A lattice-ordered group (/-group) is said to be regular il no positive element of the group is disjoint from any of its conjugates. It is well known that every simple regular /-group is totally ordered [S]. The subgroups of the reals are the most elementary examples of regular simple /-groups; other examples can be found in [2] and [ó]. In this note we investigate a class of simple /-groups at ...

Let L be an idempotent Latin square of side n, thought of as a set of ordered triples (i, j, k) where L(i, j) = k. Let I be the set of triples (i, i, i). We consider the problem of biembedding the triples of L \ I with the triples of L′ \ I, where L′ is the transpose of L, in an orientable surface. We construct such embeddings for all doubly even values of n.

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

Definition. A specific set that we often care about is the empty set, ∅ i.e. the set containing no elements. One particular quirk of the empty set is that any statement of the form ∀x ∈ ∅ . . . will always be vacuously true, as it is impossible to disprove (as we disprove ∀ claims by using ∃ quantifiers!) For example, the statement “every element of the empty set is delicious” is true. Dumb, bu...

Given an integer n 2, let H n be the set H n = {(a, b) : ab ≡ 1 (mod n), 1 a, b n − 1} and let M (n) be the maximal difference of b − a for (a, b) ∈ H n. We prove that for almost all n, n − M (n) = O n 1/2+o(1). We also improve some previously known upper and lower bounds on the number of vertices of the convex closure of H n .

a flood warning system is a non-structural measure for flood mitigation. several parameters are responsible for flood related disasters. this work  illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. in this paper, we first define ordered intuitionistic fuzzy soft sets and est...

A flood warning system is a non-structural measure for flood mitigation. Several parameters are responsible for flood related disasters. This work  illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. In this paper, we first define ordered intuitionistic fuzzy soft sets and est...

We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), ...

A t-packing is an ordered pair (V ,P) where V is a v-set and P is a collection of k-subsets (blocks) of V such that each t-subset of V occurs in at most one block of P. If each t-subset of V occurs in exactly one block of P, then (V ,P) is known as a Steiner (t, k, v)-design. In this paper, we explore a novel use of t-packings to construct d-disjunct matrices. © 2006 Elsevier B.V. All rights re...