A finite ℚ–bad space

A Finite Representation of the Narrowing Space

Narrowing basically extends rewriting by allowing free variables in terms and by replacing matching with unification. As a consequence, the search space of narrowing becomes usually infinite, as in logic programming. In this paper, we introduce the use of some operators that allow one to always produce a finite graph that still represents all the narrowing derivations. Furthermore, we introduce...

Finite Loop Space with Maximal Tori have Finite Weyl Groups

The affinity of a permutation of a finite vector space

For a permutation f of an n-dimensional vector space V over a finite field of order q we let k-affinity(f) denote the number of k-flats X of V such that f(X) is also a k-flat. By k-spectrum(n, q) we mean the set of integers k-affinity(f) where f runs through all permutations of V . The problem of the complete determination of k-spectrum(n, q) seems very difficult except for small or special val...

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

Counting the Restricted Gaussian Partitions of a Finite Vector Space

A subspace partition Π of a finite vector space V = V (n, q) of dimension n over GF(q) is a collection of subspaces of V such that their union is V , and the intersection of any two subspaces in Π is the zero vector. The multiset TΠ of dimensions of subspaces in Π is called the type of Π, or, a Gaussian partition of V . Previously, we showed that subspace partitions of V and their types are nat...