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

This paper studies the oscillation properties and asymptotic behavior of all solutions of the 2×2 system of second-order half-linear neutral differential equations. Four results are obtained in this research. The first and second results are auxiliary results while the third and fourth results are main results. All possible cases of non-oscillating bounded solutions for this system are estimated and analyzed. It is noted that the parameters that affect the volatility of the solutions are Qi,Ri on the one hand and r1 and r2 on the other hand. For this purpose, and through investigation, it is shown that there are only fourteen possible cases of non-oscillating bounded solutions for this system, so all these cases must be treated, in the fir

In The Name of Allah Most Gracious Most Merciful

In this research, I will deal with the significance of the imperative and the disagreement of the fundamentalists in the general requirement by dividing it into an introduction and two sections. , and the appropriate indication.

The current research aims to study the extent to which the Independent High Electoral Commission applies to information security risk management by the international standard (ISO / IEC27005) in terms of policies, administrative and technical procedures, and techniques used in managing information security risks, based on the opinions of experts in the sector who occupy positions (General Manager The directorate, department heads and their agents, project managers, heads of divisions, and those authorized to access systems and software). The importance of the research comes by giving a clear picture of the field of information security risk management in the organization in question because of its significant role in identifying risks and s

A twisted-fin array as an innovative structure for intensifying the charging response of a phase-change material (PCM) within a shell-and-tube storage system is introduced in this work. A three-dimensional model describing the thermal management with charging phase change process in PCM was developed and numerically analyzed by the enthalpy-porosity method using commercial CFD software. Efficacy of the proposed structure of fins for performing better heat communication between the active heating surface and the adjacent layers of PCM was verified via comparing with conventional longitudinal fins within the same design limitations of fin material and volume usage. Optimization of the fin geometric parameters including the pitch, numb

The research aims to identify the concept of green taxes and their role in reducing environmental pollution through the poll of Abnh of taxpayers and employees of the General Authority for taxes totaling 200 individual .autam adoption of the resolution as a tool head for the collection of data and information from the sample and analyzed their responses using a statistical program (spss - 10), and calculating the percentages and the arithmetic mean, standard deviation and research found to a number of conclusions, notably the lack of legislation with the challenges and the difficulty of the existence of a measure or a standard lack of planning for the application of environmental taxes that the state taxation application between the Gene

المنظومة الصورية والتعبير اللغوي في العرض المسرحي

This is a brief research in which I tried to briefly explain the care that the Holy Qur’an received during the era of the Prophet, may God bless him and grant him peace, from the Prophet, may God bless him and grant him peace, and all of his honorable companions, may God bless him and grant him peace. I made this research in an introduction and two chapters, the first chapter I made it entitled: About the Holy Qur’an, in which I talked about general investigations about the Holy Qur’an, such as the definition of the Holy Qur’an and the difference between it and the hadith Qudsi and the hadith of the Prophet, then I mentioned a part of the virtues of the Holy Qur’an in general and the virtues of some surahs in particular, and th

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.