In this paper, we propose new types of non-convex functions called strongly --vex functions and semi strongly --vex functions. We study some properties of these proposed functions. As an application of these functions in optimization problems, we discuss some optimality properties of the generalized nonlinear optimization problem for which we use, as an objective function, strongly --vex function and semi strongly --vex function.

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

Background : Gallstone disease is one of a common surgical problem and one of the most common gastrointestinal diseases throughout the world but its pathogenesis remains unclear. Many theories have been put forward to explain the mechanism of stone formation. The living organism has enzymatic and non-enzymatic antioxidant systems neutralizing the harmful effects of the endogenous oxygen free radicals products. Under certain conditions, the oxidative or anti-oxidative balance shifts towards the oxidative status as a result of increase in oxygen free radicals and/or impairment in antioxidant mechanism.

Objective :To evaluate the oxidative stress markers (total antioxidants capacity and malondialdeh

 Three of imide intermediate products  were synthesized by reacting of phthalic anhydride with glycine (2a), and tetrachloro phthalic anhydride with glycine , (S)-2-[(tert-Butoxycarbonyl)amino]-3-aminopropionic acid ( 2b,c)  respectively   in  dry toluene  with azeotropic removal of water using Dean- stark apparatus then carboxyl functional group activated by refluxing with  thionyl chloride, the resulted acid chloride (3a-c) were reacted with different amine (5-flourouracil, 4-chloroaniline, 4-bromoaniline, 2-amino thiazole, and pyrrolidine) (4a-e) , the   resulted products consider as

In this paper, some chalcone derivatives (C1, C2) were synthesized based on the reaction of equal amount of substituted acetophenone and substituted banzaldehyde in basic medium. Oxazine and thiazine derivatives were prepared from the reaction of chalcones (C1-C2) with urea and thiourea respectively in a basic medium. Pyrazole derivatives were prepared based on the reaction of chalcones with hydrazine mono hydrate or phenyl hydrazine in the presence of glacial acetic acid as a catalyst. The new synthesized compounds were identified using various physical techniques like1 H-NMR and FT-IR spectra.