Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

On the semi-Riemannian bumpy metric theorem

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the C(k)-topology, k=2, ..., infinity, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

A BROADER CONTEXT FOR MONOTONICALLY MONOLITHIC SPACES

This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically kappa-monolithic space for any infinite cardinal kappa and present the relevant results. We show, among other things, that any sigma-product of monotonically kappa-monolithic spaces is monotonically kappa-monolithic for any infinite cardinal kappa; besides, it is consistent that any strongly monotonically omega-monolithic space with caliber omega(1) is second countable. We also study (strong) monotone kappa-monolithicity in linearly ordered spaces and subspaces of ordinals.

Effect of cement type and water storage time on the push-out bond strength of a glass fiber post

This study investigated the effects of the cement type and the water storage time on the push-out bond strength of a glass fiber post. Glass fiber posts (Fibrekor, Jeneric Pentron) were luted to post spaces using a self-cured resin cement (C&B Cement [CB]), a glass ionomer cement (Ketac Cem [KC]) or a resin-modified glass ionomer cement (GC FujiCEM [FC]) according to the manufacturers’ instructions. For each luting agent, the specimens were exposed to one of the following water storage times (n=5): 1 day (T1), 7 days (T7), 90 days (T90) and 180 days (T180). Push-out tests were performed after the storage times. Control specimens were not exposed to water storage, but subjected to the push-out test 10 min after post cementation. Data (in MPa) were analyzed by Kruskal-Wallis and Dunn`s test (α=0.05). Cement type and water storage time had a significant effect (p<0.05) on the push-out bond strength. CB showed significantly higher values of retention (p<0.05) than KC and FC, irrespective of the water storage time. Water storage increased significantly the push-out bond strength in T7 and T90, regardless of the cement type (p<0.05). The results showed that fiber posts luted to post spaces with the self-cured resin cement exhibited the best bonding performance throughout the 180-day water storage period. All cements exhibited a tendency to increase the bond strength after 7 and 90 days of water storage, decreasing thereafter.

Acessibilidade em ambiente universitário: identificação de barreiras arquitetônicas no campus da USP de Bauru

A acessibilidade é um direito do cidadão assegurado por lei para que portadores de deficiência tenham a possibilidade de usufruir de recursos e ações no âmbito social. Barreiras arquitetônicas interferem na vida destes podendo deixá-los a parte da convivência e vida social. Os objetivos deste estudo foram: identificar, descrever e mapear barreiras físicas no Campus da Universidade de São Paulo de Bauru e apresentar as intervenções realizadas, durante o período de outubro de 2001 a dezembro de 2005. O estudo foi descritivo-quantitativo, no qual a coleta de dados centrou-se na análise das condições arquitetônicas das três unidades que compõe este campus, observada as normativas da Associação Brasileira de Normas técnicas e realizada intervenções. Foram identificados: 72 pontos de guias não rebaixadas, 21 pontos de acessos com diferenças de níveis sem rampas; 220m² de escadas/rampas sem corrimãos; 658m² de escadas/rampas com corrimãos em discordância com as normas vigentes; 03 rampas com inclinações superiores às determinadas nas normas técnicas; 10 banheiros parcialmente adaptados para deficientes; 02 vagas de estacionamento parcialmente adaptadas e 02 elevadores existentes. Foram executados, em 19 pontos, rebaixamentos de guias, somando 115 m², com linhas de piso tátil, pintados; 8 rampas; 14 pontos de escadas e rampas externas instaladas com corrimãos e guarda-corpos, 5 vagas exclusivas no estacionamento; instalado 2 centrais de atendimento telefônico para surdo e adquiridas 3 cadeira de rodas. As intervenções realizadas contribuíram para melhorar a acessibilidade de portadores de deficiência no campus favorecendo a utilização dos recursos existentes neste espaço público.

Variabilidade amostral das séries mensais de precipitação pluvial em duas regiões do Brasil: Pelotas-RS e Campinas-SP

O presente trabalho avaliou a variabilidade amostral dos parâmetros da distribuição gama, relativos a séries mensais de precipitação pluvial, nas regiões de Campinas-SP e Pelotas-RS, que têm dados para os períodos de 1890-2006 e 1890-2005, respectivamente. Assim, os espaços amostrais considerados foram de 58, 39 e 29 anos para Campinas e 58 e 29 anos para Pelotas. As análises foram feitas usando o teste da razão da máxima verossimilhança. Os resultados apontaram significativas alterações amostrais. Não houve indicações de tendências contínuas (redução ou aumento) no regime mensal de precipitação pluvial na região de Campinas-SP. Em contrapartida, esse teste indicou, para a localidade de Pelotas-RS, tendência de elevação no regime desse elemento meteorológico ocorrida entre as amostras relativas aos anos de 1948 a 1976 e 1977 a 2005.

A comparison of the leaf-litter ant fauna in a secondary atlantic forest with an adjacent pine plantation in southeastern Brazil

We investigated the influence of Pinus afforestation on the structure of leaf-litter ant communities in the southeastern Brazilian Atlantic Forest, studying an old secondary forest and a nearly 30 year-old never managed Pinus elliottii reforested area. A total of 12,826 individual ants distributed among 95 species and 32 genera were obtained from 50 1 m² samples/ habitat. Of these, 60 species were recorded in the pine plantation and 82 in the area of Atlantic forest; almost 50% of the species found in the secondary forest area were also present in the pine plantation. The number of species per sample was significantly higher in the secondary forest than in the pine plantation. Forest-adapted taxa are the most responsible for ant species richness differences between areas, and the pine plantation is richer in species classified as soil or litter omnivorous-dominants. The specialized ant predators registered in the pine plantation, as seven Dacetini, two Basiceros, two Attini and two Discothyrea, belong to widely distributed species. The NMDS (non-metric multidimensional scaling) ordination also suggested strong differences in similarity among samples of the two areas. Furthermore, this analysis indicated higher sample heterogeneity in the secondary forest, with two clusters of species, while in the pine plantation the species belong to a single cluster. We applied the ant mosaic hypothesis to explain the distribution of the leaf-litter fauna and spatial autocorrelation tests among samples. We argue that the results are likely related to differences in quality and distribution of the leaf-litter between the pine plantation and the secondary area.

Ant community richness and composition across a gradient from Eucalyptus plantations to secondary Atlantic Forest

Secondary forests and exotic tree plantations are expanding across tropical landscapes. However, our current understanding of the value of these human-dominated forest landscapes for invertebrate biodiversity conservation is still very poor. In this paper, we use the leaf-litter ant fauna to assess invertebrate diversity in one commercially managed Eucalyptus plantation (four years old), two abandoned plantations of different regeneration ages (16 and 31 years), and one neighboring secondary Atlantic Forest in Southeastern Brazil. There was a clear gradient in species richness from the secondary forest to the managed Eucalyptus plantation; richness and diversity peaked in secondary forest and in the older regenerating Eucalyptus plantation. Significantly more species were recorded in secondary forest samples than in Eucalyptus plantations, but Eucalyptus plantations had a similar level of richness. Furthermore, a non-metric multidimensional scaling analysis revealed clear differences in species composition between the younger managed Eucalyptus plantation (understory absent) and habitats with sub-developed or developed understory. Eucalyptus plantations were characterized by an assemblage of widespread, generalist species very different from those known to occur in core forest habitats of southeastern Brazil. Our results indicate that while older regenerating Eucalyptus plantations can provide habitat to facilitate the persistence of generalist ant species, it is unlikely to conserve most of the primary forest species, such as specialized predators, Dacetini predators, and nomadic species.

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

Estudo fotoelástico do controle vertical com o arco de dupla chave na técnica Straight wire

INTRODUÇÃO: em alguns casos, a extração de pré-molares torna-se necessária e nem sempre os espaços são completamente fechados após o alinhamento e nivelamento. O arco de dupla chave, ou Double Key Loop (DKL), é um arco retangular de aço para retração, com duas alças - uma mesial e outra distal ao canino. OBJETIVOS: este trabalho propôs-se a estudar o local onde a força é exercida, após a ativação desse arco, utilizando ativação na alça distal, ativação entre as alças e na alça distal, e ativação com Gurin®. MÉTODOS: foram montados nove modelos fotoelásticos de um arco dentário inferior, sem os primeiros pré-molares e os terceiros molares, com braquetes In-Ovation e arco DKL. O arco foi ativado e a região de incisivos, caninos e dentes posteriores foi fotografada, com interposição de filtros polarizadores de luz. RESULTADOS E CONCLUSÕES: após a análise do modelo fotoelástico, concluiu-se que a ativação com Gurin® pode produzir movimento de retração anterior com componente extrusivo; a ativação na alça distal pode produzir movimento de retração anterior sem componente extrusivo; e a ativação entre as alças e na alça distal pode produzir movimento de retração anterior com componente intrusivo.

Biogeochemical processes and the diversity of Nhecolândia lakes, Brazil

The Pantanal of Nhecolândia, the world's largest and most diversified field of tropical lakes, comprises approximately 10,000 lakes, which cover an area of 24,000 km² and vary greatly in salinity, pH, alkalinity, colour, physiography and biological activity. The hyposaline lakes have variable pHs, low alkalinity, macrophytes and low phytoplankton densities. The saline lakes have pHs above 9 or 10, high alkalinity, a high density of phytoplankton and sand beaches. The cause of the diversity of these lakes has been an open question, which we have addressed in our research. Here we propose a hybrid process, both geochemical and biological, as the main cause, including (1) a climate with an important water deficit and poverty in Ca2+ in both superficial and phreatic waters; and (2) an elevation of pH during cyanobacteria blooms. These two aspects destabilise the general tendency of Earth's surface waters towards a neutral pH. This imbalance results in an increase in the pH and dissolution of previously precipitated amorphous silica and quartzose sand. During extreme droughts, amorphous silica precipitates in the inter-granular spaces of the lake bottom sediment, increasing the isolation of the lake from the phreatic level. This paper discusses this biogeochemical problem in the light of physicochemical, chemical, altimetric and phytoplankton data.