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.
In the last few years, following the relative stability of the political, economic, and security environments, Iraq has embarked on a transformation towards an ambitious program of automation across various sectors. However, this automation program faces numerous challenges, including significant investments in technology and training, addressing social impacts, and combating widespread illiteracy
Abstract
Leadership has now become a process for applying methods and techniques that make the Organization at the top of its competitive pyramid a greater market share. Leadership has become a focus for all leaders and managers، and leaders and managers are increasingly seeking to develop their skills and leadership skills. The research started with a clear problem of specific questions to ensure that the general objective of the research is to describe the characteristics of the leader and to clarify the dimensions of empowering the workers and to highlight the role of the leader in empowering the workers. The study examines the relation between the role of the leader in
... Show MoreA novel series of liquid crystalline compounds containing 2,4-thiazolidinedione units with varying terminal alkyl chain lengths was successfully synthesized and characterized. The chemical structures of the synthesized compounds were confirmed by FT-IR, ¹H-NMR, and mass spectrometry. The mesomorphic behavior was investigated using polarized optical microscopy (POM) and differential scanning calorimetry (DSC). Compounds [V]₄, [V]₅, and [V]₆ exhibited enantiotropic nematic phases, while compound [V]₈ displayed a smectic A (SmA) phase. No liquid crystalline behavior was observed for compound [V]₃. The liquid crystalline properties were found to depend on the terminal-to-lateral chain length ratio, molecular geometry, and the nature
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This study comes as: The responsibility of the Iraqi newspapers in promoting the political culture inside society, an analytical study in newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 to 31/ 3/ 2013 to spot light on the extent to which the three mentioned newspapers are compliance with the promotion of the political culture inside society which is seen as one of the essential requirements for the success and promotion of the democratic process inside society.
The study aims to: finding out the extent to which these newspapers are compliance with their responsibility in the promoting the political culture inside society; knowing the nature of their role in pr
... Show MoreThe present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil
... Show MoreSolar photovoltaic (PV) has many environmental benefits and it is considered to be a practical alternative to traditional energy generation. The electrical conversion efficiency of such systems is inherently limited due to the relatively high thermal resistance of the PV components. An approach for intensifying electrical and thermal production of air-type photovoltaic thermal (PVT) systems via applying a combination of fins and surface zigzags was proposed in this paper. This research study aims to apply three performance enhancers: case B, including internal fins; case C, back surface zigzags; and case D, combinations of fins and surface zigzags; whereas the baseline smooth duct rep