The wake potential and wake phenomena for swift proton in an amorphous carbon target were studied by utilising various dielectric function formalisms, including the Drude dielectric function, the Drude–Lorentz dielectric function and quantum dielectric function. The Drude model results exhibited a damped oscillatory behaviour in the longitudinal direction behind the projectile; the pattern of these oscillations decreases exponentially in the transverse direction. In addition, the wake potential extends slightly ahead of the projectile which also depends on the proton coordinate and velocity. The effect of electron binding on the wake potential, characterised by the ratio to 0.1, has been studied alongside the Drude–Lorentz dielectric

Abstract

               Documentary credits are considered successful means to reduce imports, especially unnecessary imports that lead to the outflow of foreign currency from the country. However, due to the backwardness of the banking methods, the reintroduction of documentary credits after 2003 did not effectively contribute to reducing import rates. This has had a negative impact on the Iraqi economy and made it vulnerable to external markets. Documentary credits are also considered the best way to ensure payment in international trade, providing independent credit support and sufficient security for exporters and importers against commerci

An Expression for the transition charge density is investigated
where the deformation in nuclear collective modes is taken into
consideration besides the shell model transition density. The
inelastic longitudinal C2 and C4 form factors are calculated using
this transition charge density for the Ne Mg 20 24 , , Si 28 and S 32
nuclei. In this work, the core polarization transition density is
evaluated by adopting the shape of Tassie model togther with the
derived form of the ground state two-body charge density
distributions (2BCDD's). It is noticed that the core polarization
effects which represent the collective modes are essential in
obtaining a remarkable agreement between the calculated inelastic
longi

Inelastic longitudinal electron scattering form factors have been calculated for isoscaler transition
T = 0 of the (0+ ®2+ ) and (0+ ®4+ ) transitions for the 20Ne ,24Mg and 28Si nuclei. Model
space wave function defined by the orbits 1d5 2 ,2s1 2 and 1d3 2 can not give reasonable result for
the form factor. The core-polarization effects are evaluated by adopting the shape of the Tassie-
Model, together with the calculated ground Charge Density Distribution CDD for the low mass 2s-1d
shell nuclei using the occupation number of the states where the sub-shell 2s is included with an
occupation number of protons (a ) .

In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.