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.
This study aimed at some of the criteria used to determine the form of the river basins, and exposed the need to modify some of its limitations. In which, the generalization of the elongation and roundness ratio coefficient criterion was modified, which was set in a range between (0-1). This range goes beyond determining the form of the basin, which gives it an elongated or rounded feature, and the ratio has been modified by making it more detailed and accurate in giving the basin a specific form, not only a general characteristic. So, we reached a standard for each of the basins' forms regarding the results of the elongation and circularity ratios. Thus, circular is (1-0.8), and square is (between 0.8-0.6), the blade or oval form is (0.6-0
... Show MoreObesity is an escalating health problem in developing countries. One to ten children worldwide are overweight in a report showed by the International Obesity Task Force. Ghrelin, orexigenic peptide, has 28 amino acids, it is considered the greatest remarkable promotion in the last two decades for understanding the physiological changes of action regulating food intake and hunger. Obestatin is a 23-amino acid peptide nearly connected to ghrelin that secures from substitutio
... Show MoreIntroduction Periodontal diseases are ranked among the most common health problems affecting mankind. These conditions are initiated by bacterial biofilm, which is further modulated by several risk factors. Objectives To investigate the association of different risk factors with periodontal...
In this paper, thermal performance of a zig-zig solar air heater (ZZSAH) with and without using steel wire mesh on the absorber plate of the collector is experimentally investigated. The experimental work includes four inclination angles of the collector 20o, 30o, 45o, and 60o and four air mass flow rates of 0.03, 0.04, 0.06, and 0.08 kg/s under varieties of operating conditions of a geographic location of Baghdad. New correlation equations of Nusselt number are obtained from experimental results for both types of collectors where the effect of varying of the inclination angle of collector taken into consideration in the experiment. The correlations show good agreement wi
... Show MoreExperimental study has been conducted for laminar natural convection heat transfer of air flow through a rectangular enclosure fitted with vertical partition. The partition was oriented parallel to the two vertical isothermal walls with different temperatures, while all the other surfaces of the enclosure were insulated. In this study a test rig has been designed and constructed to allow studying the effect of Rayleigh number, aperture height ratio, partition thickness, the position of aperture according to the side walls and according to the height, the position of the partition according to the hot wall, and partition inclination. The experiments were carried out with air as the working fluid for Rayleigh number range (5*107 – 1.3*10
... Show MoreAim: To learn more about Oral Lichen Planus Iraqi patients, including their background information, symptoms, and prognosis. Materials and Methods: From the Oral and Maxillofacial Pathology Department, College of Dentistry, Baghdad University, we retrospectively reviewed the medical records of 68 patients with a histologically confirmed clinical diagnosis of oral lichen planus and subsequently contacted the patients by phone to evaluate their prognosis. Results: Females were more likely than males to experience severe pain; the reticular form of Oral Lichen Planus was the most prevalent at 38.2%, but the erosive type was more prevalent among females. Only 53 of 68 patients responded to phone calls. More than 37% of those respondents reporte
... Show MoreABSTRACT Background: Color changes that are detectable to human eye can affect the esthetic appearance of ceramic veneers. The purpose of this study was to evaluate and compare the effect of artificial accelerated aging on the color of ceramic veneers cemented with different resin cements. Materials and Methods: Sixty discs were prepared with 0.5 mm thickness, 30 discs made from IPS e.max press (Ivoclar Vivadent) and 30 discs were made from VITA Enamic (VITA Zahnfabrik). The discs were cemented with three resin cements: Variolink Veneer MV 0 shade (Ivoclar Vivadent), Rely X veneer Translucent shade (3M ESPE) and NX3 Nexus Clear shade (Kerr Corporation) with 0.1 mm thickness. The spectrophotometer Easyshade Advance was used to measure the co
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