Fractal index, central charge and fractons

We introduce the notion of fractal index associated with the universal class $h$ of particles or quasiparticles, termed fractons, which obey specific fractal statistics. A connection between fractons and conformal field theory(CFT)-quasiparticles is established taking into account the central charge $c[\nu]$ and the particle-hole duality $\nu\longleftrightarrow\frac{1}{\nu}$, for integer-value $\nu$ of the statistical parameter. In this way, we derive the Fermi velocity in terms of the central charge as $v\sim\frac{c[\nu]}{\nu+1}$. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. Following another route, we also established a connection between Rogers dilogarithm function, Farey series of rational numbers and the Hausdorff dimension.Comment: latex, 12 pages, To appear in Mod. Phys. Lett. A (2000

Communication, Literacy and Citizenship: a conceptual orientation in a portuguese children’s television thematic channel, K SIC

This paper highlights the consequential nature of communication, literacy and citizenship and the meta-pattern that connects everything together – the ecology of the human spirit. It argues that, just like human communication, literacy is consequential in nature for humankind. Through each of our different worlds of experience and processes of communication, we manifest both of these human conditions and co-construct everyday practices that engender a plurality of effects. Literacy is a concept common to all humankind. Thus, it forms an indivisible whole with communication. This viewpoint is at odds with that which confines literacy to being understood as the acquisition of certain competences. It is arguable that, just like communication, the human condition of literacy needs to be both encouraged and developed. We suggest here that the idea of borders in literacy should be questioned. The work of Gregory Bateson on the ecology of the human spirit – an imminent characteristic of the human species that is based on the physiological structure of the living being and is in permanent interaction and reconnection with both the biosphere and our ways of seeing the world – supports the viewpoint put forward here. From the communication mediatised by a children’s television channel, from SIC K and from the results of studies carried out into children’s use of television we draw the examples that shall illustrate the theoretical approach taken here. They also underpin two premises of an ongoing project. Firstly, television is part of the solution in that it encourages and develops communication-literacy- citizenship-education-connectivity. Secondly, human rights form a shared platform from which to orient the use of Technologies and define connection strategies for the active participation of the children

From the ecology of the human spirit to the development of the orchestral theory of communication: the inclusion of the medium-message axiom

The contributions of the biologist, anthropologist and communication theorist Gregory Bateson (1904- 1980) form the nucleus of the cross-disciplinary theoretical principles which led to the founding of the web of thought spun by Watzlawick, Weakland, Beavin, Fish, Jackson, Erickson, Foster, Haley and Satir, amongst others. These authors were united by a common theoretical standpoint which foregrounded the ecology of the human spirit and saw communication as process, a system of transactional interaction. They were also similarly influenced by cybernetics, systems theory and constructivism. Energised by the clash of the ideas in their exchanges, they constructed the orchestral theory of communication, formalised by Paul Watzlawick, Donald Jackson and Janet Beavin. Today, Watzlawick (1967) is regarded as a seminal publication in the annals of interpersonal communication studies. Moving beyond the confines of the original object of study – face-to-face communication – this theory has been increasingly applied to the analysis of institutionally mediated communication and to the understanding of the construction of learning and change in organisations. However, in current circumstances, its set of axiomatic principles would benefit from the inclusion of a medium-message axiom to allow a fuller understanding of the realities of the mediated communication process that the process contains. This paper proposes the inclusion of this new axiom, medium-message; a proposal which is based on the work of Gregory Bateson, the ecology of the human spirit, the orchestral theory of communication and the thinking of the Media Ecology Association. It aims to help build a more profound insight into the realities of the process of human communication

Global Analytic Solutions for the Nonlinear Schr\"odinger Equation

We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section

The Aveiro charter of rights for human beings: a milestone for the second decade of the 21st century

BEING HUMAN is an extraordinary privilege. Every woman and every man that is born has something to learn and a project to build throughout their lives. Designing futures in the present and affirming what makes them BE HUMAN requires work, study and fun. Since the first decade of the 21st century, the Human Rights in Action project, by Civitas Aveiro, has helped, through its work with children, young people and teachers, to construct answers to the question: what makes us truly human? What are the effects of technologies’ in our life? The Aveiro charter of rights of the Human Being is one of the results of the 10th edition of the project developed in partnership with the University of Aveiro, with the backing of the Municipality and local Businesses. Twenty-five education and teaching institutions, from Nursery School to University, and a total of eight hundred Children and Young People, joined by around fifty teachers, from various subject areas, were involved in the development of the one hundred and twenty six rights inscribed in the Charter of Rights of the Human Being, which has been turned into an agenda for 2010. The dissemination of the charter by Civitas Aveiro aims to make a contribution in order that the citizens of the city of Aveiro, upon hearing the voices that speak out in this charter, may take steps toward making Aveiro a city blessed + dreamed with the Rights of the Human Being. The purpose of this presentation is to lay out and encourage discussion on the process of collective participation in the construction of the Charter of Rights of the Human Being, in various contexts, the methodology used and the analysis of the rights inscribed in it

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$, hence it is the unique solution obtained by Huh and Oh

Information technologies and the development of professional knowledge and identity in teacher education

This paper addresses the preparation in ICT of preservice mathematics teachers. We describe the aims, assumptions, and work carried out in a course offered at the University of Lisbon and briefly discuss the processes involved in the development of professional knowledge and the formation of professional identities. Using a qualitative methodology, based on the administration of free-response questionnaires to the student teachers enrolled in the course in 1999-2000, we analyze their general perspectives about ICT, the implications of the use of ICT in their view of teaching methodologies, and their development of a professional identity. This work provides suggestions for teacher education practice and for further research

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal radial d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this radial equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.Comment: 13 pages, 10 figure