For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio

Air pollution is considered one of the major environmental problems that contain many challenges and difficulties facing most countries of the world, including Iraq. The problem has emerged widely with the emergence of the industrial revolution in the world and the tremendous increase in the population and the increase in the number of transportation and its development in addition to excavation, maintenance and work Construction and weather fluctuations, such as dust and sandstorms, pollution resulting from oil refining, extraction, diversion and other processes that cause pollution, and the start of the world using methods that limit the volume of environmental pollution. The most prominent of these methods is the imposition of

 A particle swarm optimization algorithm and neural network like self-tuning PID controller for CSTR system is presented. The scheme of the discrete-time PID control structure is based on neural network and tuned the parameters of the PID controller by using a particle swarm optimization PSO technique as a simple and fast training algorithm. The proposed method has advantage that it is not necessary to use a combined structure of identification and decision because it used PSO. Simulation results show the effectiveness of the proposed adaptive PID neural control algorithm in terms of minimum tracking error and smoothness control signal obtained for non-linear dynamical CSTR system.

Co-crystals are new solid forms of drugs that could resolve more than one problem associated with drugs formulations like solubility, stability, bioavailability, mechanical and tableting properties. A preliminary theoretical study for estimating the possible bonding between the co-crystal components (paracetamol and naproxen) was performed using the ChemOffice program. The results revealed a high possibility for bonding between paracetamol and naproxen and indicated the ability of molecular mechanics study to predict the co-crystal design.

       In this work, four different methods were used for the preparation of three different ratios 1:1, 2:1, and 1:2 of paracetamol:naproxen co-crystals. The four

The research aims to identify the effect of teaching-learning design based on the constructivism theory on the life skills of middle stage students. The sample consisted of (60) students from one of the middle schools in Baghdad's governorate. The experimental group and control group consisted of 30 students for each group, the research tool was the life skills scale composed of (78) items. The scale proved its validity and reliability, which was found to be (0.85). The results showed a statistically significant difference in life skills between the two groups of research in favor of the experimental group, which studied the educational design according to models of constructivism theory compared to the usual method of teaching.

Dam and powerhouse operation sustainability is a major concern from the hydraulic engineering perspective. Powerhouse operation is one of the main sources of vibrations in the dam structure and hydropower plant; thus, the evaluation of turbine performance at different water pressures is important for determining the sustainability of the dam body. Draft tube turbines run under high pressure and suffer from connection problems, such as vibrations and pressure fluctuation. Reducing the pressure fluctuation and minimizing the principal stress caused by undesired components of water in the draft tube turbine are ongoing problems that must be resolved. Here, we conducted a comprehensive review of studies performed on dams, powerhouses, a