João Araújo

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Industrial monitoring of complex processes with hundreds or thousands of variables is a hard task faced in this work through evolving fuzzy systems. The Visbreaker process of the Sines Oil Refinery is the case studied. Firstly dimension reduction is performed by multidimensional scaling, obtaining the process evolution in a three dimensional space. Then an(More)
The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal(More)
The rapid advancement in information and communication technologies (ICTs) has brought enormous business opportunities as well as challenges. One of these challenges is the demand for ICTs skills and expertise in adopting and implementing these emerging technologies. Coping with skills shortage poses a serious challenge across all European countries. Lack(More)
In this note we give an elementary proof of a theorem first proved by J. A. Erdos [3]. This theorem, which is the main result of [3], states that every noninvertible n × n matrix is a finite product of matrices M with the property that M = M . (These are known as idempotent matrices. Noninvertible matrices are also called singular matrices.) An alternative(More)
Suppose that a deterministic finite automata A = (Q,⌃) is such that all but one letters from the alphabet ⌃ act as permutations of the state set Q and the exceptional letter acts as a transformation with non-uniform kernel. Which properties of the permutation group G generated by the letters acting as permutations ensure that A becomes a synchronizing(More)
In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the(More)
Let X be a finite set. We denote by T (X) the monoid of all (total) transformations on X and by Sym(X) the symmetric group on X. An element a 2 T (X) \ Sym(X) is said to be singular. In 1966 Howie [4] proved that every singular transformation a 2 T (X) can be expressed as a product of idempotents of T (X). This result was generalized by Fountain and Lewin(More)
In ubiquitous streaming data sources, such as sensor networks, clustering nodes by the data they produce is an important problem that gives insights on the phenomenon being monitored by such networks. However, if these techniques require data to be gathered centrally, communication and storage requirements are often unbounded. The goal of this paper is to(More)
For any set X and any relation on X, let T (X, ) be the semigroup of all maps a : X → X that preserve . Let S(X) be the symmetric group on X. If is reflexive, the group of automorphisms of T (X, ) is isomorphic toNS(X)(T (X, )), the normalizer of T (X, ) in S(X), that is, the group of permutations on X that preserve T (X, ) under conjugation. The elements(More)
Let A be a strong independence algebra of finite rank with at most one constant, and let G be the group of automorphisms of A. Let α be a singular endomorphism of A and α = 〈{α} ∪G〉. We describe the elements of α and give additional characterisations when A is a proper independence algebra and G is a periodic group. Mathematics subject classification:(More)