For finitely generated submonoids of the integer lattice and submodules over the associated monoid algebra, we investigate Gröbner bases with respect to generalised term orders. Up to now, this theory suffered two disadvantages: The algorithm for computing the Gröbner bases was slow and it was not known whether there existed generalised term orders for arbitrary finitely generated submonoids. T...

Quasi-hereditary algebras can be viewed as a Lie theory approach to the theory of finite dimensional algebras. Motivated by the existence of certain nice bases for representations of semisimple Lie algebras and algebraic groups, we will construct in this paper nice bases for (split) quasi-hereditary algebras and characterize them using these bases. We first introduce the notion of a standardly ...

The theory of topological algebras and the theory of bases in topological vector spaces are both well-established areas of analysis but only recently have papers appeared combining these two concepts. Of course, no new information about an algebra will be provided by a basis unless some relationship is given between the basis and the multiplicative structure of the algebra. For example, orthogo...

AbstmctKnowledge present in multiple knowledge bases might need to be reviewed to make decisions based on the combined knowledge. We define the concept of combining knowledge present in a set of knowledge bases and present algorithms to maximally combine them SQ that the combination is consistent with respect to the integrity constraints associated with the knowledge bases. For this we define t...

We offer a novel theoretical model of how experienced teachers deal with the enormous complexity of classroom environments through the use of attentional skills, and report on the development of a methodology to explore the empirical basis for this model in a study of experienced mathematics teachers. In particular we address issues of the nature of the knowledge base that enables teachers to o...