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.     

On the nonuniformity of a capillary flow

It is established that the capillary rise of a liquid has an oscillatory character, in contrast to the commonly accepted opinion that a vertical capillary is filled at a monotonically varying velocity. The value of the tangential shear stress arising in an ascending liquid is evaluated for ethyl alcohol and distilled water.     

Experimental Electronuclear Setup at the Institute of Theoretical and Experimental Physics

The purpose and current construction status, at the Institute of Theoretical and Experimental Physics, of an experimental electronuclear setup, combining a pulsed proton linear accelerator (36 MeV, 0.5 mA) and a subcritical blanket thermal-power assembly 100 kW, are discussed. The main equipment is already available or is being built in industry. The setup can be used to investigate the dynamics of the interaction of a linac–driver and a subcritical reactor and problems concerning the accelerator–driver and the target–blanket assembly. The proton beams and neutron fluxes will be used for applied purposes. In the future it will be possible to increase substantially the current and energy of the proton beam.     

Vapor pressure and thermodynamic functions of TeI<Subscript>4</Subscript> and its decomposition products

Using a flow method, we have measured the vapor pressure of tellurium tetraiodide, an attractive reagent for chemical vapor deposition technology. The results, combined with earlier tensimetric data, have been used to evaluate the basic thermodynamic functions of TeI₄ and its thermolysis products.     

Phase-change optical recording: Past, present, future

We discuss specific features of Te-based compounds that made them the best materials for the phase-change data storage. It is demonstrated that the phase-change recording is due to a switch of Ge atoms between octahedral and tetrahedral symmetry positions within the Te face-centered cubic lattice. It is this nature of the transition that makes the Te-based media fast and stable. The driving force for this transition is also discussed. The chapter is concluded by introduction of a concept of the super-resolution near-field structure (super-RENS) disc that allows to reduce a bit size well below the diffraction limit and makes 100 GB/disc storage a reality.     

The structure and properties of a Cr<Subscript>3</Subscript>C<Subscript>2</Subscript>-Ni coating deposited by a high-velocity plasma jet onto a copper substrate

Chromium carbide-nickel coatings were deposited onto a technical grade copper substrate by means of a high-velocity plasma jet of a plasmatron operating in specially selected regimes. An analysis of the coatings showed evidence of the formation of a Ni-based solid solution, a complex chromium carbide (Cr₇C₃), and an fcc crystal phase with a lattice parameter of 3.614 Å. The surface of the coatings exhibits a characteristic relief resulting from a dynamic interaction between melted and fused particles of the initial powder. The local hardness on some areas of the surface and in depth of the coating reaches 66±4.5 HRC, while the coating adhesion strength varies from 25 to 300 MPa.     

The relativistic charged particles identification method based on the goodness-of-fit ωn-criterion

The statistical method of identification of relativistic charged particles by measurements of ionization losses or time-of-flights simultaneously in some detectors of an experimental plant on the basis of the new goodness-of-fit ω_n³-criterion is considered. The method proposed has been used for the secondary particles identification from the high energy -particles fragmentation on target nuclei. The efficiency of the method is excellently illustrated by reliable separation of events (rare events as well), connected with the appearence of 1- and 2-charged particles. The comparison of the ω_n³-method with the traditional methods and with the method based on the ω_n²-criterion shows that the new method outperforms the ω_n²-method and most of the traditional ones in efficiency, but compares unfavourably with the likelihood method in power, however, the former has a number of advantages as compared with the latter.     

High-resolution electron microscopy of the twinning and intergrowth in Ca4Al6SO16 and Ca3SrAl6SO16

The microstructures of unhydrated calcium aluminosulphate Ca₄Al₆SO₁₆ and Ca₃SrAl₆SO₁₆ have been studied by high-resolution electron microscopy (HREM). The results showed that twinning and twinned slabs could be introduced taking the [1 1 2] direction as the twin axis so that it seems to be coincident with the law of twinning formed in body-centred cubic structures. A previously reported superlattice with a repeat period twice that of the fundamental structure along the 〈1 1 0〉 direction has also been found in both matrix and twin variants. The close intergrowth of Ca₃SrAl₆SO₁₆ and another phase, possibly Sr₃Al₂O₆ existing as an inclusion between these two twin variants, was determined and clearly revealed by electron diffraction and HREM images. The coherent interphase boundaries and orientation relationship between them can also be deduced.