A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

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.

Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

A stronger Dunford-Pettis property

We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both l(1) and l(infinity) It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c(0) is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights 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.

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.

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.

Transiting exoplanets from the CoRoT space mission XVI. CoRoT-14b: an unusually dense very hot Jupiter

In this paper, the CoRoT Exoplanet Science Team announces its 14th discovery. Herein, we discuss the observations and analyses that allowed us to derive the parameters of this system: a hot Jupiter with a mass of 7.6 +/- 0.6 Jupiter masses orbiting a solar-type star (F9V) with a period of only 1.5 d, less than 5 stellar radii from its parent star. It is unusual for such a massive planet to have such a small orbit: only one other known higher mass exoplanet orbits with a shorter period.

Transiting exoplanets from the CoRoT space mission XVIII. CoRoT-18b: a massive hot Jupiter on a prograde, nearly aligned orbit

We report the detection of CoRoT-18b, a massive hot Jupiter transiting in front of its host star with a period of 1.9000693 +/- 0.0000028 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite combined with spectroscopic and photometric ground-based follow-up observations. The planet has a mass M(p) = 3.47 +/- 0.38 M(Jup), a radius R(p) = 1.31 +/- 0.18 R(Jup), and a density rho(p) = 2.2 +/- 0.8 g cm(-3). It orbits a G9V star with a mass M(*) = 0.95 +/- 0.15 M(circle dot), a radius R(*) = 1.00 +/- 0.13 R(circle dot), and a rotation period P(rot) = 5.4 +/- 0.4 days. The age of the system remains uncertain, with stellar evolution models pointing either to a few tens Ma or several Ga, while gyrochronology and lithium abundance point towards ages of a few hundred Ma. This mismatch potentially points to a problem in our understanding of the evolution of young stars, with possibly significant implications for stellar physics and the interpretation of inferred sizes of exoplanets around young stars. We detected the RossiterMcLaughlin anomaly in the CoRoT-18 system thanks to the spectroscopic observation of a transit. We measured the obliquity psi = 20 degrees +/- 20 degrees +/- (sky-projected value lambda = -10 degrees +/- 20 degrees), indicating that the planet orbits in the same way as the star is rotating and that this prograde orbit is nearly aligned with the stellar equator.

Transiting exoplanets from the CoRoT space mission XV. CoRoT-15b: a brown-dwarf transiting companion

We report the discovery by the CoRoT space mission of a transiting brown dwarf orbiting a F7V star with an orbital period of 3.06 days. CoRoT-15b has a radius of 1.12(-0.15)(+0.30) R(Jup) and a mass of 63.3 +/- 4.1 M(Jup), and is thus the second transiting companion lying in the theoretical mass domain of brown dwarfs. CoRoT-15b is either very young or inflated compared to standard evolution models, a situation similar to that of M-dwarf stars orbiting close to solar-type stars. Spectroscopic constraints and an analysis of the lightcurve imply a spin period in the range 2.9-3.1 days for the central star, which is compatible with a double-synchronisation of the system.