The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

In this work preparation of antireflection coating with single layer of MgO using pulsed laser deposition (PLD) method which deposit on glass substrate with different thicknesses (90 and 100) nm annealed at temperature 500 K was done.
The optical and structural properties (X-ray diffraction) have been determined. The optical reflectance was computed with the aid of MATLAB over the visible and near infrared region. Results shows that the best result obtained for optical performance of AR'Cs at 700 shots with thickness 90 nm nanostructure single layer AR'Cs and low reflection at wavelength 550 nm.

Catalytic reforming of naphtha occupies an important issue in refineries for obtaining high octane gasoline and aromatic compounds, which are the basic materials of petrochemical industries. In this study, a novel of design parameters for industrial continuous catalytic reforming reactors of naphtha is proposed to increase the aromatics and hydrogen productions. Improving a rigorous mathematical model for industrial catalytic reactors of naphtha is studied here based on industrial data applying a new kinetic and deactivation model. The optimal design variables are obtained utilizing the optimization process in order to build the model with high accuracy and such design parameters are then applied to get the best configuration of this pro

Abstract:

This study deals with the influence of the industrial buyer behavior in Channels of distribution. It concentrates on one section of management levels in the company. Which is that of administrative managers The research problem is attempt to study and analysis the influence of industrial buyer behavior in channels of distribution.. The aiming at achieving a number of applicable goals depending on one major hypotheses I set a questionnaire in collecting the data and information relating to the study، which was distributed to sample of ( 30) department manager heads of section states company .  In order to process the data resorted to many statistical methods such as arithmetic means the sta

This paper performance for preparation and identification of six new complexes of a number of transition metals Cr (lII), Mn (I1), Fe (l), Co (II), Ni (I1), Cu (Il) with: N - (3,4,5-Trimethoxy phenyl-N - benzoyl Thiourea (TMPBT) as a bidentet ligand. The prepared complexes have been characterized, identified on the basis of elemental analysis (C.H.N), atomic absorption, molar conductivity, molar-ratio ,pH effect study, I. Rand UV spectra studies. The complexes have the structural formula ML₂X₃ for Cr (III), Fe (III), and ML₂X₂ for Mn (II), Ni (II), and MLX₂ for Co (Il) , Cu (Il).

The current research aims to identify the effectiveness of a computerized program in developing mathematical skills among the first cycle students in basic education schools in the Sultanate of Oman. The two researchers used the quasi-experimental approach on an intentional sample consisting of (40) male and female students at Al Kawakeb School for Basic Education (1-4). Two of the basic fourth-grade classes and then randomly distributing them into two groups, one is experimental (20) male and female students who followed the computerized interactive program, and the other is (20) male and female students followed the traditional way. On the other hand, its reliability has reached (0.81), and the results of the research have concluded th

In this work we present a technique to extract the heart contours from noisy echocardiograph images. Our technique is based on improving the image before applying contours detection to reduce heavy noise and get better image quality. To perform that, we combine many pre-processing techniques (filtering, morphological operations, and contrast adjustment) to avoid unclear edges and enhance low contrast of echocardiograph images, after implementing these techniques we can get legible detection for heart boundaries and valves movement by traditional edge detection methods.

A sensitive spectrophotometric method was developed for the estimation of cefdinir (CFD), a cephalosporin species. This study involves two methods, and the first method includes the preparing of azo dye by the reaction of CFD diazonium salt with 4-Tert-Butylphenol (4-TBP) and 2-Naphthol (2-NPT) in alkaline medium, which shows colored dyes measured at λmax 490 and 535 nm, respectively. Beer's law was obeyed along the concentration range of (3-100) μg.ml-1. The limits of detection were 0.246, 0.447 μg.ml-1 and molar absorptivities were 0.6129×104, 0.3361×104 L.mol-1cm-1 for (CFD-4-TBP) and (CFD-2-NPT), respectively. The second method includes preconcentration for cefdinir dyes by using cloud point extraction in the presence of Triton

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all