This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-vers
... Show Moret-Self-Compacting Concrete (SCC) reduces environmental noise and has more workability. This research presents an investigation of the behavior of SCC under mechanical loading (impact loading). Two types of cement have been used to produce SCC mixtures, Ordinary Portland Cement (OPC) and Portland Limestone Cement (PLC), which reduces the emission of carbon dioxide during the manufacturing process. The mixes were reinforced with Carbon Fiber Reinforced Polymer (CFRP) which is usually used to improve the seismic performance of masonry walls, to replace lost steel reinforcements, or to increase column strength and ductility. Workability tests were carried out for fresh SCC. Prepared concrete slabs of 500×500×50mm were tested for lo
... Show MoreFG Mohammed, HM Al-Dabbas, Science International, 2018 - Cited by 2
An overall mathematical model for copper pipe corrosion in flowing water was derived based on mass transfer fundamentals where we introduced the effects of boundary layer velocity, bulk flow velocity and the surface oxide protective film on the corrosion rate. A set of experiments were conducted in a straight 10mm diameter copper pipe, flow of water include six velocities of maximum value 7.33m/sec at 200C and 350C. The good agreement between the calculated and experimental corrosion rate values were achieved , the agreement reached 92% .
Candida is the scientific name for yeast. It is a fungus that lives almost everywhere, including in human body. Usually, the immune system keeps yeast under control. If the individual is sick or taking antibiotics, it can multiply and cause an infection. Yeast infections affect different parts of the body in different ways including thrush is a yeast infection that causes white patches in oral cavity ,Candida esophagitis is thrush that spreads to esophagus, women can get vaginal yeast infections,(vaginitis) causing itchiness, pain and discharge, yeast infections of the skin cause itching and rashes ,yeast infections in bloodstream can be life-threatening . The current review article will concentrate on vaginal infection (vaginitis), project
... Show MoreDigital image is widely used in computer applications. This paper introduces a proposed method of image zooming based upon inverse slantlet transform and image scaling. Slantlet transform (SLT) is based on the principle of designing different filters for different scales.
First we apply SLT on color image, the idea of transform color image into slant, where large coefficients are mainly the signal and smaller one represent the noise. By suitably modifying these coefficients , using scaling up image by box and Bartlett filters so that the image scales up to 2X2 and then inverse slantlet transform from modifying coefficients using to the reconstructed image .
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