Optimal discrete Morse functions for 2-manifolds

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Metal concentrations in surface sediments of Paraíba do Sul River (Brazil)

Summary The Paraíba do Sul River is located in a strategic region between the most important urban and industrial centers of Brazil. In the last years, an increase in the water pollution has been reported, caused by the untreated domestic sewerage of the inhabitants, effluents discharged by various industries, mining activities and sand extraction from the riverbed. This work used total reflection X-ray fluorescence with synchrotron radiation (SRTXRF) to determine metals in the bioavailable and residual fractions from the surface sediments. The metals identified were Ti, Cr, Mn, Fe, Cu, Zn, Rb, Sr, Ba and Pb.     

Thiophene‐cored 2,2‐bis(methylol)propionic acid dendrimers for optical‐power‐limiting applications

The synthesis and characterization of dendron‐coated 2,5‐bis(phenylethynyl)thiophene chromophores are described. The dendrimers were grown divergently on the arylthiophene core with the versatile anhydride of 2,2‐bis(methylol)propionic acid. The arylthiophene core was synthesized with Sonogashira coupling reactions. Structurally well‐defined dendrimers up to the fourth generation were grown, as confirmed by size exclusion chromatography, NMR, and matrix‐assisted laser desorption/ionization time‐of‐flight analysis. The different dendritic substitution did not influence the absorption spectra of the compounds in or near the visible region. Solutions of arylthiophenes had good transparency at wavelengths greater than 400 nm. The dendritic thiophenes exhibited an optical‐power limit at the laser wavelength of 532 nm. However, the magnitude of the optical‐power limit of these compounds was slightly lower than that of a nondendritic arylthiophene with n‐pentyl substituents. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1177–1187, 2005     

Quasi-Newton acceleration for equality-constrained minimization

Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this paper quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms, with equality constraints. A periodically-restarted memoryless symmetric rank-one (SR1) correction method is introduced for that purpose. Convergence results are given and numerical experiments that confirm that the acceleration is effective are presented. This work was supported by FAPESP, CNPq, PRONEX-Optimization (CNPq / FAPERJ), FAEPEX, UNICAMP.     

Simultaneous Chemiluminometric Determination of Levodopa and Benserazide in a Multi-pumping Flow System with Multivariate Calibration

An automated multi-pumping flow system is proposed for the simultaneous chemiluminometric determination of benserazide and levodopa using multivariate calibration methods. The developed methodology is based on chemiluminescence (CL) emission generated by the reaction of benserazide with luminol, and on a concurrent inhibiting effect of levodopa on this reaction. A multi-pumping flow system comprising multiple solenoid micro-pumps as the only active components was developed to implement a stopped-flow approach for signal acquisition and processing. Artificial neural networks were used to establish a relationship between the CL emission profile and the concentration of both drugs. The concentration values used to establish the experimental calibration samples were varied between 5 and 30 mg l(-1) for levodopa and between 2.5 and 20 mg l(-1) for benserazide. The proposed method was successfully applied to the simultaneous determination of levodopa and benserazide in pharmaceutical formulations combining both drugs.     

Sodium removal and catalytic properties of HNaZSM-20 zeolite. Comparison with Y zeolite

A series of HNaZSM-20 catalysts with a varying amount of sodium cations were studied. The samples were prepared by ion exchange starting with a NaZSM-20 sample. The observedammonium-sodium exchange efficiency was slightly higher for ZSM-20 than for Y zeolite. The HNaZSM-20 series presentedhigher cracking activities in then-heptane transformation than the corresponding HNaY series. A decrease in theselectivity for coke deposition with sodium removal was also observed.