Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

An iterated sample construction with path relinking method: Application to switch allocation in electrical distribution networks

We present a metaheuristic approach which combines constructive heuristics and local searches based on sampling with path relinking. Its effectiveness is demonstrated by an application to the problem of allocating switches in electrical distribution networks to improve their reliability. Our approach also treats the service restoration problem, which has to be solved as a subproblem, to evaluate the reliability benefit of a given switch allocation proposal. Comparisons with other metaheuristics and with a branch-and-bound procedure evaluate its performance. © 2012 Published by Elsevier Ltd.

Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta formulae is developed for the efficient numerical solution of nonlinear stiff two-point boundary value problems. An analysis of the stability properties of general deferred correction schemes which are based on implicit Runge-Kutta methods is given and results which are analogous to those obtained for initial value problems are derived. A revised definition of symmetry is presented and this ensures that each deferred correction produces an optimal increase in order. Finally, some numerical results are given to demonstrate the superior performance of Lobatto formulae compared with mono-implicit formulae on stiff two-point boundary value problems. (C) 1998 Elsevier B.V. Ltd. All rights reserved.

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

Boundary of the rauzy fractal sets in R x C generated by P(x)=x(4)-x(3)-x(2)-x-1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the number of singularities in generic deformations of map germs

Let f:C-n, 0 --> C-p, 0 be a K-finite map germ, and let i = (i(1),..., i(k)) be a Boardman symbol such that Sigma(i) has codimension n in the corresponding jet space J(k)(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of Sigma(i) points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n - i(1) and, in addition, in the case p = 6, f must be a singularity of type Sigma(i2.i2).

Uma nova heurística para o problema de minimização de trocas de ferramentas

O problema de minimização de troca de ferramentas (MTSP) busca uma sequência de processamento de um conjunto de tarefas, de modo a minimizar o número de trocas de ferramentas requeridas. Este trabalho apresenta uma nova heurística para o MTSP, capaz de produzir bons limitantes superiores para um algoritmo enumerativo. Esta heurística possui duas fases: uma fase construtiva que é baseada em um grafo em que os vértices correspondem a ferramentas e existe um arco k = (i, j) que liga os vértices i e j se e somente se as ferramentas i e j são necessárias para a execução de alguma tarefa k; e uma fase de refinamento baseada na meta-heurística Busca Local Iterativa. Resultados computacionais mostram que a heurística proposta tem um bom desempenho para os problemas testados, contribuindo para uma redução significativa no número de nós gerados de um algoritmo enumerativo.

Automatic absolute orientation of scanned aerial photographs

Image orientation is a basic problem in Digital Photogrammetry. While interior and relative orientations were succesfully automated, the same can not be said about absolute orientation. This process can be automated by using an approach based on relational matching and a heuristic that uses the analytical relation between straight features in the object space and its homologous in the image space. A build-in self-diagnosis is also used in this method, that is based on the implementation of data snooping statistic test in the process of spatial resection, using the Iterated Extended Kalman Filtering (IEKF). The aim of this paper is to present the basic principles of the proposed approach and results based on real data.

Strategy to detect ground control in digital images

The identification of ground control on photographs or images is usually carried out by a human operator, who uses his natural skills to make interpretations. In Digital Photogrammetry, which uses techniques of digital image processing extraction of ground control can be automated by using an approach based on relational matching and a heuristic that uses the analytical relation between straight features of object space and its homologous in the image space. A build-in self-diagnosis is also used in this method. It is based on implementation of data snooping statistic test in the process of spatial resection using the Iterated Extended Kalman Filtering (IEKF). The aim of this paper is to present the basic principles of the proposed approach and results based on real data.

Orientação semi-automática de imagens CBERS usando rodovias como controle de campo

In this paper is proposed a methodology for semiautomatic CBERS image orientation using roads as ground control. It is based on an iterative strategy involving three steps. In the first step, an operator identifies on the image the ground control roads and supplies along them a few seed points, which could be sparsely and coarsely distributed. These seed points are used by the dynamic programming algorithm for extracting the ground control roads from the image. In the second step, it is established the correspondences between points describing the ground control roads and the corresponding ones extracted from the image. In the last step, the corresponding points are used to orient the CBERS image by using the DLT (Direct Linear Transformation). The two last steps are iterated until the convergence of the orientation process is verified. Experimental results showed that the proposed methodology was efficient with several test images. In all cases the orientation process converged. Moreover, the estimated orientation parameters allowed the registration of check roads with pixel accuracy or better.

Boundary of the rauzy fractal sets in ℝ×ℂgenerated by p(x) = x 4- x 3 - x 2 -x- 1

We study the boundary of the 3-dimensional Rauzy fractal ε ⊂ ℝ×ℂ generated by the polynomial P(x) Dx 4-x 3-x 2-x-1. The finite automaton characterizing the boundary of ε is given explicitly. As a consequence we prove that the set ε has 18 neighboors where 6 of them intersect the central tile ε in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.

A semi-automatic method for indirect orientation of aerial images using ground control lines extracted from airborne laser scanner data

This paper presents a method for indirect orientation of aerial images using ground control lines extracted from airborne Laser system (ALS) data. This data integration strategy has shown good potential in the automation of photogrammetric tasks, including the indirect orientation of images. The most important characteristic of the proposed approach is that the exterior orientation parameters (EOP) of a single or multiple images can be automatically computed with a space resection procedure from data derived from different sensors. The suggested method works as follows. Firstly, the straight lines are automatically extracted in the digital aerial image (s) and in the intensity image derived from an ALS data-set (S). Then, correspondence between s and S is automatically determined. A line-based coplanarity model that establishes the relationship between straight lines in the object and in the image space is used to estimate the EOP with the iterated extended Kalman filtering (IEKF). Implementation and testing of the method have employed data from different sensors. Experiments were conducted to assess the proposed method and the results obtained showed that the estimation of the EOP is function of ALS positional accuracy.

Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Orientação semi-automática de imagens CBERS usando rodovias como controle de campo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dimensões fractais para certos sistemas dinâmicos discretos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)