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.

Abstract:

The main objective of the research is to build an optimal investment portfolio of stocks’ listed at the Iraqi Stock Exchange after employing the multi-objective genetic algorithm within the period of time between 1/1/2006 and 1/6/2018 in the light of closing prices (43) companies after the completion of their data and met the conditions of the inspection, as the literature review has supported the diagnosis of the knowledge gap and the identification of deficiencies in the level of experimentation was the current direction of research was to reflect the aspects of the unseen and untreated by other researchers in particular, the missing data and non-reversed pieces the reality of trading at the level of compani

 Background: Mitral stenosis (MS) is the most common valve disease in developing countries and there are many ways to deal with this condition. The aim of this study was to evaluate the immediate results of percutaneous transvenous mitral commissurotomy (PTMC) in patients with severe symptomatic rheumatic mitral stenosis.
Patients and Methods: From May 2006 to August 2007, 58 patients (17 male, 41 female) with age range (16-57) years, underwent PTMC in Ibn AL- Bitar Hospital for Cardiac Surgery. All the patients were symptomatic, their MVA 1.5 cm2 with NYHA class II-IV. Clinical evaluation and echocardiographic examination were carried out before and after PTMC, mitral valve structures were assessed

A new, simple, accurate, fast and sensitive spectrophotometric method has been developed for the analysis of amiloride in pure and pharmaceutical formulations by continuous flow injection analysis. The method was based on the oxidation of the drug with Ce(IV)sulfate in acidic medium to formed a pinkish-red color species which determined using homemade Ayah 3SBGR x3-3D solar cell flow injection photometer. Optimum conditions were obtained using a high intensity green light emitted diode as a source. The linear dynamic range for the instrument response versus amiloride concentration was 0.0005- 10 mmol.L-1 while the L.O.D was of 9.471 ng / sample. The correlation coefficient (r) was 0.9824 while percentage linearity (r2%) was 96.50%. RSD%

The first flow injection spectrophotometric method is characterized by its speed and sensitivity which have been developed for the determination of promethazine-HCl in pure and pharmaceutical preparation. It is based on the in situ detection of colored cationic radicals formed via oxidation of the drug with sodium persulphate to pinkish-red species and the same species was determined by using homemade Ayah 3SX3-3D solar flow injection photometer. Optimum conditions were obtained by using the high intensive green light emitted diode as a source. Linear dynamic range for the absorbance versus promethazine-HCl concentration was 0-7 mmol.L-1, with the correlation coefficient (r) was 0.9904 while the percentage linearity (r2%) was 98.09%. the L.

This research investigated the effect of adding two groups of reinforcement materials, including bioactive materials Hydroxyapatite (HA) and halloysite nanoclay and bioinert materials Alumina (AL2O3) and Zirconia (ZrO2), each of them with various weight ratios (1,2,3,4 &5)% to the polymer matrix PMMA. The best ratios were selected, and then a hybrid was preparing Composite red from the best ratios from each group. Thermal properties, including thermal conductivity and Thermomechanical Analysis (TMA) technology, have been studied. The results showed that adding 3% Hydroxyapatite (HA) and 5% halloysite nanoclay to the polymethacrylate (PMMA) mer leads to an increase in thermal conductivity. It was also found from the Thermomechanical Analysis

Simple and sensitive batch and flow injection methods (normal and reverse flow injection analysis (nFIA and rFIA)) for spectrophotometric determination of vancomycin hydrochloride (VHC) in pharmaceutical preparations were proposed and optimized. Both methods are based on the oxidative - coupling reaction between vancomycin hydrochloride and 2,4-Dinitrophenylhydrazine (DNPH) in the presence of sodium periodate in alkaline medium to form a yellow water-soluble product that is stable and has a maximum absorption at 461 nm. Beer’s law was obeyed over the range of 1- 40, 0.5-120 and 0.5-150 μg.mL-1; the limits of detection were 0.537, 0.0823 and 0.233 μg.mL-1 for batch, normal and reverse flow injection methods respectively. The sampling