
Martins, Ernesto de Queirós Vieira; Pascoal, Marta Madalena Braz; Santos, José Luís Esteves

Rocha, Ana Maria; Fernandes, Edite M. G. P.; Soares, João
Neste artigo apresentamos resultados computacionais obtidos com o algoritmo volumétrico, uma variante do método do subgradiente, na resolução da relaxação linear que decorre da formulação estendida de fluxo desagregado para o problema do Caixeiro Viajante Assimétrico. As experiências computacionais foram realizadas numa selecção de instâncias da TSPLib e num conjunto de instâncias geradas aleatoriamente de acordo com o Dimacs Implementation Challenge. Também experimentámos a aplicação de heurísticas durante a execução do algoritmo volumétrico. As experiências computacionais mostram sucesso moderado com instâncias de média dimensão.

Ramires, Ana; Soares, João
Neste artigo explicamos como obter um limite inferior para o valor óptimo do problema do caixeiro viajante assimétrico melhor do que o que advém do problema de afectação através da resolução sucessiva de problemas de afectação. O algoritmo que propomos é um método de primeira ordem baseado na função de penalidade exponencial cujas direcções de deslocamento são definidas com base numa relaxação disjuntiva que propomos ser de dois tipos, uma baseada em ciclos e a outra baseada em cliques.

Cardoso, J. R.; Leite, F. Silva
We show that the diagonal Pade approximants methods, both for computing
the principal logarithm of matrices belonging to the Lie groupSE (n, IR) of special
Euclidean motions in IRn and to compute the matrix exponential of elements in
the corresponding Lie algebra se(n, IR), are structure preserving. Also, for the
particular cases when n == 2,3 we present an alternative closed form to compute
the principal logarithm. These low dimensional Lie groups play an important
role in the kinematic motion of many mechanical systems and, for that reason,
the results presented here have immediate applications in robotics

Henriques, Carla; Oliveira, Paulo Eduardo
Considering an associated and strictly stationary sequence of random variables we introduce an histogram estimator for the covariances between indicator functions of those random
variables. We find conditions on the covariance structure of the original random variables for
the almost sure convergence of the estimator and for the convergence in distribution of the
finite dimensional distributions. Finally we characterize the usual error criteria finding their
convergence rates under assumptions on the convergence rate of the covariances

Carvalho, F. J. Craveiro de

Neves, J. S.

Janelidze, George; Sobral, Manuela
It is shown that the descent constructions of finite preorders provide a simple motivation for
those of topological spaces, and new counterexamples to open problems in Topological descent
theory are constructed

Gonçalves, E.; Martins, C. M.; MendesLopes, N.
This paper presents a generalisation of a non classical decision procedure for simple
bilinear models with a general error process proposed by Gon calves Jacob and Mendes
Lopes This decision method involves two hypotheses on the model and its consis
tence is obtained by establishing the asymptotic separation of the sequences of probability
laws de
ned by each hypothesis Studies on the rate of convergence in the diagonal case
are presented and an exponential decay is obtained Simulation experiments are used to
illustrate the behaviour of the power and level functions in small and moderate samples
when this procedure is used as a test

Oliveira, F. Aragão
Classical finitedifference operators on uniform meshes are not appropriate for
solving singularly perturbed differential equations due to the effect of the boundary
layers.If we want uniformly convergent difference schemes (with respect to some
discrete norm), we need to adequate the numerical operator or the mesh, or both,
the operator and the mesh. We summarize some recent results about uniform
convergent methods for a general linear two point boundary value problem and
present two algorithms related with the numerical method, which give indication
about the transition points of the solution in the given domain. They are transition
point indicators

Rodrigues, Rui C.; Leite, F. Silva
We show how to generate a class of Euclidean splines, called Lsplines,
as solutions of a highorder variational problem. We also show connections
between Lsplines and optimal control theory, leading to the conclusion that
Lsplines are manifestations of an optimal behavior

Urbano, José Miguel
We consider equations of the form
atv  div(Q ( v)Vv) == 0 ,
where v E [0,1] and Q(v) degenerates for v == 0 and v == 1. We show that
local weak solutions are locally Holder continuous provided Q behaves like
a power near the two degeneracies. We adopt the technique of intrinsic
rescaling developed by DiBenedetto.

Bensaïd, Nadia; Oliveira, Paulo Eduardo
Nonparametric inference for point processes is discussed by way histograms, which provide a
nice tool for the analysis of online data. The construction of histograms depends on a sequence
of partitions, which we take to be nonembedded to allow partitions with sets of equal measure.
This presents some theoretical problems, which are addressed with an assumption on the decomposition
of second order moments. In another direction, we drop the usual independence
assumption on the sample, replacing it by a strong mixing assumption. Under this setting, we
study the convergence of the histogram in probability, which depends on approximation conditions
between the distributions of random pairs and the...

Caseiro, R.; Françoise, J. P.
The main result of this paper is the evidence of an explicit linearization
of dynamical systems of RuijsenaarsSchneider (RS) type and of the perturbations
introduced by F. Calogero of these systems with all orbits periodic
of same period. Several other systems share the existence of this explicit
linearization, among them, the CalogeroMoser system (with and without
external potential) and the CalogeroSutherland system. This explicit linearization
is compared with the notion of maximal superintegrability which
has been discussed in several articles (to quote few of them, Hietarinta [12],
Henon [11], HarnadWinternitz [10], S. Wojchiechowsky [15]).

Gutierres, Gonçalo
Among closure operators in the sense of Dikranjan and Giuli
[5] the regular
ones have a relevant role and have been widely investigated. On the contrary, the
coregular closure operators were introduced only recently in [3] and they need to
be further investigated. In this paper we study co
regular closure operators, in
connection connectednesses and disconnectednesses, in the realm of topological
spaces and modules.

Costa, J. M. Nunes da
We study the relationship between two (compatible) J acobi structures on a manifold
M, using their associated homogeneous Poisson structures on lR x M, in the case
where these Poisson tensors are related by a Nijenhuis tensor.

Urbano, José Miguel
We show that weak solutions of a free boundary problem, modeling a waterice
phase transition in the case of nonlinear heat diffusion, are continuous up to
the lateral boundary. We consider homogeneous Dirichlet boundary conditions and
assume that the lateral boundary of the spacetime domain satisfies the property of
positive geometric density. The results are a follow up from recent results by the
author concerning the interior regularity.

Carvalho, F. J. Craveiro de

Urbano, José Miguel
We exemplify the role of Free Boundary Problems as an important
source of ideas in modern analysis. With the help of a model problem we
illustrate the use of analytical, algebraic and geometrical techniques obtaining
uniqueness of weak solutions via the use of entropy inequalities, existence
through nonlinear semigroup theory, and regularity using a method, called
intrinsic scaling, based on interpreting a partial differential equation in a
geometry dictated by its own structure

Figueiredo, Isabel N.; Júdice, Joaquim J.; Oliveira, Pedro N.
The application of complementarity and genetic algorithms to an optimization
thin laminated shallow shell problem is discussed. The discrete form of the problem
leads to a Mathematical Program with Equilibrium Constraints (MPEC) [1], whose constraint
set consists of a variational inequality and a set of equality constraints. Furthermore
the variables are discrete. Special instances of the general problem are considered and indicate
that the choice of the algorithm depends on the problem to be linear or nonlinear.