In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

The research seeks to examine the ability of fifth preparatory students in solving a mathematical problem in relation to system thinking. To this end, the researcher chose (140) fifth preparatory students from four-different secondary schools in Kirkuk city for the academic year (2016-2017). Two tests were adopted to collect study data: a test of (5) items about skills in solving math problem designed by (Al-raihan, 2006); and a test of system thinking skills designed by the researcher himself consisted of (14) items. It was divided into four skills (analyzing the main system to subsystems, eliminating all inner gaps of system, identifying the inner connection of system, and reorganizing the system). The findings indicated a good ability

Reducing global warming potential (GWP) of refrigerants is needed to the decrease of ozone-depleting of refrigeration systems leakages. Refrigerant R1234yf is now used to substitute R134a inside mobile air conditioning systems. Thermodynamic properties of R1234yf are similar to R134a. Also, it has a very low GWP of 4, compared to 1430 for R134a, making it a proper choice for future automobile refrigerants. The purpose of this research is to represent the main operating and performance differences between R1234yf and R134a. Experimental analysis was carried out on the automotive air conditioning system (AACS) with 3 kW nominal capacity, to test and compare the performance of R134a with R1234yf. Experiments were accomplish

The past decades of the last century and until now have witnessed many crises in the housing sector, and these crises were the result of many problems that led to a weak quality and quantity of housing stock, especially for lowincome people, and Goal 11 of the Sustainable Development Goals states, "Make cities and human settlements inclusive, safe, and capable of enduring and being sustainable, we have prepared this research that attempts to answer the following question: Is the current empowerment in the housing sector real and efficient support for people with limited income? The research assumes that empowerment in the housing sector has an important and effective role in reducing housing problems, the research aims to reach the most imp

Compelling evidence proved that coronavirus disease (COVID-19) disproportionately affects minorities. The goal of the present study was to explore the effects of intersected discrimination and discrimination types on COVID-19, mental health, and cognition. A sample of 542 Iraqis, 55.7% females, age ranged from 18 to 73, with (M = 31.16, SD = 9.77). 48.7% were Muslims, and 51.3% were Christians (N = 278). We used measures for COVID-19 stressors, executive functions, intersected discrimination (gender discrimination, social groups-based discrimination, sexual orientation discrimination, and genocidal discrimination), posttraumatic stress disorder (PTSD), depression, anxiety, status and death, existential anxieties, and health. We conducted in

The research aims to evaluate Evaluation of the investments Iraqi fund for External development through the application of financial tools to a number of companies of the Iraqi Fund for External Development, and from the point of view to achieve the best returns from investment and the feasibility of the investments of the Iraqi Fund for External Development and the research community represents the Iraqi Fund for External Development and the amount of (28) A company, while the research sample is (4) companies (the Arab Petroleum Transportation Services Company, the Arab Iraqi Company for Livestock Development, the Bauhaus Company for prefabricated buildings and mineral installations, the Arab Fisheries Company) that were chosen

New microphotometer was constructed in our Laboratory Which deals with the determination of Molybdenum (VI) through its Catalysis effect on Hydrogen peroxide and potasum iodide Reaction in acid medium H2SO4 0.01 mM. Linearity of 97.3% for the range 5- 100 ppm. The repeatability of result was better than 0.8 % 0.5 ppm was obtanined as L.U. (The method applied for the determination of Molybdenum (VI) in medicinal Sample (centrum). The determination was compared well with the developed method the conventional method.

Fear, harvesting, hunting cooperation, and antipredator behavior are all important subjects in ecology. As a result, a modified Leslie-Gower prey-predator model containing these biological aspects is mathematically constructed, when the predation processes are described using the Beddington-DeAngelis type of functional response. The solution's positivity and boundedness are studied. The qualitative characteristics of the model are explored, including stability, persistence, and bifurcation analysis. To verify the gained theoretical findings and comprehend the consequences of modifying the system's parameters on their dynamical behavior, a detailed numerical investigation is carried out using MATLAB and Mathematica. It is discovered that the