This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine

      The service system has become a necessity of life in modern cities to be the most basic necessities of modern humans, they constitute a major base, which is based on the sustainability of life in the city and a standard measured through the degree of well-being and progress of civilized peoples and their interaction with the surrounding environment, making the services sector as a need not be an option, whenever the cities widened in population and space whenever provision of services and upgrading the quality and quantity more pressing, which made the subject of the services takes the biggest area of the trends and thinking of urban planners and those who in charge of drawing the cities policies. Consideri

Gas lift is one of the oldest methods used to produce hydrocarbon fluids from wells experiencing declining production. It works by aerating the mixture inside production tubing and forcing it to the surface. One of the reasons for declining production in oil wells is an increase in water cut or a drop in reservoir pressure, which requires one of the artificial lift methods to restore production. (A) oil field suffers from an increase in water cut, which has affected well productivity. The wells under study have a water cut of up to 66%, resulting in very low production rates. In this research, Pipesim software was used to build a physical and fluid model, then design an optimal gas lift system that achieves the highest possible prod

The logistic regression model is an important statistical model showing the relationship between the binary variable and the explanatory variables.                                                        The large number of explanations that are usually used to illustrate the response led to the emergence of the problem of linear multiplicity between the explanatory variables that make estimating the parameters of the model not accurate.    

Find cares studying the aesthetics of environmental art, one of the topics that is one of the problems of the aesthetic side in the arts of postmodernism, so this research came as an attempt to get to know the aesthetic concepts of environmental art that can be learned from functional testing in the formation of the post-modern control. The research involved four chapters: The first chapter discusses the general framework of the research methodology, as it was displayed in itThe research problem and its importance and define its objective to identify the aesthetics of environmental art at the level of the body, meaning, the receiver .ozlk in Iraq and America as the spatial limits of the time limits are period stretching from 1970 to 2006