The Gain flatness of EDFA (Eridium Dopedd Fiber Amplifier) plays a important role for WDM optical application. The purpose of this paper is to improve the gain uneveness for each channel in order to equalize the amplitude in a Wavelength Division Multiplexing (WDM) system .By using low pass Chebshev filter, tunning numerical aperature, fiber length and pump power we can improve the gain faltnes...

Big Bang models of the Universe predict rapid domination by curvature, a paradox known as the flatness problem. Solutions to this problem usually leave the Universe exactly flat for every practical purpose. Explaining a nearly but not exactly flat current Universe is a new problem, which we label the quasi-flatness problem. We show how theories incorporating time-varying coupling constants coul...

We report on numerical results for certain families of S-unimodal maps with flat critical point. For four one-parameter families, differing in their amount of flatness, we study the Feigenbaum-limits α and δ. There seems to be a finite δ and a finite α associated with each period doubling cascade in each family. Some rough numerical estimates are obtained. One would expect that these numbers sh...

We study the convergence of the proximal algorithm applied to nonsmooth functions that satisfy the Lojasiewicz inequality around their generalized critical points. Typical examples of functions complying with these conditions are continuous semialgebraic or subanalytic functions. Following Lojasiewicz’s original idea, we prove that any bounded sequence generated by the proximal algorithm conver...

An implicit finite difference scheme is derived which achieves exact results for the area, centroid, variance, skewness and kurtosis (flatness) of solutions to the unforced advection-diffusion equation ∂ t c + λ c + u ∂ x c − κ ∂ 2 x c = 0. Sufficient conditions for computational stability are that the grid spacing ∆x and time step ∆t be small enough that |u| ∆x κ < 12 1/2 , |u| ∆t ∆x < 1 2 1/2...

This paper proposes several nonlinear control strategies for trajectory trackingof a quadcopter system based on the property of differential flatness. Its origi-nality is twofold. Firstly, it provides a flat output for the quadcopter dynamicscapable of creating full flat parametrization of the states and inputs. Moreover,B-splines characterizations of the flat output and the...

Lagrangian control systems that are differentially flat with flat outputs that depend only on configuration variables are said to be configuration flat. We provide a complete characterization of configuration flatness for systems with n degrees of freedom and n−1 controls whose range of control forces only depends on configuration and whose Lagrangian has the form of kinetic energy minus potent...

Abstract: This research is aimed at improving accuracy of stereolithography (Rapid prototyping) system. The objective of this paper is to detect the flatness of freeform liquid surface. The principle of measurement is performed by obtaining grating image of total reflection from freeform liquid surface. The detection is performed by two steps, coarse detection and fine one. Coarse detection is ...

We show that the L/E-flatness of the electron-like event ratio in the Super-Kamiokande atmospheric neutrino data implies the equality of the expectation values for the muon and tau neutrino masses. We establish this result by obtaining a set of three constraints on the neutrino-oscillation mixing matrix as contained in the indicated flatness. The resulting 3× 3 neutrino-oscillation matrix depen...

In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts AS over a monoid S that can be described by means of when the functor AS ⊗ − preserves pullbacks. In this paper, we extend these results to S-posets and present equivalent descriptions of weakly kernel po-flat, principally...