In this paper, we present recursive formulas for the sequential determination of the generalized LM-inverse of a general matrix. The formulas are developed for a matrix augmented by a column. These formulas are particularized to obtain also recursive relations for the generalized L-inverse of a general matrix augmented by a column.

We introduce two generalizations of the full inverse symmetric semigroup ISX — the inverse semigroups PIPX and P̃IPX . Both of these semigroups have the same set of elements and contain ISX . The binary operations on PIPX and P̃IPX are two natural generalizations of the multiplication of partial permutations and each of the considered operations coincides with this multiplication when restricted ...

TaxoMap is an alignment tool which aims to discover rich correspondences between concepts (equivalence relations (isEq), subsumption relations (isA) and their inverse (isMoreGnl) or proximity relations (isClose)). It performs an oriented alignment (from a source to a target ontology) and takes into account labels and sub-class descriptions. This new implementation of TaxoMap uses a pattern-base...

We study generalized inverses on semigroups by means of Green’s relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class. There exist many specific generalized inverses in the literature, such as the group inverse, the Moore-Penro...

We introduce and study the partial singular braid monoid PSBn, a monoid that contains both the inverse braid monoid IBn and the singular braid monoid SBn. Our main results include a characterization of Green’s relations, a presentation in terms of generators and relations, and a proof that PSBn embeds in the semigroup algebra C[IBn].

Abstract. MacMahon’s definition of self-inverse composition is extended to n-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two ...

In this study we give recurrence relations of single and product moments of lower record values from modified-inverse Weibull distribution.

1. Relations 1 1.1. The idea of a relation 1 1.2. The formal definition of a relation 2 1.3. Basic terminology and further examples 2 1.4. Properties of relations 4 1.5. Partitions and Equivalence Relations 6 1.6. Examples of equivalence relations 7 1.7. Extra: composition of relations 8 2. Functions 9 2.1. The set of all functions from X to Y 10 2.2. Injective functions 10 2.3. Surjective func...