Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Cephalometric and three-dimensional assessment of superior posterior airway space after maxillomandibular advancement

The purpose of this study was to quantify cephalometric and three-dimensional alterations of the posterior airway space of patients who underwent maxillomandibular advancement surgery. 20 patients treated by maxillomandibular advancement were selected. The minimal postoperative period was 6 months. The treated patients underwent cone-beam computed tomography at 3 distinct time intervals, preoperative (T1), immediate postoperative period up to 15 days after surgery (T2), and late postoperative period at least 6 months after surgery. The results showed that the maxillomandibular advancement promoted an increase in the posterior airway space in each patient in all the analyses performed, with a statistically significant difference between T2 and T1, and between T3 and T1, p < 0.05. There was a statistical difference between T2 and T3 in the analysis of area and volume, which means that the airway space became narrower after 6 months compared with the immediate postoperative period. The maxillomandibular advancement procedure allowed great linear area and volume increase in posterior airway space in the immediate and late postoperative periods, but there was partial loss of the increased space after 6 months. The linear analysis of airway space has limited results when compared with analysis of area and volume.

Effect of application time of APF and NaF gels on microhardness and fluoride uptake of in vitro enamel caries

Purpose : To evaluate the effect of time of fluoride application gel, acidulated or neutral, on in vitro enamel resistance to demineralization and fluoride uptake. Materials and Methods: One hundred and ninety-two human enamel blocks were used in this study and 144 were treated with fluoride gel, acidulated or neutral, for I or 4 minutes. Ninety-six blocks treated with fluoride and 24 control blocks were submitted to a high cariogenic challenge. After the pH-cycling, enamel demineralization was assessed by surface and cross-sectional microhardness. Fluoride in the enamel blocks was also determined after removing an enamel layer by etching acid. Results: Acidulated fluoride gel formed more fluoride in enamel than neutral gel (P < 0.05), and it was also more efficient in reducing the demineralization of the enamel blocks submitted to a cariogenic challenge than the neutral one (P < 0.05). It was found that the time of application was significant in terms of fluoride uptake, but it did not render the enamel more resistant to dernineralization.

Periapical radiographs overestimate root canal wall thickness during post space preparation

Aim To evaluate differences between anatomic and radiographic measurements of root canal wall thickness (RCWT) after each root canal preparation stage during post placement.Methodology Twenty mandibular premolars with a single canal were decoronated and the roots embedded in resin using a teflon muffle. Roots were sectioned horizontally at a pre-established level and canals were prepared for post placement. Endodontic hand files were used for root canal preparation, followed by Gates Glidden drills and Peeso reamers. Standardized radiographs and photographs at pre-established measurement levels were taken before preparation, after root canal instrumentation, after Gates Glidden preparation and after Peeso enlargement. All images were digitized and RCWT at the mesial and distal walls measured (IMAGETOOL 3.0). Differences between radiographic and anatomic measurements were analysed with paired t-tests. ANOVA was used to compare the percentages of radiographic distortions.Results Regardless of the time-point evaluated, RCWT determined by radiographs were greater than the respective anatomic measurements (P < 0.05). The difference detected at each stage was similar and constant (P > 0.05).Conclusions Throughout preparation for post placement, radiographic images overestimated the RCWT by approximately 25%, regardless of the clinical stage evaluated.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

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

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

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

Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions

Some dynamical properties of a classical particle confined inside a closed region with an oval-shaped boundary are studied. We have considered both the static and time-dependent boundaries. For the static case, the condition that destroys the invariant spanning curves in the phase space was obtained. For the time-dependent perturbation, two situations were considered: (i) non-dissipative and (ii) dissipative. For the non-dissipative case, our results show that Fermi acceleration is observed. When dissipation, via inelastic collisions, is introduced Fermi acceleration is suppressed. The behaviour of the average velocity for both the dissipative as well as the non-dissipative dynamics is described using the scaling approach. (C) 2009 Elsevier B.V. All rights reserved.

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.