In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.
Chapter One – introduction
Nations managed today to achieve progress in the field of modern technology. Science has changed many beliefs and trendiness that people have held for long time, skills and scientific thinking developed, and made scientific observation and experiment replace narration and taking from others. That is attributed to examining the educational systems searching for the locations of defect, and shortage.
In the light of educational modernizations, many models of teaching incliuding a model for social tracing attributed to Herbart Thelen, which is a model to develop skills of social participation in the democratic process (Al-Khawalda,1993,335).
... Show MoreRecent research have aimed to know the effect of rational inquiry strategy on acquisition basic science processes for second intermediate students in physics. To verify the aim of this research , the researchers added the following zero hypotheses : No statistically significant differences at the level of significance (0.05) between the students mean scores of the two groups on basic science Processes test. The research was carried out on the second intermediate grade male students in Alam Al Yakeen school in Baghdad; belong to Education Directorate Al- Karkh/2, for the Academic Year (2014-2015) A.D. Prepared research requirements included ] selected the scientific subject chapters (6,7,8,9) from physics textbook, the formulation of beha
... Show MoreThe subject of the Internet of Things is very important, especially at present, which is why it has attracted the attention of researchers and scientists due to its importance in human life. Through it, a person can do several things easily, accurately, and in an organized manner. The research addressed important topics, the most important of which are the concept of the Internet of Things, the history of its emergence and development, the reasons for its interest and importance, and its most prominent advantages and characteristics. The research sheds light on the structure of the Internet of Things, its structural components, and its most important components. The research dealt with the most important search engines in the Intern
... Show MoreThe research aims to shed light on the nature of the tax gap in the income tax by the method of direct deduction and its reflection on the financial objective of the tax, and to determine the reasons for this gap in the deduction between the tax due in accordance with the laws and instructions in force and the tax actually paid. The tax gap is a real problem that cannot be ignored for what it represents loss of financial revenues due to the state.
The research problem is represented in the existence of a gap between the tax due according to direct deduction instructions and the tax actually paid according to the financial statements, and to achieve the objectives of the research and test the hypotheses, t
... Show MoreThe aim of the current research is to know the degree to which middle school teachers and female teachers in the southern border schools use electronic educational alternatives in the field of education from their point of view and its relationship to some variables, and to achieve this goal, a random sample of (200) teachers was selected in southern border schools, and a questionnaire was prepared to collect The data, as well as the descriptive approach was used to achieve this goal. T-test and analysis of variance were used for the statistical treatment. The results concluded that the educational courses provided to male and female teachers are not sufficient. It has also been concluded that the use of electronic educational alternativ
... Show MoreThe research aims to identify the concept of green taxes and their role in reducing environmental pollution through the poll of Abnh of taxpayers and employees of the General Authority for taxes totaling 200 individual .autam adoption of the resolution as a tool head for the collection of data and information from the sample and analyzed their responses using a statistical program (spss - 10), and calculating the percentages and the arithmetic mean, standard deviation and research found to a number of conclusions, notably the lack of legislation with the challenges and the difficulty of the existence of a measure or a standard lack of planning for the application of environmental taxes that the state taxation application between the Gene
... Show MoreIn this research, CNRs have been synthesized using pyrolysis of plastic waste(pp) at 1000 ° C for one hour in a closed reactor made from stainless steel, using magnesium oxide (MgO) as a catalyst. The resultant carbon nano rods were purified and characterized using energy dispersive X-ray spectroscopy (EDX), X-ray powder diffraction (XRD). The surface characteristics of carbon rods were observed with the Field emission scanning electron microscopy (FESEM). The carbon was evenly spread and had the highest concentration from SEM-EDX characterization. The results of XRD and FESEM have shown that carbon Nano rods (CNRs) were present in Nano figures, synthesized at 1000 ° C and with pyrolysis temperature 400° C. One of t
... Show MoreThe research aims to diagnose the causes of the phenomenon of Marketing deception catalog, which is now deployed in the Iraqi market and related to producers and marketers, consumers, regulators and other institutions) and their impact in the areas of prejudice to the consumer protection (product and signifying specifications, price, advertising, packaging), as well as identify differences in the sample responses according to personal variables, it has been the adoption of the resolution as a tool to collect data and information through a sample survey of consumer opinions totaling 108 people in shopping centers in the province of Baghdad and in the Karkh and Rusafa, It was the use of methods selected statistical represented by the arith
... Show MoreIn this paper we proposed a new method for selecting a smoothing parameter in kernel estimator to estimate a nonparametric regression function in the presence of missing values. The proposed method is based on work on the golden ratio and Surah AL-E-Imran in the Qur'an. Simulation experiments were conducted to study a small sample behavior. The results proved the superiority the proposed on the competition method for selecting smoothing parameter.
Terrestrial laser scanners (TLSs) are 3D imaging systems that provide the most powerful 3D representation and practical solutions for various applications. Hence this is due to effective range measurements, 3D point cloud reliability, and rapid acquisition performance. Stonex X300 TOF scanner delivered better certainty in far-range than in close-range measurements due to the high noise level inherent within the data delivered from Time of Flight (TOF) scanning sensors. However, if these errors are manipulated properly using a valid calibration model, more accurate products can be obtained even from very close-range measurements. Therefore, to fill this gap, this research presents a user-oriented target-based calibration routi
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