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 study, cloud point extraction combined with molecular spectrometry as an eco-friendly method is used for extraction, enrichment and determination of bendiocarb (BC) insecticide in different complex matrices. The method involved an alkaline hydrolysis of BC followed Emerson reaction in which the resultant phenol is reacted with 4-aminoantipyrene(4-AAP) in the presence of an alkaline oxidant of potassium ferric cyanide to form red colored product which then extracted into micelles of Triton X-114 as a mediated extractant at room temperature. The extracted product in cloud point layer is separated from the aqueous layer by centrifugation for 20 min and dissolved in a minimum amount of a mixture ethanol: water (1:1) followed

Coal fines are highly prone to be generated in all stages of Coal Seam Gas (CSG) production and development. These detached fines tend to aggregate, contributing to pore throat blockage and permeability reduction. Thus, this work explores the dispersion stability of coal fines in CSG reservoirs and proposes a new additive to be used in the formulation of the hydraulic fracturing fluid to keep the fines dispersed in the fluid. In this work, bituminous coal fines were tested in various suspensions in order to study their dispersion stability. The aggregation behavior of coal fines (dispersed phase) was analyzed in different dispersion mediums, including deionized-water, low and high sodium chloride solutions. Furthermore, the effect of Sodium

An investigation was conducted for dewaxing of lubricating oil fraction by urea to reduce the pour point.In this study mixture of 45 % methyl ethyl ketone (MEK) and 55 % toluene was used as a solvent. The studied variables are mixing time (10-70 min), solvent to oil volume ratio (0.5:1- 2:1), urea to wax weight ratio (2- 6) and constant mixing speed 1500 rpm. By analysis of the experimental results, the best operating conditions achieved are mixing time 40 min, solvent/oil 2:1 volume ratio, and urea/wax 4:1 weight ratio. At these conditions the pour point of the lubricating oil decreases from 24 ° C to -13 °C.

Transportation Sector classified as one of the services sectors which is without the production activities cannot be complete its rule. Is act asmoving actions which operate at production and non production goals for the organization and individuals insides the country and with others, that is why this sector act as one of the main which is occupied an important status on the way the economic activities and on the level of the economic institutions the transportation work on transforming all the commodities and products from productions locations to consumption location then its effect the productivity process and create the location utility and on the level of economic it considered as one of the economic supportive structure an

The study seeks to clarify the role of International Auditing Standard No. (320) of the relative importance in determining responsibility for planning and implementing the process of auditing financial statements and expressing neutral technical opinion through the analytical procedures of the auditor, whose responsibility is to obtain appropriate and reliable audit evidence that helps the auditor to form a general conclusion about whether The financial statements were consistent with the auditor's understanding of the entity. The relative importance contributes to defining the important accounts that help to set priorities for the auditor to set the necessary analytical procedures for these accounts. One of the most important co

Most of the theorists and researchers and also those interested in cinema and television attributed the fact of the existence of the dramatic works to the directors may be due to a historical justification. At the same time, the existence of the production world came as a result of the emergence of the production city (Hollywood). This is also a historic fact. The research would tackle all the formative truths to prove the relation and the timeline, i.e., before and after and the synergy that resulted in the existence of the dramatic works that benefited the humanity and those interested in this giving art. The objective of the research is to uncover the formative truth of the dramatic work between direction and production.

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The Cu(II) was found using a quick and uncomplicated procedure that involved reacting it with a freshly synthesized ligand to create an orange complex that had an absorbance peak of 481.5 nm in an acidic solution. The best conditions for the formation of the complex were studied from the concentration of the ligand, medium, the eff ect of the addition sequence, the eff ect of temperature, and the time of complex formation. The results obtained are scatter plot extending from 0.1–9 ppm and a linear range from 0.1–7 ppm. Relative standard deviation (RSD%) for n = 8 is less than 0.5, recovery % (R%) within acceptable values, correlation coeffi cient (r) equal 0.9986, coeffi cient of determination (r2) equal to 0.9973, and percentage capita

     In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel