http://hdl.handle.net/11343/294 2020-01-26T09:33:15Z 2020-01-26T09:33:15Z Doan, TS Rasmussen, M Kloeden, PE http://hdl.handle.net/11343/51722 2017-07-28T22:12:42Z 2015-05-01T00:00:00Z

The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor Doan, TS; Rasmussen, M; Kloeden, PE The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then demonstrated that a change in the sign of the dichotomy spectrum is associated with a bifurcation from a trivial to a non-trivial mean-square random attractor.

2015-05-01T00:00:00Z Archer, Shona Condon, Caroline STACEY, KAYE STEINLE, VICKI McCarthy, Heather Helme, Sue Sullivan, Gerard Tromp, Calvin http://hdl.handle.net/11343/35042 2018-12-19T04:55:08Z 2006-01-01T00:00:00Z

Learning arithmetic blocks: a concrete model for teaching decimals Archer, Shona; Condon, Caroline; STACEY, KAYE; STEINLE, VICKI; McCarthy, Heather; Helme, Sue; Sullivan, Gerard; Tromp, Calvin This booklet is an introduction to using the LAB model with your students. It outlines a number of activities using LAB to assist students in gaining an understanding of the decimal number system. Copyright confirmation in progress. Any queries to UMER-enquiries@unimelb.edu.au

2006-01-01T00:00:00Z Condon, Caroline Archer, Shona STACEY, KAYE STEINLE, VICKI Scott, Nick Helme, Sue Sullivan, Gerard Tromp, Calvin http://hdl.handle.net/11343/35041 2018-12-19T04:55:35Z 2006-01-01T00:00:00Z

Lesson ideas and activities for teaching decimals Condon, Caroline; Archer, Shona; STACEY, KAYE; STEINLE, VICKI; Scott, Nick; Helme, Sue; Sullivan, Gerard; Tromp, Calvin The Department of Science and Mathematics Education has produced this booklet to assist teachers with students learning to work confidently with decimal numbers. It contains many classroom activities that will motivate and engage students making the teaching and learning of decimals both enjoyable and effective. Copyright confirmation in progress. Any queries to UMER-enquires@unimelb.edu.au; Further information regarding the book is available at http://staff.edfac.unimelb.edu.au/~kayecs/projects/decprojlink.htm

2006-01-01T00:00:00Z Thomson, Alison ZHOU, SANMING http://hdl.handle.net/11343/33003 2018-12-14T05:19:20Z 2008-01-01T00:00:00Z

Frobenius circulant graphs of valency four Thomson, Alison; ZHOU, SANMING A first kind Frobenius graph is a Cayley graph Cay.K; S/ on the Frobenius kernel of a Frobenius group K o H such that S D aH for some a 2 K with haH i D K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4-valent circulant graph with a given diameter and maximum possible order. © 2008 Australian Mathematical Society. Online edition of the journal is available at http://journals.cambridge.org/JAZ

2008-01-01T00:00:00Z