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.     

Critical slowing down in lead magnesium niobate–zirconate ceramic

Dielectric relaxation behaviour of (1 − x)PMN − xPZ, for x = 0.10, 0.30 and 0.40 have been studied. The nature of relaxational behaviour was found to change with PZ concentration. A crossover from a static freezing to critical slowing down like behaviour is observed with increase in Zr⁴⁺ concentration. We have used Glazounov and Tangastev criterion to distinguish freezing and critical slowing down like behaviour.     

Influence of the preparation conditions on the size and morphology of nanocrystalline lanthanum orthoferrite

Nanocrystalline LaFeO₃ is prepared by the dehydration of coprecipitated lanthanum and iron(III) hydroxides. It is shown that the behavior of the samples during heating and the size distribution of LaFeO₃ nanocrystals can be considerably different depending on the scheme used for coprecipitation of lanthanum and iron hydroxides; independently of the method employed for coprecipitation of the initial compounds, sintering of the samples at 950°C leads to the formation of lanthanum orthoferrite crystals up to 100 nm in size.     

Synthesis of polyanilines with pendant fluorescent units

Functionalized polyanilines containing biphenyl, terphenyl, carbazole, anthracene, and 4-n-hexylphenyl moieties were synthesized though the reaction of polyaniline in emeraldine base form with sodium salt of corresponding vinylketoaromatics with quantitative yields. Polymers were characterized with Fourier transform infrared spectroscopy, proton nuclear magnetic resonance spectroscopy, and thermogravimetry. The emission characteristics of these polymers in N-methyl-2-pyrrolidone solution were examined. The functionalized polyanilines exhibited an intense green emission.     

Protoplast from <Emphasis Type="Italic">β</Emphasis>-carotene-producing fungus <Emphasis Type="Italic">Blakeslea trispora</Emphasis>: Preparation,regeneration and validation

The effects of key parameters on the preparation and regeneration of protoplast from the β-carotene-producing fungus Blakeslea trispora were discussed in this paper, including the combination of various enzymes, mycelial age, digesting time and temperature, pH value, osmotic stabilizers, pretreatment, culture medium and culture method. Under the condition of mixed enzymes in osmotic stabilizer (0.6 M NaCl) combined with 2% lysozyme, 3% cellulase and 3% snailase, the highest protoplast yield, as high as 7.48×106 protoplasts/mL, was obtained when mycelial age was 60 h at pH 5.0–6.0 with digesting for 14–16 h at 28 °C. After purification of the obtained protoplasts, they were regenerated in PDA regenerative medium using bilayer plate culture method. To validate the usability of the protoplasts, a novel plasmid with green fluorescent protein (GFP) was used in transformation for easy visual observation. The results showed that the protoplasts prepared by the optimized method were active and applicable in further gene manipulation experiments. This work was presented at 13 ^th YABEC symposium held at Seoul, Korea, October 20–22, 2007.     

Onset of buoyancy-driven convection in melting from below

When a horizontal homogeneous solid is melted from below, convection can be induced in a thermally unstable melt layer. In this study the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Rayleigh numbers based on the melt-layer thickness are found numerically for various conditions. For small superheats, the present predictions approach the well known results of classical Rayleigh-Bénard problems, that is, critical Rayleigh numbers are located between 1,296 and 1,708, regardless of the Prandtl number. However, for high superheats the critical Rayleigh number increases with an increase in phase change rate but with decrease in Prandtl number.