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.     

Analysis on the effectiveness of the 20-H rule for printed-circuit-board layout to reduce edge-radiated coupling

This paper presents the quantified study of the electromagnetic radiation mechanism of the 20-H rule using a numerical approach that has not yet been systematically addressed. The 20-H rule is a rule-of-thumb layout technique recommended to minimize radiated fields propagating from the edges of a printed circuit board (PCB) coupling onto nearby structures. Propagating electromagnetic fields may corrupt adjacent cable assemblies, sheet metal enclosures, and aperture openings. The magnitude of this design rule is investigated using the full-wave finite-difference time-domain (FDTD) method. An analysis on whether benefits exist from use of this rule is examined and under what conditions the rule is valid when correctly implemented. The purpose of this paper is to provide insight into the validity of the 20-H rule, recognizing that every PCB will have different simulation results. FDTD is used to capture a snapshot view of field propagation. This view allows one to determine the validity of the 20-H rule at a single point of time within a dynamic structure and what may be expected when digital components are finally added to a PCB assembly, which generally negates simulated results.     

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.     

Interfacial strength and chemistry of additive-free silicon nitride ceramics brazed with aluminium

Two kinds of additive-free silicon nitride ceramics were brazed with aluminium; one was with as-ground faying surfaces and the other was with faying surfaces heat-treated at 1073K for 1.8 ksec in air. The heat-treatment of the silicon nitride ceramics formed a silicon oxynitride layer on the faying surfaces and increased the brazing strength of the joints. A silica-alumina non-crystalline layer and a β′-sialon layer were formed successively from the aluminium side at the interface of the joints. The heat-treatment which made the former layer thicker is a necessary process in making reliable, strong brazed joints.     

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.     

Effects of contact shape on biological wet adhesion

Wet adhesion is widely adopted in biological adhesion systems in nature. Wet adhesion is studied in this paper with the focus on the effect of different contact shapes (flat, concave, convex, and ring-like) on the adhesion force. The evolution of the liquid bridge between a fiber tip and substrate during the detaching process shows two transition points. The first transition from the radius-controlled to the contact-angle controlled process is critical to influence the strength and robustness of adhesion. We show that a concave shape is more effective than a flat one, while a convex shape has no advantage. A ring-like contact shape has advantages in a hydrophobic environment and on a rough surface.     

Dielectric behavior of Cu–GeO<Subscript>2</Subscript> cermet thin films

Capacitance and dielectric loss measurements were carried out using an Al/Cu–GeO₂/Al sandwich structure for 0 to 10 vol% Cu films, 120–400 nm thick, deposited at 0.4–1.5 nm/s in the frequency and temperature range 1–10⁶ Hz and 90–573 K, respectively. The variation of capacitance and dielectric loss with frequency and temperature follows the Goswami and Goswami model. Capacitance decreases slowly with increasing thickness and also varies with the change in deposition rate of the cermet film.