A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Projections Onto Convex Sets through Particle Swarm Optimization and its application for remote sensing image restoration

Image restoration attempts to enhance images corrupted by noise and blurring effects. Iterative approaches can better control the restoration algorithm in order to find a compromise of restoring high details in smoothed regions without increasing the noise. Techniques based on Projections Onto Convex Sets (POCS) have been extensively used in the context of image restoration by projecting the solution onto hyperspaces until some convergence criteria be reached. It is expected that an enhanced image can be obtained at the final of an unknown number of projections. The number of convex sets and its combinations allow designing several image restoration algorithms based on POCS. Here, we address two convex sets: Row-Action Projections (RAP) and Limited Amplitude (LA). Although RAP and LA have already been used in image restoration domain, the former has a relaxation parameter (A) that strongly depends on the characteristics of the image that will be restored, i.e., wrong values of A can lead to poorly restoration results. In this paper, we proposed a hybrid Particle Swarm Optimization (PS0)-POCS image restoration algorithm, in which the A value is obtained by PSO to be further used to restore images by POCS approach. Results showed that the proposed PSO-based restoration algorithm outperformed the widely used Wiener and Richardson-Lucy image restoration algorithms. (C) 2010 Elsevier B.V. All rights reserved.

Prolapse-free relativistic Gaussian basis sets for the superheavy elements up to Uuo (Z=118) and Lr (Z=103)

Prolapse-free basis sets suitable for four-component relativistic quantum chemical calculations are presented for the superheavy elements UP to (118)Uuo ((104)Rf, (105)Db, (106)Sg, (107)Bh, (108)Hs, (109)Mt, (110)Ds, (111)Rg, (112)Uub, (113)Uut, (114)Uuq, (115)Uup, (116)Uuh, (117)Uus, (118)Uuo) and Lr-103. These basis sets were optimized by minimizing the absolute values of the energy difference between the Dirac-Fock-Roothaan total energy and the corresponding numerical value at a milli-Hartree order of magnitude, resulting in a good balance between cost and accuracy. Parameters for generating exponents and new numerical data for some superheavy elements are also presented. (c) 2007 Elsevier B.V. All rights reserved.

A neural system to robust Nonlinear optimization subject to disjoint and constrained sets

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel method using artificial neural networks to solve robust parameter estimation problems for nonlinear models with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Tests of one Brazilian facial reconstruction method using three soft tissue depth sets and familiar assessors

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the spectrum of stochastic perturbations of the shift and Julia sets

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Boundary of the rauzy fractal sets in R x C generated by P(x)=x(4)-x(3)-x(2)-x-1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GCHF basis sets and their application in the electronic structure study of PrMnO3

The approach called generator coordinate Hartree-Fock (GCHF) method is used in the selection of Gaussian basis set [25s18p for O ((3)p), 31s21p14d for Mn (S-6), and 33s22p16d9f for Pr ((4)J)] for atoms. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. These basis sets are contracted to (25s18p/9s5p), (31s21p14d/9s6p4d), and (33s22pl6d9f118sl2p5d3f) by segmented contraction scheme of Dunning and they are utilized in calculations of Restricted-Open-HF (ROHF) Total and Orbital energies of the (MnO+1)-Mn-3 and (PrO+1)-Pr-1 fragments, to evaluate their quality in molecular studies. The addition of one d polarization function in the contracted (9s5p) basis set for O(P-3) atom and their application with the contracted (9s6p4d), (18s21p5d3f) basis sets for Mn (S-6) and Pr-Pr ((4)j) atoms lead to the electronic structure study of PrMnO3. The dipole moment, the total energy, and total atomic charges properties were calculated and were carried out at ROHF level with the [PrMnO3](2) fragment. The calculated values show that PrMnO3 does not present piezoelectric properties. (C) 2004 Elsevier B.V. All rights reserved.

Gaussian basis sets to the theoretical study of the electronic structure of perovskite (LaMnO3)

The Generator Coordinate Hartree-Fock (GCHF) method is applied to generate extended (20s14p), (30s19p13d), and (31s23p18d) Gaussian basis sets for the 0, Mn, and La atoms, respectively. The role of the weight functions (WFs) in the assessment of the numerical integration range of the GCHF equations is shown. These basis sets are then contracted to [5s3p] and [11s6p6d] for 0 and Mn atoms, respectively, and [17s11p7d] for La atom by a standard procedure. For quality evaluation of contracted basis sets in molecular calculations, we have accomplished calculations of total and orbital energies in the Hartree-Fock-Roothaan (HFR) method for (MnO1+)-Mn-5 and (LaO1+)-La-1 fragments. The results obtained with the contracted basis sets are compared with values obtained with the extended basis sets. The addition of one d polarization function in the contracted basis set for 0 atom and its utilization with the contracted basis sets for Mn and La atoms leads to the calculations of dipole moment and total atomic charges of perovskite (LaMnO3). The calculations were performed at the HFR level with the crystal [LaMnO3](2) fragment in space group C-2v the values of dipole moment, total energy, and total atomic charges showed that it is reasonable to believe that LaMnO3 presents behaviour of piezoelectric material. (C) 2003 Elsevier B.V. All rights reserved.