Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Task design and interaction in collaborative writing: the students’ story

This article investigates student behaviour on collaborative assignments, looking at the relationship between task type and interaction, and considers the implications for task design. Students reported on interactions in a year-long workplace-focussed group communication project, comparing these with interactions on other academy based group assignments. Differences were seen in the amount of brainstorming, the criteria for dividing up work, the intensity of editing, and how conflict was managed. Contributing factors to these differences included the presence or absence of a creative element, the instrumental nature of the task, and the need for a collective approach inherent in the task design.

Building collaborative partnerships for climate change action in Maputo, Mozambique

The authors examine partnerships as a policy strategy for climate change governance in cities in the Global South. Partnerships offer the opportunity to link the actions of diverse actors operating at different scales and, thus, they may be flexible enough to deal with uncertain futures and changing development demands. However, simultaneously, partnerships may lack effectiveness in delivering action at the local level, and may constitute a strategy for some actors to legitimate their objectives in spite of the interests of other partners. Engaging with the specific example of urban governance in Maputo, Mozambique, the authors present an analysis of potential partnerships in this context, in relation to the actors that are willing and able to intervene to deliver climate change action. What, they ask, are the challenges to achieving common objectives in partnerships from the perspective of local residents in informal settlements? The analysis describes a changing context of climate change governance in the city, in which the prospects of access to international finance for climate change adaptation are moving institutional actors towards engaging with participatory processes at the local level. However, the analysis suggests a question about the extent to which local communities are actually perceived as actors with legitimate interests who can intervene in partnerships, and whether their interests are recognised.

Collabowrighting the hyper(play)text: a postdramatic digital poetics

The aim of this research is to exhibit how literary playtexts can evoke multisensory trends prevalent in 21st century theatre. In order to do so, it explores a range of practical forms and theoretical contexts for creating participatory, site-specific and immersive theatre. With reference to literary theory, specifically to semiotics, reader-response theory, postmodernism and deconstruction, it attempts to revise dramatic theory established by Aristotle’s Poetics. Considering Gertrude Stein’s essay, Plays (1935), and relevant trends in theatre and performance, shaped by space, technology and the everchanging role of the audience member, a postdramatic poetics emerges from which to analyze the plays of Mac Wellman and Suzan-Lori Parks. Distinguishing the two textual lives of a play as the performance playtext and the literary playtext, it examines the conventions of the printed literary playtext, with reference to models of practice that radicalize the play form, including works by Mabou Mines, The Living Theatre and Fiona Templeton. The arguments of this practice-led Ph.D. developed out of direct engagement with the practice project, which explores the multisensory potential of written language when combined with hypermedia. The written thesis traces the development process of a new play, Rumi High, which is presented digitally as a ‘hyper(play)text,’ accessible through the Internet at www.RumiHigh.org. Here, ‘playwrighting’ practice is expanded spatially, collaboratively and textually. Plays are built, designed and crafted with many layers of meaning that explore both linguistic and graphic modes of poetic expression. The hyper(play)text of Rumi High establishes playwrighting practice as curatorial, where performance and literary playtexts are in a reciprocal relationship. This thesis argues that digital writing and reading spaces enable new approaches to expressing the many languages of performance, while expanding the collaborative network that produces the work. It questions how participatory forms of immersive and site-specific theatre can be presented as interactive literary playtexts, which enable the reader to have a multisensory experience. Through a reflection on process and an evaluation of the practice project, this thesis problematizes notions of authorship and text.

Finite-dimensional global attractors in Banach spaces

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.