La dispersió Møller i els inicis de l’electrodinàmica quàntica: treball de recerca per al mestratge en Història de les Ciències

S’hi analitza la deducció teòrica i la contrastació experimental originals de la dispersió electró-electró (dispersió Møller, 1932), amb l’objectiu d’esbrinar quin paper van tenir en el desenvolupament de l’electrodinàmica quàntica. S’hi mostra que Christian Møller (1904-1980) va deduir la fórmula que du el seu nom mitjançant la noció de correspondència, evitant així els problemes que plantejava una incipient teoria quàntica de camps. La fórmula només va assolir el seu estatus actual d’aplicació paradigmàtica de l’electrodinàmica quàntica després de la Segona Guerra Mundial, un cop la teoria va haver superat aquests problemes a través del procés de renormalització. El treball aclareix d’aquesta manera un episodi clau en el desenvolupament d’una de les teories fonamentals de la física del segle XX.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Gas identification with tin oxide sensor array and self-organizing maps: adaptive correction of sensor drifts

Low-cost tin oxide gas sensors are inherently nonspecific. In addition, they have several undesirable characteristics such as slow response, nonlinearities, and long-term drifts. This paper shows that the combination of a gas-sensor array together with self-organizing maps (SOM's) permit success in gas classification problems. The system is able to determine the gas present in an atmosphere with error rates lower than 3%. Correction of the sensor's drift with an adaptive SOM has also been investigated

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

The determinants of capital intensity in Japan and the U.S

We estimate the determinants of capital intensity in Japan and the US, characterized by striking different paths. We augment an otherwise standard Constant Elasticity of Substitution (CES) model with demand-side considerations, which we find especially relevant in the US. In this augmented setting, the elasticity of substitution between capital and labor is placed around 0.85 in Japan, and 0.30 in the US. We also find evidence of biased technical change, which is capital-saving in Japan but labor-saving in the US. These differences help us explain the diverse experience in the capital deepening process of these economies, and lead us to conclude that demand-side drivers may also be relevant to account for different growth experiences. A close look at the nature of technological change is also needed before designing one-size-fits-all industrial, economic growth, and/or labor market policies.