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.     

A continuum-based modeling of MEMS devices for estimating their resonant frequencies

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics to conventional lumped models. The general coupled electrostatics-structure interactions are then applied for the prediction of resonant frequencies of MEMS devices due to bias-voltage changes and temperature variations. Comparisons of predicted resonant frequencies obtained by the present coupled electrostatics-structure interaction models with experimental results available in the literature demonstrate that the proposed continuum-based interaction modeling yields high-confidence predictions of resonant frequencies of MEMS devices.     

Influence of accelerated ageing on methacrylate‐based denture resins heterogeneity as viewed by ESR‐spin‐probe method

The electron‐spin‐resonance (ESR) spin‐probe method, was used to study the heterogeneity of denture resins based on poly(methyl methacrylate). Results for three resins processed by microwave energy, conventional curing and cold curing (depending on the curing procedure and exposed to ageing in various environmental conditions) were compared. All three cured resins were stored over the same time (1200 h) in distilled water at ambient temperature and in artificial saliva at 348 K. The temperature‐dependent ESR spectra of a spin probe dispersed in the denture resins are analyzed in terms of line‐shapes and line‐widths. The appearance of two spectral components was taken as an indication of resin heterogeneity. The results reveal that the cold‐cured resin has a lower local density in comparison with microwave and conventionally cured resin. The amount of residual monomer also contributes to the local motion of polymer segments. The change of denture resins exposed to ageing is influenced both by the structure of the original resin and the ageing conditions. Restricted motion of a spin probe incorporated into the acrylic resins exposed to accelerated ageing suggests additional crosslinking of polymer chains. The differences are observed for all the investigated resins, but the highest change is observed with the cold‐cured resin. The ESR results are accompanied by T_g and T_m measurements. Copyright © 2005 Society of Chemical Industry     

Cholesterol‐imprinted polymer receptor prepared by a hybrid imprinting method

A novel cholesterol‐imprinted polymer (CMIP‐H) was prepared by a hybrid method of covalent imprinting and non‐covalent imprinting. This approach involves the copolymerization of a template‐containing monomer, cholesteryl 2‐hydroxyethyl methacrylate carbonate, and a cross‐linker, followed by hydrolysis to afford a flexible guest‐binding site accompanied with the easy and efficient removal of a ‘sacrificial spacer’. The effect of solvent on the binding capacity of CMIP‐H towards cholesterol was studied, indicating that a good binding capacity towards cholesterol could be achieved in a less‐polar solvent. The binding experiments of CMIP‐H towards a series of structural analogues of cholesterol, including cholesterol acetate, progesterone and stigmasterol, were carried out in hexane. The results showed that CMIP‐H almost did not bind cholesterol acetate at all because the hydrogen‐bonding site is blocked. It exhibited a similar binding towards both cholesterol and stigmasterol, but much higher binding towards progesterone. Copyright © 2005 Society of Chemical Industry     

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     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

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.     

Visual evaluation at scale of threshold to suprathreshold color difference

Visual evaluation experiments of color discrimination threshold and suprathreshold color‐difference comparison were carried out using CRT colors based on the psychophysical methods of interleaved staircase and constant stimuli, respectively. A large set of experimental data was generated ranged from threshold to large suprathreshold color difference at the five CIE color centers. The visual data were analyzed in detail for every observer at each visual scale to show the effect of color‐difference magnitude on the observer precision. The chromaticity ellipses from this study were compared with four previous published data, of CRT colors by Cui and Luo, and of surface colors by RIT‐DuPont, Cheung and Rigg, and Guan and Luo, to report the reproducibility of this kind of experiment using CRT colors and the variations between CRT and surface data, respectively. The present threshold data were also compared against the different suprathreshold data to show the effect of color‐difference scales. The visual results were further used to test the three advance color‐difference formulae, CMC, CIE94, and CIEDE2000, together with the basic CIELAB equation. In their original forms or with optimized K_L values, the CIEDE2000 outperformed others, followed by CMC, and with the CIELAB and CIE94 the poorest for predicting the combined dataset of all color centers in the present study. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 198–208, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20106     

电容传感器在使用中存在的几个问题及处理方法

随着电容测量技术的迅速发展，电容传感器在非电量测量和自动检测中得到广泛应用，但它在使用过程中也存在一些问题，针对在使用电容传感器过程中存在的几个问题，从电容传感器的原理和工作过程两个方面进行了讨论，并提出行之有效的处理方法。