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 study, a cholera model with asymptomatic carriers was examined. A Holling type-II functional response function was used to describe disease transmission. For analyzing the dynamical behavior of cholera disease, a fractional-order model was developed. First, the positivity and boundedness of the system's solutions were established. The local stability of the equilibrium points was also analyzed. Second, a Lyapunov function was used to construct the global asymptotic stability of the system for both endemic and disease-free equilibrium points. Finally, numerical simulations and sensitivity analysis were carried out using matlab software to demonstrate the accuracy and validate the obtained results.

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Construction and operation of (2 m) parabolic solar dish for hot water application were illustrated. The heater was designed to supply hot water up to 100 oC using the clean solar thermal energy. The system includes the design and construction of solar tracking unit in order to increase system performance. Experimental test results, which obtained from clear and sunny day, refer to highly energy-conversion efficiency and promising a well-performed water heating system.

The linear segment with parabolic blend (LSPB) trajectory deviates from the specified waypoints. It is restricted to that the acceleration must be sufficiently high. In this work, it is proposed to engage modified LSPB trajectory with particle swarm optimization (PSO) so as to create through points on the trajectory. The assumption of normal LSPB method that parabolic part is centered in time around waypoints is replaced by proposed coefficients for calculating the time duration of the linear part. These coefficients are functions of velocities between through points. The velocities are obtained by PSO so as to force the LSPB trajectory passing exactly through the specified path points. Also, relations for velocity correction and exact v