The problem of reconstruction of a timewise dependent coefficient and free boundary at once in a nonlocal diffusion equation under Stefan and heat Flux as nonlocal overdetermination conditions have been considered. A Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature is used for the direct problem. While the inverse problem is reformulated as a nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from the optimization toolbox. Since the problem under investigation is generally ill-posed, a small error in the input data leads to a huge error in the output, then Tikhonov’s regularization technique is app

This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

   Fracture pressure gradient prediction is complementary in well design and it is must be considered in selecting the safe mud weight, cement design, and determine the optimal casing seat to minimize the common drilling problems. The exact fracture pressure gradient value obtained from tests on the well while drilling such as leak-off test, formation integrity test, cement squeeze ... etc.; however, to minimize the total cost of drilling, there are several methods could be used to calculate fracture pressure gradient classified into two groups: the first one depend on Poisson’s ratio of the rocks and the second is fully empirical methods. In this research, the methods selected are Huubert and willis, Cesaroni I, Cesaroni II,

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

In petroleum industry, the early knowledge of “pore pressure gradient” is the basis in well design and the extraction of these information is more direct when the pore pressure gradient is equal to normal gradient; however, this matter will be more complex if it deviate from that limit which is called “abnormal pore pressure”, if this variable does not put in consideration, then many drilling problems will occur might lead to entire hole loss. To estimate the pore pressure gradient there are several methods, in this study; Eaton method’s is selected to extract the underground pressure program using drilling data (normalized rate of penetration) and logs data (sonic and density log). The results shows that an abnormal high press

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In this paper, the computational complexity will be reduced using a revised version of the selected mapping (SLM) algorithm. Where a partial SLM is achieved to reduce the mathematical operations around 50%. Although the peak to average power ratio (PAPR) reduction gain has been slightly degraded, the dramatic reduction in the computational complexity is an outshining achievement. Matlab simulation is used to evaluate the results, where the PAPR result shows the capability of the proposed method.  

Localization is an essential demand in wireless sensor networks (WSNs). It relies on several types of measurements. This paper focuses on positioning in 3-D space using time-of-arrival- (TOA-) based distance measurements between the target node and a number of anchor nodes. Central localization is assumed and either RF, acoustic or UWB signals are used for distance measurements. This problem is treated by using iterative gradient descent (GD), and an iterative GD-based algorithm for localization of moving sensors in a WSN has been proposed. To localize a node in 3-D space, at least four anchors are needed. In this work, however, five anchors are used to get better accuracy. In GD localization of a moving sensor, the algo