The Rigged Hilbert Space of the Free Hamiltonian

We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another opportunity to see that when continuous spectrum is present, the solutions of the Schrodinger equation lie in a RHS rather than just in a Hilbert space.Comment: 18 pages. Invited, refereed contribution to the Jaca proceedings; v2: minor, cosmetic change

On the occurrence of Radio Halos in galaxy clusters - Insight from a mass-selected sample

Giant radio halos (RH) are diffuse Mpc-scale synchrotron sources detected in a fraction of massive and merging galaxy clusters. An unbiased study of the statistical properties of RHs is crucial to constrain their origin and evolution. We aim at investigating the occurrence of RHs and its dependence on the cluster mass in a SZ-selected sample of galaxy clusters, which is as close as possible to be a mass-selected sample. Moreover, we analyse the connection between RHs and merging clusters. We select from the Planck SZ catalogue (Planck Collaboration XXIX 2014) clusters with $M\geq 6\times10^{14} M_\odot$ at z=0.08-0.33 and we search for the presence of RHs using the NVSS for z<0.2 and the GMRT RH survey (GRHS, Venturi et al. 2007, 2008) and its extension (EGRHS, Kale et al. 2013, 2015) for 0.2<z<0.33. We use archival Chandra X-ray data to derive information on the clusters dynamical status. We confirm that RH clusters are merging systems while the majority of clusters without RH are relaxed, thus supporting the idea that mergers play a fundamental role in the generation of RHs. We find evidence for an increase of the fraction of clusters with RHs with the cluster mass and this is in line with expectations derived on the basis of the turbulence re-acceleration scenario. Finally, we discuss the effect of the incompleteness of our sample on this result.Comment: 11 pages, 7 figures, accepted for publication in A&

Adapting and adopting River Habitat Survey : problems and solutions for fluvial hydromorphological assessment in Portugal

The Water Framework Directive (WFD), which established the use of hydromorphological quality elements to assess the ecological status of water bodies, has influenced the purpose and content of several European methods for characterizing physical structure and assessing habitat quality in rivers. The River Habitat Survey (RHS) is a WFD compliant method developed in the UK and follows rapid and simple survey procedures using a standardised approach to characterize the physical habitat and evaluate hydromorphological quality. In Portugal, RHS was adopted for WFD purposes due to its successful long term application across the UK and other European countries. Even so, an effort was made to adapt the RHS to Portuguese regional and river characteristics, in order to accurately record habitat features, assess habitat quality and comply with legal requirements. This paper describes the constraints, adaptations, state of the art and way forward for a successful RHS implementation in Portugal. Constraints concerning the application of RHS to Mediterranean rivers are strongly related to natural hydromorphological processes, namely annual and inter-annual flow variability, which is a potential source of covariance with anthropogenic pressures. This leads to difficulties in recognizing and accurately recording some RHS features. Adaptations to RHS were introduced for survey guidelines, recording procedures and improved definitions of habitat features. Additional modifications were prepared in different sections of RHS field form to reflect Portuguese river features and incorporate components required by the WFD.La Directiva Marco del Agua (DMA), que estableció el uso de indicadores de calidad hidromorfológicos para evaluar el estado ecológico de las masas de agua, ha influido en la finalidad y el contenido de varios métodos europeos para la caracterización de la estructura física y la evaluación de la calidad del h'abitat en los ríos. El River Habitat Survey (RHS) es un método compatible con la DMA desarrollado en el Reino Unido y sigue los procedimientos de encuesta rápida y sencilla utilizando un método estándar para caracterizar el hábitat físico y evaluar la calidad hidromorfológa. En Portugal, el RHS fue adoptado a efectos de la DMA debido a su exitosa aplicación a largo plazo en el Reino Unido y otros países europeos. Aun así, se hizo un esfuerzo para adaptar el RHS a las características regionales y de los ríos de Portugal, con el fin de registrar con precisión las características del hábitat, evaluar la calidad del hábitat y cumplir con los requisitos legales. Este artículo describe las limitaciones, las adaptaciones, el estado de implementacion y la manera para una implementación exitosa de RHS en Portugal. Las restricciones relativas a la aplicación de RHS a los ríos del Mediterráneo están fuertemente relacionadas con procesos hidromorfológicos naturales, como es la variabilidad del flujo anual e interanual, la cual es una fuente potencial de covarianza con presiones antropogénicas. Esto lleva a dificultades para reconocer y registrar con precisión algunas de las caracter'ısticas del RHS. Se han introducido adaptaciones al RHS en las directrices de muestreo, en los procedimientos de registro y se han mejorado algunas definiciones de ciertas características del hábitat. Otras modificaciones adicionales se han realizado en diferentes secciones del formulario de campo del RHS para reflejar las características de los ríos por tugueses y ciertas componentes requeridas por la DMA

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Dynamic real-time hierarchical heuristic search for pathfinding.

Movement of Units in Real-Time Strategy (RTS) Games is a non-trivial and challenging task mainly due to three factors which are constraints on CPU and memory usage, dynamicity of the game world, and concurrency. In this paper, we are focusing on finding a novel solution for solving the pathfinding problem in RTS Games for the units which are controlled by the computer. The novel solution combines two AI Planning approaches: Hierarchical Task Network (HTN) and Real-Time Heuristic Search (RHS). In the proposed solution, HTNs are used as a dynamic abstraction of the game map while RHS works as planning engine with interleaving of plan making and action executions. The article provides algorithmic details of the model while the empirical details of the model are obtained by using a real-time strategy game engine called ORTS (Open Real-time Strategy). The implementation of the model and its evaluation methods are in progress however the results of the automatic HTN creation are obtained for a small scale game map

Heterogeneity, Asymmetries and Learning in InfIation Expectation Formation: An Empirical Assessment

Relying on Michigan Survey' monthly micro data on inflation expectations we try to determine the main features -- in terms of sources and degree of heterogeneity - of inflation expectation formation over different phases of the business cycle and for different demographic subgroups. We identify three regions of the overall distribution corresponding to different expectation formation processes, which display a heterogeneous response to main macroeconomic indicators: a static or highly autoregressive (LHS) group, a "nearly" rational group (middle), and a group of "pessimistic" agents (RHS), who overreact to macroeconomic fluctuations. Different learning rules have been applied to the data, in order to test whether agents' are learning and whether their expectations are converging towards rational expectations (perfect foresight). The results obtained by applying conventional and recursive methods confirm our initial conjecture that behaviour of agents in the RHS of distribution is more associated with learning dynamics. We also regard the overall distribution as a mixture of normal distributions. This strategy allows us to get a deeper understanding of the existence and the main features of convergence and learning in the data, as well as to identify the demographic participation in each subcomponentHeterogeneous Expectations, Adaptive Learning, Survey Expectations

Análise Integrada dos riscos naturais. Determinação dos índices de qualidade do habitat e do canal por troço - Rio Nabão e Lis

Com o objetivo de complementar as avaliações da qualidade da água a partir de índices físico-químicos e biológicos, neste estudo recorreu-se ao método River Habitat Survey (RHS), que considera as características importantes para os organismos e a quantificação das alterações que ocorrem nos rios. A metodologia RHS foi desenvolvida pela Environment Agency (Reino Unido) para a obtenção de informação indispensável à adequada gestão dos recursos hídricos no âmbito da aplicação da Diretiva-Quadro da Água. O método RHS avalia características como a presença de vegetação ripícola, a heterogeneidade dos habitats e das correntes, que são importantes para a comunidade de macroinvertebrados.N/

Study protocol: can a school gardening intervention improve children's diets?

BACKGROUND: The current academic literature suggests there is a potential for using gardening as a tool to improve children's fruit and vegetable intake. This study is two parallel randomised controlled trials (RCT) devised to evaluate the school gardening programme of the Royal Horticultural Society (RHS) Campaign for School Gardening, to determine if it has an effect on children's fruit and vegetable intake. METHOD/DESIGN: Trial One will consist of 26 schools; these schools will be randomised into two groups, one to receive the intensive intervention as "Partner Schools" and the other to receive the less intensive intervention as "Associate Schools". Trial Two will consist of 32 schools; these schools will be randomised into either the less intensive intervention "Associate Schools" or a comparison group with delayed intervention. Baseline data collection will be collected using a 24-hour food diary (CADET) to collect data on dietary intake and a questionnaire exploring children's knowledge and attitudes towards fruit and vegetables. A process measures questionnaire will be used to assess each school's gardening activities. DISCUSSION: The results from these trials will provide information on the impact of the RHS Campaign for School Gardening on children's fruit and vegetable intake. The evaluation will provide valuable information for designing future research in primary school children's diets and school based interventions. TRIAL REGISTRATION: ISRCTN11396528

Design and operating parameters of a fulidized bed for the combustion of municipal solid waste using standpipes air distributors

Hydrodynamic studies and combustion of simulated and actual municipal solid waste were carried out in a fluidized bed system. A wide range of parameters was investigated in hydrodynamic study after which the optimum parameters were implemented in the combustion studies. A newly fabricated standpipes air distributor (primary air inlet) was designed based on findings of the optimum orifice diameter, orifice distance and distance between pipes. Orifice diameter, orifice distance and distance between pipes of 3 mm, 10 mm and 70 mm were used in the hydrodynamic studies of circular and rectangular columns (CHS and RHS). The operating parameters investigated in the CHS and RHS included the effect of sand sizes and aspect ratios on the fluidization profile. Standpipes air distributors having the same orifice diameter and distance but with a wider pipe distance of 200 mm were used in the hydrodynamic studies of a bigger rectangular (big scale) column. Different air flow strategies were implemented to ensure good mixing between sand and samples and to investigate the penetration of the incombustibles into the sand bed. Parameters studied in the combustion of municipal solid waste included the effect of fluidizing velocity and air factor on the combustion profile in the bed as well as the freeboard region with standpipe air distributor design and dimension established from the hydrodynamic studies of a bigger scale rectangular column. Findings from the CHS and RHS showed that sand particles with mean size of 0.34 mm performed good fluidization profile compared to other coarser sand sizes. The ratio of the bed height over diameter of column (Dc) for good fluidization was determined at cDH?for the circular column whereas the ratio of the bed height (H) over the length (L) of column was observed at H<L for the rectangular columns. A two side air flow was seen as the best air flow strategy for good mixing in a bigger rectangular column. The range of fluidization number and air factor for the combustion of simulated municipal solid waste in a rectangular fluidized bed combustor was 5 – 7 mfUin which 5 mf U was found to be the optimum with air factor of 0.8 (primary air). Air factor of 0.4 (secondary air) was observed to show good temperature profile in the freeboard region for the combustion of municipal solid waste. The optimum total combined air factor for the combustion of municipal solid waste was 1.2 in which inlet primary air factor and inlet secondary air factor were 0.8 and 0.4, respectively