School of Mathematics and Statistics  Research Publications
http://hdl.handle.net/11343/294
20200117T21:20:57Z

The meansquare dichotomy spectrum and a bifurcation to a meansquare attractor
http://hdl.handle.net/11343/51722
The meansquare dichotomy spectrum and a bifurcation to a meansquare attractor
Doan, TS; Rasmussen, M; Kloeden, PE
The dichotomy spectrum is introduced for linear meansquare random dynamical systems, and it is shown that for finitedimensional meanfield 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 nontrivial meansquare random attractor.
20150501T00:00:00Z

Learning arithmetic blocks: a concrete model for teaching decimals
http://hdl.handle.net/11343/35042
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 UMERenquiries@unimelb.edu.au
20060101T00:00:00Z

Lesson ideas and activities for teaching decimals
http://hdl.handle.net/11343/35041
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 UMERenquires@unimelb.edu.au; Further information regarding the book is available at http://staff.edfac.unimelb.edu.au/~kayecs/projects/decprojlink.htm
20060101T00:00:00Z

Frobenius circulant graphs of valency four
http://hdl.handle.net/11343/33003
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 4valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4valent 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
20080101T00:00:00Z