Fitting two concentric spheres to data by orthogonal distance regression

The problem of this research tackles the process of fitting two concentric spheres to data, which arises in computational metrology. There are also many fitting criteria that could be used effectively, and the most widely used one in metrology, for example, is that of the sum of squared minimal distance. However, a simple and robust algorithm assigned for using the orthogonal distance regression will be proposed in this paper. A common approach to this problem involves an iteration process which forces orthogonality to hold at every iteration and steps of Gauss-Newton type

Higher-Order Iterative Methods for Solving Nonlinear Equations

Abstract: In this report, we presented three high-order iterative methods for solving nonlinear equations of the form 0 = ) (x f . These proposed iterative methods are obtained by combining a fourth-order iterative method with the classical Newton's method and approximating the first derivative in the third step by three different approaches of combinations of previously evaluated function values. The convergence analyses of the new methods are discussed, and several examples are given to illustrate the methods' efficiency

Flood Risk Assessment for Urban Drainage System in a Changing Climate Using Artificial Neural Network

Changes in rainfall patterns due to climate change are expected to have negative impact on urban drainage systems, causing increase in flow volumes entering the system. In this paper, two emission scenarios for greenhouse concentration have been used, the high (A1FI) and the low (B1). Each scenario was selected for purpose of assessing the impacts on the drainage system. An artificial neural network downscaling technique was used to obtain local-scale future rainfall from three coarse-scale GCMs. An impact assessment was then carried out using the projected local rainfall and a risk assessment methodology to understand and quantify the potential hazard from surface flooding. The case study is a selected urban drainage catchment in northwestern England. The results show that there will be potential increase in the spilling volume from manholes and surcharge in sewers, which would cause a significant number of properties to be affected by flooding

International commercial arbitration in Islamic law, Saudi law and the model law

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Department of Mathematics,

An important problem is that of finding a quadric surface which gives a “best ” fit to m given data points. There are many application areas, for example metrology, computer graphics, pattern recognition, and in particular quadric surfaces are often to be found in manufactured parts. There are many criteria which can be used for fitting, but one of the simplest is so-called algebraic fitting, which exploits the fact that an expression for the curve can be given which is affine in the free parameters. Here we examine a general class of such algebraic fitting problems, consider how the members of the class can be interpreted in terms of the errors in the data, and present simple algorithms which apply to all of the problems.

A Ninth-Order Iterative Method Free from Second Derivative for Solving Nonlinear Equations

Abstract In this paper, we study and analyze an iterative method for solving nonlinear equations with ninth order of convergence. The new proposed method is obtained by composing an iterative method obtained in Noor et al. Mathematics Subject Classification: 41A25, 65H05, 65K0