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

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

Trickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated z

Laser is a powerful device that has a wide range of applications in fields ranging from materials science and manufacturing to medicine and fibre optic communications. One remarkable

Atmospheric transmission is disturbed by scintillation, where scintillation caused more beam divergence. In this work target image spot radius was calculated in presence of atmospheric scintillation. The calculation depend on few relevant equation based on atmospheric parameter (for Middle East), tracking range, expansion ratio of applied beam expander's, receiving unit lens F-number, and the laser wavelength besides photodetector parameter. At maximum target range Rmax =20 km, target image radius is at its maximum Rs=0.4 mm. As the range decreases spot radius decreases too, until the range reaches limit (4 km) at which target image spot radius at its minimum value (0.22 mm). Then as the range decreases, spot radius increases due to geom

Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

The need for renewable energy sources is higher than ever due to rising global warming, climate change, and ozone depletion. For refrigeration and air conditioning applications, adsorption refrigeration systems are viable alternatives cooling techniques. This study is a topic and part of the M.Sc. thesis. A field solar-powered ice maker unit was created, studied, tested, and evaluated on the 13^th and 30^th of May, 2022. Activated carbon and methanol pair was used to set up a refrigeration system in Baghdad (Al Dora). Experimental tests were carried out outdoors to determine the coefficient of performance COP and specific cooling power SCP of the system. The results showed that the lowest temperature

Mesoporous silica (MPS) nanoparticle was prepared as carriers for drug delivery systems by sol–gel method from sodium silicate as inexpensive precursor of silica and Cocamidopropyl betaine (CABP) as template. The silica particles were characterized by SEM, TEM, AFM, XRD, and N2adsorption–desorption isotherms. The results show that the MPS particle in the nanorange (40-80 nm ) with average diameter equal to 62.15 nm has  rods particle morphology, specific surface area is 1096.122 m²/g, pore volume 0.900 cm³/g, with average pore diameter 2.902 nm, which can serve as efficient carriers for drugs. The adsorption kinetic of Ciprofloxacin (CIP) drug was studied and the data were analyzed and found to match well with

At a time when the general rules in the different legal systems require the presence of two parties to the contract, one of which is issued the first expression of the will and is called the offer, and the other is issued from the other and is called the acceptance. A special type of contracts emerged in the beginning of the last century called the “unilateral contracts”. The side sparked a major jurisprudential dispute, as well as the issuance of several contradictory judicial rulings on it. Hence, this research came to highlight this special type of contract. Key words: the definition of a unilateral contract, its distinction from other legal situations, and its effects.