The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
A comparison of double informative and non- informative priors assumed for the parameter of Rayleigh distribution is considered. Three different sets of double priors are included, for a single unknown parameter of Rayleigh distribution. We have assumed three double priors: the square root inverted gamma (SRIG) - the natural conjugate family of priors distribution, the square root inverted gamma – the non-informative distribution, and the natural conjugate family of priors - the non-informative distribution as double priors .The data is generating form three cases from Rayleigh distribution for different samples sizes (small, medium, and large). And Bayes estimators for the parameter is derived under a squared erro
... Show MoreLost circulation or losses in drilling fluid is one of the most important problems in the oil and gas industry, and it appeared at the beginning of this industry, which caused many problems during the drilling process, which may lead to closing the well and stopping the drilling process. The drilling muds are relatively expensive, especially the muds that contain oil-based mud or that contain special additives, so it is not economically beneficial to waste and lose these muds. The treatment of drilling fluid losses is also somewhat expensive as a result of the wasted time that it caused, as well as the high cost of materials used in the treatment such as heavy materials, cement, and others. The best way to deal with drilling fluid losses
... Show MoreLowering the emission, fuel economy and torque management are the essential
requirements in the recent development in the automobile industry. The main engine control
input that satisfies the above requirements is the throttling angle which adjusts the air mass
flow rate to the engine port. Due to the uncertainty and the presence of the nonlinear
components in its dynamical model, the sliding mode control theory is utilized in this work
for the throttle valve angle control system to design a robust controller for this system in the
presence of a nonlinear spring and Coulomb friction. A continuous sliding mode control law
which consists of a saturation function, instead of a signum function, and the integral of
ano
Computations of the relative permeability curves were made through their representation by two functions for wetting and nonwetting phases. Each function contains one parameter that controls the shape of the relative permeability curves. The values of these parameters are chosen to minimize an objective function, that is represented as a weighted sum of the squared differences between experimentally measured data and the corresponding data calculated by a mathematical model simulating the experiment. These data comprise the pressure drop across core samples and the recovery response of the displacing phase. Two mathematical models are constructed in this study to simulate incompressible, one-dimensional, two-phase flow. The first model d
... Show MoreA Modified version of the Generlized standard addition method ( GSAM) was developed. This modified version was used for the quantitative determination of arginine (Arg) and glycine ( Gly) in arginine acetyl salicylate – glycine complex . According to this method two linear equations were solved to obtain the amounts of (Arg) and (Gly). The first equation was obtained by spectrophotometic measurement of the total absorbance of (Arg) and (Gly) colored complex with ninhydrin . The second equation was obtained by measuring the total acid consumed by total amino groups of (Arg) and ( Gly). The titration was carried out in non- aqueous media using perchloric acid in glacial acetic acid as a titrant. The developed metho
... Show MoreThis research prepared polymer blend contains from epoxy resin (Ep) and polyurethane
)Pu) as a matrix material of percentage (90 %) from epoxy and ) 10 (% polyurethane and
reinforced by PVC fibers and aluminum fibers two dimension knitted mat with fractional
volume(15 %), and study impact strength before and after reinforcing at temperatures of
(20,40,60(
o
CØŒand the results have shown that the reinforcing matrix materials by fibers
increased impact strength values that rise from(3.387kJ/m2) to (151.62kJ/m2) of composite
material (Ep+Pu+PVC(and thus ) Ep+Pu+PVC+Al.F) at last (Ep+Pu+Al.F (. following
composite material so that temperatures increase led to rise impact strength values except the
polymer
This researchs the preparation of particulate polymer composites from Alkyd resin and Iraqi Burn Kaolin which were added as (20%,30%,40%,50%)and comparing with the polymer. It studied Thermal conductivity and Dielectric strength for both of the Alkyd resin and the Composite Material. The result showed an increase in Dielectric strength after adding the Iraqi Burn Kaolin , also the Thermal conductivity was increased by adding the Iraqi Burn Kaolin .