Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
According to the current situation of peroxidase (POD), the relevant studies on this enzyme indicated its importance as a tool in clinical biochemistry and different industrial fields. Most of these studies used the fruits and vegetables as source of this enzyme. So that in order to couple the growing requirements for POD with the recent demands for reduc-ing disposal volume by recycling the plant waste, the aim of the present study was to extract POD through management of municipal bio-waste of Iraqi maize species. A simple, green and economical method was used to extract this enzyme. Our results revealed that maize cobs are rich sources of POD, where the activity of this enzyme was found to be 7035.54 U/g of cobs. In pilot experiments thi
... Show More<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA<sup>®</sup> 9.0.</p>
The aim of this paper is to study the quaternary classical continuous optimal control for a quaternary linear parabolic boundary value problems(QLPBVPs). The existence and uniqueness theorem of the continuous quaternary state vector solution for the weak form of the QLPBVPs with given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method. In addition, the existence theorem of a quaternary classical continuous optimal control vector governinig by the QLPBVPs is stated and demonstrated. The Fréchet derivative for the cost function is derived. Finally, the necessary conditions for the optimality theorem of the proposed problem is stated and demonstrated.
In this paper, the blow-up solutions for a parabolic problem, defined in a bounded domain, are studied. Namely, we consider the upper blow-up rate estimate for heat equation with a nonlinear Neumann boundary condition defined on a ball in Rn.
This paper presents the design, construction and investigates an experimental study of a parabolic Trough Solar Collector (PTSC). It is constructed of multi – piece glass mirror to form the parabolic reflector (1.8 m ? 2.8 m) its form were checked with help of a laser and carbon steel rectangular as receiver. Sun tracker has been developed (using two – axis) to track solar PTSC according to the direction of beam propagation of solar radiation. Using synthetic oil as a heat transfer its capability to heat transfer and load high temperature (?400 oc). The storage tank is fabricated with stainless steel of size 50 L. The experimental tests have been carried out in Baghdad climatic conditions (33.3o N, 44.4o E) during selective days of the
... Show MoreThe Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.
A demonstration of the inverse kinematics is a very complex problem for redundant robot manipulator. This paper presents the solution of inverse kinematics for one of redundant robots manipulator (three link robot) by combing of two intelligent algorithms GA (Genetic Algorithm) and NN (Neural Network). The inputs are position and orientation of three link robot. These inputs are entering to Back Propagation Neural Network (BPNN). The weights of BPNN are optimized using continuous GA. The (Mean Square Error) MSE is also computed between the estimated and desired outputs of joint angles. In this paper, the fitness function in GA is proposed. The sinwave and circular for three link robot end effecter and desired trajectories are simulated b
... Show MoreDesalination is a process where fresh water produces from high salinity solutions, many ways used for this purpose and one of the most important processes is membrane distillation (MD). Direct contact membrane distillation (DCMD) can be considered as the most prominent type from MD types according to ease of design and modus operandi. This work studies the efficiency of using DCMD operation for desalination brine with different concentration (1.75, 3.5, 5 wt. % NaCl). Frame and plate cell was used with flat sheet PTFE hydrophobic type membrane. The study proves that MD is an effective process for desalination brines with feed temperature less than 60˚C especially for feed with low TDS. 37˚C, 47˚C, and 57˚C was feed t
... Show MoreAdvances in gamma imaging technology mean that is now technologically feasible to conduct stereoscopic gamma imaging in a hand-held unit. This paper derives an analytical model for stereoscopic pinhole imaging which can be used to predict performance for a wide range of camera configurations. Investigation of this concept through Monte Carlo and benchtop studies, for an example configuration, shows camera-source distance measurements with a mean deviation between calculated and actual distances of <5 mm for imaging distances of 50–250 mm. By combining this technique with stereoscopic optical imaging, we are then able to calculate the depth of a radioisotope source beneath a surfa
This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition. This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.