
MartinsFerreira, Nelson; Sobral, Manuela
We characterize pointed categories having semidirect products in the
sense of D. Bourn and G. Janelidze ([3]) providing necessary and sufficient conditions
for a pointed category to admit semidirect products and interpreting these
conditions in terms of protomodularity and exactness of certain split chains.

Almeida, Jorge; Costa, Alfredo
In previous work, the first author established a natural bijection between
minimal subshifts and maximal regular J classes of free profinite semigroups.
In this paper, the Sch¨utzenberger groups of such J classes are investigated in particular
in respect to a conjecture proposed by the first author concerning their profinite
presentation. The conjecture is established for several types of minimal subshifts
associated with substitutions. The Sch¨utzenberger subgroup of the J class corresponding
to the ProuhetThueMorse subshift is shown to admit a somewhat simpler
presentation, from which it follows that it satisfies the conjecture, that it has rank
three, and that it is nonfree relatively to any pseudovariety of groups.

Bourn, Dominique; Rodelo, Diana
We show that, under suitable left exact conditions on a re
ection functor
I, the construction of the associated universal Icentral extension is reduced
to the comprehensive factorization of a speci c internal functor. This observation
produces some existence conditions which hold in particular for any re
ection from
a Mal'cev variety to any Birkho subvariety

Urbano, José Miguel; Vorotnikov, Dmitry
We prove a series of results concerning the emptiness and nonemptiness
of a certain set of Sobolev functions related to the wellposedness of a twophase
minimization problem, involving both the p(x)norm and the in nity norm. The
results, although interesting in their own right, hold the promise of a wider applicability
since they can be relevant in the context of other problems where minimization
of the penergy in a part of the domain is coupled with the more local minimization
of the L1norm on another region

Santana, Ana Paula; Yudin, Ivan
In a perfect category every object has a minimal projective resolution.
We give a sufficient condition for the category of modules over a categorygraded
algebra to be perfect

Abrunheiro, Lígia; Camarinha, Margarida; Cariñena, José F.; ClementeGallardo, Jesús; Martínez, Eduardo; Santos, Patricia
In this paper we study optimal control problems for nonholonomic systems
defined on Lie algebroids by using quasivelocities. We consider both kinemactic,
i.e. systems whose cost functional depends only on position and velocities, and
dynamic optimal control problems, i.e. systems whose cost functional depends also
on accelarations. Formulating the problem directly at the level of Lie algebroids
turns out to be the correct framework to explain in detail similar results appeared
recently [48]. We also provide several examples to illustrate our construction

Branquinho, A.; Rebocho, M. N.

Gutiérrez García, Javier; Picado, Jorge
This paper deals with the algebra F(L) of real functions of a frame L
and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous
real functions. It is wellknown that F(L) is a latticeordered ring; this paper
presents explicit formulas for its algebraic operations which allow to conclude about
their behaviour in LSC(L) and USC(L).
As applications, idempotent functions are characterized and the results of [10]
about strict insertion of functions are signi cantly improved: general pointfree formulations
that correspond exactly to the classical strict insertion results of Dowker
and Michael regarding, respectively, normal countably paracompact spaces and perfectly
normal spaces are derived.
The paper ends with a...

Branquinho, A.; Marcellán, F.; Mendes, A.
In this paper we study sequences of matrix polynomials that satisfy a
nonsymmetric recurrence relation. To study this kind of sequences we use a vector
interpretation of the matrix orthogonality. In the context of these sequences of
matrix polynomials we introduce the concept of the generalized matrix Nevai class
and we give the ratio asymptotics between two consecutive polynomials belonging to
this class. We study the generalized matrix Chebyshev polynomials and we deduce
its explicit expression as well as we show some illustrative examples. The concept of
a Dirac delta functional is introduced. We show how the vector model that includes
a Dirac delta functional is a representation...

Gran, Marino; Rodelo, Diana
We present a new characterisation of Goursat categories in terms of
special kind of pushouts, that we call Goursat pushouts. This allows one to prove
that, for a regular category, the Goursat property is actually equivalent to the
validity of the denormalised 3by3 Lemma. Goursat pushouts are also useful to
clarify, from a categorical perspective, the existence of the quaternary operations
characterising 3permutable varieties

Jacob, Pierre; Oliveira, Paulo Eduardo
In models using categorical data one may use adjacency relations to
justify smoothing to improve upon simple histogram approximations of the probabilities.
This is particularly convenient for sparsely observed or rather peaked
distributions. Moreover, in a few models, prior knowledge of a marginal distribution
is available. We adapt local polynomial estimators to include this partial
information about the underlying distribution and give explicit representations for
the proposed estimators. An application to a set of anthropological data is included.

Ferreira, J. A.; Oliveira, P. de; Silva, P. M. da; Murta, J. N.
Mathematical models to describe drug concentration profiles of topically
administered drug in the anterior chamber aqueous humor have been proposed
by several authors. The aim of this paper is to present a mathematical model to
predict the drug concentration in the anterior chamber when a therapeutical contact
lens with the drug is entrapped in nanoparticles is used.

Ferreira, J. A.; Oliveira, P. de; Silva, P. M. da; Simon, L.
The dynamics of diffusive and stressinduced transport in polymeric
delivery systems was investigated. Partial and ordinary differential equations were
first written to describe drug release behaviors in Maxwell and MaxwellVoigt materials.
The time constants governing the flux and concentration responses of a
permeating species were determined from a Laplace transform solution of the original
model. A ”tracking strategy”, based on the estimated characteristic times,
was proposed to estimate the delivery rate and the concentration near the exit side
of the membrane. The methodology was more efficient at times greater than the
time constant and the prediction error decreased further as the process approached
steady state. Numerical illustrations and comparisons...

Oliveira, Paulo Eduardo

Vorotnikov, Dmitry
We study the
ashing ratchet model of a Brownian motor, which consists
in cyclical switching between the FokkerPlanck equation with an asymmetric
ratchetlike potential and the pure di usion equation. We show that the motor really
performs unidirectional transport of mass, for proper parameters of the model,
by analyzing the attractor of the problem and the stationary vector of a related
Markov chain

Conn, Andrew R.; Vicente, L. N.
We address bilevel programming problems when the derivatives of both
the upper and the lower level objective functions are unavailable.
The core algorithms used for both levels are trustregion interpolationbased
methods, using minimum Frobenius norm quadratic models when the number of
points is smaller than the number of basis components. We take advantage of the
problem structure to derive conditions (related to the global convergence theory of
the underlying trustregion methods, as far as possible) under which the lower level
can be solved inexactly and sample points can be reused for model building. In addition,
we indicate numerically how effective these expedients can be. A number of
other issues...

Vicente, L. N.
In this paper we prove that direct search of directional type shares
the worst case complexity bound of steepest descent when sufficient decrease is
imposed using a quadratic function of the step size parameter. This result is proved
under smoothness of the objective function and using a framework of the type of
GSS (generating set search). We also discuss the worst case complexity of direct
search when only simple decrease is imposed and when the objective function is
nonsmooth.

Custódio, A. L.; Madeira, J. F. A.; Vaz, A. I. F.; Vicente, L. N.
In practical applications of optimization it is common to have several
conflicting objective functions to optimize. Frequently, these functions are subject to
noise or can be of blackbox type, preventing the use of derivativebased techniques.
We propose a novel multiobjective derivativefree methodology, calling it direct
multisearch (DMS), which does not aggregate any of the objective functions. Our
framework is inspired by the search/poll paradigm of directsearch methods of directional
type and uses the concept of Pareto dominance to maintain a list of nondominated
points (from which the new iterates or poll centers are chosen). The aim
of our method is to generate as many points in the Pareto...

Kuusi, Tuomo; Siljander, Juhana; Urbano, José Miguel
We give a proof of the Hölder continuity of weak solutions of certain degenerate
doubly nonlinear parabolic equations in measure spaces. We only assume
the measure to be a doubling nontrivial Borel measure which supports a Poincaré
inequality. The proof discriminates between large scales, for which a Harnack inequality
is used, and small scales, that require intrinsic scaling methods.

Figueiredo, Isabel N.; Figueiredo, Pedro; Almeida, Nuno
The administration of dyes and subsequent examination, with a colorimetry
visual criterium, is a gastroenterology procedure for distinguishing, in
endoscopic images, normal and aberrant colonic crypts. These are thought to be
possible precursors of colon cancer. In this paper a combined image segmentation
and parameter estimation model is proposed for in vivo colonic crypts’ images,
obtained with chromoscopic colonoscopy. The parameter estimation is an inverse
problem. It is formulated as a partial differential equation constrained optimization
problem, and involves an absorptiondiffusion equation. A Lagrange multiplier formulation
is employed and analyzed for resolving this inverse problem. Using only
the segmentation of the medical endoscopic image, which separates normal and
aberrant crypts,...