Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

Finiteness obstructions and Euler characteristics of categories

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

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

Accés i Recuperació de Continguts en Líni@ (ARC@) : la gestió dels materials docents a la UOC

Arc@ té per objectiu millorar el procés d'aprenentatge de l'estudiant i facilitar l'eficiència en els processos de gestió docent i de continguts. Amb independència de la ubicació del material docent, s'han establert mecanismes en XML que permeten importar/exportar la informació des dels diferents aplicatius existents, indexar i organitzar aquesta informació per a la seva transformació i tractament posterior.

Euler characteristics of categories and homotopy colimits

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

Estimation of zero-sequence impedance of undergrounds cables for single-phase fault location in distribution systems with electric arc

This paper focus on the problem of locating single-phase faults in mixed distribution electric systems, with overhead lines and underground cables, using voltage and current measurements at the sending-end and sequence model of the network. Since calculating series impedance for underground cables is not as simple as in the case of overhead lines, the paper proposes a methodology to obtain an estimation of zero-sequence impedance of underground cables starting from previous single-faults occurred in the system, in which an electric arc occurred at the fault location. For this reason, the signal is previously pretreated to eliminate its peaks voltage and the analysis can be done working with a signal as close as a sinus wave as possible

On a series of Goldbach and Euler

Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.

On the Chern classes and the Euler characteristic for nonsingular complete intersections

It is shown that Hirzebruch's result on the Chern classes of a complete intersection of nonsingular hypersurfaces in general position in PN(C), is also valid for any nonsingular complete intersection. Then rela- tions between Euler characteristic, class and Milnor number are pointed out.

Faint arc-minute extended radio emission around Cygnus X-3

Aims.We revisit the vicinity of the microquasar Cygnus X-3 at radio wavelengths. We aim to improve our previous search for possible associated extended radio features/hot spots in the position angle of the Cygnus X-3 relativistic jets focusing on shorter angular scales than previously explored. Methods.Our work is mostly based on analyzing modern survey and archive radio data, mainly including observations carried out with the Very Large Array and the Ryle Telescopes. We also used deep near-infrared images that we obtained in 2005. Results.We present new radio maps of the Cygnus X-3 field computed after combining multi-configuration Very Large Array archive data at 6 cm and different observing runs at 2 cm with the Ryle Telescope. These are probably among the deepest radio images of Cygnus X-3 reported to date at cm wavelengths. Both interferometers reveal an extended radio feature within a few arc-minutes of the microquasar position, thus making our detection more credible. Moreover, this extended emission is possibly non-thermal, although this point still needs confirmation. Its physical connection with the microquasar is tentatively considered under different physical scenarios. We also report on the serendipitous discovery of a likely Fanaroff-Riley type II radio galaxy only away from Cygnus X-3.

Late Neogene lacustrine record and paleogeography in the Quillagua-Llamara basin, Central Andean fore-arc (Northern Chile)

The Cenozoic QuillaguaLlamara basin (northern Chile, Central Andes) is an asymmetrical, intramassif fore-arc basin with a relatively wide northern sector separated from a narrower southward extension by a basement threshold. The north- ern sector was characterised by a noticeable Oligocene?late Neogene alluvial-fan and lacustrine dominated deposition which resulted in sequences up to 900 m thick, whereas the southern sector was often a bypass zone with thinner fluvial and lacustrine sediment accumulation.

Morphological and Magnetic Properties of Superparamagnetic Carbon-Coated Fe Nanoparticles Produced by Arc Discharge.

Spherical carbon coated iron particles of nanometric diameter in the 510 nm range have been produced by arc discharge at near-atmospheric pressure conditions (using 58·10 4 Pa of He). The particles exhibit a crystalline dense iron core with an average diameter 7.4 ± 2.0 nm surrounded by a sealed carbon shell, shown by transmission electron microscopy (TEM), selected-area diffrac- tion (SAED), energy-dispersive X-ray analysis (STEM-EDX) and electron energy loss spectroscopy (EELS). The SAED, EDX and EELS results indicate a lack of traces of core oxidized phases showing an efficient protection role of the carbon shell. The magnetic properties of the nanoparticles have been investigated in the 5300 K temperature range using a superconducting quantum interference device (SQUID). The results reveal a superparamagnetic behaviour with an average monodomain diameter of 7.6 nm of the nanoparticles. The zero field cooled and field cooled (ZFC-FC)magnetization curves show a blocking temperature (TB)at room temperature very suitable for biomedical applications (drug delivery, magnetic resonance imaging MRI, hyperthermia).