In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddl...

In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [3]. This relation is deeper than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci of diffe...

We consider difference equations y(s+1) = A(s)y(s), where A(s) is an n × n-matrix meromorphic in a neighborhood of ∞ with detA(s) ≡ 0. In general, the formal fundamental solutions of this equation involve gamma-functions which give rise to the critical variable s log s and a level 1. We show that, under a mild condition, formal fundamental matrices of the equation can be summed uniquely to anal...

We study the equivalence relation on states of labelled transition systems of satisfying the same formulas in Computation Tree Logic without the next state modality (CTL−X). This relation is obtained by De Nicola & Vaandrager by translating labelled transition systems to Kripke structures, while lifting the totality restriction on the latter. They characterised it as divergence sensitive branch...

In this paper, we provide a new approach for computing regular solutions of first-order linear difference systems. We use the setting of factorial series known to be very well suited for dealing with difference equations and we introduce a sequence of functions which play the same role as the powers of the logarithm in the differential case. This allows us to adapt the approach of [5] where we ...

We use a relational characterization of binary direct sums to model sequences within the relation-algebraic manipulation and prototyping system RelView in a simple way. As an application we formally derive a RelView program for computing equivalence classes of an equivalence relation, where we combine relation-algebraic calculations with the so-called Dijkstra-Gries program development method. ...

I. Basic concepts 1. Recursive enumerability and recursiveness. We consider infinite sequences of non-negative integers, free from repetitions. A familiar equivalence relation between such sequences is that based on sets: two sequences are equivalent when they enumerate the same set. The equivalence classes under this relation, with the necessary operations introduced, form a system isomorphic ...

In this paper we will introduce a certain collection of fuzzy subsets of a nonempty set X. This certain collection gives raise to a useful new fuzzy partition. This new fuzzy partition gives us a way of generating a fuzzy equivalence relation as in the ordinary case; any partition generates an equivalence relation. Mathematics Subject Classification: 03E72, 46S40, 26E50

We give an elementary proof that there are two topological generators for the full group of every aperiodic hyperfinite probability measure preserving Borel equivalence relation. Our proof explicitly constructs topological generators for the orbit equivalence relation of the irrational rotation of the circle, and then appeals to Dye’s theorem and a Baire category argument to conclude the genera...