This is joint work with Ana Dias (University of Porto). A coupled cell network consists of a finite set of nodes (the cells) and a finite number of arrows. The cells represent the individual dynamics and the arrows the interactions between the individuals. An equivalence relation on the set of nodes can be defined symbolizing the following; two nodes are in the same cell equivalence class if th...

The central notion of a rough set is indiscernibility based on equivalence relation. Since equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between upper and lower approximations is lost. We here introduce two different equivalence relations, the one for upper approximation, and the other for lower approximation, and construct co...

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

This paper aims to create a class [O] concerning the groups associated with Gromov hyperbolic over correspondence and equivalence through Fuchsian, Kleinian, Schottky when subject Laplace – Beltrami in Teichmüller space where for 3-manifold fundamental of Dehn extended any occurrence Švarc-Milnor lemma satisfies same quotient Jørgensen inequality. Thus relation (and class) Mostow Prasad Rigidit...

A second-order generalization of the fundamental Lepage form geometric calculus variations over fibered manifolds with 2-dimensional base is described by means insisting on (i) an equivalence relation “Lepage differential 2-form closed if and only associated Lagrangian trivial” (ii) principal component form, extending well-known Poincaré–Cartan preserving order prescribed a given Lagrangian. Th...

We prove that the equivalence of pure states of a separable C*-algebra is either smooth or it continuously reduces [0, 1]N/l2 and it therefore cannot be classified by countable structures. The latter was independently proved by Kerr–Li–Pichot by using different methods. We also give some remarks on a 1967 problem of Dixmier. If E and F are Borel equivalence relations on Polish spaces X and Y , ...

We deene an equivalence relation on-terms called shuue-equivalence which attempts to capture the notion of reductional equivalence on strongly normalizing terms. The shuue-equivalence classes are shown to divide the classes of-equal terms into smaller ones consisting of terms with similar reduction behaviour. We reene-reduction from a relation on terms to a relation on shuue-equivalence classes...

We define an analog of Voiculescu’s free entropy for n-tuples of unitaries u1, . . . , un in a tracial von Neumann algebra M which normalize a unital subalgebra L[0, 1] = B ⊂ M. Using this quantity, we define the free dimension δ0(u1, . . . , un G B). This number depends on u1, . . . , un only up to orbit equivalence over B. In particular, if R is a measurable equivalence relation on [0, 1] gen...

A connection is established between the semantic theories of concurrency and communication in the works of de Bakker and Zucker, who develop a denotational semantics of concurrency using metric spaces instead of complete partial orders, and Milner, who develops an algebraic semantics of communication based upon observational equivalence between processes. His rigid synchronization trees (RSTs) ...

Let ďc be computable reducibility on ceers. We show that for every computably enumerable equivalence relation (or ceer) R with infinitely many equivalence classes, the index sets ti : Ri ďc Ru (with R non-universal), ti : Ri ěc Ru, and ti : Ri ”c Ru are Σ3 complete, whereas in case R has only finitely many equivalence classes, we have that ti : Ri ďc Ru is Π2 complete, and ti : Ri ěc Ru (with R...