Critical Configurations for 1-View in Projections from ℙ<Superscript>k</Superscript> → ℙ<Superscript>2</Superscript>

In this paper we describe, from a theoretical point of view, critical configurations for the projective reconstruction of a set of points, for a single view, i.e. for calibration of a camera, in the case of projections from ℙ^k to ℙ² for k ≥ 4. We give first a general result describing these critical loci in ℙ^k, which, if irreducible, are algebraic varieties of dimension k−2 and degree 3. If k=4 they can be either a smooth ruled surface or a cone and if k = 5 they can be a smooth three dimensional variety, ruled in planes, or a cone. If k≥ 6, the variety is always a cone, the vertex of which has dimension at least k − 6. The reducible cases are studied in Appendix A. These results are then applied to determine explicitly the critical loci for the projections from ℙ^k which arise from the dynamic scenes in ℙ³ considered in [13]. Marina Bertolini is currently Associate Professor of Geometry at the Department of Mathematics at the Università degli Studi di Milano, Italy. Her main field of research is Complex Projective Algebraic Geometry, with particular interest for the classification of projective varieties and for the geometry of Grassmann varieties. On these topics M. Bertolini has published more than twenty reviewed papers on national and international journals. She has been for some years now interested also in applications of Algebraic Geometry to Computer Vision problems. Cristina Turrini is Associate Professor of Geometry at the Department of Mathematics of Università degli Studi di Milano, Italy. Her main research interest is Complex Projective Algebraic Geometry: subvarieties of Grassmannians, special varieties, automorphisms, classification. In the last two years she has started to work on applications of Algebraic Geometry to problems of Computer Vision. She is author or co-author of about thirty reviewed papers. She is also involved in popularization of Mathematics, and on this subject she is co-editor of some books.     

The impacts of a GTL plant on Brazil's oil products supply and refinery expansion

This paper assesses the impacts of a GTL plant on the expansion of Brazil's oil refining segment. The GTL plant (50,000 bpd) was sized to start up operations in 2015, producing diesel and naphtha through the indirect route (FT-synthesis). This plant will consume the non-associated natural gas production from the recent discoveries at the Santos Basin (around 419 Bm³), and the associated gas production from the Campos Basin. Both basins are located in the Southeast of Brazil, the most populated, rich and industrialized region of the country. Two different criteria for refinery expansion were simulated in order to meet oil product demand scenarios. Findings show that depending on the refinery expansion criteria considered GTL will play a fundamental hole to meet the oil product demand forecast to Brazil in the next 10 years.     

Retaining maximum antioxidative potency of wheat germ oil refined by molecular distillation

A process of physical refining wheat germ oil using the technique of molecular distillation (MD) is presented in this work. Wheat germ oil was obtained from the germ by solvent extraction using hexane and also by cold pressing. The oil extracted with hexane was degummed and bleached before deacidification in order to modify the parameters of phosphorus and color. The goal in carrying out the stage of physical refining by MD was to preserve the maximum amount of original antioxidative potential obtained from extraction of the crude oil. The effect of evaporation temperature of one‐stage MD on the efficiency of free fatty acid elimination was studied. The antioxidant portion was followed by means of analytic determination of tocopherols by high‐performance liquid chromatography. Tocopherol retention up to 98% was achieved in the oil extracted by pressing, and yields of up to 96% were achieved in the oil extracted with hexane. Copyright © 2007 Society of Chemical Industry     

Mechanism of the skeletal isomerisation of linear butenes over ferrierite: analysis of side reactions

An investigation of the effect of reaction conditions on product distribution in the skeletal isomerisation reaction of linear butenes has been carried out. The main reaction routes over ferrierite have been identified. Beside the main product isobutene, major by-product formation occurs. The unwanted reactions include dimerisation of butene to form octenes, hydrogen transfer yielding small amounts of saturated C₃ and C₄ hydrocarbons and disproportionation producing propene and pentenes. The most abundant by-products were pentene and propene, though these were not formed in equimolar amounts as could be expected. Oligomerisation experiments of propene over ferrierite produced large amounts of butene and pentene, revealing the presence of adsorbed nonene. The cracking of this surface species to hexene and propene is the most likely reaction route for the excess propene formation. This additional path to propene formation operates mainly at temperatures above 623 K.     

Microwave-Assisted Reaction Sintering of Bismuth Titanate-Based Ceramics

Bismuth titanate-based ceramics, pure and doped with 5 mol% WO₃, were prepared by reaction-sintering using a microwave oven. High densities, ≥96% of theoretical density were achieved with very short thermal treatments, with soaking time ranging from 5 to 15 min. Relatively small platelet-like grains were formed, and microstructure seemed not to be strongly affected by doping nor soaking time. Electrical measurements were performed and, as expected, a decrease of electrical conductivity was observed in WO₃-doped materials. The results of reaction-sintered samples, both conventional as well as microwave sintered, are compared with those of samples prepared with previously calcined powders and sintered using microwaves as well as a conventional electric furnace.     

Metal sorption by biomass of melanin‐producing fungi grown in clay‐containing medium

The sorption of toxic metals by fungal mycelia grown in clay‐containing medium is reported in this work. Biomass of melanin‐producing microfungi of the genus Cladosporium (C cladosporioides, C resinae and C herbarum) and Aureobasidium pullulans, clay minerals and fungal mycelia grown in clay‐containing medium were compared for their equilibrium Cu and Cd uptake from pH‐buffered solutions using experimental sorption isotherms. Bentonite (Cherkassy) in the natural form was shown to be the best Cu sorbent compared with the other clays and clay minerals tested. Cu sorption isotherms fitted the Langmuir sorption model for all cases. Comparison of Cu and Cd uptake for biomass and bentonite showed a lower biomass uptake capacity but a considerably higher affinity of the biosorbent for the solute. The presence of kaolinite and palygorskite in the medium generally reduced both Cu and Cd sorption capacity and the metal‐binding ability of the fungal–clay mixtures. In contrast, addition of bentonite into the medium did not appreciably alter the Cd sorption ability but increased the sorption of Cu by A pullulans and C cladosporioides grown in this medium. A common feature for all fungi grown in the presence of bentonite was an increase in the Cu sorption capacity (Q_max) of the biomineral sorbents and a reduction in their affinity (Langmuir parameter b) compared with control biomass. A difference between predicted and experimental data obtained for biomass grown on bentonite medium was also observed. The connection between the sorption capacity of biomass grown in clay‐containing medium, mycelial morphology and the structure of fungal pellets is discussed and a mechanism for the changed sorption capacity of the combined biomineral sorbents is proposed which involves blocking or modification of binding sites on biotic and abiotic components of the ‘biomineral’ association. © 2002 Society of Chemical Industry     

Lyapunov analysis of the approximate motion equations of flexible structures

In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the RitzKantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two ‘extreme’ cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.     

Preparation and sintering behaviour of submicronic Bi4Ti3O12 powders

Submicronic powders of Bi₄Ti₃O₁₂ with different morphologies were prepared by both the oxalate coprecipitation and the conventional mixing oxides methods. Compacts of the two calcined powders were sintered at 850–1100 °C in air, and the densification process was studied by non-isothermal and dilatometric experiments. A rapid densification (> 97% theoretical density) below 875 °C took place in the Bi₄Ti₃O₁₂ oxalate powder which was attributed to an extremely uniform pore-size distribution in the green compact. The possible formation of a transient liquid which promotes densification also was taken into account. The development of plate-like morphology in the conventional Bi₄Ti₃O₁₂ powder, broad pore-size distribution, and the plate-like colony formation, hindered rapid densification of the green compacts at low temperature. Microstructural development was studied; preliminary dielectric and electrical results are also reported.     

Contextual void patching for digital elevation models

Digital terrain models can be created by gathering a set of measurements from geometric objects. For various reasons, these models may be incomplete and thus fail to meet the requirements defined by their potential applications. In this work, we develop a novel multiresolution approach to repair the voids commonly found in digital elevation models (DEM). We use the overall shape and structure of the surrounding terrain to build a smooth patch for the void. Then, using a multiresolution approach obtained from reverse Chaikin subdivision, we extract the low-scale characteristics from the surrounding terrain and apply them to the smooth patch. The results demonstrate that our approach is effective in synthesizing models with realistic characteristics.