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.

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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This study investigates the implementation of Taguchi design in the estimation of minimum corrosion rate of mild-steel in cooling tower that uses saline solution of different concentration. The experiments were set on the basis of Taguchi’s L16 orthogonal array. The runs were carried out under different condition such as inlet concentration of saline solution, temperature, and flowrate. The Signal-to- Noise ratio and ANOVA analysis were used to define the impact of cooling tower working conditions on the corrosion rate. A regression had been modelled and optimized to identify the optimum level for the working parameters that had been founded to be 13%NaCl, 35ᴼC, and 1 l/min. Also a confirmation run to establish the p

The current research illustrates experimentally the effect of series and parallel connection (Z-I Configurations) of flat plate water solar collectors array on the thermal performance of closed loop solar heating system. The study includes the effect of changing the water flow rate on the thermal efficiency. The results show that, the collector's efficiency in series connection is higher than the parallel connection within flow rate level less than (100) ℓ/hr. Moreover, the collector efficiency in parallel connection of (I-Configurations) is more than the (Z- Configurations) with increasing the water flow rate .The maximum daily efficiency for parallel (I-Configurations) and (Z- Configurations) are (55%) and (51%) at w

Exploitation of mature oil fields around the world has forced researchers to develop new ways to optimize reservoir performance from such reservoirs. To achieve that, drilling horizontal wells is an effective method. The effectiveness of this kind of wells is to increase oil withdrawal. The objective of this study is to optimize the location, design, and completion of a new horizontal well as an oil producer to improve oil recovery in a real field located in Iraq. “A” is an oil and gas condensate field located in the Northeast of Iraq. From field production history, it is realized the difficulty to control gas and water production in this kind of complex carbonate reservoir with vertical producer wells. In this study, a horizont

This study focuses on producing wood-plastic composites using unsaturated polyester resin reinforced with Pistacia vera shell particles and wood industry waste powder. Composites with reinforcement ratios of 0%, 20%, 30%, and 40% were prepared and tested for thermal conductivity, impact strength, hardness, and compressive strength. The results revealed that thermal conductivity increases with reinforcement, while maintaining good thermal insulation, reaching a peak value of 0.633453 W/m·K. Hardness decreased with increased reinforcement, reaching a minimum nominal hardness value of 0.9479. Meanwhile, impact strength and compressive strength improved, with peak values of 14.103 k/m² and 57.3864568 MPa, respectively. The main aim is to manu

Results showed that the optimum conditions for production of inulunase from isolate Kluyveromyces marxianus AY2 by submerged culture could be achieved by using inulin as carbon source at a concentration of 2% with mixture of yeast extract and ammonium sulphate in a ratio of 1:1 in a concentration of 1% at initial pH 5.5 after incubation for 42 hours at 30ºC.

Background: Cluster of differentiation 14 (CD14) is a serum/cell surface glycoprotein; and it is a pattern recognition receptor. CD14 expressed on the surface of various cells, or it found soluble in saliva and other body fluids. It has been proposed that soluble CD14 (sCD14) may play a protective role by controlling Gram negative bacterial infections through its capacity to bind lipopolysaccharide. This study was conducted to assess the level of soluble CD14 in saliva of patients with different periodontal diseases and healthy subjects and determine its correlation with clinical periodontal parameters. Materials & Methods: A total of 80 subjects, age ranged (25-50) years old, divided into three main groups, group ? consisted of 45 chronic