In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr

In this paper the method of singular value decomposition  is used to estimate the ridge parameter of ridge regression estimator which is an alternative to ordinary least squares estimator when the general linear regression model suffer from near multicollinearity.

This research is concerned with the re-analysis of optical data (the imaginary part of the dielectric function as a function of photon energy E) of a-Si:H films prepared by Jackson et al. and Ferlauto et al. through using nonlinear regression fitting we estimated the optical energy gap and the deviation from the Tauc model by considering the parameter of energy photon-dependence of the momentum matrix element of the p as a free parameter by assuming that density of states distribution to be a square root function. It is observed for films prepared by Jackson et al. that the value of the parameter p for the photon energy range is is close to the value assumed by the Cody model and the optical gap energy is which is also close to the value

Protection study of the corrosion behavior of Copper surface was conducted with several concentrations of drug. Experimentally, voltammetric measurements were used to check the inhibition eciency (% IE) in saline solution of 3.5% NaCl. The results showed an increase in the inhibition eciency with increasing the concentration of the drug was 95.90%. Theoretical treatment of the drug in the gas phase was performed using the (hyperchem-8.07) program for molecular mechanics and semi-empirical computations. The (PM3) approach was used to determine the heat of formation (1H°f), binding energy (1Eb), and total energ

Protection study of the corrosion behavior of Copper surface was conducted with several concentrations of drug. Experimentally, voltammetric measurements were used to check the inhibition efficiency (% IE) in saline solution of 3.5% NaCl. The results showed an increase in the inhibition efficiency with increasing the concentration of the drug was 95.90%. Theoretical treatment of the drug in the gas phase was performed using the (hyperchem-8.07) program for molecular mechanics and semi-empirical computations. The (PM3) approach was used to determine the heat of formation (1H˚f), binding energy (1Eb), and total energy (ET

Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process when the objective function is
fraction .