The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

System oriented neural networks - Problem formulation, methodology and application

A novel methodology is proposed for the development of neural network models for complex engineering systems exhibiting nonlinearity. This method performs neural network modeling by first establishing some fundamental nonlinear functions from a priori engineering knowledge, which are then constructed and coded into appropriate chromosome representations. Given a suitable fitness function, using evolutionary approaches such as genetic algorithms, a population of chromosomes evolves for a certain number of generations to finally produce a neural network model best fitting the system data. The objective is to improve the transparency of the neural networks, i.e. to produce physically meaningful

Analysis procedure for calculation of electron energy distribution functions from incoherent Thomson scattering spectra

Incoherent Thomson scattering (ITS) provides a nonintrusive diagnostic for the determination of one-dimensional (1D) electron velocity distribution in plasmas. When the ITS spectrum is Gaussian its interpretation as a three-dimensional (3D) Maxwellian velocity distribution is straightforward. For more complex ITS line shapes derivation of the corresponding 3D velocity distribution and electron energy probability distribution function is more difficult. This article reviews current techniques and proposes an approach to making the transformation between a 1D velocity distribution and the corresponding 3D energy distribution. Previous approaches have either transformed the ITS spectra directly from a 1D distribution to a 3D or fitted two Gaussians assuming a Maxwellian or bi-Maxwellian distribution. Here, the measured ITS spectrum transformed into a 1D velocity distribution and the probability of finding a particle with speed within 0 and given value v is calculated. The differentiation of this probability function is shown to be the normalized electron velocity distribution function. (C) 2003 American Institute of Physics.

Objective assessment of cardiopulmonary resuscitation skills of 10-11 year-old schoolchildren using two different external chest compression to ventilation ratios

Study which shows that 10-11 yr olds are capable of effective CPR after a single 2 hour training session using the ABC for Life programme. However they perfrom more effective CPR when using a ratio of 15:2 rather than 30:2 chest compressions : ventilations