Modelling and identification of non-linear deterministic systems in the delta-domain

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

Transverse modulational instability of partially incoherent soliton stripes

Based on the Wigner distribution approach, an analysis of the effect of partial incoherence on the transverse instability of soliton structures in nonlinear Kerr media is presented. It is explicitly shown, that for a Lorentzian incoherence spectrum the partial incoherence gives rise to a damping which counteracts, and tends to suppress, the transverse instability growth. However, the general picture is more complicated and it is shown that the effect of the partial incoherence depends crucially on the form of the incoherence spectrum. In fact, for spectra with finite rms-width, the partial incoherence may even increase both the growth rate and the range of unstable, transverse wave numbers.Comment: 5 pages, submitted to Phys. Rev.

A case study of effective practice in mathematics teaching and learning informed by Valsiner’s zone theory

The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated ‘best practice’ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsiner’s zone theory. A finding of the study is that ‘successful’ practice is strongly tied to school context and the cultural practices that have been developed by school leaders and teachers to optimise student learning opportunities. We illustrate such an alignment of school culture and practice through a vignette based on a case of one ‘successful’ school

Ionization experiment

Mariner space probe ionization chamber and Geiger counter experiments on galactic radiation entering solar syste

Heat-transfer thermal switch

Thermal switch maintains temperature of planetary lander, within definite range, by transferring heat. Switch produces relatively large stroke and force, uses minimum electrical power, is lightweight, is vapor pressure actuated, and withstands sterilization temperatures without damage

High-temperature bearing-cage materials

Evaluation tests conducted at temperatures of 500 and 700 degrees F reveal that S-Monel and AISI M-1 steel are suitable as high temperature cage materials for precision bearings. The area of the wear scar in the cage pocket that developed during the test was used as the measure of wear