Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadística de Catalunya) with the Chambers of Commerce (Cámaras de Comercio) of Sabadell and Terrassa.

Experimental investigation of transient natural convection cooling of high prandtl number fluid with variable viscosity

Report for the scientific sojourn at the James Cook University, Australia, between June to December 2007. Free convection in enclosed spaces is found widely in natural and industrial systems. It is a topic of primary interest because in many systems it provides the largest resistance to the heat transfer in comparison with other heat transfer modes. In such systems the convection is driven by a density gradient within the fluid, which, usually, is produced by a temperature difference between the fluid and surrounding walls. In the oil industry, the oil, which has High Prandtl, usually is stored and transported in large tanks at temperatures high enough to keep its viscosity and, thus the pumping requirements, to a reasonable level. A temperature difference between the fluid and the walls of the container may give rise to the unsteady buoyancy force and hence the unsteady natural convection. In the initial period of cooling the natural convection regime dominates over the conduction contribution. As the oil cools down it typically becomes more viscous and this increase of viscosity inhibits the convection. At this point the oil viscosity becomes very large and unloading of the tank becomes very difficult. For this reason it is of primary interest to be able to predict the cooling rate of the oil. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of high Prandtl fluid considering the variable viscosity effects.

Computation of an integral basis of a quartic number field

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Computation of an integral basis of quartic number field

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Els dermatoglifs: estudi dermatoglífic sobre la població de Llançà

El treball està basat en un mètode d'investigació antropològic que s'ha dut a terme al municipi de Llançà, on s'ha pres com a mostra 100 habitants, 50 homes i 50 dones, als quals se'ls ha agafat les empremtes dels dits índex d'ambdues mans, amb l'objectiu de demostrar que els dermatoglifs venen marcats genèticament amb diferències entre mans i entre sexes. Es demostra seguint la metodologia de l'anàlisi dels caràcters dermatoglifs de Cummins i Midlo (1943), descobridors i autors d'aquest estil. Aquesta tècnica té dos aspectes a valorar. Primerament s'ha d'estudiar el valor qualitatiu de cada empremta, alhora que es crea una base de dades on quedin registrades cadascuna de les observacions; i darrerament s'estudia el valor quantitatiu de cada mostra, anotant els valors obtinguts en una sèrie de taules. En la segona part del treball, creades ja, les taules, es compara els resultats extrets d'aquestes, amb la teoria universal de Holt, la qual estableix les primeres característiques generals obtingudes a través de la metodologia de Cummins i Midlo. I a partir d aquí, s'estableixen les primeres possibles conclusions, que en la tercera part del treball, es comproven de manera estadística, utilitzant dos mètodes matemàtics. Aquest tractament al qual es sotmeten les dades és la prova de la 2, que és la que ens comprovarà els resultats qualitatius; i el test T-Student, que ens verificarà els resultats quantitatius. I finalment arrel d'aquest anàlisis estadístics obtenim els resultats.

On the number of higher order Delaunay triangulations

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

A functional equation related to the product in a quadratic number field

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Gender gap index in Spain by regions

Every year, the World Economic Forum publishes the World Gender Gap Report mainly based on the results of the Global Gender Gap Index (GGGI) computed by country. This index is made out of four subindexes to capture the magnitude of the gender gap in 4 areas: educational attainment, economic participation and opportunity, political empowerment, and health and survival; its methodology was reformed in 2006. In this paper we adapt the GGGI to construct a Regional Gender Gap Index (RGGI) and we compute it by regions (Comunidades Autónomas) in Spain with 2006 data. The RGGI could be applied to other regions. Results of the RGGI show that not only are there gender gap differences between Spanish regions in Spain, but that there are at the political empowerment and economic participation and opportunity categories that those differences are strongest. Geographic distribution of the gender gap shows that the deepest gaps are, in general, located in the northern regions (Euskadi, with a high score, and Murcia and Extremadura, with low scores, being exceptions); this is mainly due to the poor participation in politics of women in those regions.

Ethnic and religious polarization and social conflict

In this paper we examine the link between ethnic and religious polarization and conflict using interpersonal distances for ethnic and religious attitudes obtained from the World Values Survey. We use the Duclos et al (2004) polarization index. We measure conflict by means on an index of social unrest, as well as by the standard conflict onset or incidence based on a threshold number of deaths. Our results show that taking distances into account significantly improves the quality of the fit. Our measure of polarization outperforms the measure used by Montalvo and Reynal-Querol (2005) and the fractionalization index. We also obtain that both ethnic and religious polarization are significant in explaining conflict. The results improve when we use an indicator of social unrest as the dependent variable.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Variability of North Atlantic hurricanes: seasonal versus individual-event features

Tropical cyclones are affected by a large number of climatic factors, which translates into complex patterns of occurrence. The variability of annual metrics of tropical-cyclone activity has been intensively studied, in particular since the sudden activation of the North Atlantic in the mid 1990’s. We provide first a swift overview on previous work by diverse authors about these annual metrics for the North-Atlantic basin, where the natural variability of the phenomenon, the existence of trends, the drawbacks of the records, and the influence of global warming have been the subject of interesting debates. Next, we present an alternative approach that does not focus on seasonal features but on the characteristics of single events [Corral et al., Nature Phys. 6, 693 (2010)]. It is argued that the individual-storm power dissipation index (PDI) constitutes a natural way to describe each event, and further, that the PDI statistics yields a robust law for the occurrence of tropical cyclones in terms of a power law. In this context, methods of fitting these distributions are discussed. As an important extension to this work we introduce a distribution function that models the whole range of the PDI density (excluding incompleteness effects at the smallest values), the gamma distribution, consisting in a powerlaw with an exponential decay at the tail. The characteristic scale of this decay, represented by the cutoff parameter, provides very valuable information on the finiteness size of the basin, via the largest values of the PDIs that the basin can sustain. We use the gamma fit to evaluate the influence of sea surface temperature (SST) on the occurrence of extreme PDI values, for which we find an increase around 50 % in the values of these basin-wide events for a 0.49 C SST average difference. Similar findings are observed for the effects of the positive phase of the Atlantic multidecadal oscillation and the number of hurricanes in a season on the PDI distribution. In the case of the El Niño Southern oscillation (ENSO), positive and negative values of the multivariate ENSO index do not have a significant effect on the PDI distribution; however, when only extreme values of the index are used, it is found that the presence of El Niño decreases the PDI of the most extreme hurricanes.

Influència del clima en la fenologia de la floració de Globularia alypum: anàlisi a partir de mostres d'herbari

Globularia alypum és un arbust termòfil típic de la regió oest del Mediterrani. Aquest nanofaneròfit té un patró de floració molt ampli. Les poblacions primerenques floreixen des del Juliol fins al Desembre i les poblacions tardanes des del Gener fins a l’Abril. L’objectiu del projecte és esbrinar quins factors climàtics determinen la fenologia de la floració de l’espècie a partir de mostres d’herbari i conèixer l’abast geogràfic d’ambdós patrons de floració a la península Ibèrica i França. També l’estudi d’altres característiques fenològiques en relació amb el clima: els braquiblasts i les espigues de capítols. Els plecs d’herbari han estat georeferenciats per ser utilitzats en un entorn SIG junt amb les dades del clima i s’ha realitzat una anàlisi estadística. El resultats mostren que les poblacions primerenques creixen majoritàriament en zones costaneres mentre que les tardanes ho fan en zones continentals. Les poblacions primerenques creixen en àrees on les temperatures (mitjana, mínima, màxima i mínima del mes més fred) són més altes que les tardanes per l’efecte temperador del mar. Al analitzar totes les poblacions, el nombre de mesos des de la transició floral es correlaciona negativament amb la temperatura mínima mensual i la temperatura mitjana mensual en tots els mesos, mentre que amb la temperatura màxima mensual entre Octubre i Abril. Al estudiar sols les poblacions tardanes les correlacions són similars, però no en les primerenques on no se’n troba cap. Les correlacions entre el nombre de mesos des de la transició floral i les variables climàtiques anuals són iguals, a més de trobar-se una correlació negativa amb la temperatura mínima del mes més fred i l’índex tèrmic, i positiva amb l’índex de continentalitat. No s’ha trobat cap diferència en presència de braquiblasts segons la població, però sí en les espigues de capítols, essent més freqüents en les poblacions primerenques. Es suggereix que la temperatura és un factor més determinant per a les poblacions tardanes, mentre que es desconeix si és la precipitació en les primerenques. Tampoc es té coneixement sobre si les diferències entre els dos patrons són genètiques o fenotípiques i quin mecanisme possibilita el desenvolupament de braquiblasts i espigues de capítols.