Finding invariant tori in the problem of a periodically corrugated waveguide

Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.

Structural studies of AgPO3-MoO3 glasses using solid state NMR and vibrational spectroscopies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reading, equivalence, and recombination of units: A replication with students with different learning histories

First graders, preschoolers, special education students, and adults received a reading program in which they learned to match printed to dictated words and to construct (copy) printed words. The students not only learned to match the training words but also learned to read them. In addition, most of the students learned to read new words that involved recombinations of the syllables of the training words. The results replicate and extend the generality of a prior analysis of a reading program based on stimulus equivalence and recombination of units.

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Biosynthetic origins of the isoprene units of gaudichaudianic acid in Piper gaudichaudianum (Piperaceae)

The biosynthesis of (2S)-2-methyl-2-(4'-methyl-3-pentenyl)-8-(3-methyl-2-butenyl)-2H-1-benzopyran-6-carboxylic acid (gaudichaudianic acid), the major metabolite in leaves and roots of Piper gaudichaudianum Kunth (Piperaceae), has been investigated employing [1(-13) C]-D-glucose as precursor. The labelling pattern in the isolated gaudichaudianic acid was determined by quantitative 13 C NMR spectroscopy analysis and was consistent with involvement of both mevalonic acid and 2-C-methyl-D-erythritol-4-phosphate pathways in the formation of the dimethylallyl- and geranyl-derived moieties. The results confirmed that both plastidic and cytoplasmic pathways are able to provide isopentenyl diphosphate units for prenylation of p-hydroxybenzoic acid. (c) 2007 Elsevier Ltd. All rights reserved.

Nanostructured films employed as sensing units in an electronic tongue system

Nanostructured films of lignin (macromolecule extracted from sugar cane bagasse), polypyrrole (conducting polymer) and bis butylimido perylene (organic dye) were used in the detection of trace levels of fluorine (from H2SiF6), chlorine (from NaCIO), Pb+2, Cu+2, and Cd+2 in aqueous solutions. Langmuir monolayers on ultrapure water were characterised by surface pressure-mean molecular area (II-A) isotherms. Langmuir-Blodgett (LB) films were transferred onto gold interdigitated electrodes and used as individual sensing units of an electronic tongue system. Impedance spectroscopy measurements were taken with the sensor immersed into aqueous solutions containing the ions described above in different molar concentrations. Fourier transform infrared absorption (FTIR) was employed to identify possible interactions between the LB films and the analytes in solution, and no significant changes could be observed in the FTIR spectra of BuPTCD and Ppy. Therefore, the results for lignin point to an interaction involving the electronic cloud of the phenyl groups with the metallic ions.

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

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.

Relaxation and tunnelling of structural units within the LTO phase of La2CuO4

The anelastic relaxation (elastic energy loss and Young modulus) of nearly stoichiometric La2CuO4+delta with LTO structure was measured. Extraordinarily intense effects are present below room temperature in the elastic dynamic susceptibility, indicating relaxational dynamics of a relevant fraction of the lattice. The involved degrees of freedom are identified as rotations of the CuO6 octahedra. Two distinct processes are found at frequencies around 1 kKz: one is observed around 150 K and is characterized by a mean activation energy of 2800 K; the second one occurs below 30 K and is governed by atomic tunnelling. Two explanations are proposed for the faster process: i) formation of fluctuating LTT domains on a scale of few atomic cells; ii) the LTO phase is a dynamical Jahn-Teller phase with all the octahedra tunneling between two LTT-like tilts. In both cases there would be important implications regarding the mechanisms giving rise to charge nanophase separation and strong electron-phonon coupling.

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.