An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

The effect of simultaneous contractions of ipsilateral muscles on changes in corticospinal excitability induced by paired associative stimulation (PAS)

Consideration was given to means of increasing the reliability and muscle specificity of paired associative stimulation (PAS) by utilising the phenomenon of crossed-facilitation. Eight participants completed three separate sessions: isometric flexor contractions of the left wrist at 20% of maximum voluntary contraction (MVC) simultaneously with PAS (20s intervals; 14 min duration) delivered at the right median nerve and left primary motor cortex (MI); isometric contractions at 20% of MVC: and PAS only ( 14 min). Eight further participants completed two sessions of longer duration PAS (28 min): either alone or in conjunction with flexion contractions of the left wrist. Thirty motor potentials (MEPs) were evoked in the right flexor (rFCR) and extensor (rECR) carpi radialis muscles by magnetic stimulation of left M1 Prior to the interventions, immediately post-intervention, and 10 min post-intervention. Both 14 and 28 min of combined PAS and (left wrist flexion) contractions resulted in reliable increases in rFCR MEP amplitude, which were not present in rECR. In the PAS only conditions, 14 min of stimulation gave rise to unreliable increases in MEP amplitudes in rFCR and rECR, whereas 28 min of PAS induced small (unreliable) changes only for rFCR. These results support the conclusion that changes in the excitability of the corticospinal pathway induced by PAS interact with those associated with contraction of the muscles ipsilateral to the site of cortical stimulation. Furthermore, focal contractions applied by the opposite limb increase the extent and muscle specificity of the induced changes in excitability associated with PAS. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Application of auto-associative neural networks to transient fault detection in an IC engine

The tailpipe emissions from automotive engines have been subject to steadily reducing legislative limits. This reduction has been achieved through the addition of sub-systems to the basic four-stroke engine which thereby increases its complexity. To ensure the entire system functions correctly, each system and / or sub-systems needs to be continuously monitored for the presence of any faults or malfunctions. This is a requirement detailed within the On-Board Diagnostic (OBD) legislation. To date, a physical model approach has been adopted by me automotive industry for the monitoring requirement of OBD legislation. However, this approach has restrictions from the available knowledge base and computational load required. A neural network technique incorporating Multivariant Statistical Process Control (MSPC) has been proposed as an alternative method of building interrelationships between the measured variables and monitoring the correct operation of the engine. Building upon earlier work for steady state fault detection, this paper details the use of non-linear models based on an Auto-associate Neural Network (ANN) for fault detection under transient engine operation. The theory and use of the technique is shown in this paper with the application to the detection of air leaks within the inlet manifold system of a modern gasoline engine whilst operated on a pseudo-drive cycle. Copyright © 2007 by ASME.