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.

Reconsideration of dimensions and curve fitting practice in economics ellaborating on Georgescu-Roegen’s economic methodology

This paper is to examine the proper use of dimensions and curve fitting practices elaborating on Georgescu-Roegen’s economic methodology in relation to the three main concerns of his epistemological orientation. Section 2 introduces two critical issues in relation to dimensions and curve fitting practices in economics in view of Georgescu-Roegen’s economic methodology. Section 3 deals with the logarithmic function (ln z) and shows that z must be a dimensionless pure number, otherwise it is nonsensical. Several unfortunate examples of this analytical error are presented including macroeconomic data analysis conducted by a representative figure in this field. Section 4 deals with the standard Cobb-Douglas function. It is shown that the operational meaning cannot be obtained for capital or labor within the Cobb-Douglas function. Section 4 also deals with economists "curve fitting fetishism". Section 5 concludes thispaper with several epistemological issues in relation to dimensions and curve fitting practices in economics.

Dimensions of national culture and the accounting environment -The Spanish case-

Gray (1988) has put forward a hypothesis on how a national accountingenvironment might reflect the cultural dimensions identified by Hofstede (1980, 1983). A number of studies have tested Gray's hypothesis, including one by Pourjalali and Meek (1995) which identified a match between changes in cultural dimensions and the accounting environment in Iran following the revolution. In this paper we replicate this work in the context of Spain following the death of Franco in 1975 and the emergence of a democratic constitution in 1978. Specifically, we: 1) Consider Gray's hypothesis built on Hofstede's cultural dimensions and review some empirical tests of the hypotheses.2) Building on the work of Hofstede and Gray, we: put forward some hypotheses on how we would expect cultural dimensions to change in Spain with the transition to democracy.3) Review developments in accounting in Spain following the transition to democracy, in order to identify how well these fit with our hypotheses.

Ground-state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values x~0.001 . The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same x.