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.

The results of the historical review of social and political realities in general show that the practical and procedural applications of social engineering as a particular activity primarily of the social and political characteristics of man and society emerged in modern Western societies before appearing in other societies, These results also show that the emergence of these practical reasons and their applications in the West has also seen the emergence of modern theoretical foundations there, which seems to be the usual and usual context everywhere and in most or not all areas of life. Since the social and political dimensions are intertwined in human life and are in full, comprehensive and lasting harmony, interest in this geometry h

In Iraq most of the small buildings deployed a conventional air conditioning technology which typically uses electrically driven compressor systems which exhibits several clear disadvantages such as high energy consumption, high electricity at peak loads. In this work a thermal performance of air conditioning system combined with a solar collector is investigated theoretically. The hybrid air conditioner consists of a semi hermetic compressor, water cooled shell and tube condenser, thermal expansion valve and coil with tank evaporator. The theoretical analysis included a simulation for the solar assisted air-conditioning system using EES software to analyze the effect of different parameters on the power consumption of c

   In this research the effect of grain size and effect of La2O3 doping on densification  rate for the  initial and intermediate  stages of sintering were studied .The experimental results for α – cristobilite powder are modeled using ( L2-Regression ) technique in studying  the effect of grain size and La2O3 doping using  three particles size (6.12, 8.92, 13.6 ) µm, with undoped  initial powder and with La2O3 doping . The mathematical simulation showes that the densification rates increase as the initial particles sizes decrease and vice versa. This shows that the densification depends directly on the initial compact density which reflects the contacts area between the particles . How