Poincaré maps often prove to be invaluable tools in the study of long-term behaviour and qualitative properties of a given dynamical system. While the analytic theory of these maps is fully explored, finding numerical algorithms that allow the computation of Poincaré maps in concrete problems is far from trivial. For the verification it is desirable to approximate the Poincaré map over as large...

rayleigh-taylor (rt) instability has a growing importance in many fields including aircraft industry and astrophysics. the development and the growth of rt instability were investigated using sinusoidal disturbances with different wavelength at the interface of two fluids. numerical simulations were performed by solving navier-stokes unsteady equations with the vof formulation. results of the 2...

A common problem in nonlinear control is the need to consider systems of high complexity. Here we consider systems, which although may be low order, have high complexity due to a complex right hand side of a differential equation (e.g. a right hand side which has many terms – such systems arise from coordinate transformations in constructive nonlinear control designs). This contribution develop...

Model compensation approach has been successfully applied to various noise robust speech recognition tasks. In this paper, based on Continuous Time (CT) approximation, the dynamic mismatch function is derived without further approximation. With such mismatch function, a novel approach to deriving the formula for calculating the dynamic statistics is presented. Besides, we also provide an insigh...

This document provides proofs of the following: • The binomial distribution can be approximated with a Gaussian distribution at large values of N . • The arcsin square-root transform is the variance stabilising transform for the binomial distribution. • The Gaussian approximation for the binomial distribution is more accurate at smaller values of N after the variance stabilising transform has b...

Abstract. The convergence of a Fourier series on an interval can be interpreted naturally as the convergence of a Laurent series on the unit circle in the complex plane. In turn this Laurent series can be interpreted as the sum of an analytic and a co-analytic Taylor series.The Gibbs phenomenon in this context can be seen as an attempt to approximate a logarithmic branch cut with such series. C...

Fluid-approximation or mean-field techniques are currently very popular approaches to the efficient analysis of massivelyparallel Markov models. In this paper, we exploit the ODE-representation of these approximations to develop efficient techniques for simultaneous partially-symbolic numerical integration over parameter ranges. In particular, we borrow the Taylor model data structure of Makino...

In this paper we show that the first-order results of the recent many-body theory of inelastic electron scattering (Csanak, Taylor and Yaris) can be derived quite simply by a direct application of the distorted-wave and random phase approximations to the usual expression for the inelastic scattering amplitude. The result is derived both in the second quantized formalism and by the standard appl...