Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

A non-malleable group key exchange protocol robust against active insiders

In this paper we make progress towards solving an open problem posed by Katz and Yung at CRYPTO 2003. We propose the first protocol for key exchange among n ≥2k+1 parties which simultaneously achieves all of the following properties: 1. Key Privacy (including forward security) against active attacks by group outsiders, 2. Non-malleability — meaning in particular that no subset of up to k corrupted group insiders can ‘fix’ the agreed key to a desired value, and 3. Robustness against denial of service attacks by up to k corrupted group insiders. Our insider security properties above are achieved assuming the availability of a reliable broadcast channel.

Diversifying Information Literacy Research : An Informed Learning Perspective

This article uses the idea of informed learning, an interpretation of information literacy that focuses on people’s information experiences rather than their skills or attributes, to analyse the character of using information to learn in diverse communities and settings, including digital, faith, indigenous and ethnic communities. While researchers of information behaviour or information seeking and use have investigated people’s information worlds in diverse contexts, this work is still at its earliest stages in the information literacy domain. To date, information literacy research has largely occurred in what might be considered mainstream educational and workplace contexts, with some emerging work in community settings. These have been mostly in academic libraries, schools and government workplaces. What does information literacy look like beyond these environments? How might we understand the experience of effective information use in a range of community settings, from the perspective of empirical research and other sources? The article concludes by commenting on the significance of diversifying the range of information experience contexts, for information literacy research and professional practice.

Health and safety regulatory reform in Australia : challenges and issues for smaller ethnic firms

In recent times significant change has occurred to the Australian health and safety regulatory context. In this paper we consider the potential response of smaller firms in general, and ethnic owned and/or operated smaller firms in particular. We draw on literature examining smaller firms' responses to regulation and apply this to what little we know about smaller ethnic firms in Australia in the context of the regulatory change. We highlight the challenges to owner managers and what could be done to engage and support smaller ethnic firms to realise the opportunities resulting from this regulatory change.

Forms of capital, intra-ethnic variation and Polish entrepreneurs in Leicester

A study of ten Polish entrepreneurs operating in Leicester, UK is reported in this article. The concepts of social, cultural and economic capital are used as the lens through which to explore the way the capital they access is employed and converted into entrepreneurial activity. Ethnic entrepreneurship takes place within wider social, political and economic institutional frameworks and opportunity structures and so this is taken into account by differentiating two groups – post-war and contemporary Polish entrepreneurs. The differing origins and amounts of forms of capital they can access are shown as is how these are converted into valued outcomes. Combining the mixed embeddedness approach with a forms-of-capital analysis enables looking beyond social capital to elaborate on intra-ethnic variation in the UK’s Polish entrepreneurial community.

Testing the international linkage in the platinum-group metal futures markets

This study tests whether an international market exists in the platinum-group metal (PGM) futures markets. For this purpose, we tested the law of one price (LOP) and the causality between the U.S. and Japanese platinum and palladium futures markets. We also performed the test when structural breaks are considered. Long-run price relationships were found in both platinum and palladium markets but the LOP only sustained in the palladium market. The causality test revealed that it is the U.S. market that leads the price to transmit information between the U.S. and Japanese markets. Structural breaks had large impacts on the test results, suggesting that incorporating breaks is important when investigating the international price linkage in the PGM futures markets.

Architecture in the South Pacific : the Ocean of Islands

Architecture in the South Pacific: The Ocean of Islands recounts the recent developments of the South Pacific and its fascinating architecture. This volume traces the European architectural overlay onto this scattered group of islands as well as the transition of these same islands towards a regional identity that has been fashioned by the remoteness of each location, the incomparable setting, and the distinctive ethnic mix of its inhabitants. A series of themed essays present the story of architectural development in the Solomon Islands, Vanuatu, New Caledonia, Fiji, Wallis and Futuna, Tonga, the Cook Islands, Samoa and American Samoa, and French Polynesia. Recent architecture typifies the evolution of the islands as they have been subjected to the transformative waves of alien trade, religion, colonization, war and tourism, followed by post-colonialism and revived nationalism. As with the Pacific region itself, the most prominent characteristic of the architecture is its diversity. The blending of the universal and the local sets the stage for a fresh vision of the South Pacific across a wide range of building types, from spectacular mission churches to sensational resorts in paradise. This book, in full colour, will appeal to architects, armchair-tourists, students and all those for whom the South Pacific is the idyll of their dreams.

Sentencing and public confidence in Australia: The dynamics and foci of small group deliberations

This study is the first of its kind in Australia to use the deliberative small group methodology to explore participants’ deeper, nuanced thoughts on specific criminal justice issues in order to gain insight into the underlying beliefs that influence people’s opinions on sentencing. The use of small group discussions allows an analysis of the dynamics of people’s interactions and the potential of these to elicit deeper, more thoughtful deliberation. Participants’ comments around two policy areas – mandatory sentencing and the use of alternatives to imprisonment – were founded on concerns about the need for judges to tailor the sentence to fit the specific circumstances of each case. The methodology itself has shown that people may change their initial opinions on complex issues when given the opportunity to discuss and reflect on their beliefs.

Drinking games participation among female students at a regional Australian university

Participation in drinking games (DGs) by university students is often associated with heavy drinking and negative social and health impacts. Although research in Australia indicates that university students tend to drink at risky levels, there is paucity of literature on DGs among students, especially those residing at regional universities. This research examined drinking among female college students of white background. Eighteen female students participated in face-to-face in-depth interviews to describe their DG experiences. Most women played DGs for social and monetary reasons, with many drinking high volumes of alcohol during the game. Excessive drinking was linked with the type of beverage consumed. Despite knowing the health risks associated with DGs, there was a strong social imperative for these young women to play these games. Research and public health initiatives to better understand and address problematic drinking activities in rural and regional Australia have tended to ignore women and the dominant white populations whose heavy drinking has been largely restricted to private spheres.

‘It's all scientific to me’ : focus group insights into why young people do not apply safe-sex knowledge

Despite rising levels of safe-sex knowledge in Australia, sexually transmitted infection notifications continue to increase. A culture-centred approach suggests it is useful in attempting to reach a target population first to understand their perspective on the issues. Twenty focus groups were conducted with 89 young people between the ages of 14 and 16 years. Key findings suggest that scientific information does not articulate closely with everyday practice, that young people get the message that sex is bad and they should not be preparing for it and that it is not appropriate to talk about sex. Understanding how young people think about these issues is particularly important because the focus groups also found that young people disengage from sources of information that do not match their own experiences.