Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Hybrid approaches to estimating freeway travel times using point traffic detector data

The accurate and reliable estimation of travel time based on point detector data is needed to support Intelligent Transportation System (ITS) applications. It has been found that the quality of travel time estimation is a function of the method used in the estimation and varies for different traffic conditions. In this study, two hybrid on-line travel time estimation models, and their corresponding off-line methods, were developed to achieve better estimation performance under various traffic conditions, including recurrent congestion and incidents. The first model combines the Mid-Point method, which is a speed-based method, with a traffic flow-based method. The second model integrates two speed-based methods: the Mid-Point method and the Minimum Speed method. In both models, the switch between travel time estimation methods is based on the congestion level and queue status automatically identified by clustering analysis. During incident conditions with rapidly changing queue lengths, shock wave analysis-based refinements are applied for on-line estimation to capture the fast queue propagation and recovery. Travel time estimates obtained from existing speed-based methods, traffic flow-based methods, and the models developed were tested using both simulation and real-world data. The results indicate that all tested methods performed at an acceptable level during periods of low congestion. However, their performances vary with an increase in congestion. Comparisons with other estimation methods also show that the developed hybrid models perform well in all cases. Further comparisons between the on-line and off-line travel time estimation methods reveal that off-line methods perform significantly better only during fast-changing congested conditions, such as during incidents. The impacts of major influential factors on the performance of travel time estimation, including data preprocessing procedures, detector errors, detector spacing, frequency of travel time updates to traveler information devices, travel time link length, and posted travel time range, were investigated in this study. The results show that these factors have more significant impacts on the estimation accuracy and reliability under congested conditions than during uncongested conditions. For the incident conditions, the estimation quality improves with the use of a short rolling period for data smoothing, more accurate detector data, and frequent travel time updates.

Extensões multidimensionais para correntropia e suas aplicações em estimativas robustas

This present work uses a generalized similarity measure called correntropy to develop a new method to estimate a linear relation between variables given their samples. Towards this goal, the concept of correntropy is extended from two variables to any two vectors (even with different dimensions) using a statistical framework. With this multidimensionals extensions of Correntropy the regression problem can be formulated in a different manner by seeking the hyperplane that has maximum probability density with the target data. Experiments show that the new algorithm has a nice fixed point update for the parameters and robust performs in the presence of outlier noise.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Prevalence of inadequate nutrient intake in a group of adolescents using dietary reference intake- based methods

O objetivo do presente estudo foi avaliar a prevalência de ingestão inadequada de nutrientes em um grupo de adolescentes de São Bernardo do Campo-SP. Dados de consumo de energia e nutrientes foram obtidos por meio de recordatórios de 24 horas aplicados em 89 adolescentes. A prevalência de inadequação foi calculada utilizando o método EAR como ponto de corte, após ajuste pela variabilidade intrapessoal, utilizando o procedimento desenvolvido pela Iowa State University. As Referências de Ingestão Dietética (IDR) foram os valores de referência para ingestão. Para os nutrientes que não possuem EAR estabelecida, a distribuição do consumo foi comparada com a AI. As maiores prevalências de inadequação em ambos sexos foram observadas para o magnésio (99,3 por cento para o sexo masculino e 81,8 por cento para o feminino), zinco (44,0 por cento para o sexo masculino e 23,5 por cento para o feminino), vitamina C (57,2 por cento para o sexo masculino e 59,9 por cento para o feminino) e folato (34,8 por cento para o sexo feminino). A proporção de indivíduos com ingestão superior à AI foi insignificante (menor que 2,0 por cento) em ambos os sexos

Minimal Nielsen Root Classes and Roots of Liftings

Given a continuous map f : K -> M from a 2-dimensional CW complex into a closed surface, the Nielsen root number N(f) and the minimal number of roots mu(f) of f satisfy N(f) <= mu(f). But, there is a number mu(C)(f) associated to each Nielsen root class of f, and an important problem is to know when mu(f) = mu(C)(f)N(f). In addition to investigate this problem, we determine a relationship between mu(f) and mu((f) over tilde), when (f) over tilde f is a lifting of f through a covering space, and we find a connection between this problems, with which we answer several questions related to them when the range of the maps is the projective plane.

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

Energy gain induced by boundary crisis

We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

Loss minimization by the predictor-corrector modified barrier approach

This paper presents a new approach, predictor-corrector modified barrier approach (PCMBA), to minimize the active losses in power system planning studies. In the PCMBA, the inequality constraints are transformed into equalities by introducing positive auxiliary variables. which are perturbed by the barrier parameter, and treated by the modified barrier method. The first-order necessary conditions of the Lagrangian function are solved by predictor-corrector Newton`s method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, reaching the limits of the inequality constraints. The feasibility of the proposed approach is demonstrated using various IEEE test systems and a realistic power system of 2256-bus corresponding to the Brazilian South-Southeastern interconnected system. The results show that the utilization of the predictor-corrector method with the pure modified barrier approach accelerates the convergence of the problem in terms of the number of iterations and computational time. (C) 2008 Elsevier B.V. All rights reserved.

Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

Texture alignment in simple shear

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is coupled to a director theory to add specific orientation of grains to describe anisotropic microstructure. The numerical solution is based on an implicit form of the Material Point Method developed by Moresi et al. [1].

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.