Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Multi-View Weighted Network

Extensive investigation has been conducted on network data, especially weighted network in the form of symmetric matrices with discrete count entries. Motivated by statistical inference on multi-view weighted network structure, this paper proposes a Poisson-Gamma latent factor model, not only separating view-shared and view-specific spaces but also achieving reduced dimensionality. A multiplicative gamma process shrinkage prior is implemented to avoid over parameterization and efficient full conditional conjugate posterior for Gibbs sampling is accomplished. By the accommodating of view-shared and view-specific parameters, flexible adaptability is provided according to the extents of similarity across view-specific space. Accuracy and efficiency are tested by simulated experiment. An application on real soccer network data is also proposed to illustrate the model.

MiLK: Transforming everyday places into dynamic learning spaces with mobile and web technologies

This paper explores how game authoring tools can teach processes that transform everyday places into engaging learning spaces. It discusses the motivation inherent in playing games and creating games for others, and how this stimulates an iterative process of creation and reflection and evokes a natural desire to engage in learning. The use of MiLK at the Adelaide Botanic Gardens is offered as a case in point. MiLK is an authoring tool that allows students and teachers to create and share SMS games for mobile phones. A group of South Australian high school students used MiLK to play a game, create their own games and play each other’s games during a day at the gardens. This paper details the learning processes involved in these activities and how the students, without prompting, reflected on their learning, conducted peer assessment, and engaged in a two-way discussion with their teacher about new technologies and their implications for learning. The paper concludes with a discussion of the needs and requirements of 21st century learners and how MiLK can support constructivist and connectivist teaching methods that engage learners and will produce an appropriately skilled future workforce.

Designing learning spaces for (partially) online lives : recombinant architecture

The notion of recombinant architecture signals a loosening of spatial connections between physical and digital-online environments (Mitchell, 1996; 2000; 2003). Such an idea also points to the transformative nature of the designing approaches concerned with the creation of spaces where bits meet bodies to fulfil human needs and desires and, at the same time, pursuing those human dimensions of space and place which are so important to our senses of belonging, physical comfort and amenity. This paper proposes that recombinant spaces and places draw on familiar architectural forms and functions and on the transforming functions of digital-online modes. Perspectives, approaches and resources outlined in the paper support designing and re-designing enterprises and aim to stimulate discussion in the Digital Environments strand of this online conference: 'Under Construction: a world without walls'.

There is nothing that 'identifies me to that place' : Aboriginal Women's perceptions of health spaces and places

There is a growing body of literature within social and cultural geography that explores notions of place, space, culture, race and identity. The more recent works suggest that places are experienced and understood in multiple ways and are embedded within an array of politics. Memmott and Long, who have undertaken place-based research with Australian Indigenous people, present the theoretical position that ‘place is made and takes on meaning through an interaction process involving mutual accommodation between people and the environment’. They outline that places and their cultural meanings are generated through one or a combination of three types of people–environment interactions. These include: a place that is created by altering the physical characteristics of a piece of environment and which might encompass a feature or features which are natural or made; a place that is created totally through behaviour that is carried out within a specific area, therefore that specific behaviour becomes connected to that specific place; and a place created by people moving or being moved from one environment to another and establishing a new place where boundaries are created and activities carried out. All these ideas of places are challenged and confirmed by what Indigenous women have said about their particular use of, and relationship with, space within several health services in Rockhampton, Central Queensland. As my title suggests, Indigenous women do not see themselves as ‘neutral’ or ‘non-racialised’ citizens who enter and ‘use’ a supposedly neutral health service. Instead, Aboriginal women demonstrate they are active recognisers of places that would identify them within the particular health place. That is, they as Aboriginal women didn’t just ‘make’ place, the places and spaces ‘make’ them. The health services were identified as sites within which spatial relations could begin to grow with recognition of themselves as Aboriginal women in place, or instead create a sense of marginality in the failure of the spaces to identify them. The women’s voices within this paper are drawn from interviews undertaken with twenty Aboriginal women in Rockhampton, Central Queensland, Australia, who participated in a research project exploring ‘how the relationship between health services and Aboriginal women can be more empowering from the viewpoints of Aboriginal women’. The assumption underpinning this study was that empowering and re-empowering practices for Aboriginal women can lead to improved health outcomes. Throughout the interviews women shared some of their lived realities including some of their thoughts on identity, the body, employment in the health sector, service delivery and their notions of health service spaces and places. Their thoughts on health service spaces and places provide an understanding of the lived reality for Aboriginal women and are explored and incorporated within this paper.

Recent Italian cinema : spaces, contexts, experiences

The book is an in-depth view of recent Italian cinema - bringing an interdisciplinary knowledge to the study of a complex cinema industry. The book aims to address a number of questions about Italian cinema of the last twenty years, bringing interdisciplinary knowledge to a cinema that eschews traditional definitions and categories, and challenges critical assumption about a film industry that is struggling to find a new direction. In doing so, Recent Italian Cinema offers a transverse analysis of the Italian cinema industry in its dealings with national and international production, and of the themes and issues that have emerged in films produced during the period 1980-2006.