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.
Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions as a whole.
The topic of attention was drawn to the attention of the speakers, as it made me ponder it carefully, and my goal in that is to know the reason for the interest of the speakers and their care for it, and to clarify from their books the purpose of making this topic one of the advanced investigations with them.
The idea of writing a paper on the subject of consideration was not absent from my thinking, because I saw the attention of speakers on this issue, as they made it one of the first issues that they deal with studying in their work
... Show MoreSampling is the selection of a representative portion of a material, and it’s as important as testing. The minimum weight of gravel field or lab sample depends on the nominal maximum particle size. The weight of the sample will always be greater than that portion required for testing. The approximate precision desired for the testing will control the weight of the gravel sample. In this study, gravel sample has been simulated by using multilinear approximated function for Fuller’s curve on the logarithmic scale. Gravel particles are divided into classes according to their medium diameter and each class was simulated separately. A stochastic analysis, by using 100 realizations in s
Fine aggregate (Sand) is a necessary material used in concrete construction purposes, it’s naturally available and it’s widely used around the world for different parts of construction in any building mainly for filling the voids between gravel. Sand gradation is important for different composite materials, and it gives good cohesion when compared with coarse sand that provides strength for the building. Therefore, sand is necessary to be tested before it is used and mixed with other building materials in construction and the specimen must be selected carefully to represent the real material in the field. The specimen weight must be larger than the required weight for test. When t
This paper presents a study of a syndrome coding scheme for different binary linear error correcting codes that refer to the code families such as BCH, BKLC, Golay, and Hamming. The study is implemented on Wyner’s wiretap channel model when the main channel is error-free and the eavesdropper channel is a binary symmetric channel with crossover error probability (0 < Pe ≤ 0.5) to show the security performance of error correcting codes while used in the single-staged syndrome coding scheme in terms of equivocation rate. Generally, these codes are not designed for secure information transmission, and they have low equivocation rates when they are used in the syndrome coding scheme. Therefore, to improve the transmiss
... Show MoreThis study aims to identify the level of quality of Islamic banking services in the Kingdom of Saudi Arabia. It also investigates the importance of the various dimensions of the quality of banking services. The sample of the study included 69 clients of Al Rajhi Bank and Al-Bilad Bank. The study concluded that the overall level quality of services that Islamic banking offer is high. However, their relative importance varies from one dimension to another. The security, confidence and physical aspects are very high which this is a good point. On the other hand, the application aspects do not get the same importance. These aspects include the customer's wishes, helping them to improve the services offered to them,
... Show MoreThe need for detection and investigation of the causes of pollution of the marshes and submit a statistical study evaluated accurately and submitted to the competent authorities and to achieve this goal was used to analyze the factorial analysis and then obtained the results from this analysis from a sample selected from marsh water pollutants which they were: (Electrical Conductivity: EC, Power of Hydrogen: PH, Temperature: T, Turbidity: TU, Total Dissolved Solids: TDS, Dissolved Oxygen: DO). The size of sample (44) sites has been withdrawn and examined in the laboratories of the Iraqi Ministry of Environment. By illustrating SPSS program) the results had been obtained. The most important recommendation was to increase the pumping of addit
... Show MoreSolar energy is one of the immeasurable renewable energy in power generation for a green, clean and healthier environment. The silicon-layer solar panels absorb sun energy and converts it into electricity by off-grid inverter. Electricity is transferred either from this inverter or from transformer, consumed by consumption unit(s) available for residential or economic purposes. The artificial neural network is the foundation of artificial intelligence and solves many complex problems which are difficult by statistical methods or by humans. In view of this, the purpose of this work is to assess the performance of the Solar - Transformer - Consumption (STC) system. The system may be in complete breakdown situation due to failure of both so
... Show MoreAbstract: A home-made dc sputtering is characterized by cathode potential of 250-2500 V and sputtering gas pressures of (3.5×10-2 – 1.5) mbar. This paper studies in experiment the breakdown of argon, nitrogen, and oxygen in a uniform dc electric field at different discharge gaps and cathode potentials. Paschen curves for Argon, Nitrogen, and oxygen are obtained by measuring the breakdown voltage of gas within a stainless steel vacuum chamber with two planar, stainless steel electrodes. The Paschen curves in Ar, N2, and O2 gases show that the breakdown voltage between two electrodes is a function of pd (The product of the pressure inside the chamber and distance between the electrodes). Current-voltage characteristics visualization of the
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