the non commuting graph of a non-abelian finite group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [2]. we also prove that if $g_1$, $g_2$, ..., $...

We investigate the power of regular leaf languages with respect to three diierent tree shapes: the rst one is the case of arbitrary (and thus potentially non-regular) computation trees; the second one is the case of balanced computation trees (these trees are initial segments of full binary trees); and the third one is the case of full binary computation trees. It is known that the class charac...

Typically, a (Boolean) query is a finite formula that defines a possibly infinite set of database instances that satisfy it (positive examples), and implicitly, the set of instances that do not satisfy the query (negative examples). We investigate the following natural question: for a given class of queries, is it possible to characterize every query with a finite set of positive and negative e...

We propose an algorithm for transforming a characteristic decomposition of a radical differential ideal from one ranking into another. The algorithm is based on a new bound: we show that, in the ordinary case, for any ranking, the order of each element of the canonical characteristic set of a characterizable differential ideal is bounded by the order of the ideal. Applying this bound, the algor...

School of thought analysis is an important yet not-well-elaborated scientific knowledge discovery task. This paper makes the first attempt at this problem. We focus on one aspect of the problem: do characteristic school-of-thought words exist and whether they are characterizable? To answer these questions, we propose a probabilistic generative School-Of-Thought (SOT) model to simulate the scien...

Hertrampf's locally de nable acceptance types show that many complexity classes can be de ned in terms of polynomial time bounded NTM's with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce a modi cation of Hertrampf's locally de nable acceptance types which allows to get a larger number of characterizable...