The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

When scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems,  it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin

Most of the water pollutants with dyes are leftovers from industries, including textiles, wool and others. There are many ways to remove dyes such as sorption, oxidation, coagulation, filtration, and biodegradation, Chlorination, ozonation, chemical precipitation, adsorption, electrochemical processes, membrane approaches, and biological treatment are among the most widely used technologies for removing colors from wastewater. Dyes are divided into two types: natural dyes and synthetic dyes.

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

Four different spectrophotometric methods are used in this study for the determination of Sulfamethoxazole and sulfanilamide drugs in pharmaceutical compounds, synthetic samples, and in their pure forms. The work comprises four chapters which are shown in the following: Chapter One: Includes a brief for Ultraviolet-Visible (UV-VIS) Absorption spectroscopy, antibacterial drugs and sulfonamides with some methods for their determination. The chapter lists two methods for optimization; univariate method and multivariate method. The later includes different types, two of these were mentioned; simplex method and design of experiment method. Chapter Two: Includes reaction of the two studied drugs with sodium nitrite and hydrochloric acid for diazo

Background: Morphology of the root canal system is divergent and unpredictable, and rather linked to clinical complications, which directly affect the treatment outcome. This objective necessitates continuous informative update of the effective clinical and laboratory methods for identifying this anatomy, and classification systems suitable for communication and interpretation in different situations. Data: Only electronic published papers were searched within this review. Sources: “PubMed” website was the only source used to search for data by using the following keywords "root", "canal", "morphology", "classification". Study selection: 153 most relevant papers to the topic were selected, especially the original articles and review pa