Reconceptualising public spaces of (IN)equality: sensing and creating layers of visibility

Tese apresentada para cumprimento dos requisitos necessários à obtenção do grau de Doutor em Geografia e Planeamento Territorial - Especialidade: Geografia Humana

Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

2010 Mathematics Subject Classification: 47B33, 47B38.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Internet Geography: New Spaces of Information

The objective of great investments in telecommunication networks is to approach economies and put an end to the asymmetries. The most isolated regions could be the beneficiaries of this new technological investments wave disseminating trough the territories. The new economic scenarios created by globalisation make high capacity backbones and coherent information society polity, two instruments that could change regions fate and launch them in to an economic development context. Technology could bring international projection to services or products and could be the differentiating element between a national and an international economic strategy. So, the networks and its fluxes are becoming two of the most important variables to the economies. Measuring and representing this new informational accessibility, mapping new communities, finding new patterns and localisation models, could be today’s challenge. In the physical and real space, location is defined by two or three geographical co-ordinates. In the network virtual space or in cyberspace, geography seems incapable to define location, because it doesn’t have a good model. Trying to solve the problem and based on geographical theories and concepts, new fields of study came to light. The Internet Geography, Cybergeography or Geography of Cyberspace are only three examples. In this paper and using Internet Geography and informational cartography, it was possible to observe and analyse the spacialisation of the Internet phenomenon trough the distribution of the IP addresses in the Portuguese territory. This work shows the great potential and applicability of this indicator to Internet dissemination and regional development studies. The Portuguese territory is seen in a completely new form: the IP address distribution of Country Code Top Level Domains (.pt) could show new regional hierarchies. The spatial concentration or dispersion of top level domains seems to be a good instrument to reflect the info-structural dynamic and economic development of a territory, especially at regional level.

Internet Geography: Spaces of Innovation

Information Society plays an important role in all kinds of human activity, inducing new forms of economic and social organization and creating knowledge. Over the last twenty years of the 20th century, large investments in telecommunication networks were made to approach economies and put an end to the asymmetries. The most isolated regions were the beneficiaries of this new technological investment’s wave disseminating trough the territories. The new economic scenarios created by globalisation make high capacity backbones and coherent information society polity, two instruments that could change regions fate and launch them in to an economic development context. Technology could bring international projection to services, products and could be the differentiating element between a national and an international economic strategy. So, the networks and its fluxes are becoming two of the most important variables to the economies. Measuring and representing this new informational accessibility, mapping new communities, finding new patterns and localisation models, could be today’s challenge. In the physical/real space, location is defined by two or three geographical co-ordinates. In the network/virtual space or in cyberspace, geography seems incapable to define location, because it doesn’t have a good model. Trying to solve the problem and based on geographical theories and concepts, new fields of study came to light. Internet Geography is one example. In this paper and using Internet Geography and informational cartography, it was possible to observe and analyse the spacialisation of the Internet phenomenon trough the distribution of the IP addresses in the Portuguese territory. This work shows the great potential and applicability of this indicator to regional development studies, and at the same time. The IP address distribution of Country Code Top Level Domains (.pt for Portugal) could show the same economic patterns, reflecting territorial inflexibility or, by opposition, new regional hierarchies. The spatial concentration or dispersion of top level domains seems to be a good instrument to analyse the info-structural dynamic and economic development of a territory, especially at regional level. At the same time it shows that information technologies are essential to innovation and competitive advantage.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs up to level li about the state of nature coincide, weobtain quotient type spaces that are typically smaller than the original ones, preserve basic topologicalproperties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash(li; l-i)-equilibria capture players inability to distinguish types belonging to the same equivalence class.The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustratethe constructions.

Extensions of maps defined on many fibres

Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.

Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots.

The configuration space available to randomly cyclized polymers is divided into subspaces accessible to individual knot types. A phantom chain utilized in numerical simulations of polymers can explore all subspaces, whereas a real closed chain forming a figure-of-eight knot, for example, is confined to a subspace corresponding to this knot type only. One can conceptually compare the assembly of configuration spaces of various knot types to a complex foam where individual cells delimit the configuration space available to a given knot type. Neighboring cells in the foam harbor knots that can be converted into each other by just one intersegmental passage. Such a segment-segment passage occurring at the level of knotted configurations corresponds to a passage through the interface between neighboring cells in the foamy knot space. Using a DNA topoisomerase-inspired simulation approach we characterize here the effective interface area between neighboring knot spaces as well as the surface-to-volume ratio of individual knot spaces. These results provide a reference system required for better understanding mechanisms of action of various DNA topoisomerases.

Kollektiivista muistia etsimässä : How Collectivities Remember : Structures and Spaces of Social and Cultural Memory

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