COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper. we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests. (C) 2010 Elsevier B.V. All rights reserved.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Influence of the length of remaining root canal filling and post space preparation on the coronal leakage of Enterococcus faecalis

This study evaluated the sealing ability of different lengths of remaining root canal filling and post space preparation against coronal leakage of Enterococcus faecalis. Forty-one roots of maxillary incisors were biomechanically prepared, maintaining standardized canal diameter at the middle and coronal thirds. The roots were autoclaved and all subsequent steps were undertaken in a laminar flow chamber. The canals of 33 roots were obturated with AH Plus sealer and gutta-percha. The root canal fillings were reduced to 3 predetermined lengths (n=11): G1=6 mm, G2=4 mm and G3=2 mm. The remaining roots served as positive and negative controls. Bacterial leakage test apparatuses were fabricated with the roots attached to Eppendorf tubes keeping 2 mm of apex submerged in BHI in glass flasks. The specimens received an E. faecalis inoculum of 1 x 107 cfu/mL every 3 days and were observed for bacterial leakage daily during 60 days. Data were submitted to ANOVA, Tukey's test and Fisher's test. At 60 days, G1 (6 mm) and G2 (4 mm) presented statistically similar results (p>0.05) (54.4% of specimens with bacterial leakage) and both groups differed significantly (p<0.01) from G3 (2 mm), which presented 100% of specimens with E. faecalis leakage. It may be concluded that the shortest endodontic obturation remnant leaked considerably more than the other lengths, although none of the tested conditions avoids coronal leakage of E. faecalis.

Ensino de astronomia em um espaço não formal: observação do Sol e de manchas solares

O presente artigo analisa os resultados obtidos num minicurso sobre o Sol e sua dinâmica realizado no Observatório Astronômico do Centro de Divulgação Científica e Cultural (CDCC) pertencente à Universidade de São Paulo (USP) na cidade de São Carlos para alunos do ensino fundamental. As atividades foram desenvolvidas na recente inaugurada, Sala Solar. Ela é dedicada ao estudo do Sol, enfatizando a observação de manchas solares e do espectro do Sol. A metodologia adotada no minicurso consistiu em pequenos experimentos, observações e diálogos expositivos. Isto incentivou os estudantes a tomarem decisões, fazerem questionamentos e refletirem gerando pensamentos mais críticos e produzindo um maior número de conexões entre o real e o abstrato que contribuiu para níveis de maior complexidade conceitual verificados durante entrevistas semiestruturadas e nas respostas ao questionário final.

Técnicas de diagnóstico de influência local na análise espacial da produtividade da soja

A modelagem da estrutura de dependência espacial pela abordagem da geoestatística é fundamental para a definição de parâmetros que definem esta estrutura, e que são utilizados na interpolação de valores em locais não amostrados pela técnica de krigagem. Entretanto, a estimação de parâmetros pode ser muito afetada pela presença de observações atípicas nos dados amostrados. O desenvolvimento deste trabalho teve por objetivo utilizar técnicas de diagnóstico de influência local em modelos espaciais lineares gaussianos, utilizados em geoestatística, para avaliar a sensibilidade dos estimadores de máxima verossimilhança e máxima verossimilhança restrita na presença de dados discrepantes. Estudos com dados experimentais mostraram que tanto a presença de valores atípicos como de valores considerados influentes, pela análise de diagnóstico, pode exercer forte influência nos mapas temáticos, alterando, assim, a estrutura de dependência espacial. As aplicações de técnicas de diagnóstico de influência local devem fazer parte de toda análise geoestatística a fim de garantir que as informações contidas nos mapas temáticos tenham maior qualidade e possam ser utilizadas com maior segurança pelo agricultor.

Modelos da Química Quântica no espaço de momento: diferentes representações de um mesmo sistema

The conventional approach to simple quantum chemistry models is contrasted with that known as momentum representation, where the wavefunctions are momentum dependent. Since the physical interactions are the same, state energies should not change, and whence the energy differences correlating with the real world as spectral lines or bands. We emphasize that one representation is not more fundamental than the other, and the choice is a matter of mathematical convenience. As spatial localization is rooted in our brains, to think in terms of the momentum present us a great mental challenge that can lead to complementary perspectives of a model.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Validation of reference genes for gene expression studies in the honey bee, Apis mellifera, by quantitative real-time RT-PCR

For obtaining accurate and reliable gene expression results it is essential that quantitative real-time RT-PCR (qRT-PCR) data are normalized with appropriate reference genes. The current exponential increase in postgenomic studies on the honey bee, Apis mellifera, makes the standardization of qRT-PCR results an important task for ongoing community efforts. For this aim we selected four candidate reference genes (actin, ribosomal protein 49, elongation factor 1-alpha, tbp-association factor) and used three software-based approaches (geNorm, BestKeeper and NormFinder) to evaluate the suitability of these genes as endogenous controls. Their expression was examined during honey bee development, in different tissues, and after juvenile hormone exposure. Furthermore, the importance of choosing an appropriate reference gene was investigated for two developmentally regulated target genes. The results led us to consider all four candidate genes as suitable genes for normalization in A. mellifera. However, each condition evaluated in this study revealed a specific set of genes as the most appropriated ones.

TRAVELLING THROUGH PITCH SPACE SPEEDS UP MUSICAL TIME

SEVERAL MODELS OF TIME ESTIMATION HAVE BEEN developed in psychology; a few have been applied to music. In the present study, we assess the influence of the distances travelled through pitch space on retrospective time estimation. Participants listened to an isochronous chord sequence of 20-s duration. They were unexpectedly asked to reproduce the time interval of the sequence. The harmonic structure of the stimulus was manipulated so that the sequence either remained in the same key (CC) or travelled through a closely related key (CFC) or distant key (CGbC). Estimated times were shortened when the sequence modulated to a very distant key. This finding is discussed in light of Lerdahl's Tonal Pitch Space Theory (2001), Firmino and Bueno's Expected Development Fraction Model (in press), and models of time estimation.

The role of heritage in revalorization politicos of urban space

Certain areas of the city of Sao Paulo, as many others around the world, including in Lisbon, Barcelona and Buenos Aires, have been going through a process of requalification, in special the ones commonly known as old and/or traditional city. Regarding Sao Paulo, some exceptional actions have been taken downtown with investments in rehabilitation/requalification of areas that concentrated the historical, urbanistic and cultural heritages, such as Praca da S and its cathedral, as well as the revaluation/rehabilitation projects of other squares like Praca da Republica, other areas as the previously called Cracolandia (due to high consumption/deal of crack), known today as Nova Luz, besides propositions to reevaluate areas already modified, such as Vale do Anhangabau. In all propositions to modify sites, it is firstly underlined its deterioration, litter and the presence of low-income populations (passer-bys, street vendors or residents), generally stigmatized as ""potential suspects"", emphasizing danger and lack of security in those places. This belief, which has become consensual, results in that: public as well as private companies promote the rehabilitation of the areas basing their reasoning in the necessity of adding value to the existing urban heritage, although, as it will be discussed in this paper, part of this heritage might be destroyed in this very process, under the allegation that upon completion, the action would allow the social, cultural and economical revaluation/requalification of the area. This paper is intended to provide a contribution to this discussion.

Living Our Lives on the Edge: Power, Space and Sexual Orientation in Cape Town Townships, South Africa

Much of social science literature about South African cities fails to represent its complex spectrum of sexual practices and associated identities. The unintended effects of such representations are that a compulsory heterosexuality is naturalised in, and reiterative with, dominant constructions of blackness in townships. In this paper, we argue that the assertion of discreet lesbian and gay identities in black townships of a South African city such as Cape Town is influenced by the historical racial and socio-economic divides that have marked urban landscape. In their efforts to recoup a positive sense of gendered personhood, residents have constructed a moral economy anchored in reproductive heterosexuality. We draw upon ethnographic data to show how sexual minorities live their lives vicariously in spaces they have prised open within the extant sex/gender binary. They are able to assert the identities of moffie and man-vrou (mannish woman) without threatening the dominant ideology of heterosexuality.

Development of Hepatitis C Virus Genotyping by Real-Time PCR Based on the NS5B Region

Background: Hepatitis C virus (HCV) genotyping is the most significant predictor of the response to antiviral therapy. The aim of this study was to develop and evaluate a novel real-time PCR method for HCV genotyping based on the NS5B region. Methodology/Principal Findings: Two triplex reaction sets were designed, one to detect genotypes 1a, 1b and 3a; and another to detect genotypes 2a, 2b, and 2c. This approach had an overall sensitivity of 97.0%, detecting 295 of the 304 tested samples. All samples genotyped by real-time PCR had the same type that was assigned using LiPA version 1 (Line in Probe Assay). Although LiPA v. 1 was not able to subtype 68 of the 295 samples (23.0%) and rendered different subtype results from those assigned by real-time PCR for 12/295 samples (4.0%), NS5B sequencing and real-time PCR results agreed in all 146 tested cases. Analytical sensitivity of the real-time PCR assay was determined by end-point dilution of the 5000 IU/ml member of the OptiQuant HCV RNA panel. The lower limit of detection was estimated to be 125 IU/ml for genotype 3a, 250 IU/ml for genotypes 1b and 2b, and 500 IU/ml for genotype 1a. Conclusions/Significance: The total time required for performing this assay was two hours, compared to four hours required for LiPA v. 1 after PCR-amplification. Furthermore, the estimated reaction cost was nine times lower than that of available commercial methods in Brazil. Thus, we have developed an efficient, feasible, and affordable method for HCV genotype identification.