The combined trace (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is defined from two relations simultaneity and serializability on events. They also showed that comtraces correspond to some class of labeled stratified order structures, bu...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

In this paper, we give an algorithm for presenting S-unit groups of an order O in a definite rational quaternion algebra B such that, for every p ∈ S at which B splits, the localization of O at p is maximal and all left ideals of O of norm p are principal. We then apply this to give presentations for projective S-unit groups of the Hurwitz order in Hamilton’s quaternions over the rational field...

0. INTRODUCTION. Although the word problem for free lattices is well known to be solvable (cf. Dean [1]), the question still remains open to characterize the finite partial lattices P for which the free lattice F (P ) over P is finite. There are partial answers to this question. In Wille [5] the problem is solved for the partial lattices P that are both meet– and join–trivial in the sense that ...

A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes correspond to classes of equivalent elements in P. The two well known normal forms in P correspond to endpoints of intervals in the weak Bruhat order that determine the Tamari classes. In the monoid P thes...

The congruence between the order of cladistic branching and the first appearance dates of fossil lineages can be quantified using a variety of indices. Good matching is a prerequisite for the accurate time calibration of trees, while the distribution of congruence indices across large samples of cladograms has underpinned claims about temporal and taxonomic patterns of completeness in the fossi...

It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist of a distribution of a perfect (non–dissipative) fluid, whereas the same spacetime as seen by a “tilted” (Lorentz–boosted) congruence of observers may exhibit the presence of dissipative processes. As we shall see, the appearance of entropy-producing pr...

To every morphism of X∗ a congruence fR on X ∗, called kernel congruence, and defined by ufRv iff f(u) = f(v) can be associated. We characterize morphisms having a commutative kernel congruence and, introducing the notion of the index of a morphism, we give a classification of the morphisms of X∗. Moreover, a congruence with special properties, called hp-congruence is considered; every kernel c...

We focus on the Ferrers property of fuzzy preference relations. We study the connection between the Ferrers property and fuzzy interval orders. A crisp total interval order is characterized by the Ferrers property of its strict preference relation. Also, a crisp preference structure is a total interval order if and only if its large preference relation satisfies the Ferrers property. For fuzzy ...

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We pre...