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.     

Rheological and drug‐release behaviour of a scleroglucan gel matrix at different drug loadings

The aim of this study was to investigate the drug‐loading effects on release and mechanical properties of a scleroglucan gel, with the intention of considering them in delivery systems formulations. The rheological and kinetic properties of a 2 % w/w scleroglucan gel matrix loaded with 0, 0.02, 0.04, 0.06, 0.2 and 0.4 % w/w of theophylline (Th, used as a model drug) were investigated. Rheological measurements were performed in a controlled‐stress rotational‐shear rheometer under isothermal conditions. For theophylline release from the gel a flat Franz cell was used and the kinetic parameters were derived applying a semi‐empirical power law. The influence of scleroglucan molar weight on kinetic and rheological behaviour was also studied. Results suggest two possible effects of drug loading on the gel network: in the 0.04–0.06 % w/w Th range a plasticizing effect and in the 0.2–0.4 % w/w Th range a rigidization effect. In the first range mentioned, the changes in the gel structural properties tested by means of rheological measurements are coincident with changes in drug‐release kinetics. Copyright © 2005 Society of Chemical Industry     

Precision equipment for symmetrical bending— Part 1. The loading system

The design and performance of precision bending equipment for testing straight beams with constant rectangular section under a pure bending moment is described. Part 1 deals with the loading arrangements and Part 2 with the rig for measuring beam deflection. The methods for recording deflection of strain gauges applied on the beam have been described elsewhere.^1–4
The reactions to the deadweight gravity loads are taken via ball bearings. The total bending moment inaccuracy, i.e. the sum of estimated systematic errors and random errors, the latter expressed as the 2Ga confidence interval about the mean (2G_cim), is about ± 25 x. 10^-4%, for 23 tests with a steel beam with 15 mm × 75 mm cross sectional dimensions, loaded to 1-1.5 mm/m strain.
The measuring rig stands on the beam via hardened and polished spherical segment feet and uses a capacitive transducer system with less than 5nm resolution. Various application tasks are described. The total inaccuracy of the measured deflection, i.e. apart from bending moment inaccuracy, is about ± 35 times 10^4% for about 10 reproduced, not repeated, tests with the same steel beam. The deflection for such a beam is of the order of 2 to 4 mm.     

Effect of refraction on optical microscopic measurement of internal blood-vessel diameter and its correction

In optical microscopic measurement of internal blood-vessel diameters, the effect of refraction must be taken into account to ensure accuracy of the result. This effect is discussed and an analytical correction formula derived. Phantom blood vessels with known internal and external diameters were used to test the validity of the correction formula. The errors obtained prior to correction were reduced significantly after correction.     

The solution of the inverse problem of gravitational potential using a set of measurements of different field elements

A numerical solution of the inverse problem of the gravitational field at a single point is obtained using six field elements for a point, a spherical cap, a differential spherical sector and a vertical segment. In the system of six equations obtained, the unknowns are the mass of the body, the depth of its center, and the second, third, and fourth degree moments. The accuracy of the solution of this system is ten times higher than when using three field elements. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 3–8, May, 2007.     

Feasibility study of absolute activity measurement with metallic magnetic microcalorimeters

We report on a feasibility study on precise determination of mass-specific activity of low-energy emitting radioisotopes. Conventional methods of activity measurement suffer from source self-absorption and a strong decrease in detection efficiency for low-energy electrons and photons. We propose a new method based on metallic magnetic microcalorimeters with the source embedded in the detector target in a 4π geometry. First results with a ⁵⁵Fe source show that electrons and photons are detected with a detection efficiency close to unity and with little loss of energy for electrons. The aim of this study is to provide standards of activity with very low uncertainties in the framework of radiation metrology.     

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.     

纳米颗粒的测量与表征

介绍了用于纳米颗粒测量的电镜观察法、X射线衍射线宽法、激光粒度分析法、比表面积法、颗粒沉降法、扫描探针显微术以及小角X射线散射等,并对其测量原理、测量过程、适用范围及测量方法的优缺点进行了讨论。     

Specific interactions in blends containing Chitosan and functionalized polymers. Molecular dynamics simulations

Chitosan (CS)/poly(vinyl alcohol) (PVA) and Chitosan/poly(2-hydroxyethyl methacrylate) (P2HEM) blends have been studied through molecular dynamic simulations. In a previous work it was found miscibility between these polymers and it was attributed to hydrogen bonding formation. However, the experimental information obtained was not enough to know which of the interacting groups of Chitosan, i.e. -CH₂OH or -NH₂, are responsible of the interaction. Therefore, we have performed molecular dynamics simulation runs of 1 ns in order to calculate radial distribution functions (RDF) for the groups tentatively involved in the interaction. The results are correlated with our previous experimental data. This way, we have obtained a more precise conclusive information about the interactions involved as function of the blends composition. For low compositions of PVA and P2HEM the interaction is predominantly with the hydroxymethyl groups of CS while as the composition of PVA and P2HEM increases, the interaction with the amine groups increases.