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.

An indecomposable Banach space of continuous functions which has small density

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

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.

Diet and cancer in Northeast Brazil: evaluation of eating habits and food group consumption in relation to breast cancer

Realizou-se um estudo do tipo caso-controle de base hospitalar no Município de João Pessoa, Paraíba, Brasil. Participaram 183 indivíduos (89 casos e 94 controles) na faixa etária entre 30 e 80 anos, com pareamento por idade. O consumo alimentar de casos e controles foi avaliado por alimentos e grupos de alimentos categorizados em tercis de consumo. A estimativa dos valores da odds ratio (OR) e intervalos de confiança de 95% (IC95%) foi realizada por regressão logística múltipla não-condicional. O consumo de frutas e sucos, feijão e leite e derivados apresentou uma forte associação com a redução no risco de câncer de mama. O consumo de carnes vermelhas e de carnes fritas esteve positivamente associado ao risco de câncer de mama (carne vermelha - OR = 4.30; IC95%: 1,74-10,67; p = 0,00). Não foi observada associação entre o consumo dos grupos de vegetais e embutidos com o câncer de mama. Carne vermelha e carnes fritas podem ser fatores de risco, e o consumo de frutas, feijão e leite e derivados pode atuar como protetor do câncer de mama

Multistability and Self-Similarity in the Parameter-Space of a Vibro-Impact System

The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets. Copyright (C) 2009 Silvio L.T. de Souza et al.

Evaluation of serum trace element, biochemical and hematological data of a healthy elderly group residing in So Paulo city, Brazil

In this study, blood serum trace elements, biochemical and hematological parameters were obtained to assess the health status of an elderly population residing in So Paulo city, SP, Brazil. Results obtained showed that more than 93% of the studied individuals presented most of the serum trace element concentrations and of the hematological and biochemical data within the reference values used in clinical laboratories. However, the percentage of elderly presenting recommended low density lipoprotein (LDL) cholesterol concentrations was low (70%). The study indicated positive correlation between the concentrations of Zn and LDL-cholesterol (p < 0.06).

Sexual System, Sex Ratio, and Group Living in the Shrimp Thor amboinensis (De Man): Relevance to Resource-Monopolization and Sex-Allocation Theories

The sexual system of the symbiotic shrimp Thor amboinensis is described, along with observations on sex ratio and host-use pattern of different populations. We used a comprehensive approach to elucidate the previously unknown sexual system of this shrimp. Dissections, scanning electron microscopy, size-frequency distribution analysis, and laboratory observations demonstrated that T amboinensis is a protandric hermaphrodite: shrimp first mature as males and change into females later in life. Thor amboinensis inhabited the large and structurally heterogeneous sea anemone Stichoclactyla helianthus in large groups (up to 11 individuals) more frequently than expected by chance alone. Groups exhibited no particularly complex social structure and showed male-biased sex ratios more frequently than expected by chance alone. The adult sex ratio was male-biased in the four separate populations studied, one of them being thousands of kilometers apart from the others. This study supports predictions central to theories of resource monopolization and sex allocation. Dissections demonstrated that unusually large males were parasitized by an undescribed species of isopod (family Entoniscidae). Infestation rates were similarly low in both sexes (approximate to 11%-12%). The available information suggests that T. amboinensis uses pure search promiscuity as a mating system. This hypothesis needs to be formally tested with mating behavior observations and field measurements on the movement pattern of both sexes of the species. Further detailed studies on the lifestyle and sexual system of all the species within this genus and the development of a molecular phylogeny are necessary to elucidate the evolutionary history of gender expression in the genus Thor.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

Landau analog levels for dipoles in non-commutative space and phase space - Landau analog levels for dipoles

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov-Casher and He-McKellar-Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.

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.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space

In this paper we give a partially affirmative answer to the following question posed by Haizhong Li: is a complete spacelike hypersurface in De Sitter space S(1)(n+1)(c), n >= 3, with constant normalized scalar curvature R satisfying n-2/nc <= R <= c totally umbilical? (C) 2008 Elsevier B.V. All rights reserved.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.