The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Surface morphology and optical characterization of OC1 OC6-PPV films

We report optical and morphological properties of poly(2-methoxy-5-hexyloxy-p-phenylenevinylene) (OC1OC6-PPV) films processed by casting, spin-coating (SC) and Langmuir-Blodgett (LB) techniques. The absorption spectra are practically the same, with an absorption maximum at approximately at 500 nm. For the photoluminescence (PL) spectra at low temperature (T=10K), a small but significant difference was noted in the cast film, in comparison with the LB and SC films. The zero-phonon transition shifted from 609 nm for the LB film to 615 and 621 nm for the SC and cast films, respectively. At room temperature, the PL spectra are similar for all films, and blue shifted by ca. 25 nm in comparison with the spectra at low temperature due to thermal disorder. Using atomic force microscopy (AFM) we inferred that the distinctive behavior of the cast film, probably associated with structural defects, is related to the large thickness of this film. The surface roughness, which was surprisingly higher for the LB film, apparently played no role in the emission properties of OC1OC6-PPV films.

Interference of robust tori on the resonance overlap

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

Virasoro constraints and flavor-topology duality in QCD

We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge v. The constraints depend on the topological charge only through the combination N-f +betav/2 where the value of the Dyson index beta is determined by the reality type of the fermions. This duality between flavor and topology is inherited by the small-mass expansion of the partition function and all spectral sum rules of inverse powers of the eigenvalues of the Dirac operator. For the special case beta =2 but arbitrary topological charge the Virasoro constraints are solved uniquely by a generalized Kontsevich model with the potential V(X) = 1/X.

WO3 and ZnO-doped SnO2 ceramics as insulating material

SnO2 ceramics doped with ZnO and WO3 were prepared by mixed oxide method. The effect of ZnO and WO3 additives could be explained by the substitution of Sn4+ by Zn2+ and W6+. The addition of WO3 inhibits the grain growth due to the segregation of SnZnWO8 and ZnWO6 at the grain boundaries without strong influence on the densification process. The electrical characterization (log E x log J) shows that the ternary system SnO2-ZnO-WO3 exhibits a very high resistivity of around 10(14) Omega M. Independently of the WO3 concentration, the electrical conductivity of the Sn02-ZnO-WO3 system is always lower than that of the undoped tin dioxide. (C) 2005 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

QED(3) RADIATIVE-CORRECTIONS IN THE HEISENBERG PICTURE

We evaluate the vacuum polarization tensor for three-dimensional quantum electrodynamics (QED3) via Heisenberg equations of motion in order to clarify the problem arising from the use of different regularization prescriptions in the interaction picture. We conclude that the photon does acquire physical mass of topological origin when such contribution is taken into account for the photon propagator.

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

The use of classification methods for modeling the antioxidant activity of flavonoid compounds

A study using two classification methods (SDA and SIMCA) was carried out in this work with the aim of investigating the relationship between the structure of flavonoid compounds and their free-radical-scavenging ability. In this work, we report the use of chemometric methods (SDA and SIMCA) able to select the most relevant variables (steric, electronic, and topological) responsible for this ability. The results obtained with the SDA and SIMCA methods agree perfectly with our previous model, in which we used other chemometric methods (PCA, HCA and KNN) and are also corroborated with experimental results from the literature. This is a strong indication of how reliable the selection of variables is.

Fractals de Rauzy

We study arithmetical and topological properties of a class of Rauzy Fractals. In particular, we give a parametrization of the boundaries of these sets and show that they are quasi-disks.

Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund couphng J(H) is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-held approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and (3x(2) - r(2))/(3y(2) - r(2))-type orbital ordering are successfully reproduced based on the JT-phononic model with large JH for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized t(2g) spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic (large JH) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

Perturbative bosonization from two-point correlation functions

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive QED(2) and QED(3) with N fermion flavors including also a Thirring coupling. We start from two-point correlators involving the U(1) fermionic current and the gauge field. From the tensor structure of those correlators we prove that the U(1) current must be identically conserved (topological) in the corresponding bosonized theory in both D=2 and D=3 dimensions. We find an effective generating functional in terms of bosonic fields which reproduces these two-point correlators and from that we obtain a map of the Lagrangian density (ψ) over bar (r)(ipartial derivative-m)psi(r) into a bosonic one in both dimensions. This map is nonlocal but it is independent of the electromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant.

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Using shifts in the electronic emission curve to evaluate polymer surface degradation

The polymer surface degradation and/or modification evolution of Teflon FEP and Mylar C films caused by a low energy electron beam were analyzed using a new method that consists in measuring the second crossover energy shift in the electronic emission curve. Upon prolonged irradiation, the second crossover energy shifts irreversibly to lower values in Teflon FEP but to higher values in Mylar C, indicating distinct mechanisms of surface degradation for the two polymers. The method represents a relatively inexpensive way to monitor early stages of surface degradation since the secondary electron emission comes from a maximum depth below the geometric surface of 100 mn in insulators. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.