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.     

Investigation for long wavelength fir laser lines for EPR studies: New lines from CH2=CF2

The results described in this work are part of a systematic search for long wavelength laser lines to be used in high magnetic field EPR applications and in plasma diagnostic. Four new far-infrared laser lines of CH₂ = CF₂ (1,1 difluoroethylene), optically pumped by a waveguide CO₂ laser, have been discovered and characterized in wavelength, polarization relative to the pumping radiation and offset relative to the CO₂ center frequency. New measurements of polarization and offset of 5 already known laser lines are also reported. A table of all of the known CO₂ pumped FIR laser lines from this molecule is given.     

On the specific reactivity of platinum segregated layers on Pt80X20 (111) (X= Ni,Co, Fe) alloys

The influence of alloying of Pt with 20 at.% of Ni, Co and Fe has been studied in the hydrogenation of 1,3 butadiene. Iron induces the more important modifications, with both higher activity and selectivity. The results are discussed in terms of the surface segregation, the local order in surface and the electronic properties measured by photoemission of core levels.     

Pd deposited on Cu(110): a highly performant catalyst for the 1,3-butadiene hydrogenation reaction

The catalytic properties, with respect to the 1,3-butadiene hydrogenation reaction, of strained Pd films on Cu(110) (lattice mismatch 8%) has been probed as a function of the film thickness. The characterization of the adlayer has been made by the combined use of STM with LEED and AES. For deposits below 10¹⁵ Pd/cm² (i.e., about 1 ML) the catalytic activity is near zero. This is the consequence of the formation of a Pd–Cu surface alloy with tendency for Cu to migrate/segregate to the surface. The catalytic activity suddenly increases to reach a maximum value for about 3 ML; the activity is then one order of magnitude higher than that of the pure Pd(110) surface. This is the consequence of the presence of a strained Pd overlayer, with Pd surface atoms having very unusual geometry, and hence very peculiar electronic and chemical properties. The catalytic activity then decreases as the Pd coverage is increased, and tends to values near that of the pure Pd(110). Gradual relaxation of the film geometry towards that of the normal fcc Pd structure probably exists.     

Linear pose estimate from corresponding conics

We propose here a new method to recover the orientation and position of a plane by matching at least three projections of a conic lying on the plane itself. The procedure is based on rearranging the conic projection equations such that the non linear terms are eliminated. It works with any kind of conic and does not require that the shape of the conic is known a-priori. The method was extensively tested using ellipses, but it can also be used for hyperbolas and parabolas. It was further applied to pairs of lines, which can be viewed as a degenerate case of hyperbola, without requiring the correspondence problem to be solved first. Critical configurations and numerical stability have been analyzed through simulations. The accuracy of the proposed algorithm was compared to that of traditional algorithms and of a trinocular vision system using a set of landmarks.     

Use of cryogenic machining to improve the adhesion of sphene bioceramic coatings on titanium substrates for dental and orthopaedic applications

Rods of commercially pure titanium were machined using standard oil-based emulsion and cryogenic cooling, and were then coated with sphene (CaTiSiO₅) bioceramic by spray coating using an automatic airbrush. The sphene bioceramic was synthesized in-situ starting from a suspension of polysiloxane that used as SiO₂ precursor, CaCO₃ and TiO₂ nanoparticles. The suspension was deposited on the machined substrates, which were heat treated up to 950?°C in order to promote the formation of sphene ceramic. The produced coated prototypes were characterized to evaluate the effect of the machining conditions on surface roughness and microstructure of the substrate, and thereby their effect on coating adhesion. Nanoindentation tests were employed to determine the hardness and elastic modulus of the coating through its thickness. Results showed that the reduced amount of defects on the surface of the cryo-machined substrates, contributed to increase the hardness, elastic modulus and adhesion strength of the coating-substrate interfaces compared to standard machined samples, therefore improving adhesion of the coating to the underlying substrate.     

Pd catalysts supported on silicon nitride for the combustion of methane: Influence of the crystalline and amorphous phases of the support and of the preparation method on the catalytic performances

Non-oxide refractory materials, such as silicon nitride having high thermal stability and thermal conductivity can be used as catalytic supports. The influence of the Si₃N₄ support nature and of the chemical compounds used for preparations on the physical-chemistry and catalytic properties of the palladium systems in the total oxidation of methane was investigated. A strong influence of the phase composition and the crystalline state of supports on the catalytic properties in the total oxidation of methane of the Pd catalysts was found. The activity of Pd catalysts increases with the -Si₃N₄ content and crystallization state of the support. The catalytic activity of Pd/-Si₃N₄ is also strongly affected by the preparation procedure. The Pd/-Si₃N₄ catalyst obtained by aqueous impregnation is less active and less stable. It was proposed that if water is used as an impregnation solvent, the surface acid-based properties of Si₃N₄ support and/or of the Pd active phase are irreversibly damaged. Pd supported on -Si₃N₄, prepared by impregnation of the Pd precursors in toluene solutions are found to be the most active and stable under reaction conditions.     

Pd(111) versus Pd–Au(111) in carbon monoxide oxidation under elevated pressures

The oxidation of CO on Pd(111) and Pd₇₀Au₃₀(111) has been studied under pressures upto 100 Torr. Gold is found to decrease the surface activity by inhibiting oxygen dissociation. For a sufficient conversion time depending on the CO coverage and the surface identity, a dramatic boost of activity occurs. This is ascribed to a switch from CO-induced inhibition of O₂ adsorption to a regime determined by CO adsorption. The other kinetic features are explained by oxidation of palladium and adsorption-induced restructuring of the surfaces.