was studied by taking several different values for the constant α and fixing the other three variables β, c and d with the values 25.58, -0.7142857, and -1.142, respectively. The purpose of this paper is to know the values by which the system transforms from a steady state to a chaotic state under the initial conditions x, y, and z that equal -1.6, 0 and 1.6 respectively. It was found that when the value of α is equal to 0, the Chua system is in a steady state, and when the value of α is equal to 9.5 and the wave is sinusoidal, the system is in oscillation, and when α is equal 13.4 the system is in a Quasi-chaotic state, and finally the system turns to the chaotic state when the value of α equals 15.0

      In this article, the boundary value problem of convection propagation through the permeable fin in a natural convection environment is solved by the Haar wavelet collocation method (HWCM). We also compare the solutions with the application of a semi-analytical method , namely the Temimi and Ansari (TAM), that is characterized by accuracy and efficiency.The proposed method is also characterized by simplicity and efficiency. The possibility of applying the proposed method to many types of  linear or nonlinear ordinary and partial differential equations.

The object of this work is to investigate the effect of the addition of methanol on the shelf life and color characteristics of novolak resin. Different percentages were added and two mechanisms were suggested for the addition. High ortho structure (1, 2-3) novolak resin was prepared and used in the above investigation. Experimental determination using FT-IR and UV-spectroscopy showed that on the addition of 30% of methanol and according to the second mechanism of addition novolak shelf life increased to 12 months without obvious decomposition and color change. It is suggested that methanol plays an important role in the inhabitation of the reactive sites on the resin that are responsible for the oxidation of the polymer when exposed to

     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

Pandemic COVID-19 is a contagious disease affecting more than 200 countries, territories, and regions. Recently, Iraq is one of the countries that have immensely suffered from this outbreak. The Kurdistan Region of Iraq (KRI) is also prone to the disease. Until now, more than 23,000 confirmed cases have been recorded in the region. Since the onset of the COVID-19 in Wuhan, based on epidemiological modelling, researchers have used various models to predict the future of the epidemic and the time of peak, yielding diverse numbers in different countries. This study aims to estimate the basic reproductive number [R₀] for COVID-19 in KRI, using the standard SIR (Susceptible-Infected-Removed) epidemic model. A system of non

The present work presents design and implementation of an automated two-axis solar tracking system using local materials with minimum cost, light weight and reliable structure. The tracking system consists of two parts, mechanical units (fixed and moving parts) and control units (four LDR sensors and Arduino UNO microcontroller to control two DC servomotors). The tracking system was fitted and assembled together with a parabolic trough solar concentrator (PTSC) system to move it according to information come from the sensors so as to keep the PTSC always perpendicular to sun rays. The experimental tests have been done on the PTSC system to investigate its thermal performance in two cases, with tracking system (case 1) and without trackin

Influence of combined square nozzle with helical tape inserted in a constant heat flux tube on heat transfer enhancement for turbulent airflow for Reynolds number ranging from 7000 to 14500 were investigated experimentally. Three different pitch ratios for square nozzle (PR = 5.8, 7.7 and 11.6) according to three different numbers of square nozzle (N = 3, 4 and 5) and constant pitch ratios for helical tape were used. The results observed that the Nusselt number and friction factor for combination with winglets were found to be up to 33.8 % and 21.4 %, respectively higher than nozzle alone for pitch ratio PR=5.8. The maximum value of thermal performance for using combination with winglets was about 1.351 for pitch ratio= 5.8. Nusselt numb

Mixed convection heat transfer to air inside an enclosure is investigated experimentally. The bottom wall of the enclosure is maintained at higher temperature than that of the top wall which keeps in oscillation motion, whereas the left and right walls are well insulated. The differential temperature of the bottom and top walls changed several times in order to accurately characterize the temperature distribution over a considerable range of Richardson number. Adjustable aspect ratio box was built as a test rig to determine the effects of Richardson number and aspect ratio on the flow behavior of the air inside the enclosure. The flow fields and the average Nusselt number profiles were presented in this wo