This paper proposes a new structure for a Fractional Order Sliding Mode Controller (FOSMC) to control a Twin Rotor Aerodynamic System (TRAS). The new structure is composed by defining two 3-dimensional sliding mode surfaces for the TRAS model and introducing fractional order derivative integral in the state variables as well as in the control action. The parameters of the controller are determined so as to minimize the Integral of Time multiplied by Absolute Error (ITAE) performance index. Through comparison, this controller outperforms its integer counterpart in many specifications, such as reducing the delay time, rise time, percentage overshoot, settling time, time to reach the sliding surface, and amplitude of chattering in control inpu

Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.

MCA has gained a reputation for being a very useful statistical method for determining the association between two or more categorical variables and their graphical description. For performance this method, we must calculate the singular vectors through (SVD). Which is an important primary tool that allows user to construct a low-dimensional space to describe the association between the variables categories. As an alternative procedure to use (SVD), we can use the (BMD) method, which involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, the (HD) is formed. The aim of study is to use alternative method of (MCA) that is appropriate with order

In this work we prepared some schiff bases by condensation urea and benzaldehyde or its derevative ( bromo benzaldehyde or hydroxy benzaldehyde ) as ( 1 : 1 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A1 , B1 , C1 , D1 , E1 , F1 , G1 ) and ( 1 : 2 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A2 , B2 , C2 , D2 , E1 , F2 , G2 ) . The prepared compounds identified spectroscopic by infrared spectroscopy FT-IR and Thin layer chromotography T.L.C . The force constant calculated from the wave number for the carbonyl stretching from FT-IR chart and by using the following equation K = 4?2C2?'2? The change in double bond order for carbonyl deteremined in according with some past re

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

Total Quality Assurance Concept have appeared in Higher Education Institutions as a result of the continuous criticism for the lower quality of the outputs of these institutions and their inappropriacy to the needs of the job market. The faculty, i.e. teaching staff member, is one of the most important output for his/her responsibility to achieve the stated goals in higher education. This represents a problem that may influence the construction of society which has to limit his tasks, responsibilities, and competencies that should be found in a faculty, and evaluating his teaching profession in light of the prerequisites of the century to become an input to achieve quality assurance in Higher Education. Therefore, the present study aims

Abstract:

Borago officinalis is highly interesting amongst nutritional and medical source relate to its high composition of some useful phytochemical compound. It is great plants with bright blue star-shaped flowers present in most world regions and usually known as borage. The Borago phytochemical analysis showed the presence of alkaloids, tannins, flavonoids, phenolic acids, essential oil, vitamins and others. Borage is cultivated all over the world and used in traditional medicine as a demulcent, diuretic, emollient, tonic, expectorant, for the treatment of coughs, inflammation and swelling, and other diseases. In herbal medicine, Borage seed oil (BSO) has been utilized for many progres­sive illnesse

A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.

Discotic liquid crystal compounds were synthesized and characterized. Liquid crystalline texture of these compounds was investigated by polarized optical microscopy (POM). The Hartree-Fock approximation (HF) was used to calculate theoretical molecular parameters for synthesized compounds such as optimization, hardness, EHOMO, ELUMO, and energy gap using the Gaussian 09W program.