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.
The researcher focused on the importance of the physical abilities of the tennis game, as this game is one of the games that are characterized by its specificity in performance as this game is characterized by continuous movement and dealing with different elements, so this game requires the development of muscle strength, which plays an important role in Performance skills in the game of tennis. There are several methods to develop strength, including flat hierarchical technique, which is one of the most common forms of training in the development of muscle strength. As for the research problem, the researcher found a method that has an effect on the development of force. Therefore, the researcher tried to diversify a
... Show MoreTitanium dioxide nanorods have been prepared by sol-gel template
method. The structural and surface morphology of the TiO2 nanorods was
investigated by X-ray diffraction (XRD) and atomic force microscopy
(AFM), it was found that the nanorods produced were anatase TiO2 phase.
The photocatalytic activity of the TiO2 nanorods was evaluated by the
photo degradation of methyl orange (MO). The relatively higher
degradation efficiency for MO (D%=78.2) was obtained after 6h of exposed
to UV irradiation.
The nuclear charge density distributions, form factors and
corresponding proton, charge, neutron, and matter root mean square
radii for stable 4He, 12C, and 16O nuclei have been calculated using
single-particle radial wave functions of Woods-Saxon potential and
harmonic-oscillator potential for comparison. The calculations for the
ground charge density distributions using the Woods-Saxon potential
show good agreement with experimental data for 4He nucleus while
the results for 12C and 16O nuclei are better in harmonic-oscillator
potential. The calculated elastic charge form factors in Woods-Saxon
potential are better than the results of harmonic-oscillator potential.
Finally, the calculated root mean square
The nuclear charge density distributions, form factors andcorresponding proton, charge, neutron, and matter root mean squareradii for stable 4He, 12C, and 16O nuclei have been calculated usingsingle-particle radial wave functions of Woods-Saxon potential andharmonic-oscillator potential for comparison. The calculations for theground charge density distributions using the Woods-Saxon potentialshow good agreement with experimental data for 4He nucleus whilethe results for 12C and 16O nuclei are better in harmonic-oscillatorpotential. The calculated elastic charge form factors in Woods-Saxonpotential are better than the results of harmonic-oscillator potential.Finally, the calculated root mean square radii usingWoods-Saxonpotentials ho
... Show MoreObjective: Geographic differences in clinical and pathological aspects of ameloblastoma have been suggested, therefore the purpose of this study was to analyze cases of ameloblastoma in terms of clinical and radiographic manifestations, histopathological types, treatment modalities and recurrence rate and compare them with reports from other parts of the world. Methods: The medical reports of patients diagnosed with ameloblastoma were reviewed and the data concerning the age, gender, chief complaint, the anatomical site of the lesion, radiographic appearance, histopathological diagnosis, treatment approach and recurrence were retrieved. Surgical treatment consisted of either enucleation with curettage and peripheral ostectomy or resection;
... Show MoreA shocking third species emerged from a family of coronaviruses (CoV) in late 2019 following viruses causing SARS (Severe Acute Respiratory Syndrome-CoV) in 2003 and MERS (Middle East Respiratory Syndrome-CoV) in 2012; it’s a novel coronavirus now called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; formerly called 2019-nCoV). First emerging in China, it has spread rapidly across the globe, giving rise to significant social and economic costs and imposing severe strain on healthcare systems. Since many attempts to control viral spread has been futile, the only old practice of containment including city lockdown and social distancing are working to some extent. Unfortunately, specific antiviral drugs and vaccines remain u
... Show MoreWellbore instability is a significant problem faced during drilling operations and causes loss of circulation, caving, stuck pipe, and well kick or blowout. These problems take extra time to treat and increase the Nonproductive Time (NPT). This paper aims to review the factors that influence the stability of wellbores and know the methods that have been reached to reduce them. Based on a current survey, the factors that affect the stability of the wellbore are far-field stress, rock mechanical properties, natural fractures, pore pressure, wellbore trajectory, drilling fluid chemicals, mobile formations, naturally over-pressured shale collapse, mud weight, temperature, and time. Also, the most suitable ways to reduce well
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