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.     

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.     

Structure and properties of CE/CTBN/EP blends: II. Effect of EP on the mechanical properties and thermostability of the CE/CTBN system

Carboxyl‐terminated butadiene‐acrylonitrile rubber (CTBN) has often been used to improve the toughness of cyanate ester (CE) resin while sacrificing modulus and thermostability. In this paper, the addition of the appropriate amount of epoxy resin (EP) to the CE/CTBN system is shown to not only increase the modulus and thermostability of the blend, but also improve the toughness. The values of impact strength showed a maximum for the CE/CTBN/EP 100/5/5 blend. The temperature of 10 % weight loss (T₁₀) improves from 376 °C for CE/CTBN 100/5 to 407 °C for the CE/CTBN/EP 100/5/2.5 blend. It is proposed that addition of the appropriate amount of EP can decrease the mobility and increase the stability of CTBN via the reaction between the terminal carboxyl group of CTBN and the hydroxyl group of EP. But a very high EP concentration will decrease the crosslinking density of CE, consequently reducing the mechanical properties and thermostability of the blends. Copyright © 2004 Society of Chemical Industry     

Application of a multi-channel system for continuous monitoring and an early warning system.

A multi-channel continuous toxicity monitoring system developed in our laboratory, based on two-stage mini-bioreactors, was successfully implemented in the form of computer-based data acquisition. The multi-channel system consists of a series of a two-stage minibioreactor systems connected by a fiber optic probe to a luminometer, and uses genetically engineered bioluminescent bacteria for the detection of the potential toxicity from the soluble chemicals. This system can be stably and continuously operated due to the separation of the culture reactor from the test reactor and accomplish easy and long-term monitoring without system shut down by abrupt inflows of severe polluting chemicals. Four different recombinant bioluminescent bacteria were used in different channels so that the modes of the samples toxicities can be reasonably identified and evaluated based upon the response signature of each channel. The bioluminescent signatures were delivered from four channels by switching one at once, while the data is automatically logged to an IBM compatible computer. We also achieved the enhancement of the system through the manipulation of the dilution rate and the use of thermo-lux fusion strains. Finally, this system is now being implemented to a drinking water reservoir and river for remote sensing as an early warning system.     

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.     

Fabrication of multi-walled carbon nanotube reinforced polyelectrolyte hollow nanofibers by electrospinning

Hybrid hollow multi-walled carbon nanotubes (MWCNTs)/polyelectrolytes (PE) nanofibers were prepared by a combination of the electrospinning method and layer-by-layer (LbL) technique. The mixed polystyrene (PS)/MWCNTs nanofibers were obtained by electrospinning method, which were employed as templates to self-assembly multilayered polyelectrolytes by LbL technique. Hollow MWCNTs/PE nanofibers were obtained by selectively removed part of the template: PS, which is confirmed by Raman spectra, transmission electron microscopy (TEM) and scanning electron microscopy (SEM).