Twisted conjugacy in braid groups

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A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

Embedding theorems of function classes, IV

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Embedding theorems of function classes, II

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Embedding theorems of function classes, I

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Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

Classes of measures generated by capacities

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Twisted Reidemeister torsion for twist knots

The aim of this paper is to give an explicit formula for the SL2(C)-twisted Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables given approximations of the twisted Reidemeister torsion for twist knots on some concrete examples are also enclosed.

Proposta de migració segura d'agents amb sol·licitud de classes sota demanda per a la plataforma JADE

Aquest projecte consisteix en la implementació d'una migració d'agents mòbils amb sol·licitud de classes sota demanda de manera segura per a la plataforma JADE. En aquest projecte hem desenvolupat dos protocols de control d'accés i autentificació sobre agents i/o plataformes. Però la línia central de desenvolupament d'aquest projecte radica en la creació d'un protocol de migració sota demanda d'agents. Hem implementat dues versions d'aquest protocol. La primera versió del protocol de migració es centra en la sol·licitud de classes sota demanda i la segona versió, per tal de millorar-ne el rendiment de la primera, emmagatzema les classes que ha demanat sota demanada en una cache de la plataforma.

Orbit decidability and the conjugacy problem for some extensions of groups

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Aproximació a les conceptualitzacions gramaticals d’alumnes de secundària a propòsit de les classes de mots

El treball vol aprofundir en les conceptualitzacions gramaticals dels alumnes de secundària, particularment en els sabers que mobilitzen quan han de determinar la classe lèxica de certes paraules (els mots analitzats pertanyen a categories “simples” com les de nom, verb, adjectiu i adverbi). Per a tal fi s’han enquestat 141 alumnes i se n’han entrevistat 18 (es tracta d’estudiants de tots els nivells de secundària d’un mateix institut). L’estudi posa en evidència la diversitat de procediments i de conceptualitzacions mobilitzats, progressivament complexos a mesura que avança l’escolarització, però també la freqüent manca de coherència entre els procediments aplicats –sovint mecànics– i els conceptes que afloren –sovint purament memorístics– en el discurs metalingüístic d’aquests estudiants.

On the growth rate of minor-closed classes of graphs

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Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.