have been changed with the change of its mission and expanding its operation scope with the leadership of the USA in the international scens. The latter has made this organization as the military arm to tighten its control over strategic regions.

            The research supposes that NATO state members confront security concerns and political and military issues that push to expand the organization. The importance of this study lies in knowing the new roles of NATO imposed by the United States. Therefore, the continuity and affi

The goal (purpose) from using development technology that require mathematical procedure related with high Quality & sufficiency of solving complex problem called Dynamic Programming with in recursive method (forward & backward) through  finding series of associated decisions for reliability function of Pareto distribution estimator by using two approach Maximum likelihood & moment .to conclude optimal policy

One of the most common metabolic illnesses in the world is diabetes mellitus. This metabolic disease is responsible for a large percentage of the burden of kidney damage and dysfunction. The goal of this study was to look into the renal function of diabetic patients using metformin monotherapy who came to Mosul's Al-Wafaa diabetes care and research facility. During the period 1 January 2021 to 30 April 2021, 47 patients with T2DM (age 50.48 7.74 years) were enrolled in this case-control study. These patients' results were compared to a control group of 47 seemingly healthy people (age 45.89 9.06 years). All participants' demographic and medical histories were acquired through the delivery of a questionnaire. Blood samples were collected