A RELATIVE COHOMOLOGICAL INVARIANT FOR GROUP PAIRS

We define a cohomological invariant E(G, S, M) where G is a group, S is a non empty family of (not necessarily distinct) subgroups of infinite index in G and M is a F2G-module (F2 is the field of two elements). In this paper we are interested in the special case where the family of subgroups consists of just one subgroup, and M is the F2G-module F2(G/S). The invariant E(G, {S}, F2(G/S)) will be denoted by E(G, S). We study the relations of this invariant with other ends e(G) , e(G, S) and e(G, S), and some results are obtained in the case where G and S have certain properties of duality.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Barrier penetration for supersymmetric shape-invariant potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wavefunctions obtained via the introduction of new generalized ladder operators. The general form of the wavefunction is obtained by the use of the F(-infinity, +infinity)-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wavefunction coefficients.

Supersymmetric and shape-invariant generalization for nonresonant and intensity-dependent Jaynes-Cummings systems

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the coupled-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent Jaynes-Cummings Hamiltonians, widely used in quantized theories of lasers. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.

Critical exponents for a transition from integrability to non-integrability via localization of invariant tori in the Hamiltonian system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coordination of Eu3+ ions in siliceous nanohybrids containing short polyether chains and bridging urea cross-links

Infrared and photoluminescence spectroscopies have been used to investigate the local environment of the Eu3+ ions in luminescent sol-gel derived materials-di-ureasils-based on a hybrid framework represented by U(600). This host is composed of a siliceous backbone grafted, through urea cross-links, to both ends of polymer segments incorporating 8.5 oxyethylene repeat units. The active centers have been introduced as europium perchlorate, Eu(ClO4)3. Samples with compositions n = 232, 62, 23, 12, and 6 (where n denotes the ratio of (OCH2CH2) moieties per lanthanide ion) have been examined. The combination of the information retrieved from the analysis of characteristic bands of the FTIR spectra-the perchlorate and the Amide I/Amide II features-with that obtained from the photoluminescence data demonstrates that at compositions n = 232 and 62 the anions are free, whereas the Eu3+ ions are complexed by the heteroatoms of the polyether chains. At higher salt concentration, the cations are bonded, not only to the ClO4 - ions, but also to the ether oxygen atoms of the organic segments and to the carbonyl oxygen atoms of the urea linkages. The dual behavior of U(600) with respect to cation coordination has been attributed to the presence in this nanohybrid of strong hydrogen-bonded urea-urea structures, which, at low salt content, cannot be disrupted, thus inhibiting the formation of Eu3+-O=C(urea) contacts and promoting the interaction between the lanthanide ions and the (OCH2CH2) moieties. The present work substantiates the claim that the activation of the coordinating sites of the di-ureasil framework can be tuned by varying either the guest salt concentration at constant chain length or the length of the.organic segments at constant salt concentration. This relevant property opens challenging new prospects in the fields of application of this class of hybrids. © 2001 American Chemical Society.

Generalized ladder operators for shape-invariant potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

North-western Africa-North-eastern Brazil. Major tectonic links and correlation problems

The establishment of a geological correlation between northwest Africa and northeast Brazil faces a series of problems of both a virtual and a real nature. Several aspects are summarised in this work that include pre-Mesozoic and Mesozoic features on both continental sides. © 2002 Elsevier Science Ltd. All rights reserved.

Comment on 'Relativistic extension of shape-invariant potentials'

This comment criticizes the recently published approach of Alhaidari for solving relativistic problems. It is shown that his gauge considerations are inaccurate and that the class of exactly solvable relativistic problems is not as large as the author claims.

Behavior of the PMD coefficient of optical links under influence of mechanical and thermal effects

This papers presents results on the variation of the PMD coefficient of optical links under influence of mechanical tests, such as tensile strength, bending and compression, and also during the application of a thermal cycle. Results revealed that the link coefficient is more influenced by the application of a tension load and also suffers significant variation under strong temperature changes. Copyrigth © SBMO.

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the regularization via relocalization scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples. © 2006 The American Physical Society.

Overcoming Latin America's growth frustrations: the macro and mesoeconomic links

Includes bibliography

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

Weak links between exports and economic growth in Latin America and the Caribbean

Includes bibliography

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. All rights reserved.