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.

CuO nanoparticles were synthesized in two different ways, firstly by precipitation method using copper acetate monohydrate Cu(CO₂CH₁₃)₂·H2O, glacial acetic acid (CH3COOH) and sodium hydroxide(NaOH), and secondly by sol-gel method using copper chloride(CuCl₂), sodium  hydroxide (NaOH) and ethanol (C₂H₆O). Results of scanning electron microscopy (SEM) showed that different CuO nanostructures (spherical and Reef) can be formed using precipitation and sol- gel process, respectively, at which the particle size was found to be less than 2 µm. X-ray diffraction (XRD)manifested that the pure synthesized powder has no inclusions that may exist during preparations. XRD result

Two series of bent and liner core mesogen containing 1,2,4-traizole ring [VI]a,g and series were synthesized by many steps starting from esterification of isophthalic acid and terephathalic acid with methanol to yield diester compound [I]a,b which was converted to their acid hydrazide [II]a,b and the acid hydrazide reacted with ammonium thiocyanate or diester reacted with thiosemicarbazide to yield compounds [III]a,b. Then cyclization by 4% NaOH to yielded 1,2,4 traizole-3- thiol compounds [IV]a,b , afterword adding hydrazine hydrate to yield compounds [V]a,b. These compounds condensated with different substituted aldehyde to give new Schiff bases[VI]a,b ,[VII]a,b . Also , reaction acid hydrazide [II]a,b with aldehyde [VII] to yielded Schif

In the present study benzofuran based chalcones 1 (a, b) are synthesized by condensing aromatic aldehydes with 2-acetylbenzofuran in the presence suitable base. These chalcones are very useful precursors for the synthesis of pyrazoline, isoxazoline, pyrmidine, cyclohexenone and indazole derivatives. All these compounds are characterized by their melting points, FTIR and 1 HMNR (for some of them) spectral dat

Polycystic ovary syndrome (PCOS) is a prevalent condition in women of reproductive age. It is characterized by androgen excess and chronic anovulation. Some trace elements, macroelements, and heavy metals have been linked to pathophysiological mechanisms of PCOS .

To study the alterations in the serum levels of the trace element manganese (Mn), some macroelements, magnesium(Mg) and calcium (Ca), and the heavy metals cadmium (Cd) and lead (Pb), in obese and non-obese PCOS patients; and the association of these alterations with some of the hormonal changes occurring in PCOS.

The study was carried out at Kamal Al-Samarrai Hospital (Center for Infertility treatment and in vitro Fertilization "IVF") Baghdad- Iraq. Eig