Decentralized model reference control of flexible cable-stayed beam structures

A decentralized model reference controller is designed to reduce the magnitude of the transversal vibration of a flexible cable-stayed beam structure induced by a seismic excitation. The controller design is made based on the principle of sliding mode such that a priori knowledge

Modifications in the Si valence band after ion-beam-induced oxidation

The changes undergone by the Si surface after oxygen bombardment have special interest for acquiring a good understanding of the Si+-ion emission during secondary ion mass spectrometry (SIMS) analysis. For this reason a detailed investigation on the stoichiometry of the builtup surface oxides has been carried out using in situ x-ray photoemission spectroscopy (XPS). The XPS analysis of the Si 2p core level indicates a strong presence of suboxide chemical states when bombarding at angles of incidence larger than 30°. In this work a special emphasis on the analysis and interpretation of the valence band region was made. Since the surface stoichiometry or degree of oxidation varies with the angle of incidence, the respective valence band structures also differ. A comparison with experimentally measured and theoretically derived Si valence band and SiO2 valence band suggests that the new valence bands are formed by a combination of these two. This arises from the fact that Si¿Si bonds are present on the Si¿suboxide molecules, and therefore the corresponding 3p-3p Si-like subband, which extends towards the Si Fermi level, forms the top of the respective new valence bands. Small variations in intensity and energy position for this subband have drastic implications on the intensity of the Si+-ion emission during sputtering in SIMS measurements. A model combining chemically enhanced emission and resonant tunneling effects is suggested for the variations observed in ion emission during O+2 bombardment for Si targets.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

The complexity of random ordered structures

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On the stability of cooperation structures

Qin [J. Eco. Th., 1996] recently showed that in a game of endogenous formation of cooperation structure, if the underlying TU-game is superadditive, then the full cooperation structure is stable. In this note, we characterize the class of games that ensure the stability of the full cooperation structure, and show that this class is much larger than that of superadditive TU-games.

Stable coalition structures with fixed decision scheme

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction's choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This class contains all the decision schemes whose choice lies between the Rawlsian decision scheme and the median voter with mid-distance of the two median voters when there are ties. We show that for non-monotone distribution, there is no decision scheme that can ensure the stability of coalitions. In the last part of the paper, we prove the non-emptiness of the core of this coalition formation game

Fabricació de Lents Zonals de Fresnel per aplicació als raigs X tous

Estudi elaborat a partir d’una estada al Paul Scherrer Institut del Maig a l’Octubre del 2006 amb l’ajuda i supervisió dels Dr. Konstantins Jefimovs i Dr. Christian David. Focalitzar raigs X tous és una necessitat essencial per al microanàlisis, la microscopia, i fer imatges en moltes Instal·lacions de Radiació Sincrotró. Les Lents Zonals de Fresnel (FZP, de la denominació anglesa “Fresnel Zone Plates”) han demostrat donar uns punts focals amb una resolució espacial destacada i una baixa il·luminació de fons. Tanmateix, la fabricació de FZP és complexa i no totalment reproduïble. A més a més, el temps de vida de les FZP és força curt, ja que estant situades sobre membranes de nitrur de silici molt fines i altament absorbents. Per tant, hem fet esforços per implementar FZP de silici, que s’espera que siguin més resistents. L’element està fet d’una oblia de cristall de silici poc absorbent, i no presenta cap interfase entre materials. Així doncs, aquestes lents són especialment adequades per a aguantar les extremes càrregues de radiació de les fonts de raigs X més brillants. Particularment, això és molt important per a les aplicacions a les pròximes generacions de fonts de raigs X, com els Làsers d’Electrons Lliures (FEL, de la denominació anglesa “Free Electron Laser”). El silici també garanteix que no hi hagi cap banda d’absorció en el rang d’energies de la finestra de l’aigua (200-520 eV), fent aquestes lents ideals per a fer imatges de mostres biològiques. En aquest informe, hi ha una descripció detallada de tots els passos involucrats en la fabricació de les Lents Zonals de Fresnel de silici. En resum, les estructures de FZP es modelen sobre una resina utilitzant litografia per feix d’electrons i llavors el patró es transmet al silici mitjançant un gravat d’ions reactius (RIE, de la denominació anglesa ‘Reactive Ion Etching’) utilitzant una fina (20 nm) màscara de Crintermitja. Les membranes de silici es poden aprimar després de la fabricació de les estructures per a garantir una transmissió suficient fins i tot a baixes energies. Aquest informe també inclou l’anàlisi i la discussió d’alguns experiments preliminars per avaluar el rendiment de les Si FZPs fets a la línia de llum PolLux del Swiss Ligth Source amb l’ajuda dels Dr. Jörg Raabe i Dr. George Tzvetkov.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

Free Mobility and Taste-Homogeneity of Jurisdiction Structures

We consider a population of agents distributed on the unit interval. Agents form jurisdictions in order to provide a public facility and share its costs equally. This creates an incentive to form large entities. Individuals also incur a transportation cost depending on their location and that of the facility which makes small jurisdictions advantageous. We consider a fairly general class of distributions of agents and generalize previous versions of this model by allowing for non-linear transportation costs. We show that, in general, jurisdictions are not necessarily homogeneous. However, they are if facilities are always intraterritory and transportation costs are superadditive. Superadditivity can be weakened to strictly increasing and strictly concave when agents are uniformly distributed. Keywords: Consecutiveness, stratification, local public goods, coalition formation, country formation. JEL Classification: C71 (Cooperative Games), D71 (Social Choice; Clubs; Committees; Associations), H73 (Interjurisdictional Differentials and Their Effects).

Moduli of flat conformal structures of hyperbolic type

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Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Isomorphism relations on computable structures

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