Existence results for elliptic equations with singular terms

Esta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de equações que envolve o operador Laplaciano, um termo singular e nãolinearidade com o exponente crítico de Sobolev, (II) uma classe de equações com singularidade dupla, o expoente crítico de Hardy-Sobolev e um termo côncavo e (III) uma classe de equações em forma divergente, que envolve um termo singular, um operador do tipo Leray-Lions, e uma função definida nos espaços de Lorentz. As não-linearidades consideradas nos problemas (I) e (II), apresentam dificuldades adicionais, tais como uma singularidade forte no ponto zero (de modo que um "blow-up" pode ocorrer) e a falta de compacidade, devido à presença do exponente crítico de Sobolev (problema (I)) e Hardy-Sobolev (problema (II)). Pela singularidade existente no problema (III), a definição padrão de solução fraca pode não fazer sentido, por isso, é introduzida uma noção especial de solução fraca em subconjuntos abertos do domínio. Métodos variacionais e técnicas da Teoria de Pontos Críticos são usados para provar a existência de soluções nos dois primeiros problemas. No problema (I), são usadas uma combinação adequada de técnicas de Nehari, o princípio variacional de Ekeland, métodos de minimax, um argumento de translação e estimativas integrais do nível de energia. Neste caso, demonstramos a existência de (pelo menos) quatro soluções não triviais onde pelo menos uma delas muda de sinal. No problema (II), usando o método de concentração de compacidade e o teorema de passagem de montanha, demostramos a existência de pelo menos duas soluções positivas e pelo menos um par de soluções com mudança de sinal. A abordagem do problema (III) combina um resultado de surjectividade para operadores monótonos, coercivos e radialmente contínuos com propriedades especiais do operador de tipo Leray- Lions. Demonstramos assim a existência de pelo menos, uma solução no espaço de Lorentz e obtemos uma estimativa para esta solução.

Multiplicity results for some classes of Schrödinger-Poisson systems

In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp 2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq 2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.

The Well London program - a cluster randomized trial of community engagement for improving health behaviors and mental wellbeing: baseline survey results

Background The Well London programme used community engagement, complemented by changes to the physical and social neighbourhood environment, to improve physical activity levels, healthy eating and mental wellbeing in the most deprived communities in London. The effectiveness of Well London is being evaluated in a pair-matched cluster randomised trial (CRT). The baseline survey data are reported here. Methods The CRT involved 20 matched pairs of intervention and control communities (defined as UK census lower super output areas; ranked in the 11% most deprived LSOAs in London by Index of Multiple Deprivation) across 20 London boroughs. The primary trial outcomes, sociodemographic information and environmental neighbourhood characteristics were assessed in three quantitative components within the Well London CRT at baseline: a cross-sectional, interviewer-administered adult household survey; a self-completed, school-based adolescent questionnaire; a fieldworker completed neighbourhood environmental audit. Baseline data collection occurred in 2008. Physical activity, healthy eating and mental wellbeing were assessed using standardised, validated questionnaire tools. Multiple imputation was used to account for missing data in the outcomes and other variables in the adult and adolescent surveys. Results There were 4107 adults and 1214 adolescent respondents in the baseline surveys. The intervention and control areas were broadly comparable with respect to the primary outcomes and key sociodemographic characteristics. The environmental characteristics of the intervention and control neighbourhoods were broadly similar. There was greater between cluster variation in the primary outcomes in the adult population compared to the adolescent population. Levels of healthy eating, smoking and self-reported anxiety/depression were similar in the Well London population and the national Health Survey for England. Levels of physical activity were higher in the Well London population but this is likely to be due to the different measurement tools used in the two surveys. Conclusions Randomisation of social interventions such as Well London is acceptable and feasible and in this study the intervention and control arms are well balanced with respect to the primary outcomes and key sociodemographic characteristics. The matched design has improved the statistical efficiency of the study amongst adults but less so amongst adolescents. Follow-up data collection will be completed 2012.

EU water framework directive: will the nitrate load reduction from diffuse sources produce the same results in all estuaries?

The impact of urban waste-water and non-point nitrate discharges in estuarine and near-shore coastal waters are analyzed. The study is focused on the effects of applying the European directives 91/271/EEC and 91/676/EEC to these systems. 4 Portuguese estuaries and two coastal lagoons with different characteristics are studied. A modelling system is applied and calibrated in each system. Three nitrate load scenarios are examined. It is shown that the morphologic and hydrodynamic characteristics of the domain largely control the ecological processes in these systems. The primary production limitation factors are split into “biologic” and “hydrodynamic” components. The physical limitation due to hydrodynamic and residence time is the most important factor. The combined limitation of “biologic” factors (temperature, light and nutrients availability) control productivity only in the systems where physical limitation is not important.

Cyanobacteria blooms and cyanotoxin occurrence in the Guadiana (SE - Portugal): preliminary results

Cyanobacteria are a recognised public health hazard, because the majority of species is able to produce toxins. The monitoring is usually restricted to freshwater environments, like lakes or dams used for water supply. Cyanobacteria blooms have been regularly reported in the Guadiana River and high estuary and most of the observed cyanobacteria were toxin producers.

Do Girls and Boys Perceive Themselves as Equally Engaged in School? The Results of an International Study from 12 Countries

This study examined gender differences in student engagement and academic performance in school. Participants included 3420 students (7th, 8th, and 9th graders) from Austria, Canada, China, Cyprus, Estonia, Greece, Malta, Portugal, Romania, South Korea, the United Kingdom, and the United States. The results indicated that, compared to boys, girls reported higher levels of engagement in school andwere rated higher by their teachers in academic performance. Student engagement accounted for gender differences in academic performance, but gender did not moderate the associations among student engagement, academic performance, or contextual supports. Analysis of multiple-group structural equation modeling revealed that perceptions of teacher support and parent support, but not peer support, were related indirectly to academic performance through student engagement. This partial mediation model was invariant across gender. The findings from this study enhance the understanding about the contextual and personal factors associated with girls' and boys' academic performance around the world.

Release of Bet v 1 from Birch Pollen 1 from 5 European 2 Countries. Results from the HIALINE Study

Exposure to allergens is pivotal in determining sensitization and allergic symptoms in individuals. Pollen grain counts in ambient air have traditionally been assessed to estimate airborne allergen exposure. However, the exact allergen content of ambient air is unknown. We therefore monitored atmospheric concentrations of birch pollen grain and the matched major birch pollen allergen Bet v 1 simultaneously across Europe within the EU-funded project HIALINE (Health Impacts of Airborne Allergen Information Network). Pollen count was assessed with Hirst type pollen traps at 10 l/min at sites in France, United Kingdom, Germany, Italy and Finland. Allergen concentrations in ambient air were sampled at 800l/min with a Chemvol high-volume cascade impactor equipped with stages PM>10μm, 10 μm>PM>2.5μm, and in Germany also 2.5 μm>PM>0.12μm. The major birch pollen allergen Bet v 1 was determined with an allergen specific ELISA. Bet v 1 isoform patterns were analyzed by 2D-SDS-PAGE blots and mass spectrometric identification. Basophil activation was tested in an FcεR1-humanized rat basophil cell line passively sensitized with serum of a birch pollen lmptomatic patient. Compared to 10 previous years, 2009 was a representative birch pollen season for all stations. About 90% of the allergen was found in the PM>10μm fraction at all stations. Bet v 1 isoforms pattern did not varied substantially neither during ripening of pollen nor between different geographical locations. The average European allergen release from birch pollen was 3.2 pg Bet v 1/pollen and did not vary much between the European countries. However, in all countries a >10-fold difference in daily allergen release per pollen was measured which could be explained by long range transport of pollen with a deviating allergen release. Basophil activation by ambient air extracts correlated better with airborne allergen than with pollen concentration. Although Bet v 1 is a mixture of different isoforms, its fingerprint is constant across Europe. Bet v 1 was also exclusively linked to pollen. Pollen from different days varied >10-fold in allergen release. Thus exposure to allergen is inaccurately monitored by only monitoring birch pollen grains. Indeed, a humanized basophil activation test correlated much better with allergen concentrations in ambient air than with pollen count. Monitoring the allergens themselves together with pollen in ambient air might be an improvement in allergen exposure assessment.

Application of the WRF-Chem Model for a High Ozone Episode in SW Poland – Preliminary Results

The Weather Research and Forecasting model, integrated online with chemistry module, is a multi-scale model suitable for both research and operational forecasts of meteorology and air quality. It is used by many institutions for a variety of applications. In this study, the WRF v3.5 with chemistry (WRF-Chem) is applied to the area of Poland, for a period of 3-20 July 2006, when high concentrations of ground level ozone were observed. The meteorological and chemistry simulations were initiated with ERA-Interim reanalysis and TNO MACC II emissions database, respectively. The model physical parameterization includes RRTM shortwave radiation, Kain-Fritsch cumulus scheme, Purdue Lin microphysics and ACM2 PBL, established previously as the optimal configuration. Chemical mechanism used for the study was RADM2 with MADE/SORGAM aerosols. Simulations were performed for three one-way nested domains covering Europe (36 km x 36 km), Central Europe (12 km x 12 km) and Poland (4 km x 4 km). The results from the innermost domain were analyzed and compared to measurements of ozone concentration at three stations in different environments. The results show underestimation of observed values and daily amplitude of ozone concentrations.

Cultural universality and specificity of student engagement in school: The results of an international study from 12 countries

The Hong Kong subproject was supported by the Quality Education Fund of the Education Bureau in Hong Kong, whereas the Portuguese subproject was supported by the Portuguese Foundation for Science and Technology and by the Institute of Education of the University of Lisbon. The data of this paper were part of the data collected in a multinational project initiated by the International School Psychology Association.

The attractive female body weight and female body dissatisfaction in 26 countries across 10 world regions: results of the International Body Project I

This study reports results from the first International Body Project (IBP-I), which surveyed 7,434 individuals in 10 major world regions about body weight ideals and body dissatisfaction. Participants completed the female Contour Drawing Figure Rating Scale (CDFRS) and self-reported their exposure to Western and local media. Results indicated there were significant cross-regional differences in the ideal female figure and body dissatisfaction, but effect sizes were small across high-socioeconomic-status (SES) sites. Within cultures, heavier bodies were preferred in low-SES sites compared to high-SES sites in Malaysia and South Africa (ds = 1.94-2.49) but not in Austria. Participant age, body mass index (BMI), and Western media exposure predicted body weight ideals. BMI and Western media exposure predicted body dissatisfaction among women. Our results show that body dissatisfaction and desire for thinness is commonplace in high-SES settings across world regions, highlighting the need for international attention to this problem.

Analysing the results of UK urban freight studies

The paper is based on work carried out as part of the Green Logistics project1. The paper provides a review of urban freight studies that have taken place in the UK over approximately a thirty year period from the early 1970 s to the present (this is the first attempt at such a review in the UK as far as the authors are aware). Coverage of both goods collection and delivery vehicle activity and service vehicle activity is included. This review covers the survey techniques used, as well as the survey results obtained. Comparisons are made between the results of studies from the 1970 s and those carried out in the last decade in order to gain insight to changes in urban freight transport operations. The data provided in the studies reviewed is extremely important as it provides insight into urban freight operations that is unavailable from any other data source, including national freight surveys conducted by government. However, until now, the results of these studies have not been widely disseminated or compared.

Climatology of the Iberia coastal low-level wind jet: weather research forecasting model high-resolution results

Coastal low-level jets (CLLJ) are a low-tropospheric wind feature driven by the pressure gradient produced by a sharp contrast between high temperatures over land and lower temperatures over the sea. This contrast between the cold ocean and the warm land in the summer is intensified by the impact of the coastal parallel winds on the ocean generating upwelling currents, sharpening the temperature gradient close to the coast and giving rise to strong baroclinic structures at the coast. During summertime, the Iberian Peninsula is often under the effect of the Azores High and of a thermal low pressure system inland, leading to a seasonal wind, in the west coast, called the Nortada (northerly wind). This study presents a regional climatology of the CLLJ off the west coast of the Iberian Peninsula, based on a 9km resolution downscaling dataset, produced using the Weather Research and Forecasting (WRF) mesoscale model, forced by 19 years of ERA-Interim reanalysis (1989-2007). The simulation results show that the jet hourly frequency of occurrence in the summer is above 30% and decreases to about 10% during spring and autumn. The monthly frequencies of occurrence can reach higher values, around 40% in summer months, and reveal large inter-annual variability in all three seasons. In the summer, at a daily base, the CLLJ is present in almost 70% of the days. The CLLJ wind direction is mostly from north-northeasterly and occurs more persistently in three areas where the interaction of the jet flow with local capes and headlands is more pronounced. The coastal jets in this area occur at heights between 300 and 400 m, and its speed has a mean around 15 m/s, reaching maximum speeds of 25 m/s.