We investigate the interaction of proton with a solid target, describing the wake effects by taking fitted parameters with experimental values of energy loss function ELF for copper using the dielectric function of random phase approximation (RPA). The results exhibited a damped oscillatory behavior in the longitudinal direction behind the projectile. In addition, the wake potential becomes asymmetric around the z-axis with proton velocity values higher than Fermi velocity, as well as it depends on the position of projectile in cylindrical coordinates.

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the

An analytical expression for the charge density distributions is derived based on the use of occupation numbers of the states and the single particle wave functions of the harmonic oscillator potential with size parameters chosen to reproduce the observed root mean square charge radii for all considered nuclei. The derived expression, which is applicable throughout the whole region of shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- of shell nuclei, such as and nuclei. It is found that introducing an additional parameters, namely and which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkabl

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

In wireless broadband communications using single-carrier interleave division multiple access (SC-IDMA) systems, efficient multiuser detection (MUD) classes that make use of joint hybrid decision feedback equalization (HDFE)/ frequency decision-feedback equalization (FDFE) and interference cancellation (IC) techniques, are proposed in conjunction with channel coding to deal with several users accessing the multipath fading channels. In FDFE-IDMA, the feedforward (FF) and feedback (FB) filtering operations of FDFE, which use to remove intersymbol interference (ISI), are implemented by Fast Fourier Transforms (FFTs), while in HDFE-IDMA the only FF filter is implemented by FFTs. Further, the parameters involved in the FDFE/

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.