Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

Analysis of Apical Root Transportation Associated with Protaper Universal F3 and F4 Instruments by Using Digital Subtraction Radiography

Introduction: The aim of this study was to assess the occurrence of apical root transportation after the use of Pro Taper Universal rotary files sizes 3 (F3) and 4 (F4). Methods: Instruments were worked to the apex of the original canal, always by the same operator. Digital subtraction radiography images were produced in buccolingual and mesiodistal projections. A total of 25 radiographs were taken from root canals of human maxillary first molars with curvatures varying from 23-31 degrees. Quantitative data were analyzed by intraclass correlation coefficient and Wilcoxon nonparametric test (P = .05). Results: Buccolingual images revealed a significantly higher degree of apical transportation associated with F4 instruments when compared with F3 instruments in relation to the original canal (Wilcoxon test, P = .007). No significant difference was observed in mesiodistal images (P = .492). Conclusions: F3 instruments should be used with care in curved canals, and F4 instruments should be avoided in apical third preparation of curved canals. (J Endod 2010;36:1052-1055)

The anatomy of two-rooted mandibular canines determined using micro-computed tomography

P>Aim To investigate the internal and external anatomy of extracted human mandibular canines with two roots and two distinct canals using micro-computed tomography (mu CT). Methodology Fourteen two-rooted human mandibular canines were scanned using a high-resolution mu CT system (SkyScan 1174v2; SkyScan N.V., Kontich, Belgium). The images were processed to evaluate the size of the roots, the furcation regions, the presence of accessory canals, the mean distances between several anatomical landmarks, the position of the apical foramina, the direction of root curvatures, the cross-sectional appearances (SMI index), the volume and surface areas of the root canals. Results Root bifurcation was located in both apical (44%, n = 6) and middle (58%, n = 8) thirds of the root. The size of the buccal and lingual roots was similar in 29% of the sample. From a buccal view, no curvature towards the lingual or buccal direction occurred in either roots. From a proximal view, no straight lingual root occurred. In both views, S-shaped roots were found in 21% of the specimens. Location of the apical foramen varied considerably, tending to the mesio-buccal aspect of both roots. Lateral and furcation canals were observed mostly in the cervical third in 29% and 65% of the sample, respectively. The structure model index (SMI) index ranged from 1.87 to 3.86, with a mean value of 2.93 +/- 0.46. Mean volume and area of the root canals were 11.52 +/- 3.44 mm3 and 71.16 +/- 11.83 mm2, respectively. Conclusions The evaluation of two-rooted mandibular canines revealed that bifurcations occurred in the apical and middle third. S-shaped roots were found in 21% of the specimens. Mean volume, surface area and SMI index of the root canals were 11.52 mm3, 71.16 mm2 and 2.93, respectively.

Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data the local influence curvatures are derived and some diagnostic graphics are proposed A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors The local influence approach is used to compare the sensitivity of the model estimates (C) 2010 Elsevier B V All rights reserved

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.

Influence diagnostics for linear models with first-order autoregressive elliptical errors

We introduce in this paper the class of linear models with first-order autoregressive elliptical errors. The score functions and the Fisher information matrices are derived for the parameters of interest and an iterative process is proposed for the parameter estimation. Some robustness aspects of the maximum likelihood estimates are discussed. The normal curvatures of local influence are also derived for some usual perturbation schemes whereas diagnostic graphics to assess the sensitivity of the maximum likelihood estimates are proposed. The methodology is applied to analyse the daily log excess return on the Microsoft whose empirical distributions appear to have AR(1) and heavy-tailed errors. (C) 2008 Elsevier B.V. All rights reserved.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.