Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

ASERA : an uncontroversial evolution

The Australasian Science Education Research Association Ltd. (ASERA) is the oldest educational research association in Australasia. Starting as an informal meeting of science educators at Monash University in May 1970, it has evolved progressively without major controversy into a formally constituted limited company that promotes science education at all levels and contexts. There are no revelations of fractures within the association, and no accounts of major controversy, other than reference to a few grumbles here and there when changes were proposed. So, has the ASERA experience been positive and uplifting for all? Are there unspoken controversies? Can the uncontroversial be made controversial?

Multi-level order, friction and contradiction : the evolution of Australian film industry policy

Cultural policy studies have previously highlighted the importance of multiple logics, friction and contradiction in cultural policy. Recent developments in institutional theory provide a framework for analysing change in cultural policy which explores movement between these multiple and sometimes contradictory logics. This paper analyses the role of friction in the evolution of Australian film industry policy and in particular the tension between competing logics regarding nationalism, commercialism and the state. The paper is suggestive of the relevance of institutional theory as a framework for understanding cultural policy evolution.

Defining an Identity : The Evolution of Science Education

Research in science education is now an international activity. This book asks for the first time, Does this research activity have an identity?-It uses the significant studies of more than 75 researchers in 15 countries to see to what extent they provide evidence for an identity as a distinctive field of research.-It considers trends in the research over time, and looks particularly at what progression in the research entails.-It provides insight into how researchers influence each other and how involvement in research affects the being of the researcher as a person.-It addresses the relation between research and practice in a manner that sees teaching and learning in the science classroom as interdependent with national policies and curriculum traditions about science. It gives graduate students and other early researchers an unusual overview of their research area as a whole. Established researchers will be interested in, and challenged by, the identity the author ascribes to the research and by the plea he makes for the science content itself to be seen as problematic.

The evolution of a community of practice at the Queensland University of Technology for lecturers involved in large first year units

Communities of practice (CoPs) may be defined as groups of people who are mutually bound by what they do together (Wenger, 1998, p. 2), that is, they “form to share what they know, to learn from one another regarding some aspects of their work and to provide a social context for that work” (Nickols, 2000, para. 1). They are “emergent” in that the shape and membership emerges in the process of activity (Lees, 2005, p. 7). People in CoPs share their knowledge and experiences freely with the purpose of finding inventive ways to approach new problems (Wenger & Snyder, 2000, p. 2). They can be seen as “shared histories of learning” (Wenger, 1998, p. 86). For some time, QUT staff have been involved in a number of initiatives aimed at sharing ideas and resources for teaching first year students such as the Coordinators of Large First Year Units Working Party. To harness these initiatives and maximise their influence, the leaders of the Transitions In Project (TIP)1 decided to form a CoP around the design, assessment and management of large first year units.

The Evolution of the creative industries : creative clusters, creative citizens and social network markets 創意產業的演化 : 創意集群 ,創意公民, 社會網絡市場 [published in Chinese]

The creative industries are important because they are clustered at the point of attraction for a billion or more young people around the world. They're the drivers of demographic, economic and political change. They start from the individual talent of the creative artist and the individual desire and aspiration of the audience. These are the raw materials for innovation, change and emergent culture, scaled up to form new industries and coordinated into global markets based on social networks.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Why creative industries matter to economic evolution

This paper proposes that the 'creative industries'(CIs) play an important yet widely unexamined function in economic evolution through their role in the innovation process. This occurs in terms of the facilitation of demand for novelty, the provision and development of social technologies for producer-consumer interactions, and the adoption and embedding of new technologies as institutions. The incorporation of CIs into the Schumpeterian model of economic evolution thus fills a notable gap in the social technologies of the origination, adoption and retention of innovation.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.