A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Differential activation of the thoracic multifidus and longissimus thoracis during trunk rotation

Study Design. Cross-sectional study. Objective. To develop a technique to measure electromyographic (EMG) activity of deep and superficial paraspinal muscles at different thoracic levels and to investigate activity of these muscles during seated trunk rotation. Summary of Background Data. Few studies have compared activity of deep and superficial paraspinal muscles of the thorax during trunk rotation, and conflicting results have been presented. Conflicting data may result from recording techniques or variation in activity between thoracic regions. Methods. EMG recordings were made from deep (multifidus/ rotatores) and superficial ( longissimus) paraspinal muscles at T5, T8, and T11 using selective intramuscular electrodes. Ten subjects rotated the trunk to end of range in each direction. EMG amplitude was measured in neutral, at end of range, and during four epochs, which represented four quarters of the movement. Results. During trunk rotation in sitting, longissimus EMG either increased with ipsilateral rotation ( T5) or decreased with contralateral rotation ( T5, T8, T11). In contrast, multifidus EMG was more variable and was either active with rotation in both directions ( particularly T5) or with one movement direction. Conclusions. The deep and superficial muscles of the thorax are differentially active, and the patterns of activity differ between the regions of the thorax. Data from this study support the hypothesis that multifidus may have a role in control of segmental motion at T5. Variability in multifidus activity at T8 and T11 suggests that this muscle may also control coupling between rotation and lateral flexion.

Embedding partial G-designs where G is a 4-cycle with a pendant edge

Let D denote the graph consisting of a cycle of length 4 with a pendant edge. In this paper, two very different small embeddings of partial D-designs are presented. (c) 2005 Elsevier B.V. All rights reserved.

Effect of gaze direction on neck muscle activity during cervical rotation

Control of the neck muscles is coordinated with the sensory organs of vision, hearing and balance. For instance, activity of splenius capitis (SC) is modified with gaze shift. This interaction between eye movement and neck muscle activity is likely to influence the control of neck movement. The aim of this study was to investigate the effect of eye position on neck muscle activity during cervical rotation. In eleven subjects we recorded electromyographic activity (EMG) of muscles that rotate the neck to the right [right obliquus capitis inferior (OI), multifides (MF), and SC, and left sternocleidomastoid (SCM)] with intramuscular or surface electrodes. In sitting, subjects rotated the neck in each direction to specific points in range that were held statically with gaze either fixed to a guide (at three different positions) that moved with the head to maintain a constant intra-orbit eye position or to a panel in front of the subject. Although right SC and left SCM EMG increased with rotation to the right, contrary to anatomical texts, OI EMG increased with both directions and MF EMG did not change from the activity recorded at rest. During neck rotation SCM and MF EMG was less when the eyes were maintained with a constant intra-orbit position that was opposite to the direction of rotation compared to trials in which the eyes were maintained in the same direction as the head movement. The inter-relationship between eye position and neck muscle activity may affect the control of neck posture and movement.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Visualising energy data

The Australian energy market is in the final stages of deregulation. These changes have created a dynamic environment which is highly volatile and competitive with respect to both demand and price. Our current research seeks to visualise aspects of the National Energy Market with a view to developing techniques which may be useful in identifying significant characteristics and/or drivers of these characteristics. In order to capture the complexity of the problem we explore a suite of different visualisation techniques, which, when combined into a unified package, highlight aspects of the problem. The particular problem visualised here is "Does the date exhibit characteristics which suggest that the time of day, day of the week, or the season, aflect the variation in demand and/or price?" © Austral. Mathematical Soc. 2005.