In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The present study analyzes the effect of couple stress fluid (CSF) with the activity of connected inclined magnetic field (IMF) of a non-uniform channel (NUC) through a porous medium (PM), taking into account the sliding speed effect on channel walls and the effect of nonlinear particle size, applying long wavelength and low Reynolds count estimates. The mathematical expressions of axial velocity, stream function, mechanical effect and increase in pressure have been analytically determined. The effect of the physical parameter is included in the present model in the computational results. The results of this algorithm have been presented in chart form by applying the mathematical program.

In this work, has been a studied the effect of thermal treatment using different annealing temperatures (373, 423 and 473) K in vacuum on structural and morphological properties of organic semiconductor Alq₃:C₆₀ thin films which are prepared by the spin coating on a glass, silicon and porous silicon.  These films have been coated on substrates with speed of 2000 rpm. The structure properties of Tris(8-hydroxyquinoline) aluminum (III) (Alq₃) and fullerene (C₆₀) (100:1) and (100:10) blend as-deposited and treated have been studied by X-ray diffraction (XRD) for glass only and morphological properties by Atomic Force Microscope (AFM) for silicon and porous silicon substrates. The results of X

This study aims at identifying the role played by Public Relations in the field of security awareness of the dangers of terrorism. The research is directed to the employees at the Directorate General of Public Relations and Media at the Ministry of Interior. And that on the basis that those who play an important role in the security awareness are the security institutions, primarily the Ministry of Interior, since this Directorate is responsible for all subjects related to the public security using public relations science. It aims at identifying the functions, methods and communication tools used by the Directorate to raise awareness about the dangers of terrorism. In order to achieve the research objectives, the researcher uses the sur

This investigation was conducted to examine some physical and chemical properties of sand dunes collected from Basrah (1 '2 and 3) 'Nassiriya (4 and 5) and Amara (6) provinces that situated in lower Mesopotamia plain.

The results indicate clearly that the dominant particles in the samples were sand that were ranging from (81) % to (97) %, however the aggregated size of (0.1 - 0.25) mm were predominates in the investigated sand dunes of the region . Also the study shows that the content of the organic matter and potassium ions were very low (0.1- 0.4% '0.02 -0.22 meq I 100 gm soil. Further more the current result shows high a percentage of calcium carbonate (20.3 - 42.5%). In addition, the study has found a

An attempt was made to evaluate the PV performance of one-axis daily tracking and fixed system for Baghdad, Iraq. Two experimental simulations were conducted on a PV module for that purpose. Measurements included incident solar radiation, load voltage and load current. The first experiment was carried out for six months of winter half of year to simulate the one-axis daily tracking. The azimuth angle was due south while the tilt angle was being set to optimum according to each day of simulation. The second experiment was done at one day to simulate the PV module of fixed angles. It is found that there is a significant power gain of 29.6% for the tracking system in respect to the fixed one. The one-axis daily tracking was much more effect

This paper aims to improve the voltage profile using the Static Synchronous Compensator (STATCOM) in the power system in the Kurdistan Region for all weak buses. Power System Simulation studied it for Engineers (PSS\E) software version 33.0 to apply the Newton-Raphson (NR) method. All bus voltages were recorded and compared with the Kurdistan region grid index (0.95≤V ≤1.05), simulating the power system and finding the optimal size and suitable location of Static Synchronous Compensator (STATCOM)for bus voltage improvement at the weakest buses. It shows that Soran and New Koya substations are the best placement for adding STATCOM with the sizes 20 MVAR and 40 MVAR. After adding STATCOM with the sizes [20MVAR and 40MV

In this article, the backstepping control scheme is proposed to stabilize the fractional order Riccati matrix differential equation with retarded arguments in which the fractional derivative is presented using Caputo's definition of fractional derivative. The results are established using Mittag-Leffler stability. The fractional Lyapunov function is defined at each stage and the negativity of an overall fractional Lyapunov function is ensured by the proper selection of the control law. Numerical simulation has been used to demonstrate the effectiveness of the proposed control scheme for stabilizing such type of Riccati matrix differential equations.

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of