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 ACTUAL SOCIETY MODEL
Our society model has been showing signs of exhaustion since the end of the XX century. The recent appearance of the Covid-19 virus is another consequence of humanity's distance from Nature and the environment it inhabits. Also, climate change, environmental deterioration, loss of biodiversity, overexploitation of natural resources, and social inequality are some of the consequences derived from this separation between society and Nature. We must change our operating habits. Inevitably from a society based on the market, hyper consumption, fossil energy and individual enrichment at all costs, we will have to change to another
... Show MoreDecision-making in Operations Research is the main point in various studies in our real-life applications. However, these different studies focus on this topic. One drawback some of their studies are restricted and have not addressed the nature of values in terms of imprecise data (ID). This paper thus deals with two contributions. First, decreasing the total costs by classifying subsets of costs. Second, improving the optimality solution by the Hungarian assignment approach. This newly proposed method is called fuzzy sub-Triangular form (FS-TF) under ID. The results obtained are exquisite as compared with previous methods including, robust ranking technique, arithmetic operations, magnitude ranking method and centroid ranking method. This
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Seeking happiness and searching for it have been among the priorities of mankind from the beginning of his creation and will remain so until the end of this world, and even in the next life, he seeks happiness, but the difference is that a person can work in this world to obtain it, but in the next life he is expected to get what he done in this world. And among these reasons are practical actions that a person undertakes while he intends to draw close to God Almighty, so they lead him to attain his desired perfection, and to attain his goals and objectives, which is the minimum happiness in this life, and ultimate happiness after the soul separates the body, and on the day of the judgment, Amon
... Show MoreThe aim of the current research is to find out the extent to which algebraic thinking skills are included in the mathematics textbook for the third intermediate grade for the academic year (2020-2021) by answering the main research question:What algebraic thinking skills are included in the mathematics textbook for middle third grade?The descriptive and analytical approach was used, and to achieve the goal of the research, a list of the main algebraic thinking skills and the sub-skills were prepared, and after analyzing the content of the mathematics textbook, the stability of the analysis was verified through the analysis over time and across individuals using the Holsti equation, and
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Abstract
Natural gas is characterized by features that made from it a fuel and a raw material for many industries. Deepening its position as a favorite fossil supplier between other types of fossil fuel is the efficiency, diversity of its uses, low costs and compatibility with the environment which leads to increasing of its uses then increased global demand. So, the natural gas must take its place as an important resource in Iraq and participate the oil in the economic development process of building and financing of the general budget.
Iraq is planning to continue of increasing the export capacity of raw oil to meet ambitious production targets emanating from the mai
... Show MoreThe study showed flow rates and the interaction between the settlements served by applying the model of gravity theory to measure depending on the number of the population between city Najaf and the rest of the other settlements served and using three functions of disability, time and cost, as recorded an increase in the interaction index with some settlements like them Kufa, Abbasid and Manathira, while the indicator contrast was in other settlements, either when the application of the gravity model depending on trips and socio-economic characteristics accuracy rate was more pronounced.
Earth cover of the city of Baghdad was studied exclusively within its administrative border during the period 1986-2019 using satellite scenes every five years, as Landsat TM5 and OLI8 satellite images were used. The land has been classified into ten subclasses according to the characteristics of the land cover and was classified using the Maximum Likelihood classifier. A study of the changing urban reality of the city of Baghdad during that period and the change of vegetation due to environmental factors, human influences and some human phenomena that affected the accuracy of the classification for some areas east of the city of Baghdad is presented. The year 2019 has been highlighted because of its privacy in changing the land cover of th
... Show MoreSoil is the cardinal resource for agricultural crops. Healthy soil will produce healthy plants. Since healthy soil is the important goal for the farmers, they need to select the best tillage system to achieve that goal. There are two main types of tillage systems. Conservation tillage (no-tillage farming) uses agricultural machinery that performs a double function; tillage and seed farming simultaneously. In contrast, conventional tillage farming uses multiple agricultural machines to till and seed the soil. The farmers in the northern governorates of Iraq have used the conservation farming system for a long time. However, the farmers who live in the middle and southern governorates in Iraq use conventional tillage farming. Because most of
... Show MoreThe process of selection assure the objective of receiving for chosen ones to high levels more than other ways , and the problem of this research came by these inquires (what is the variables of limits we must considered when first preliminaries selections for mini basket ? and what is the proper test that suits this category ? and is there any standards references it can be depend on it ?) also the aims of this research that knowing the limits variables to basketball mini and their tests as a indicators for preliminaries for mini basketball category in ages (9-12) years and specifies standards (modified standards degrees in following method) to tests results to some limits variables for research sample. Also the researchers depends on (16)
... Show MoreThis investigation was conducted to recognize the structure for (RHETI version 2.5 1999) by using exploratory and confirmatory factor analysis. Sample of (620) student of Al-Mustansrya University were administered the (RHETI).
The data of their responses was analyzed by using (PAF) and oblique rotating .
The findings explored (9) factors as one factor for each type and (184) items were loaded by the factors: (60) item for feeling center, (61) items for instinctive center and (63) items for thinking center.
Results of confirmatory factorial analysis supported a model designed by the researcher depended upon a theoretical views of Riso and Hudson
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