This research deals with unusual approach for analyzing the Simple Linear Regression via Linear Programming by Two - phase method, which is known in Operations Research: “O.R.”. The estimation here is found by solving optimization problem when adding artificial variables: Ri. Another method to analyze the Simple Linear Regression is introduced in this research, where the conditional Median of (y) was taken under consideration by minimizing the Sum of Absolute Residuals instead of finding the conditional Mean of (y) which depends on minimizing the Sum of Squared Residuals, that is called: “Median Regression”. Also, an Iterative Reweighted Least Squared based on the Absolute Residuals as weights is performed here as another method to

The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

Background: Poly-ether-ether-ketone(PEEK) has been introduced to many dental fields. Recently it was tested as a retainer wire‎ following orthodontic treatment. This study aimed to investigate the effect of changing the bonding spot size and location on the performance of PEEK retainer wires. Methods: A biomechanical study involving four three-dimensional finite element models was performed. The basic model was with a 0.8 mm cylindrical cross-section PEEK wire, bonded at the center of the lingual surface of the mandibular incisors with 4 mm in diameter composite spots. Two other models were designed with 3 mm and 5 mm composite sizes. The last model was created with the composite bonding spot of the canine away from the center

Background: Poly-ether-ether-ketone(PEEK) has been introduced to many dental fields. Recently it was tested as a retainer wire‎ following orthodontic treatment. This study aimed to investigate the effect of changing the bonding spot size and location on the performance of PEEK retainer wires. Methods: A biomechanical study involving four three-dimensional finite element models was performed. The basic model was with a 0.8 mm cylindrical cross-section PEEK wire, bonded at the center of the lingual surface of the mandibular incisors with 4 mm in diameter composite spots. Two other models were designed with 3 mm and 5 mm composite sizes. The last model was created with the composite bonding spot of the canine away from the center of t

The second half of the last century witnessed a great scientific revolution that was able to bring about wide changes in various fields, including the field of physical education, which plays a fundamental role in the process of change for the better, and which knocked all the doors of modern science in various aspects and from this perspective we see that students have different capabilities And interests and motives, which require providing a differentiated education, and this depends on the necessity of knowing each student and on the school’s ability to know appropriate strategies for teaching each student so there is no single way to teach so the research problem comes in experimenting with an educational method that works on

In this research, the performance of asphalt mixtures modified with polyethylene polymer (PE) by adding 2%, 4%, and 6% percentages was evaluated. Two kinds of PE are employed: Low-Density PE (LDPE) and High-Density PE (HDPE). The semi-wet mixing technique (SWM) was conducted to avoid stability issue for PE-modified binder during storage condition. Many experimental tests were conducted to evaluate the ability of these mixtures to withstand the effects of loads and moisture. The hardness index of these mixtures was also measured to determine their resistance to the effects of high temperatures without causing permanent deformations. The results showed that adding PE led to a remarkable enhancement in the performance of PE-modified mixtures.

Is in this research review of the way minimum absolute deviations values ​​based on linear programming method to estimate the parameters of simple linear regression model and give an overview of this model. We were modeling method deviations of the absolute values ​​proposed using a scale of dispersion and composition of a simple linear regression model based on the proposed measure. Object of the work is to find the capabilities of not affected by abnormal values by using numerical method and at the lowest possible recurrence.