Ordered hydroxyls on Ca3Ru2O7(001)

On fuzzy convex lattice-ordered subgroups

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

On k-ordered graphs

Ng and Schultz [J Graph Theory 1 (1997), 45±57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k-ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k-ordered Hamiltonian. We give sum of degree conditions for nonadja...

On Partly Ordered Fields

On Linear Ordered Codes

We consider linear codes in the metric space with the Niederreiter-Rosenbloom-Tsfasman (NRT) metric, calling them linear ordered codes. In the first part of the paper we examine a linear-algebraic perspective of linear ordered codes, focusing on the distribution of “shapes” of codevectors. We define a multivariate Tutte polynomial of the linear code and prove a duality relation for the Tutte po...

On Ordered Divisible Groupso)

Introduction and remarks. In the theory of r)a-sets three main theorems stand out: that an r/0-set is universal for totally ordered sets of power not exceeding Xa, that any two 7/a-sets of power Na are isomorphic and that 7/a-sets of power Xa exist provided Ka is a regular cardinal number and 2~2i<<> 2t*sS&a. L. Gillman and M. Jerison [6] have shown that a real closed (totally ordered) field wh...