The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

A Boolean algebra and a Banach space obtained by push-out iteration

Under the assumption that c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(omega)/fin has under CH and in the N(2)-Cohen model. We prove a similar result in the category of Banach spaces. (C) 2011 Elsevier B.V. All rights reserved.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Countability and star covering properties

Whenever P is a topological property, we say that a topological space is star P if whenever U is an open cover of X, there is a subspace A subset of X with property P such that X = St(A, U). We study the relationships of star P properties for P is an element of {Lindelof, sigma-compact, countable} with other Lindelof type properties. (C) 2010 Elsevier B.V. All rights reserved.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

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.

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 FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

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.

A inclusão da criança com Síndrome de Down na rede regular de ensino: desafios e possibilidades

O estudo teve como objetivo buscar evidências na literatura acerca da inclusão de crianças com Síndrome de Down na rede regular de ensino. Elaboraram-se revisão da literatura e busca dos artigos nas bases de dados PubMed e PsycINFO, utilizando as palavras-chave Down syndrome, schools, mainstreaming (education), education, infant, newborn, adolescent, child e preschool, no período de 1994 a 2007. Selecionaram-se oito artigos e sua análise permitiu a identificação do tema: experiências e recomendações para a inclusão. Os dados desta revisão, em sua maioria provenientes de relatos de experiências, indicaram que os fatores que colaboraram ou dificultaram o processo de inclusão da criança com síndrome de Down na rede regular de ensino relacionaram-se à escola, aos pais e ao professor. Os resultados deste estudo oferecem possibilidades para melhorar o processo de inclusão, apresentam os desafios e ainda apontam a necessidade do desenvolvimento de novas pesquisas, cujos resultados possam ser aplicados na prática.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

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.

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.