Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

THE SOUTHERN BRAZILIAN SHELF: GENERAL CHARACTERISTICS, QUATERNARY EVOLUTION AND SEDIMENT DISTRIBUTION

Extending from latitude 34 degrees S to 22 degrees S the Southern Brazilian shelf constitutes the only part of the Brazilian shelf with a subtropical to temperate environment. The studies on the different geological aspects of the area began in the 1960`s and have recently been reassessed after studies related to the determination of the Economic Exclusive Zone. In terms of morphology, the Southern Brazilian shelf may be divided into three sectors, the Sao Paulo Bight, the Florianopolis-Mostardas Sector and the Rio Grande Cone, characterized by conspicuous differences in terms of geological determining factors, bathymetry, declivities and the presence of canyons and channels. Despite the existence of hundreds of radiocarbon datings the sea level changes curve of southern Brazil during the Last Glacial Cycle is still a matter of debate. A recent controversy on the Middle and late Holocene sea level changes curve raised the question of the amplitude of the oscillations which occurred in the period. Also, a few but relatively consistent radiocarbon datings suggest the occurrence of a high sea level during Isotope Stage 3. In terms of sedimentary cover the Southern Brazilian shelf exhibits a very strong hydrodynamic control, both latitudinal and bathymetrical. The sector southward from 25 degrees S is characterized by the influence of the plume of water carrying sediments originating from the Rio de La Plata. Actually its presence is conspicuous up to 28 degrees S, with the area between this latitude and 25 degrees S constituting a transitional zone. In terms of bathymetry the outer shelf is marked by the ""floor-polisher"" effect of the Brazil Current, which is responsible for the maintenance of a relict facies in areas deeper than 100 meters.

Drizzle and Fog Analysis in the Sao Paulo Metropolitan Area: Changes 1933-2005 and Correlations with other Climate Factors

In order to improve our understanding of climate change, the aim of this research project was to study the climatology and the time trends of drizzle and fog events in the Sao Paulo Metropolitan Area, and the possible connections of this variability with the sea surface temperature (SST) of the Atlantic and Pacific Oceans. The climatology of both phenomena presents differences and similarities. Fog shows a marked maximum frequency in winter and a minimum frequency in summer, while the seasonal differences of drizzle occurrence are less pronounced, there is a maximum in spring, whereas the other seasons present smaller and similar numbers of events. Both phenomena present a negative trend from 1933 to 2005 which is stronger for fog events. A multivariate statistical analysis indicates that the South Atlantic SST could increase warm temperature advection to the continent. This could be one of the responsible factors for the negative tendency in the number of both fog and drizzle events.

MODIS aerosol optical depth Retrievals with high spatial resolution over an urban area using the critical reflectance

[1] The retrieval of aerosol optical depth (Ta) over land by satellite remote sensing is still a challenge when a high spatial resolution is required. This study presents a tool that uses satellite measurements to dynamically identify the aerosol optical model that best represents the optical properties of the aerosol present in the atmosphere. We use aerosol critical reflectance to identify the single scattering albedo of the aerosol layer. Two case studies show that the Sao Paulo region can have different aerosol properties and demonstrates how the dynamic methodology works to identify those differences to obtain a better T a retrieval. The methodology assigned the high single scattering albedo aerosol model (pi o( lambda = 0.55) = 0.90) to the case where the aerosol source was dominated by biomass burning and the lower pi(o) model (pi(o) (lambda = 0.55) = 0.85) to the case where the local urban aerosol had the dominant influence on the region, as expected. The dynamic methodology was applied using cloud-free data from 2002 to 2005 in order to retrieve Ta with Moderate Resolution Imaging Spectroradiometer ( MODIS). These results were compared with collocated data measured by AERONET in Sao Paulo. The comparison shows better results when the dynamic methodology using two aerosol optical models is applied (slope 1.06 +/- 0.08 offset 0.01 +/- 0.02 r(2) 0.6) than when a single and fixed aerosol model is used (slope 1.48 +/- 0.11 and offset - 0.03 +/- 0.03 r(2) 0.6). In conclusion the dynamical methodology is shown to work well with two aerosol models. Further studies are necessary to evaluate the methodology in other regions and under different conditions.

High specific surface area LaFeCo perovskites-Synthesis by nanocasting and catalytic behavior in the reduction of NO with CO

LaFe(1-x)CO(x)O(3) perovskites were conventionally or nanocasting synthesized. The nanocasting involved the preparation of a micro-mesoporous carbon mould using a Silica Aerosil 200 and a carbon source. Then, perovskites were carbon cast at 800 degrees C. The solids were characterized by XRD, N(2) sorption, FTIR, TGA/DTG, SEM and TEM. N(2) sorption evidenced that the nanocast perovskites did not show significant intraparticle porosity in despite of their enhanced (30-50 m(2)/g) specific surface area (SSA). Nevertheless, TEM images, XRD and Rietveld refinement data showed that the solids are constituted at least by 97 wt% of perovskite phase and by agglomerates smaller than 100 nm constituted by crystallites of about 6 nm. TGA/DTG results demonstrated carbon oxidation during the perovskite formation, thus eliminating the template effect and facilitating the occurrence of sintering, which limited the SSA increase. The nanocast perovskites were more active in the reduction of NO than the uncast ones, behavior that was attributed to the increase in their SSA that allows the exposure of a higher number of accessible active sites. However, the perovskite composition and the presence of impurities can reduce the effect of the improvement of the textural properties. The nanocast perovskites also showed high thermal and catalytic stability, corroborating their potential as catalysts for the studied reaction. (C) 2009 Elsevier B.V. All rights reserved.