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 paper, variable gain nonlinear PD and PI fuzzy logic controllers are designed and the effect of the variable gain characteristic of these controllers is analyzed to show its contribution in enhancing the performance of the closed loop system over a conventional linear PID controller. Simulation results and time domain performance characteristics show how these fuzzy controllers outperform the conventional PID controller when used to control a nonlinear plant and a plant that has time delay.

A simple, environmentally benign, cost-effective, and sensitive colorimetric determination for the pharmaceutical drug dexamethasone sodium phosphate (DXP) has been developed by the formation of a colored complex with fluoranil. The process was sensitive and linear over the range 1 to 40 μg/mL, excellent correlation coefficient 0.9989, recovery% 99.80 ± 1.3, limit of detection (LOD) and limit of quantification (LOQ) were 0.23 and 0.9 μg/mL, respectively, and good RSD ~1.63%. The experimental conditions were optimized after an intensive study. The approach was validated statistically for the quantification of the analyte in its pure and/or pharmaceutical form. Despite the proposed approach is selective, it still can be applied for

Background: An oily calcium hydroxide formulation proved over the last years to be highly efficient in promoting bone regeneration in closed defects as periapical lesions, cysts, or post-extraction defects. The aim of the present study is the assessment of the outcome of treatment of deep intrabony periodontal defects with an Open Flap Debridement) (OFD) + combination of {(30% Hydroxyapatite HAp + 70% ?-Tricalcium Phosphate granules mixed with an Oily Calcium Hydroxide Suspension (OCHS )} and compare the results with {(OFD) alone)}. The combination of OCHS& TCP was used in humans with a sort of positive results, and more conduction of studies was recommended. Material and method: The sample of this study composed of sixteen patients;

In the present survey 18 species of endo and ecto-parasites were recorded during the examination of 50 Mus musculus (Linnaeus, 1758) among 10 localities in Erbil city, of which 7 species were protozoan and as follows : Chilomastix bettencourti (da Fonseca 1915)82%; Giardia muris (Filice, 1952) 68%; Tritrichomonas muris (Grassi,1879)36%; Entamoeba histolytica (Schaudinn,1903) 24%; Entamoeba coli (Grassi,1879)32%; Eimeria sp. 28% and Trypanosoma musculi (Kendall,1906)2%; and 8 species were helminthes as follows: 4 Cestodes: Rodentolepis nana (von Siebold, 1852) 8%; Hymenolepis diminuta (Rudolphi, 1819)2%; larval stage of Echinococcus granulosus (Batsch, 1786)8%, Cysticercus fasciolaris (Rudolphi, 1808)6%, 4 Nematodes: Aspiculuris tetrapter