Isolated horizons [1], much like Killing horizons [2], were introduced in order to deal with the more practical problems involving black holes. Both formulations are local, in contrast with the global nature of event horizons [3]. However, isolated horizons, unlike Killing horizons, do not require a Killing vector field in their neighbourhood. Thus, isolated horizons are characterized by a weak...

Throughout the 25-year history of research on stimulus equivalence, one feature of the training procedure has remained constant, namely, the requirement of operant responding during the training procedures. The present investigation compared the traditional match-to-sample (MTS) training with a more recent respondent-type (ReT) procedure. Another consistent feature of the equivalence paradigm i...

We study two observational equivalences of Fickle programs. Fickle is a class-based object oriented imperative language, which extends Java with object re-classification. The first is a contextual equivalence of expressions with respect to a given program. We provide an adequate coalgebraic semantics for it, which is compositional w.r.t. the operators of the language. The second observational e...

Sequential pattern mining first proposed by Agrawal and Srikant has received intensive research due to its wide range applicability in many real-life domains. Various improvements have been proposed which include mining a closed set of sequential patterns. Sequential patterns supported by the same sequences in the database can be considered as belonging to an equivalence class. Each equivalence...

The modular Catalan numbers Ck,n, introduced by Hein and Huang in 2016 count equivalence classes of parenthesizations x0⁎…⁎xn, where ⁎ is a binary k-associative operation k positive integer. classical notion associativity coincides with 1-associativity, which case C1,n=1 the single 1-equivalence class has size given number Cn. In this paper we introduce Fuss-Catalan Ck,nm k-equivalence x0⁎…⁎xn ...

For an equivalence relation E on the words in some finite alphabet, we consider the recognition problem (decide whether two words are equivalent), the invariant problem (calculate a function constant on precisely the equivalence classes), the normal form problem (calculate a particular member of an equivalence class, given an arbitrary member) and the first member problem (calculate the first m...

In this note we introduce a new equivalence relation θ∗ on a (semi)hyperring R and we show that it is strongly regular. Also we prove that, R/θ∗, the equivalence class of this equivalence relation under usual operations consists a commutative (semi-)ring. Finally we introduce the notion of θ-parts of hyperrings and investigate the important properties of them. Mathematics Subject Classification...

We will study the smooth and piecewise linear manifolds within a given homotopy equivalence class. In the first part we find an obstruction theory for deforming a homotopy equivalence between manifolds to a diffeomorphism or a piecewise linear homeomorphism. In the second part we analyze the piecewise linear case and characterize the obstructions in terms of a geometric property of the homotopy...