Complete classification of 3-multisets up to combinatorial equivalence

A classification of the harmonic frames up to unitary equivalence

Up to unitary equivalence, there are a finite number of tight frames of n vectors for C which can be obtained as the orbit of a single vector under the unitary action of an abelian group G (for nonabelian groups there may be uncountably many). These so called harmonic frames (or geometrically uniform tight frames) have recently been used in applications including signal processing (where G is t...

Classification of Lie Subalgebras up to an Inner Automorphism

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...

Equivalence of Geometric and Combinatorial Dehn Functions 3

We prove that if a finitely presented group acts properly discontinuously, cocompactly and by isometries on a simply connected Riemannian manifold, then the Dehn function of the group and the corresponding filling function of the manifold are equivalent, in a sense described below. 1. Dehn functions and their equivalence Let X be a simply connected 2-complex , and let w be an edge circuit in X....

Structural Classification of XML Documents Using Multisets

In this paper, we investigate the problem of clustering XML documents based on their structure. We represent the paths in an XML document as a multiset and use the symmetric difference operation on multisets to define certain metrics. These metrics are then used to obtain a measure of similarity between any two documents in a collection. Our technique was successfully applied to real and synthe...

Complete Combinatorial Generation of