Groups, graphs and mutually unbiased bases

A new characteristic free approach to constructing large sets of mutually unbiased bases in Hilbert space is developed. We associate with a seed set of bases a finite subgroup of which defines a strongly regular graph. Large sets of mutually unbiased bases are obtained as the cliques of the graph.

Quantitative assessment of through-thickness crack size based on Lamb wave scattering in aluminium plates

The interaction of Lamb wave modes at varying frequencies with a through-thickness crack of different lengths in aluminium plates was analysed in terms of finite element method and experimental study. For oblique-wave incidence, both numerical and experimental results showed that the wave scattering from a crack leads to complicated transmission, reflection and diffraction accompanied by possible wave-mode conversion. A dual-PZT actuation scheme was therefore applied to generate the fundamental symmetrical mode (S0) with enhanced energy to facilitate the identification of crack-scattered wave components. The relationship between crack length and the reflection/transmission coefficient obtained with the aid of the Hilbert transform was established, through which the crack length was quantitatively evaluated. The effects of wavelength of Lamb waves and wave diffraction on the properties of the reflection and transmission coefficients were analysed.

On the classification of image features

While the primary purpose of edge detection schemes is to be able to produce an edge map of a given image, the ability to distinguish between different feature types is also of importance. In this paper we examine feature classification based on local energy detection and show that local energy measures are intrinsically capable of making this classification because of the use of odd and even filters. The advantage of feature classification is that it allows for the elimination of certain feature types from the edge map, thus simplifying the task of object recognition.

Zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy

The first 12000 zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy. Format: the zeroes are in text file listed consecutively in decimal representation, each zero starts on a new line.

Zeroes of zeta function presented in this file were calculated on MASSIVE cluster (www.massive.org.au) using Python and packages MPmath version 0.17 and gmpy version 2.1, with a Newton based algorithm proposed by Fredrik Johansson with precision set to 20000 decimal digits. Partial recalculation with higher precision didn't show any loss of accuracy so we expect that the values are correct up to, possibly, a few last digits. We express our thanks to Fredrik Johansson for this algorithm and for development of MPmath as well.

Zeroes of Riemann's zeta function on the critical line with 40000 decimal digits accuracy

The project aims at computing Riemann's zeroes with high accuracy through an analysis of large determinants using Matyasievich's Artless method. Location of Riemann's zeroes is the famous 8th Hilbert problem, and one of Clay's Institute millennium problems.

Zeros of Dirichlet L-functions on the critical line with the accuracy of 40000 decimal places

The zeros of Dirichlet L-functions for various moduli and characters are being computed with very high accuracy on a cluster of workstations at Deakin University. This collection is growing to include more zeros (other moduli and characters).

Qualitative and historiometric methods in leadership research: a review of the first 25 years of the leadership quarterly

In the spirit of the 25th anniversary edition of The Leadership Quarterly, as the world's premier outlet for leadership research, we have reviewed qualitative and historiometric research across those 25. years. Qualitative research is a complex and cluttered area of scholarship. This is not because there is an inherent confusion about it. Rather, it is because 'qualitative' research is a cover-all term for a wide range of research strategies, paradigms, parent disciplines, sources of data, and methods of analysis for them. More so than in previous journal review articles, we explored variation in qualitative analysis as well as variety in qualitative data. In terms of methodologies, our efforts concentrated on case study, content analysis, grounded theory and historiometrics. We also examined trends toward post-positivism, post-modernity and liquid modernity, and their resultant benefits for researching leadership. Future directions for leadership research are posited. © 2013 Elsevier Inc.

Disentangling quality and safety indicator data: a longitudinal, comparative study of hand hygiene compliance and accreditation outcomes in 96 Australian hospitals.

The study aims are twofold. First, to investigate the suitability of hand hygiene as an indicator of accreditation outcomes and, second, to test the hypothesis that hospitals with better accreditation outcomes achieve higher hand hygiene compliance rates.