In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica^®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum

   Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. In this paper, we consider the multi-criteria scheduling problem of n jobs on single machine to minimize a function of five criteria denoted by total completion times (∑), total tardiness (∑), total earliness (∑), maximum tardiness () and maximum earliness (). The single machine total tardiness problem and total earliness problem are already NP-hard, so the considered problem is strongly NP-hard.

We apply two local search algorithms (LSAs) descent method (DM) and simulated annealing method (SM) for the 1// (∑∑∑

     In this paper, one of the Machine Scheduling Problems is studied, which is the problem of scheduling a number of products (n-jobs) on one (single) machine with the multi-criteria objective function. These functions are (completion time, the tardiness, the earliness, and the late work) which formulated as . The branch and bound (BAB) method are used as the main method for solving the problem, where four upper bounds and one lower bound are proposed and a number of dominance rules are considered to reduce the number of branches in the search tree. The genetic algorithm (GA) and the particle swarm optimization (PSO) are used to obtain two of the upper bounds. The computational results are calculated by coding (progr

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo

This paper focuses on the most important element of scientific research: the research problem which is confined to the concept of concern or concern surrounding the researcher about any event or phenomenon or issue paper and need to be studied and addressed in order to find solutions for them, to influence the most scientific research steps from asking questions and formulating hypotheses, to employ suitable methods and tools to choose the research and sample community, to employ measurement and analysis tools. This problem calls for a great effort by the researcher intellectually or materially to develop solutions.

All modern critical approaches attempt to cover the meanings and overtones of the text, claiming that they are better than others in the analysis and attainment of the intended meanings of the text. The structural approach claims to be able to do so more than any other modern critical approach, as it claimed that it is possible to separate what is read from the reader, on the presumed belief that it is possible to read the text with a zero-memory. However, the studies in criticism of criticism state that each of these approaches is successful in dealing with the text in one or more aspects while failing in one or more aspects. Consequently, the criticism whether the approach possesses the text, or that the text rejects this possession, r

     This paper introduces a relation between resultant and the Jacobian determinant
by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:  ,            and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.