Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Limit Cycles for a class of three dimensional polynomial differential systems

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Polynomial and linearized normal forms for almost periodic differential systems

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On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Television and the construction of identity: Barcelona, Olympic host

This document, originally published as part of the book The Keys of success: the social, sporting, economic and communications impact of Barcelona’92, comes from a larger study that looked at all aspects of television in the Olympics and can be found in its original version, in Miquel de Moragas Spà, Nancy K. Rivenburgh and James F. Larson (1996). Television in the Olympics. London: John Libbey.

The identity type weak factorisation system

We show that the classifying category C(T)of a dependent type theory T with axioms for identity types admits a nontrivial weak factorisation system. After characterising this weak factorisation system explicitly, we relate it to the homotopy theory of groupoids.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Polynomial functors and polynomial monads

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

An algorithm for semi-infinite polynomial optimization

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Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

Contextual effects on subjective national identity and nationalist vote in Catalonia

The important inflow of foreign population to western countries has boosted the study of acculturation processes among scholars in the last decades. By using the case of Catalonia, a receiver region of international and national migration since the fifties, this paper seeks to intersect a classic acculturation model and a newly reemerging literature in political science on contextual determinants on individual behavior. Does the context matters for understanding individual’s subjective national identity and, therefore, its voting behavior? Multilevel models show that environment matters. Percentage of Spain-born population in the town is statistically significant to account for variance in the subjective national identity and nationalist vote, even after controlling for age, sex, origin, language and left – right orientation and other contextual factors. This conclusion invites researchers not to underestimate the direct effect of the environment on individual outcomes such as feelings of belonging and vote orientation in contexts of rival identities.

Identity based encription with tate pairing

L'objectiu principal del projecte és l'estudi, la implementació d'algoritmes i protocols amb criptografia basada en la identitat. Aquesta o Identity Based Encryption (IBE) s'utilitza per simplificar el procés de comunicacions segures, com per exemple el correu electrònic. IBE permet a les polítiques de seguretat ser codificades directament sense la necessitat d'usar certificats. Aquests esquemes van ser proposats inicialment per A. Shamir a l'any 1984 i han estat objecte d'estudi per D. Boneh, S. Galbraith, etc. En aquest farem l'estudi dels emparellaments de Werl i Tate a través de l'algorisme de Miller, que ens permetrà implementar aquests emparellaments sobre corbes el·líptiques supersingulars.

Symbolic meaning of local identity – A case study on Barcelona place brand representation

The core objective of this research process was to design an operational tool for place brand analysis. By modelling the emotional significance and the deeper-lying symbols associated to a specific place identity I expected to create a semiotic tool that could be applied, mutatis mutandis, on other similar place brands. As a field case study to develop the instrument, my choice of the research arena was Barcelona city, the capital of Catalonia Autonomous Community, Spain. Barcelona brand identity was approached in the line of the Chicago Urban Anthropology School. The research methods were designed according to the prescriptions of the urban anthropology, namely qualitative methods: in-depth interviews and discourse analysis. The final research outcome was a model summarizing a range of specific emotional values that support a place brand to position in the collective mindset and to assume a positively valued status and identity in the world order.