Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

An electronic voting platform with elliptic curve cryptography

The future of elections seems to be electronic voting systems du to its advantatges over the traditional voting. Nowadays, there are some different paradigms to ensure the security and reliability of e-voting. This document is part of a wider project which presents an e-Voting platform based on elliptic curve cryptography. It uses an hybrid combination of two of the main e-Voting paradigms to guarantee privacy and security in the counting phase, these are precisely, the mixnets and the homomorphic protocols. This document is focused in the description of the system and the maths and programming needed to solve the homomorphic part of it. In later chapters, there is a comparison between a simple mixing system and our system proposal.

Algorithms and cryptographic protocols using elliptic curves

En els darrers anys, la criptografia amb corbes el.líptiques ha adquirit una importància creixent, fins a arribar a formar part en la actualitat de diferents estàndards industrials. Tot i que s'han dissenyat variants amb corbes el.líptiques de criptosistemes clàssics, com el RSA, el seu màxim interès rau en la seva aplicació en criptosistemes basats en el Problema del Logaritme Discret, com els de tipus ElGamal. En aquest cas, els criptosistemes el.líptics garanteixen la mateixa seguretat que els construïts sobre el grup multiplicatiu d'un cos finit primer, però amb longituds de clau molt menor. Mostrarem, doncs, les bones propietats d'aquests criptosistemes, així com els requeriments bàsics per a que una corba sigui criptogràficament útil, estretament relacionat amb la seva cardinalitat. Revisarem alguns mètodes que permetin descartar corbes no criptogràficament útils, així com altres que permetin obtenir corbes bones a partir d'una de donada. Finalment, descriurem algunes aplicacions, com són el seu ús en Targes Intel.ligents i sistemes RFID, per concloure amb alguns avenços recents en aquest camp.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Global eriodicity and complete integrability of discrete dynamical systems

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Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Preventive health care and payment systems to providers

Prevention has been a main issue of recent policy orientations in health care. This renews the interest on how different organizational designs and the definition of payment schemes to providers may affect the incentives to provide preventive health care. We present, both the normative and the positive analyses of the change from independent providers to integrated services. We show the evaluation of that change to depend on the particular way payment to providers is done. We focus on the externality resulting from referral decisions from primary to acute care providers. This makes our analysis complementary to most works in the literature allowing to address in a more direct way the issue of preventive health care.

Sources of Competitiveness in Tourist Local Systems

At the end of the XIX Century, Marshall described the existence of some concentrations of small and medium enterprises specialised in a specific production activity in certain districts of some industrial English cities. Starting from his contribute, Italian scholars have paid particular attention to this local system of production coined by Marshall under the term industrial district. In other countries, different but related territorial models have played a central role as the milieu or the geographical industrial clusters. Recently, these models have been extended to non-industrial fields like culture, rural activities and tourism. In this text, we explore the extension of these territorial models to the study of tourist activities in Italy, using a framework that can be easily applied to other countries or regions. The paper is divided in five sections. In the first one, we propose a review of the territorial models applied to tourism industry. In the second part, we construct a tourist filiere and we apply a methodology for the identification of local systems through GIS tools. Thus, taxonomy of the Italian Tourist Local Systems is presented. In the third part, we discuss about the sources of competitiveness of these Tourist Local Systems. In the forth section, we test a spatial econometrics model regarding different kinds of Italian Tourist Local Systems (rural systems, arts cities, tourist districts) in order to measure external economies and territorial networks. Finally, conclusions and policy implications are exposed.

Knowledge, networks of cities and growth in regional urban systems

The objective of this paper is to measure the impact of different kinds of knowledge and external economies on urban growth in an intraregional context. The main hypothesis is that knowledge leads to growth, and that this knowledge is related to the existence of agglomeration and network externalities in cities. We develop a three-tage methodology: first, we measure the amount and growth of knowledge in cities using the OCDE (2003) classification and employment data; second, we identify the spatial structure of the area of analysis (networks of cities); third, we combine the Glaeser - Henderson - De Lucio models with spatial econometric specifications in order to contrast the existence of spatially static (agglomeration) and spatially dynamic (network) external economies in an urban growth model. Results suggest that higher growth rates are associated to higher levels of technology and knowledge. The growth of the different kinds of knowledge is related to local and spatial factors (agglomeration and network externalities) and each knowledge intensity shows a particular response to these factors. These results have implications for policy design, since we can forecast and intervene on local knowledge development paths.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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