The problem we want to handle in this p a p e r is vagueness. A notion of space, which we basically have, plays an important part in the faculty of thinking and speech. In this paper, we concentrate on a particular class of spatial descriptions, namely descriptions about positional relations on a two-dimensional space. A theoretical device we present in this paper is called the potential model ...

This paper contains a number of estimations of the split domination number and the maximal domination number of a graph with a deleted subset of edges which induces a complete subgraph Kp. We discuss noncomplete graphs having or not having hanging vertices. In particular, for p = 2 the edge deleted graphs are considered. The motivation of these problems comes from [2] and [6], where the authors...

We consider the inequation XA ⊆ BX where A, B and X are formal languages, X is unknown. It has been proved in [9] that if B is a regular language then the maximal solution is also regular. However, the proof, based on Kruskal’s Tree Theorem, does not give any effective construction of the solution. Here we give such an effective construction in the case where A and B are both finite and are suc...

In the recent literature of Arti cial Intelligence, an intensive research e ort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractab...

In this paper we prove that for a type II1 factor N with a Cartan maximal abelian subalgebra (masa), the Hochschild cohomology groups Hn(N, N)=0, for all n ≥ 1. This generalizes the result of Sinclair and Smith, who proved this for all N having separable predual.

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for...

Let S ⊆ Zn satisfy the property that conv(S) ∩ Zn = S. Then a convex set K is called an S-free convex set if int(K) ∩ S = ∅. A maximal S-free convex set is an S-free convex set that is not properly contained in any S-free convex set. We show that maximal S-free convex sets are polyhedra. This result generalizes a result of Basu et al. [6] for the case where S is the set of integer points in a r...

In recent times there has been some interest in studying partial latin squares which have no completions or precisely one completion, and which are critical with respect to this property. Such squares are called, respectively, premature partial latin squares and critical sets. There has also been interest in related maximal partial latin squares. This paper will explore the connection between t...