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.

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.