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 hot blow forming of AZ31 Mg sheet: Formability assessment and application development

The hot blow forming of magnesium sheet offers significant opportunity for forming complex, lightweight parts for automotive applications. This paper characterizes the elevated-temperature formability of AZ31 magnesium sheet materials and the effect of processing conditions on the performance of these materials. In addition, magnesium sheet application development at General Motors Corporation is reviewed.     

Simulation of Strength Distribution in Ground Ceramics by Incorporating Residual Stress Effect

Strength of ground ceramics may be affected by residual stress as well as surface flaws induced by grinding. Strength prediction for ground ceramics is convenient for mechanical design of ceramic components. In this article, a numerical procedure based on fracture mechanics was proposed to estimate strength distribution of ground ceramics by considering grinding-induced residual stress. Bending strength and residual stress of ground ceramics were measured for three grinding-conditions. By comparison of simulated results with experimental ones, it was revealed that strength characteristics in experiments were well simulated by using the proposed procedure.     

Spalling of Flat Plates by Thermal Shock

A model is presented for the thermal shock damage in plates subjected to a sudden rise in temperature. Spalling is assumed to follow localized buckling caused by the thermally induced compressive stresses above subsurface flaws. The minimum size o flaw required to cause spalling is determined as a function of the material properties of the plate, the temperature rise, the position of the paw, and the time after the thermal shock.     

Phase Studies Concerning Sintering in Aluminas Doped with Ti4+

Previous solid state analyses of sintering in Ti⁴⁺-doped-commercial alumina are shown to be in error because a liquid phase exists in the appropriate region of the Al₂O₃−TiO₃−Na₂Ophase diagram at least by 1350^°C, a temperature lower than that at which "solid state" studies were conducted. It is suggested that liquid-phase sintering is a much more common occurrence than was realized formerly.     

Retention of Escherichia coli in municipal sewage by means of planted soil filters in two-stage pilot plant systems.

Different types of constructed wetlands in a pilot-plant system were fed with identical municipal waste water to compare the sanitisation process in two-stage systems. With combinations of a vertical and a horizontal flow filter an E. coli reduction of 5 log10 with an E. coli influent concentration of 10(7) MPN/100 ml was achieved. Using different filter materials in each stage the total performance of the two-stage system was independent from the sequence of these materials. However, using coarser filter material in the first stage makes the filter less prone to clogging and is thus the preferential option with regard to operational reliability.     

Olfactory discrimination of individual littermates in rats (Rattus norvegicus).

Tested the ability of 4 adult male Sprague-Dawley rats to use odors in discrimination among littermates living as a group. Ss were trained in a Y-maze to discriminate the presence of a littermate from its absence. Results from transfer of training in 3 subsequent testing periods indicated that the animals were capable of distinguishing among individuals when relatedness and familiarity were held constant, that this ability was not due to training, and that performance was based solely on odor cues. Results suggest that laboratory rats exhibit odor sensitivities conmensurate with very complex social processes. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Production of maraging steel grades and the influence of specified and nonspecified elements for special applications

The material properties of maraging steels are greatly affected by the alloy and inclusion content and hence by the production route. This paper describes various past and current production routes at Böhler Edelstahl GmbH and the effect of these routes on the specified element (alloy) and non-specified element (inclusion) contents. Non-metallic inclusions were investigated by EDX analysis. The effects of various alloying and tramp elements on the material properties are presented as a statistical evaluation of previous melts. Nitrogen solubility was calculated with Thermo–Calc for maraging steel Mat.-No. 1.6354 and the precipitation of nitrides is discussed. A proposal is made for the production of melts with improved properties.     

Phase relations in the ternary system Cu-In-Se

The phase relations of the ternary system Cu-In-Se were studied at 750° C by quenching experiments. Special attention was given to the region CuInSe₂In₂Se₃-In₄Se₃. Only four ternary phases with extended homogeneity ranges were found to exist. They were characterized by X-ray powder diffraction, electron microprobe analysis (EK8PA)' end optical microscopy. Differential thermal analysis (DTA) investigations allowed us to construct theT-x diagram of the Cu₂Se-In₂Se₃. out between 47 and 100 mol% In₂Se₃. Besides, it was also possible to give a tentative diagram of the solid-liquid equilibria at 750° C and to get some information on the sub-solid existence fields beside the Cu₂Se-In₂Se₃ cut.