Leanne Rylands

Matrix Generators for Exceptional Groups of Lie Type

This paper gives a uniform method of constructing generators for matrix representations of finite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimension representation of an associated Lie algebra. These generators have been implemented in the computer algebra system Magma and this completes the provision of pairs of matrix generators for all finite groups of Lie type.

On a relationship between completely separating systems and antimagic labeling of regular graphs

A completely separating system (CSS) on a finite set [n] is a collection C of subsets of [n] in which for each pair a ≠ b ∈ [n], there exist A, B ∈ C such that a ∈; A, b ∉ A and b ∈ B, a ∉ B. An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs.

Scientists and mathematicians collaborating to build quantitative skills in undergraduate science

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.

Matrix Generators for the Orthogonal Groups

In 1962 Steinberg gave pairs of generators for all finite simple groups of Lie type. In this paper, for each finite orthogonal group we provide a pair of matrices which generate its derived group: the matrices correspond to Steinbergs generators modulo the centre. These generators have been implemented in the computer algebra system MAGMA and this completes the provision of pairs of generators in MAGMA for all (perfect) finite classical groups.

On antimagic labeling for generalized web and flower graphs

An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. Completely separating systems arose from certain problems in information theory and coding theory. Recently these systems have been shown to be useful in constructing antimagic labelings of particular graphs.

Curriculum Development for Quantitative Skills in Degree Programs: A Cross-Institutional Study Situated in the Life Sciences.

ABSTRACT Higher education policies are increasingly focused on graduate learning outcomes, which infer an emphasis on, and deep understanding of, curriculum development across degree programs. As disciplinary influences are known to shape teaching and learning activities, research situated in disciplinary contexts is useful to further an understanding of curriculum development. In the life sciences, several graduate learning outcomes are underpinned by quantitative skills or an ability to apply mathematical and statistical thinking and reasoning. Drawing on data from a national teaching project in Australia that explored quantitative skills in the implemented curricula of 13 life sciences degree programs, this article presents four program-level curricular models that emerged from the analysis. The findings are interpreted through the lens of discipline-specific research and general curriculum design theories to further our understanding of curriculum development for graduate learning outcomes. Implications for future research and to guide curriculum development practices in higher education are discussed.

An Application of Completely Separating Systems to Graph Labeling

In this paper a known algorithm used for the construction of completely separating systems (CSSs), Roberts’ Construction, is modified and used in a variety of ways to build CSSs. The main interest is in CSSs with different block sizes. A connection between CSSs and vertex antimagic edge labeled graphs is then exploited to prove that various non-regular graphs are antimagic. An outline for an algorithm which produces some of these non-regular graphs together with a vertex antimagic edge labeling is presented.

Constructions for Octonion and Exceptional Jordan Algebras

In this note we reverse theusual process of constructing the Lie algebras of types G2and F4 as algebras of derivations of the splitoctonions or the exceptional Jordan algebra and instead beginwith their Dynkin diagrams and then construct the algebras togetherwith an action of the Lie algebras and associated Chevalley groups.This is shown to be a variation on a general construction ofall standard modules for simple Lie algebras and it is well suitedfor use in computational algebra systems. All the structure constantswhich occur are integral and hence the construction specialisesto all fields, without restriction on the characteristic, avoidingthe usual problems with characteristics 2 and 3.

Antichains and completely separating systems-A catalogue and applications

This paper extends known results on the existence, number and structure of antichains and completely separating systems. Both these structures are classified in several ways, and both an enumeration and listing of each type of object are given in a catalogue, which is described in detail in this paper. The antichain catalogue provides a complete listing of all non-isomorphic antichains on m points for m@?7.

Power quality disturbance recognition employing state vector machine methods

This paper presents a power quality disturbance recognition system employing support vector machine (SVM) techniques. Based on site measurements, a waveform generator is designed to emulate different power quality disturbances existing in modern power distribution systems. Digital wavelet transform (DWT) is then applied to the sampled waveforms for feature extraction. Thereby obtained DWT coefficients are further exploited to identify the associated disturbances through constructing an SVM classifier for each type of waveforms. Simulation results demonstrate that the SVM based classifiers can achieve significantly higher recognition rates compared with conventional methods.