Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Recerca de producció de gravitons en escenaris amb dimensions extres al Tevatron amb el detector CDF

Les dimensions extres plantegen una solució al problema de la jerarquia de les forces i proposen una explicació a l’aparent feblesa de la força de la gravetat en front de les altres forces. Utilitzant dades simulades i dades proporcionades pel detector CDF situat en l’accelerador Tevatron a Fermilab (Chicago, EEUU), s’ha realitzat una recerca de dimensions extres i de producció de gravitons.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

"Vegeu el resum a l'inici del document del fitxer adjunt."

Politics and the Olympics: some new dimensions

Paper given at the Institut de Ciències Polítiques i Socials, Barcelona in 1995 analysing the relationship between politics, the Olympic Games and the Olympic Movement and their influences.

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.

Art en tres dimensions: construcció de renders 3D amb renders 3D studio max

Treball de recerca realitzat per un alumne d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. Existeixen diversos programes informàtics per a la generació d’imatges en format 3D. S’analitza breument l’oferta del mercat actual de la tecnologia de programari més emprada en la producció de gràfics 3D amb ordinador, identificant les vessants positives i negatives de cadascun. Posteriorment s’examina en profunditat el programa 3D Studio Max, per tal de conèixer-ne les eines de creació d’escenes virtuals i les seves funcionalitats. Finalment s’han desenvolupat projectes d’escenaris 3D en els quals es puguin aplicar els coneixements tècnics obtinguts en la recerca, sempre conceptualitzant aquestes propostes amb un cert criteri artístic.

Comparació de la cobertura de bàlec després de diferents pertorbacions amb foc, tenint en compte l'autocorrelació espacial en transectes de dos dimensions

Projecte de recerca elaborat a partir d’una estada a la University of Alberta entre juliol i octubre del 2007. Es pot comparar la cobertura d'arbustos després d'incendis i de cremes controlades en transectes amb 2 dimensions, tenint en compte l'autocorrelació espacial? Canvia el patró espacial dels arbustos després d'aquestes pertorbacions?

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

Reliable acetabular cup orientation with a new gravity-assisted guidance system.

Acetabular cup orientation is a key factor determining hip stability, and standard mechanical guides have shown little help in improving alignment. An in vitro study was carried out to compare the accuracy and precision of a new gravity-assisted guidance system with a standard mechanical guide. Three hundred ten cups were impacted by 5 surgeons, and the final cup orientation was measured. With the new guide, the average error in anteversion was 0.4 degrees , compared with 10.4 degrees with the standard guide and 0.3 degrees and -4.7 degrees , respectively, for abduction angles. The average time required for orienting the cups was similar for both guides. The accuracy and reproducibility obtained with the new guide were better (P < .0001). These good results would require a clinical validation.