An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian National University, 22 January to 9 February, 1996. They have subsequently been updated and expanded…
Groups
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" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a oneline explanation as any. The concept of a group is surely one of the central ideas of…

These notes are a selfcontained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in greater…

Investigators have modeled oceanic and atmospheric vortices in the laboratory in a number of different ways, employing background rotation, density effects, and geometrical confinement. In this article, we address barotropic vortices in a rotating…

Computational fluid dynamics (CFD) modeling of tricklebed reactors with detailed interstitial flow solvers has remained elusive mostly due to the extreme CPU and memory intensive constraints. Here, we developed a comprehensible and scalable CFD…

We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are noncommensurate and the connectivity is simple (no parallel bonds…

The heat shock promoter is useful for regulating transgene expression in small waterliving organisms. In zebrafish embryos, downstream gene expression can be greatly induced throughout the body by raising the temperature from 28.5 degrees C to 38.0…

The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "P" for the function which is 1 when the Boolean condition…

We survey the known results regarding the boundaries of wordhyperbolic groups.

Recently, rightangled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications. This survey…

The Poisson boundary of a group G with a probability measure \mu is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral…

Let G be a finite group. The table of marks of G arises from a characterization of the permutation representations of G by certain numbers of fixed points. It provides a compact descrip tion of the subgroup lattice of G and enables explicit…

In this note we discuss techniques for determining the automorphism group of a genus g hyperelliptic curve Xg defined over an algebraically closed field k of characteristic zero. The first technique uses the classical GL2 (k)invariants of binary…

We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x ∈ G the subgroup of G generated by x and y is solvable. This confirms a conjecture of Flavell. We present analogues…

Key to a computational study of the finite classical groups in odd characteristic are efficient methods for constructing involutions and their centralisers. Constructing an involution in a given conjugacy class is usually achieved by finding an…

Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out…

Mycotoxins are small (MW approximately 700), toxic chemical products formed as secondary metabolites by a few fungal species that readily colonise crops and contaminate them with toxins in the field or after harvest. Ochratoxins and Aflatoxins are…

Abstract Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to…

Introduction This is a concise summary of recommended features in LATEX and a couple of extension packages for writing math formulas. Readers needing greater depth of detail are referred to the sources listed in the bibliography, especially…

DAVID bioinformatics resources consists of an integrated biological knowledgebase and analytic tools aimed at systematically extracting biological meaning from large gene/protein lists. This protocol explains how to use DAVID, a highthroughput and…
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