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.

    تعد مراجعة النظير واحدة من الأســاليب الحديثة فــي مجال الرقابة والتدقيق ونشــأة كأداة لقياس مــدى فاعليــة الرقابــة علــى الجــودة هو لبنة أساسية في إدارة الجودة الشاملة ووسيلة لتحســين أدوات الرقابــة المعمول بها، وللتحقق من مدى الانسجام بين المعايير الدولية للأجهزة العليا للرقابة المالية والمحاسبة والاجراءات المعمول بها من قبل الاجهزة العليا للرقابة وعليه فأن مراجعة النظير أداة تستخدم ف

The indirect monetary policy tools led to financial stability for the period being studied through the use of indicators of financial stability (aggregate) to show the effect of the foreign reserves of the Central Bank of Iraq and its indirect instruments in achieving financial and economic stability, especially after the significant decline in oil prices and dependence of the Iraqi economy on Oil (rent) and lower reserves of the Central Bank of Iraq after 2014 and now compared to previous years, the goal of this research is to achieve financial stability according to selected indicators and achieve an optimal monetary policy to achieve the development goals of The economic policy in the country. Standard models were used to test

In this work, the effect of the addition of bright nickel plating and silver carried out by the electroplating method has been studied, on the coating of copper nanoparticles on the copper base metal via the process of thermal evaporation. The improvement of the solar absorber using CuNP in combination with the bright nickel and silver was obtained to be better than copper nanoparticles individually. A bright nickel enhanced the absorbed thermal stability. Also, other optical properties, absorptions, and emissivity slightly decreased from (93% to 87%), while the existence of silver had a slight impact on absorption of about (86.50%). On the other hand, thermal conductivity was evaluated using hot disk analyzer. The results showed a good

Taxes are an essential axis in the economy as the most effective and effective economic tool in any country (economy). Expanding the scope of taxation without adequate study has produced a dangerous result with a negative impact that is almost apparent, namely (tax evasion), which stands as a barrier preventing the state from reaching Therefore, the research sought to study strategic tax planning and its importance in reducing tax evasion, and the research aims from that to prove the importance of adopting strategic planning in the field of taxes according to modern and effective scientific foundations to reduce tax evasion to enhance the achievement of tax evasion. The financing objective is in addition to the other objectives,

The measurement of vitamin B1 in pure and pharmaceutical formulations was proposed by using a straightforward and sensitive spectrophotometric approach. Sulfacetamide (SFA) is diazotized, then coupled with vitamin B1 in alkaline media to produce a colored azo dye complex with a stability constant of 5.597 × 105 L/mol. The product is stable, with a maximum absorption wavelength of 489.5 nm, molar absorptivity of 10108 L/mol∙cm, Sandell's sensitivity of 0.0334 μg/cm2, detection limit of 0.0135 μg/mL, and Beer's law being observed over the concentration range of 0.2–20.0 μg/mL. The stability constant and stoichiometry of the produced azo dye were calculated using the continuous variation (Job's) and mole ratio methods. The suggested ap

A batch adsorption system was applied to study the adsorption of methylene blue from aqueous solution by Iraqi bentonite and treated bentonite with different amount of zinc oxide (ZnO). The adsorption capacities of methylene blue onto bentonite were evaluated. The equilibrium between liquid and solid phase was described by Langmuir model better than the Freundlich model. Langmuir and Freundlich constants have been determined. The separation factor or equilibrium parameter, RL which is used to predict if an adsorption system is favourable or unfavourable was calculated for all cases.

This paper describes the digital chaotic signal with ship map design. The robust digital implementation eliminates the variation tolerance and electronics noise problems common in analog chaotic circuits. Generation of good non-repeatable and nonpredictable random sequences is of increasing importance in security applications. The use of 1-D chaotic signal to mask useful information and to mask it unrecognizable by the receiver is a field of research in full expansion. The piece-wise 1-D map such as ship map is used for this paper. The main advantages of chaos are the increased security of the transmission and ease of generation of a great number of distinct sequences. As consequence, the number of users in the systems can be increased. Rec

In this research, Zinc oxide (ZnO)/epoxy nanocomposite was synthesized by simple casting method with 2wt. % ZnO concentration. The aim of this work was to study the effect of pH and composite dosage on the photocatalytic activity of ZnO/ epoxy nanocomposite. Scanning electron microscopy (SEM) technique images proof the homogeneous distribution of ZnO nanoparticles in epoxy. A synthesized nanocomposite samples were characterized by Fourier Transform Infrared spectrometer (FTIR) measurements. Two spectra for epoxy and 2wt.% ZnO/epoxy nanocomposites were similar and there are no new bonds formed from the incorporation of ZnO nanoparticles. Using HCl and NaOH were added to Methylene blue (MB) dye (5ppm) to gat pH values 3 and 8. The degradat

In this research, porous silicon (PS) prepared by anodization etching on surface of single crystalline p-type Si wafer, then Gold nanoparticle (AuNPs) prepared by pulsed laser ablation in liquid. NPs deposited on PS layer by drop casting. The morphology of PS, AuNPs and AuNPs/PS samples were examined by AFM. The crystallization of this sample was characterized by X-ray diffraction (XRD). The electrical properties and sensitivity to CO2 gas were investigated to Al/AuNPs/PS/c-Si/Al, we found that AuNPs plays crucial role to enhance this properties.