Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

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

DNA Psi-condensation and reentrant decondensation: Effect of the PEG degree of polymerization

psi-Condensation of DNA fragments of about 4 kbp was induced by poly(ethylene glycol) (PEG), with degrees of polymerization ranging from 45 to 182, and univalent salt (NaCl). Using circular dichroism spectroscopy, we were able to accurately determine the critical amount of PEG needed to induce condensation, as a function of the NaCl concentration. A significant dependence on the PEG degree of polymerization was found. Phase boundaries determined for the multimolecular condensation were very similar to those observed previously for the monomolecular collapse, with two asymptotic regimes at low and high salt concentrations. We analyze our data using a theoretical model that properly takes into account both the polyelectrolyte nature of the DNA and the liquid crystallinity of the condensed phase. The model assumes that all PEG is excluded from the condensates and shows reentrant decondensation only at low salt. We also systematically study reentrant decondensation and find a very strong dependence on PEG molecular weight. At low PEG molecular weight, decondensation occurs at relatively low concentrations of PEG, and over a wide range of salt concentrations. This suggests that in the reentrant decondensation the flexible polymers used are not completely excluded from the condensed phase.

Solutions of the Fokker-Planck equation for a Morse isospectral potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A General Solution of the Fokker-Planck Equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Particular solution for anomalous diffusion equation with source term

In literature the phenomenon of diffusion has been widely studied, however for nonextensive systems which are governed by a nonlinear stochastic dynamic, there are a few soluble models. The purpose of this study is to present the solution of the nonlinear Fokker-Planck equation for a model of potential with barrier considering a term of absorption. Systems of this nature can be observed in various chemical or biological processes and their solution enriches the studies of existing nonextensive systems.

Discussion on the limit cycles of the Lev Ginzburg equation by M. Bellamy and R.E. Mickens, Journal of Sound and Vibration 308 (2007) 337-342

The authors M. Bellamy and R.E. Mickens in the article "Hopf bifurcation analysis of the Lev Ginzburg equation" published in Journal of Sound and Vibration 308 (2007) 337-342, claimed that this differential equation in the plane can exhibit a limit cycle. Here we prove that the Lev Ginzburg differential equation has no limit cycles. (C) 2012 Elsevier Ltd. All rights reserved.

ON THE MINIMUM ABSOLUTE VALUE of THE DISCRIMINANT of ABELIAN FIELDS of DEGREE p(2)

Let p be a prime number. A formula for the minimum absolute value of the discriminant of all Abelian extensions of Q of degree p(2) is given in terms of p.

Global dynamics of stationary solutions of the extended Fisher-Kolmogorov equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

pK determination. A mean field, Poisson-Boltzmann approach

A model describing dissociation of monoprotonic acid and a method for the determination of its pK value are presented. The model is based on a mean field approximation. The Poisson-Boltzmann equation, adopting spherical symmetry, is numerically solved, and the solution of its linearized form is written. By use of the pH values of a dilution experiment of galacturonic acid as the entry data, the proposed method allowed estimation of the value of pK = 3.25 at a temperature of 25 degrees C. Values for the complex dimensions and dissociation degree are calculated using experimental pH values for solution concentration values ranging from 0.1 to 60 mM. The present analysis leads to the conclusion that the Poisson-Boltzmann equation or its linear form is equally suited for the description of such systems.

Conversion Degree of Indirect Resin Composites and Effect of Thermocycling on Their Physical Properties

Purpose: This study evaluated the degree of conversion (DC) of four indirect resin composites (IRCs) with various compositions processed in different polymerization units and investigated the effect of thermal aging on the flexural strength and Vicker's microhardness.Materials and Methods: Specimens were prepared from four IRC materials, namely Gr 1: Resilab (Wilcos); Gr2: Sinfony (3M ESPE); Gr3: VITA VMLC (VITA Zahnfabrik); Gr4: VITA Zeta (VITA Zahnfabrik) using special molds for flexural strength test (N = 80, n = 10 per group) (25 x 2 x 2 mm(3), ISO 4049), for Vicker's microhardness test (N = 80, n = 10 per group) (5 x 4 mm(2)) and for DC (N = 10) using FT-Raman Spectroscopy. For both flexural strength and microhardness tests, half of the specimens were randomly stored in distilled water at 37 degrees C for 24 hours (Groups 1 to 4), and the other half (Groups 5 to 8) were subjected to thermocycling (5000 cycles, 5 to 55 +/- 1 degrees C, dwell time: 30 seconds). Flexural strength was measured in a universal testing machine (crosshead speed: 0.8 mm/min). Microhardness test was performed at 50 g. The data were analyzed using one-way and two-way ANOVA and Tukey's test (alpha = 0.05). The correlation between flexural strength and microhardness was evaluated with Pearson's correlation test (alpha = 0.05).Results: A significant effect for the type of IRC and thermocycling was found (p = 0.001, p = 0.001) on the flexural strength results, but thermocycling did not significantly affect the microhardness results (p = 0.078). The interaction factors were significant for both flexural strength and microhardness parameters (p = 0.001 and 0.002, respectively). Thermocycling decreased the flexural strength of the three IRCs tested significantly (p < 0.05), except for VITA Zeta (106.3 +/- 9.1 to 97.2 +/- 14 MPa) (p > 0.05) when compared with nonthermocycled groups. Microhardness results of only Sinfony were significantly affected by thermocycling (25.1 +/- 2.1 to 31 +/- 3.3 Kg/mm(2)). DC values ranged between 63% and 81%, and were not significantly different between the IRCs (p > 0.05). While a positive correlation was found between flexural strength and microhardness without (r = 0.309) and with thermocycling (r = 0.100) for VITA VMLC, negative correlations were found for Resilab under the same conditions (r = -0.190 and -0.305, respectively) (Pearson's correlation coefficient).Conclusion: Although all four IRCs presented nonsignificant DC values, flexural strength and microhardness values varied between materials with and without thermocycling.

The adhesive system and root canal region do not influence the degree of conversion of dual resin cement

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

Bond strengths, degree of conversion of the cement and molecular structure of the adhesive-dentine joint in fibre post restorations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vortices in nonlocal Gross-Pitaevskii equation

We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to the polar angle, the unstable modes of the axial n-fold vortex have orbital numbers l satisfying 0 < \l\ < 2\n\, as in the local model. Numerical simulations show that nonlocality slightly decreases the threshold rotation frequency above which the nonvortex state ceases to be the global energy minimum and decreases the frequency of the anomalous mode of the 1-vortex. In the case of higher axial vortices, nonlocality leads to instability against splitting with the creation of antivortices and gives rise to additional anomalous modes with higher orbital numbers. Despite new instability channels with the creation of antivortices, for a stationary solution comprised of vortices and antivortices there always exists another vortex solution, composed solely of vortices, with the same total vorticity but with a lower energy.

Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation

A new version of the relaxation algorithm is proposed in order to obtain the stationary ground-state solutions of nonlinear Schrodinger-type equations, including the hyperbolic solutions. In a first example, the method is applied to the three-dimensional Gross-Pitaevskii equation, describing a condensed atomic system with attractive two-body interaction in a non-symmetrical trap, to obtain results for the unstable branch. Next, the approach is also shown to be very reliable and easy to be implemented in a non-symmetrical case that we have bifurcation, with nonlinear cubic and quintic terms. (c) 2006 Elsevier B.V. All rights reserved.