In the present paper, the problem of multi-pumping all Raman amplifier has been investigated to obtain a maximum flatness gain and increases the bandwidth of the cascaded Raman amplifiers over a wide range of optical signal wavelengths for long-haul ultra-wide wavelength division multiplexing (UW-WDM) transmission systems due to multi-pumping wavelengths and pumping power . Three cases are anal...

The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness ~kurtosis! is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation ...

We show that ( n + 1)-dimensional Myers–Perry metrics, ≥ 4, have a conformal completion at space-like infinity of C n−3,1 differentiability class and the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.

In this work we consider the concept of differential flatness defined by Fliess, Levine, Martin and Rouchon. The structural property of k-flatness (the case in which flat outputs depends up to the kth derivative of the inputs) is studied based on the properties of the dynamic extension algorithm and the Cartan-Kähler theorems on the existence of integral manifolds of exterior differential syste...

The objective of this paper is to study the impact of scheduling flexibility on both demand profile flatness and user inconvenience in residential smart grid systems. Temporal variations in energy consumption by end users result in peaks and troughs in the aggregated demand profile. In a residential smart grid, some of these peaks and troughs can be eliminated through appropriate load balancing...

in this paper, the effects of reflected waves of the facets on the internal optical intensity of semiconductor dfb lasers are investigated. the uniformity of optical intensity along the cavity length is evaluated with flatness parameter. the dependence of this parameter on coupling coefficient, reflectivity and grating phase at the facets is also studied. this investigation shows that in some s...