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.

A prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc

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

The survival analysis is one of the modern methods of analysis that is based on the fact that the dependent variable represents time until the event concerned in the study. There are many survival models that deal with the impact of explanatory factors on the likelihood of survival, including the models proposed by the world, David Cox, one of the most important and common models of survival, where it consists of two functions, one of which is a parametric function that does not depend on the survival time and the other a nonparametric function that depends on times of survival, which the Cox model is defined as a semi parametric model, The set of parametric models that depend on the time-to-event distribution parameters such as

A total of 60 samples of drinking water filtrated by Reverser 0smosis Filtration System from April to October 2012, from different houses in Baghdad – Al Resafa, so as to identify the eggs and cysts of protozoa. Two methods applied direct smear and staining technique with zeal nelson stain, which appeared Tape warm eggs, Ascaris lumbrecoides eggs and oocyst of Cryptospordium sp. This study revealed that total contamination rate with intestinal parasites in tap water were 96.6% this high rate, refers to filtrate tap water by reverse osmosis system was useful to prevent or reduce the contamination of drinking water, in order to reduce risks to public health; So recommended to apply this method at water purification stations. Dis

A fixed firefighting system is a key component of fire safeguarding and reducing fire danger. It is installed as a permanent component in a structure to protect the entire or a portion of the building and its contents. The study aims to review the previous studies that deal with the evaluation of fire safety measures and their use in resolving problems associated with fire threats in buildings. For this reason, a number of previous studies in this field were reviewed compared with the NFPA code. The findings revealed that regulatory developments over the last several decades had created an atmosphere conducive to innovation. This has resulted in a growth in the number of fixed firefighting system types now obtainable. Th

The research study is important since it establishes predicted rates for various nervous system functional indicators.In terms of performing the skill of Dribbling in basketball for young players in Baghdad Governorate in order to reach scientific results that serve researchers, coaches, and players uniformly. The study's goal is to create predictive equations for specific functional indicators of the nervous system in relation to the Dribbling skill performance of young basketball players in Baghdad Governorate. The researchers used a descriptive approach with a survey method on (8) youth basketball league clubs in Baghdad Governorate for the 2022-2023 sports season, totaling (96) players . Three tests were used to measure the nervous sy