In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

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Many water supplies are now contaminated by anthropogenic sources such as domestic and agricultural waste, as well as manufacturing activities, the public's concern about the environmental effects of wastewater contamination has grown. Several traditional wastewater treatment methods, such as chemical coagulation, adsorption, and activated sludge, have been used to eliminate pollution; however, there are several drawbacks, most notably high operating costs, because of its low operating and repair costs, the usage of aerobic waste water treatment as a reductive medium is gaining popularity. Furthermore, it is simple to produce and has a high efficacy and potential to degrade pollu

This article studies a comprehensive methods of edge detection and algorithms in digital images which is reflected a basic process in the field of image processing and analysis. The purpose of edge detection technique is discovering the borders that distinct diverse areas of an image, which donates to refining the understanding of the image contents and extracting structural information. The article starts by clarifying the idea of an edge and its importance in image analysis and studying the most noticeable edge detection methods utilized in this field, (e.g. Sobel, Prewitt, and Canny filters), besides other schemes based on distinguishing unexpected modifications in light intensity and color gradation. The research as well discuss

Optimization of gas lift plays a substantial role in production and maximizing the net present value of the investment of oil field projects. However, the application of the optimization techniques in gas lift project is so complex because many decision variables, objective functions and constraints are involved in the gas lift optimization problem. In addition, many computational ways; traditional and modern, have been employed to optimize gas lift processes. This research aims to present the developing of the optimization techniques applied in the gas lift. Accordingly, the research classifies the applied optimization techniques, and it presents the limitations and the range of applications of each one to get an acceptable level of accura

Objectives: Although the Frankfort Horizontal (FH) and sella-nasion were routinely used as craniofacial reference planes, the inter-individual orientations were changeable when related to true horizontal (HOR). Natural head position (NHP) is a reproducible, standardized position, with the head in an upright posture and eyes focused on a point in the distance at eye level so that the visual axis is horizontal. The natural head position has importance in anthropological as well as in orthodontic fields, as this position has a relatively fixed relationship to the true horizontal and vertical planes. However, NHP is clinically not simple and it takes long time to be recorded, in addition to a deficiency in the tools utilized in the NHP and l

During the course of fixed orthodontic therapy, patients should be instructed to eat specific food stuffs and beverages in order to maintain good health for the dentition and supporting structures and prevent frequent attachment debonding that prolong the treatment duration. After searching and collecting articles from 1930 till July 2021, the current review was prepared to emphasize various types of foods that should be taken during the course of fixed orthodontic therapy and to explain the effect of various food stuffs and beverages on the growth and development of craniofacial structures, tooth surfaces, root resorption, tooth movement, retention and stability after orthodontic treatment and the effect on the components of fixed ortho

Optimization of well placement plays a considerable role in the production and maximizing the net present value of the investment of oil field developments. However, the application of the optimization techniques in well placement developments is so complicated because many decision variables, objective functions, and constraints are involved in the well placement optimization case. Furthermore, many computational techniques; conventional and non-conventional, have been utilized to optimize well placement operations. This study displays the advancement of the optimization methods applied in the well placement. Subsequently, the study assorted the applied optimization methods, and it demonstrates the restriction and the range of implementati

Image Fusion Using A Convolutional Neural Network

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.