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.

Background: Periodontal diseases are inflammatory diseases affecting the supporting tissues of the teeth. One of the leading environmental factors that are closely related not only to the risk but also to the prognosis of periodontitis is smoking. This study aimed to evaluate the influence of smoking on periodontal health status and to measure the levels of matrix metalloproteinase-9 in smokers and nonsmokers chronic periodontitis patients, also it aimed to test the correlation between the levels of matrix metalloproteinase-9 and the clinical periodontal parameters. Materials and Methods: Five milliliters samples of un-stimulated whole saliva and full-mouth clinical periodontal recordings (plaque index, gingival index, bleeding on probing,

A new series of metal ions complexes of VO(II), Cr(III), Mn(II), Zn(II), Cd(II) and Ce(III) have been synthesized from the Schiff bases (4-chlorobenzylidene)-urea amine (L1) and (4-bromobenzylidene)-urea amine (L2). Structural features were obtained from their elemental microanalyses, magnetic susceptibility, molar conductance, FT-IR, UV–Vis, LC-Mass and 1HNMR spectral studies. The UV–Vis, magnetic susceptibility and molar conductance data of the complexes suggest a tetrahedral geometry around the central metal ion except, VOII complexes that has square pyramidal geometry, but CrIII and CeIII octahedral geometry. The biological activity for the ligand (L1) and its Vanadium and Cadmium complexes were studied. Structural geometries of com

In this research, a Co-polymer (Styrene / Allyl-2.3.4.6-tetra-O-acetyl-β-D-glucopyranoside) was synthesized from glucose in four steps using Addition Polymerization according to the radical mechanism using Benzoyl Peroxide (BP) as initiator. Initially, Allyl-2.3.4.6-tetra-O-acetyl-β-D-glucopyranoside monomer was prepared in three steps and the reaction was followed by (HPLC, FT-IR, TLC), in the fourth step the monomer was polymerized with Styrene and the structure was determined by FT-IR and NMR spectroscopy. The reaction conditions (temperature, reaction time, material ratios) were also studied to obtain the highest yield, the relative, specific and reduced viscosity of the prepared polymer was determined, from which the viscosity ave

The research aimed to demonstrate the possibility of benefiting from the coordination between real estate and income tax as the independent variable on the tax outcome as the dependent variable as the dependent variable. Which were practiced within rented buildings, as information was obtained from real estate owners, and the annual controls for the year 2021 were relied upon in the process of calculating the tax amounts expected to be obtained. used in the tax inventory process lacks seriousness and continuous updating

The present study was conducted to examine toxicological effects of copper sulfate (Cu) in common carp fish (Cyprinus carpio L.). The LC50 (median lethal concentrations) of copper on Cyprinus carpio were 3.64, 3.36, 3.04, 2.65 mg/L respectively. In general, behavioral responses of the fishes exposed to copper included uncontrolled swimming, erratic movements, loss of balance, swam near the water surface with sudden jerky movements. Haematological parameters such, red blood cells (RBC), white blood cells (WBC), haemoglobin (Hb), Packed cell volume (PCV), mean cell volume (MCV) mean cell haemoglobin (MCH), and mean corpuscular hemoglobin concentration (MCHC) were studied. The obtained results indicated that the (RBC) and (WBC) have increas

Left bundle branch block (LBBB) is a common finding in electrocardiography, there are many causes of LBBB.