Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Relationship Between Oral Health-Related Quality of Life and the Position of the Lower Third Molar: Postoperative Follow-Up

Purpose: The aim of this study was to verify possible associations between oral health-related quality of life (QoL) and the position of the lower third molar among patients undergoing lower third molar surgery during the first postoperative week. Materials and Methods: We performed an interventional prospective study of 86 patients for whom the preoperative treatment plan included the removal of 2 third molar teeth from the same side in a 1-time procedure. The patients were divided into 2 groups depending on the position of the lower third molar. QoL was evaluated before and after the surgical procedure (during the first 7 days) with the Oral Health Impact Profile (OHIP) 14 questionnaire. Data were treated according to Stata 10.0 (StataCorp, College Station, TX). Variables were evaluated by use of split-plot analysis of variance for the repeated-measures analysis to identify the association between QoL and the position of the lower third molar. Results: Patients can have deterioration in their QoL immediately after surgery, especially during the first and second postoperative days, and subsequently show rapid improvement. The variation in the total OHIP score during the days after surgery was significant, whereas a decrease in QoL was observed immediately after the procedure (P = .001), which returned to initial value (preoperative) levels after the sixth postoperative day. The OHIP domains with higher scores (ie, those that had an impact) were physical pain, psychological discomfort, and physical disability (domains 2, 3, and 4, respectively). Conclusions: Teeth considered to be associated with technical difficulties for extraction based on their position had a higher score on the OHIP-14 questionnaire and worse health-related QoL score. QoL outcomes may be as important as clinical signs in decisions regarding third molar extractions. (C) 2012 American Association of Oral and Maxillofacial Surgeons J Oral Maxillofac Surg 70:779-786, 2012

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Assessing Pathogenicity for Novel Mutation/Sequence Variants: The Value of Healthy Older Individuals

Improvement in DNA technology is increasingly revealing unexpected/unknown mutations in healthy persons and generating anxiety due to their still unknown health consequences. We report a 44-year-old healthy father of a 10-year-old daughter with bilateral coloboma and hearing loss, but without muscle weakness, in whom a whole-genome CGH revealed a deletion of exons 38-44 in the dystrophin gene. This mutation was inherited from her asymptomatic father, who was further clinically and molecularly evaluated for prognosis and genetic counseling (GC). This deletion was never identified by us in 982 Duchenne/Becker patients. To assess whether the present case represents a rare case of non-penetrance, and aiming to obtain more information for prognosis and GC, we suggested that healthy older relatives submit their DNA for analysis, to which several complied. Mutation analysis revealed that his mother, brother, and 56-year-old maternal uncle also carry the 38-44 deletion, suggesting it an unlikely cause of muscle weakness. Genome sequencing will disclose mutations and variants whose health impact are still unknown, raising important problems in interpreting results, defining prognosis, and discussing GC. We suggest that, in addition to family history, keeping the DNA of older relatives could be very informative, in particular for those interested in having their genome sequenced.

Investigating Smart Sampling as a population initialization method for Differential Evolution in continuous problems

Recently, researches have shown that the performance of metaheuristics can be affected by population initialization. Opposition-based Differential Evolution (ODE), Quasi-Oppositional Differential Evolution (QODE), and Uniform-Quasi-Opposition Differential Evolution (UQODE) are three state-of-the-art methods that improve the performance of the Differential Evolution algorithm based on population initialization and different search strategies. In a different approach to achieve similar results, this paper presents a technique to discover promising regions in a continuous search-space of an optimization problem. Using machine-learning techniques, the algorithm named Smart Sampling (SS) finds regions with high possibility of containing a global optimum. Next, a metaheuristic can be initialized inside each region to find that optimum. SS and DE were combined (originating the SSDE algorithm) to evaluate our approach, and experiments were conducted in the same set of benchmark functions used by ODE, QODE and UQODE authors. Results have shown that the total number of function evaluations required by DE to reach the global optimum can be significantly reduced and that the success rate improves if SS is employed first. Such results are also in consonance with results from the literature, stating the importance of an adequate starting population. Moreover, SS presents better efficacy to find initial populations of superior quality when compared to the other three algorithms that employ oppositional learning. Finally and most important, the SS performance in finding promising regions is independent of the employed metaheuristic with which SS is combined, making SS suitable to improve the performance of a large variety of optimization techniques. (C) 2012 Elsevier Inc. All rights reserved.