Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Growth kinetics of CdS in germanium oxide glassy matrix

In the present work we revisit the size data of CdS microcrystals previously collected in the glassy matrix of Germanium oxide. The CdS clusters analyzed using electron microscopy images have shown a wurtzite structure. The mean average radius, dispersion and volume evaluated from the histograms showed good agreement for t(1/3), t(2/3) and t laws, respectively. We observed that the amount of microcrystals remains constant throughout the heat treatment process, as well as that the radii distribution has a lower limit and increases with heat treatment. The distribution of radii follows a distribution similar to the Lifshitz-Slyozov-Wagner distribution limited in the origin. Discussions led to the conclusion that the growth of CdS is a process that occurs after the fluctuating nucleation and coalescence phases. We then analyze the growth process, assuming that the evaporation is overcome by the precipitation rate, stabilizing all clusters with respect to dissolution back into the matrix. The problem was simplified neglecting anisotropy and the assuming a spherical shape for clusters and particles. The low interface tension was described in terms of an empirical potential barrier in the surface of the cluster. The growth dynamics developed considering that the number of clusters remains constant, and that the minimum size of these clusters grow with time, as the first order approximation showed a good agreement with the flaw. (C) 2012 Elsevier B.V. All rights reserved.

Impact of Protease Inhibitors on Dentin Matrix Degradation by Collagenase

This proof-of-concept study assessed whether the reduction of the degradation of the demineralized organic matrix (DOM) by pre-treatment with protease inhibitors (PI) is effective against dentin matrix loss. Bovine dentin slices were demineralized with 0.87 M citric acid, pH 2.3, for 36 hrs. In sequence, specimens were treated or not (UT, untreated) for 1 min with gels containing epigallocatechin 3-gallate (EGCG, 400 A mu M), chlorhexidine (CHX, 0.012%), FeSO4 (1 mM), NaF (1.23%), or no active compound (P, placebo). Specimens were then stored in artificial saliva (5 days, 37 degrees C) with the addition of collagenase (Clostridium histolyticum, 100 U/mL). We analyzed collagen degradation by assaying hydroxyproline (HYP) in the incubation solutions (n = 5) and evaluated the dentin matrix loss by profilometry (n = 12). Data were analyzed by ANOVA and Tukey's test (p < 0.05). Treatment with gels containing EGCG, CHX, or FeSO4 led to significantly lower HYP concentrations in solution and dentin matrix loss when compared with the other treatments. These results strongly suggest that the preventive effects of the PI tested against dentin erosion are due to their ability to reduce the degradation of the DOM.

Surface modification by metal ion implantation forming metallic nanoparticles in insulating matrix.

There is special interest in the incorporation of metallic nanoparticles in a surrounding dielectric matrix for obtaining composites with desirable characteristics such as for surface plasmon resonance, which can be used in photonics and sensing, and controlled surface electrical conductivity. We investigated nanocomposites produced through metallic ion implantation in insulating substrate, where the implanted metal self-assembles into nanoparticles. During the implantation, the excess of metal atom concentration above the solubility limit leads to nucleation and growth of metal nanoparticles, driven by the temperature and temperature gradients within the implanted sample including the beam-induced thermal characteristics. The nanoparticles nucleate near the maximum of the implantation depth profile (projected range), that can be estimated by computer simulation using the TRIDYN. This is a Monte Carlo simulation program based on the TRIM (Transport and Range of Ions in Matter) code that takes into account compositional changes in the substrate due to two factors: previously implanted dopant atoms, and sputtering of the substrate surface. Our study suggests that the nanoparticles form a bidimentional array buried few nanometers below the substrate surface. More specifically we have studied Au/PMMA (polymethylmethacrylate), Pt/PMMA, Ti/alumina and Au/alumina systems. Transmission electron microscopy of the implanted samples showed the metallic nanoparticles formed in the insulating matrix. The nanocomposites were characterized by measuring the resistivity of the composite layer as function of the dose implanted. These experimental results were compared with a model based on percolation theory, in which electron transport through the composite is explained by conduction through a random resistor network formed by the metallic nanoparticles. Excellent agreement was found between the experimental results and the predictions of the theory. It was possible to conclude, in all cases, that the conductivity process is due only to percolation (when the conducting elements are in geometric contact) and that the contribution from tunneling conduction is negligible.