A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

The developments and transformations taking place in the era and the growth of knowledge economies and communication technology led this development to compel higher education institutions in Iraq to reconsider their objectives to keep pace with development. And one of the most important tools of development was the application of e-learning standards and its long-term impact on the performance of the educational institution. Performance auditing plays an important role in verifying the extent to which these institutions have implemented their activities and programs that auditing performance by adopting e-learning standards helps the institutions’ management by providing appropriate information on the extent to which they achieve thei

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

Hand-lay up method was used to prepare the samples made of epoxy (EP) as a matrix reinforced with chopped carbon fibers (CCF). The fatigue behavior of epoxy resin /chopped carbon fiber composites was studied with different weight percentage of chopped carbon fibers (2.5%,5%,7.5%,10%,12.5%). The fatigue test was carried out under alternate bending method, which was made by applying sinusoidal wave with constant displacement (15mm), stress ratio R=-1,and loading frequency 10Hz, which is believed to give a negligible temperature rise during the test. The results of the maximum stress, fatigue strength, fatigue limit and fatigue life of the tested composites are calculated from stress(S)-number of cycles(N) (S-N) curves.
It was shown that

Overlapped have been prepared from epoxy resin material added to carbon Nanotube and percentages weight (0.1, 0.05, 0.01) % Studied the mechanical properties of the composite (bending, tensile an d hardness) has been found that the Flexural and tensile modulus of the composites were higher than the pure epoxy resin this may be due to the high mechanical strength of carbon nano tube (CNT). The hardness of the epoxy carbon Nanotube composites increased and the reason is due to increased overlap and stacking between the additives and material basis, which reduces the movement of polymer molecules leading to increased resistance to scratching material and cutting, will become more resistance to plastic deformation.