Let be a partial order on a countable set V such that there exists a minimum element a ∈ V and {u ∈ V : u v} is finite for each v ∈ V . An item of information is to be broadcast to the elements of V according to the policy in the following sense: a is initially informed and broadcasting to v 6= a begins as soon as all elements u ≺ v are informed; the time required to broadcast the information i...

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...

Fuchs [6] called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and ...

We employ partially ordered sets to describe the stratification of a social system, using rank to define the strata. We present a simple method of computing the matrix corresponding to the Hasse diagram and prove its correctness. This methodology is applied to analyze the hierarchy of countries that have won at least one Olympic medal. Four different definitions of dominance are given, leading ...

In this paper, coupled xed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V.Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, NonlinearAnalysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotonemappings instead mappings with mixed monotone property. Also, an example is given to supportthese improvements.

A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable, an extension of generalized permutation patterns introduced by Babson and Steingŕımsson. POPs were introduced in the symmetric group by Kitaev [19, 21], and studied in the set of k-ary words by Kitaev and Mansour [22]. Moreover, Kitaev et al. [23] introduced segmented POPs in composi...

The Constraint Problems usually addressed fall into one of two models: the Constraint Satisfaction Problem (CSP) and the Constraint Optimization Problem (COP). However, in many real-life applications, more functions should be optimized at the same time, and solutions are ranked by means of a Partial Order. Also, when dealing with Null values, the solution set is ranked through a Partial Order, ...

Let P be a partially ordered set. A function φ : P → P is an endomorphism of P if for every two elements x, y of P , the inequality φ(x) 6 φ(y) holds whenever x 6 y. Obviously, the identity mapping is a (trivial ) endomorphism. Here, however, we will be interested in endomorphisms with an image of size less than |P |, i.e. endomorphisms which are not automorphisms of P . We will refer to them a...

This paper introduces a method to correctly order events in modelbased testing for concurrent systems, in particular multi-threaded programs, whose events are only partially ordered. For a sequential, centralized tester, we need to merge (local) traces of each component into a (global) trace of a system in such a way that the ordering constraints are observed. To this end, we instrument a multi...

The recent development of abstract algebraic logic has led to a reconsideration of the universal algebraic theory of ordered algebras from a new perspective. The familiar equational logic of Birkhoff can be naturally viewed as one of the deductive systems that constitute the main object of study in abstract algebraic logic; technically it is a deductive system of dimension two. Large parts of u...