Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Isotopic, trace element and nutrient characterization of coastal waters from Ubatuba inner shelf area, south-eastern Brazil

Stable isotopes, tritium, radium isotopes, radon, trace elements and nutrients data were collected during two sampling campaigns in the Ubatuba coastal area (south-eastern Brazil) with the aim of investigating submarine groundwater discharge (SGD) in the region. The isotopic composition (delta D, delta(18)O, (3)H) of submarine waters was characterised by significant variability and heavy isotope enrichment. The stable isotopes and tritium data showed good separation of groundwater and seawater groups. The contribution of groundwater in submarine waters varied from a few % to 17%. Spatial distribution of (222)Rn activity concentration in surface seawater revealed changes between 50 and 200 Bq m(-3) which were in opposite relationship with observed salinities. Time series measurements of (222)Rn activity concentration in Flamengo Bay (from 1 to 5 kBq m(-3)), obtained by in situ underwater gamma-spectrometry showed a negative correlation between the (222)Rn activity concentration and tide/salinity. This may be caused by sea level changes as tide effects induce variations of hydraulic gradients, which increase (222)Rn concentration during lower sea level, and opposite, during high tides where the (222)Rn activity concentration is smaller. The estimated SGD fluxes varied during 22-26 November between 8 and 40 cm d(-1), with an average value of 21 cm d(-1) (the unit is cm(3)/cm(2) per day). The radium isotopes and nutrient data showed scattered distributions with offshore distance and salinity. which implies that in a complex coast with many small bays and islands, the area has been influenced by local currents and groundwater-seawater mixing. SGD in the Ubatuba area is fed by coastal contaminated groundwater and re-circulated seawater (with small admixtures of groundwater). which claims for potential environmental concern with implications on the management of freshwater resources in the region. (C) 2007 Elsevier Ltd. All rights reserved.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Characteristics of violence against children in a Brazilian Capital

The purpose of this exploratory, descriptive and retrospective study with a quantitative approach was to characterize violence against children in Curitiba. Reports of 2004 through 2008 about compulsory denouncements of violence cases were analyzed. The results showed an increase in violence, with home violence as the most frequent type and five to nine-year-olds as the most affected group, and negligence and physical violence as the most denounced forms of violence. Almost 81% of the sexual violence is performed against girls and the father is the main aggressor, showing inequality in gender relations and between generations. The importance of notification as a visibility instrument is highlighted. Other confrontation measures are necessary though, such as the promotion of equitable relationships of gender and generation, and cross-sectional policies that involve the social segments in a praxis that transforms reality.

Genes involved in thoracic exoskeleton formation during the pupal-to-adult molt in a social insect model, Apis mellifera

Background: The insect exoskeleton provides shape, waterproofing, and locomotion via attached somatic muscles. The exoskeleton is renewed during molting, a process regulated by ecdysteroid hormones. The holometabolous pupa transforms into an adult during the imaginal molt, when the epidermis synthe3sizes the definitive exoskeleton that then differentiates progressively. An important issue in insect development concerns how the exoskeletal regions are constructed to provide their morphological, physiological and mechanical functions. We used whole-genome oligonucleotide microarrays to screen for genes involved in exoskeletal formation in the honeybee thoracic dorsum. Our analysis included three sampling times during the pupal-to-adult molt, i.e., before, during and after the ecdysteroid-induced apolysis that triggers synthesis of the adult exoskeleton. Results: Gene ontology annotation based on orthologous relationships with Drosophila melanogaster genes placed the honeybee differentially expressed genes (DEGs) into distinct categories of Biological Process and Molecular Function, depending on developmental time, revealing the functional elements required for adult exoskeleton formation. Of the 1,253 unique DEGs, 547 were upregulated in the thoracic dorsum after apolysis, suggesting induction by the ecdysteroid pulse. The upregulated gene set included 20 of the 47 cuticular protein (CP) genes that were previously identified in the honeybee genome, and three novel putative CP genes that do not belong to a known CP family. In situ hybridization showed that two of the novel genes were abundantly expressed in the epidermis during adult exoskeleton formation, strongly implicating them as genuine CP genes. Conserved sequence motifs identified the CP genes as members of the CPR, Tweedle, Apidermin, CPF, CPLCP1 and Analogous-to-Peritrophins families. Furthermore, 28 of the 36 muscle-related DEGs were upregulated during the de novo formation of striated fibers attached to the exoskeleton. A search for cis-regulatory motifs in the 5′-untranslated region of the DEGs revealed potential binding sites for known transcription factors. Construction of a regulatory network showed that various upregulated CP- and muscle-related genes (15 and 21 genes, respectively) share common elements, suggesting co-regulation during thoracic exoskeleton formation. Conclusions: These findings help reveal molecular aspects of rigid thoracic exoskeleton formation during the ecdysteroid-coordinated pupal-to-adult molt in the honeybee.

Identificação de ondas de Rossby a partir de diagramas de Hovmoller da concentração de clorofila entre as latitudes de 25o S e 45o S do Oceano Atlântico

Ondas de Rossby são ondas planetárias oceânicas de ocorrência quase global com comprimentos de onda da ordem de centenas a milhares de quilômetros, períodos da ordem de meses a anos e amplitudes superficiais da ordem de centímetros, causando anomalia da altura da superfície do mar (AASM). Transportando grandes quantidades de energia e influenciando diretamente a circulação de larga escala e o clima global, sua propagação de fase acontece sempre para oeste e sua velocidade é predominantemente uma função da latitude. É sabido que relações entre AASM e concentração de clorofila (CC) podem ser encontradas em todas as bacias oceânicas, evidenciando uma clara influência de fenômenos físicos em fenômenos biológicos. O presente trabalho visa a identificação de ondas de Rossby através da visualização de dados de CC, que, quando comparados a de AASM, apresentaram comprimento, período e velocidade de fase conforme previsto teoricamente para ondas de Rossby baroclínicas do primeiro modo vertical. A região de estudo, entre as latitudes de 25o S e 45o S, é caracterizada pela presença da Corrente do Atlântico Sul, da convergência subtropical e da faixa de rotacional nulo do vento e é, portanto, sede de importantes fenômenos oceanográficos de larga escala. Ambos os conjuntos de dados foram obtidos por sensoriamento remoto e submetidos a uma cadeia de filtros bidimensionais de resposta impulsiva finita (FIR2D) cujo funcionamento de baseia no princípio de convolução entre a série temporal e uma matriz-filtro. Os sinais filtrados foram decompostos em componentes propagantes e não-propagantes e entre os propagantes foi feita a separação das componentes em diversas bandas espectrais definidas por seus períodos centrais. Diagramas de Hovmoller foram confeccionados e as velocidades de fase foram obtidas através da transformada de Radon. A conclusão do trabalho evidenciou uma clara influência das ondas de Rossby sobre a distribuição de clorofila ao longo da região estudada.

Identificação de ondas de Rossby a partir de diagramas de Hovmoller da concentração de clorofila entre as latitudes de 25o S e 45o S do Oceano Atlântico

Ondas de Rossby são ondas planetárias oceânicas de ocorrência quase global com comprimentos de onda da ordem de centenas a milhares de quilômetros, períodos da ordem de meses a anos e amplitudes superficiais da ordem de centímetros, causando anomalia da altura da superfície do mar (AASM). Transportando grandes quantidades de energia e influenciando diretamente a circulação de larga escala e o clima global, sua propagação de fase acontece sempre para oeste e sua velocidade é predominantemente uma função da latitude. É sabido que relações entre AASM e concentração de clorofila (CC) podem ser encontradas em todas as bacias oceânicas, evidenciando uma clara influência de fenômenos físicos em fenômenos biológicos. O presente trabalho visa a identificação de ondas de Rossby através da visualização de dados de CC, que, quando comparados a de AASM, apresentaram comprimento, período e velocidade de fase conforme previsto teoricamente para ondas de Rossby baroclínicas do primeiro modo vertical. A região de estudo, entre as latitudes de 25o S e 45o S, é caracterizada pela presença da Corrente do Atlântico Sul, da convergência subtropical e da faixa de rotacional nulo do vento e é, portanto, sede de importantes fenômenos oceanográficos de larga escala. Ambos os conjuntos de dados foram obtidos por sensoriamento remoto e submetidos a uma cadeia de filtros bidimensionais de resposta impulsiva finita (FIR2D) cujo funcionamento de baseia no princípio de convolução entre a série temporal e uma matriz-filtro. Os sinais filtrados foram decompostos em componentes propagantes e não-propagantes e entre os propagantes foi feita a separação das componentes em diversas bandas espectrais definidas por seus períodos centrais. Diagramas de Hovmoller foram confeccionados e as velocidades de fase foram obtidas através da transformada de Radon. A conclusão do trabalho evidenciou uma clara influência das ondas de Rossby sobre a distribuição de clorofila ao longo da região estudada