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.     

A comparison of three approaches for predicting C4 species cover of northern mixed grass prairie

The C4 composition of Canadian mixed-grass communities is more sensitive to environmental change than other grasslands. Reliable methods of detecting such changes are necessary if these landscapes are to be properly managed. One approach is to use satellite remote sensing systems. Various studies have shown that the asynchronous seasonality of C3 and C4 species allows the relative abundance of each photosynthetic type to be estimated using temporal trajectory indices (TTIs) of sensor-derived normalized difference vegetation index (NDVI). In this study, we compared three approaches for predicting C4 species cover at Grasslands National Park (GNP) (Saskatchewan, Canada). TTIs related to Approach I were calculated from plots of NDVI vs. day-of-year (DOY). TTIs related to Approach II were calculated from plots of normalized cumulative NDVI vs. growing degree day (GDD). TTIs related to Approach III were calculated as ratios of early-season NDVI to late-season NDVI. Our analyses were conducted at two separate ecological scales. A within-community analysis used field-sampled data from upland grassland to compare techniques at sampling resolutions of 0.5, 2.5, 10, and 50 m. An across-community analysis compared techniques using a vegetation survey of the GNP region and TTIs calculated from Advanced Very High Resolution Radiometer (AVHRR) data (1 km). At both scales, TTIs related to the timing of specific phenological events were the best predictors of C4 species cover. While all techniques performed well in the within-community study, Approach III performed best. Here, the predictive ability of each approach was weak at a resolution of 0.5 m but stronger at 2.5, 10, and 50 m resolutions. We also found that the optimal sampling dates for Approach III fell within a certain GDD range. This is encouraging for the a priori selection of sample dates, which would make the need for full seasonal time series redundant. In the across-community analysis, the AVHRR-derived Approach II TTIs were better able to discriminate among grasslands of different C4 composition than any other technique (overall accuracy=74%). However, for some C4 cover classes, the predictive accuracy of this approach was low. While these results are encouraging for the use of spectral data in monitoring the C4 cover of northern prairie, various research issues remain. At the within-community level, these include (a) further attempts to define objective criteria for the a priori identification of sampling dates for Approach III, and (b) and the extension of such studies to other growing seasons and community types/grassland regions. At the across-community level, these include the expansion of such techniques to a larger geographical region that contains a wider range in C4 cover values and land use types (e.g. ungrazed vs. grazed grasslands).     

Phase equilibria of the ternary Al-Cu-Ni system and interfacial reactions of related systems at 800 °C

A series of Al-Cu-Ni alloys of various compositions were made and annealed at 800 °C. The equilibrium phases were studied by metallography, X-ray diffraction (XRD) analysis, and electron probe microanalysis. The isothermal section of the ternary Al-Cu-Ni system at 800 °C was then determined based on these experimental results and the available phase relationship knowledge of the three constituent binary systems. No ternary compound was found. All three phases, AlNi₃, AlNi, and Al₃Ni₂, have very high ternary solubility, especially the AlNi phase, which almost reaches the binary Al-Cu side. However, no continuous solid solution was formed between the AlNi phase and any of the binary Al-Cu phases. Interfacial reactions of Al/Ni, Al/Cu, Al-Cu/Ni, and Al-Ni/Cu at 800 °C were investigated by using reaction couple techniques. The results showed that Al₃Ni and Al₃Ni₂ phases were formed in the Al/Ni couples; β-AlCu₄, γ ₁-Al₄Cu₉, and ɛ ₂-Al₂Cu₃ phases were formed in the Al/Cu couples. As for the results in the Al-2 at. pct Ni/Cu, Al-5 at. pct Ni/Cu, and Al-2 at. pct Cu/Ni, Al-4.5 at. pct Cu/Ni, and Al-6 at. pct Cu/Ni were similar to those in the binary Al/Cu and Al/Ni couples, respectively. A different reaction path was found in the Al-7.5 at. pct Cu/Ni couples, and an AlNi solid solution layer was formed instead of the Al₃Ni and Al₃Ni₂ phases.     

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.     

The function of bleaching earths in the processing of palm,palm kernel and coconut oils

The results presented in the literature, which attempt to elucidate the mechanisms by which triglyceride oils are bleached by earths, are reviewed. The impact of this work and how the mechanistic proposals affect changes in oil properties are considered, with particular emphasis on the needs of the palm oil processor. Important properties include color, metals and phosphorus content and oxidative stability of the oil. Investigations made in our own laboratories have been aimed at elucidating the effect of varying physical and chemical properties of the bleaching earth on the quality of bleached and deodorized oils. Techniques used in this work are pore-size distribution, surface area, scanning and transmission electron microscopy and a variety of chemical and X-ray analysis methods. The ability to vary such parameters in montmorillonite clays by alteration of process conditions to give materials with specific performance characteristics is demonstrated. Comparisons are made between acid-activated montmorillonites and other clay types.     

The preparation of high purity Mg2Ni

The intermetallic compound Mg₂Ni has been prepared by the vapour exchange/diffusion reaction of the elements sealed in a stainless steel container. The product has been characterised by powder X-ray diffractometry with Mo-K_α radiation, using step-scanning and profile refinement techniques. The hexagonal unit cell has constants a = 5.2117(4), $\text{c}\text{= 13.2538(9)}\text{A}\text{?}$.     

Synthesis,characterization and ion exchange properties of zirconium(IV) tungstoiodophosphate,a new cation exchanger

Zirconium(IV) tungstoiodophosphate has been synthesized under a variety of conditions. The most chemically and thermally stable sample is prepared by adding a mixture of aqueous solutions of 0·5 mol L⁻¹ sodium tungstate, potassium iodate and 1 mol L⁻¹ orthophosphoric acid to aqueous solution of 0·1 mol L⁻¹ zirconium(IV) oxychloride. Its ion exchange capacity for Na⁺ and K⁺ was found to be 2·20 and 2·35 meq g⁻¹ dry exchanger, respectively. The material has been characterized on the basis of chemical composition, pH titration, Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis. The effect on the exchange capacity of drying the exchanger at different temperatures has been studied. The analytical importance of the material has been established by quantitative separation of Pb²⁺ from other metal ions.     

A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.