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.
In this paper we shall prepare an sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).
In this paper, we present some numerical methods for solving systems of linear FredholmVolterra integral equations of the second kind. These methods namely are the Repeated Trapezoidal Method (RTM) and the Repeated Simpson's 1/3 Method (RSM). Also some numerical examples are presented to show the efficiency and the accuracy of the presented work.
Solid state blue laser source is a solid state laser include generation of IR laser light 1064 nm and companied with other wavelength 810 nm that invented from other active medium (Tm:ZBLAN) and non-linear crystal (CLBO) are used to generate fourth harmonic of the resultant wavelength 1874 nm that is blue laser light of 460nm. Several optical component have been designed by multilayer dielectric structure and anti reflection coating analysis. By using MATLAB soft ware, the simulation done and used the following non linear material (ZrO2, HfO2, MgO, SiO, Ta2O5 CaF2) and other linear material (ZnO, MgF2, GaAs, AlAs, BaF2, LiF, TiO2) as coating material. The result showed that as more quarter wave layers are added to the structure, the refl
... Show Moreان الغرض من هذا البحث هو المزج بين القيود الضبابية والاحتمالية. كما يهدف الى مناقشة اكثر حالات مشكلات البرمجة الضبابية شيوعا وهي عندما تكون المشكلة الضبابية تتبع دالة الانتماء مرة دالة الاتنماء المثلثية مرة اخرى، من خلال التطبيق العملي والتجريبي. فضلا عن توظيف البرمجة الخطية الضبابية في معالجة مشكلات تخطيط وجدولة الإنتاج لشركة العراق لصناعة الأثاث، وكذلك تم استخدام الطرائق الكمية للتنبؤ بالطلب واعتماده
... Show MoreObjectives. The current study aimed to predict the combined mesiodistal crown widths of maxillary and mandibular canines and premolars from the combined mesiodistal crown widths of maxillary and mandibular incisors and first molars. Materials and Methods. This retrospective study utilized 120 dental models from Iraqi Arab young adult subjects with normal dental relationships. The mesiodistal crown widths of all teeth (except the second molars) were measured at the level of contact points using digital electronic calipers. The relation between the sum mesiodistal crown widths of the maxillary and mandibular incisors and first molars and the combined mesiodistal crown widths of the maxillary and mandibular canines and premolars was as
... Show MoreIn this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the informative and non- informative prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.
Foreign direct investment (FDI) has been viewed as a power affecting economic growth (EG) directly and indirectly during the past few decades. This paper reviewed an amount of researches examining the relationships between FDI and EG, especially the effects of FDI on EG, from 1994 up to 2012. The results show that the main finding of the FDI-EG relation is significantly positive, but in some cases it is negative or even null. And within the relation, there exist several influencing factors such as the adequate levels of human capital, the well-developed financial markets, the complementarity between domestic and foreign investment and the open trade regimes, etc.
Direct field-orientation Control (DFOC) of induction motor drives without mechanical speed sensors at the motor shaft has the attractions of low cost and high reliability. To replace the sensor, information on the rotor speed and position are extracted from measured stator currents and from voltages at motor terminals. In this paper presents direct field-orientation control (DFOC) with two type of kalman filter (complete order and reduced order extended kalman filter) to estimate flux, speed, torque and position. Simulated results show how good performance for reduced order extended kalman filter over that of complete order extended kalman filter in tracking performance and reduced time of state estimation.