Let A be a nite dimensional hereditary algebra over a nite eld, H(A) and C(A) be respectively the Ringel-Hall algebra and the composition algebra of A. Deene r d to be the element P M] 2 H(A), where M] runs over the isomorphism classes of the regular A?modules with dimension vector d. We prove that r d and the exceptional A?modules all lie in C(A). Let K be the Kronecker algebra, P (resp. I) th...

Some results from [2], [5], [6] are generalized for nite automata over arbitrary groups. The accepting power is smaller when abelian groups are considered, in comparison with the non-abelian groups. We prove that this is due to the commutativity. Each language accepted by a nite automaton over an abelian group is actually a unordered vector language. Finally, deterministic nite automata over gr...

This paper analyzes a connection between risk-sensitive and minimax criteria for discrete-time, nite-states Markov Decision Processes (MDPs). We synthesize optimal policies with respect to both criteria, both for nite horizon and discounted in nite horizon problem. A generalized decision-making framework is introduced, which includes as special cases a number of approaches that have been consid...

The G-graph Γ(G,S) is a graph from the group G generated by S ⊆ G, where the vertices are the right cosets of the cyclic subgroups 〈s〉, s ∈ S with k-edges between two distinct cosets if there is an intersection of k elements. In this thesis, after presenting some important properties of G-graphs, we show how the G-graph depends on the generating set of the group. We give the G-graphs of the sym...

Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classiied. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, a...

We give some observations on association schemes with a relation of valency 2 from the representation theory of Bose–Mesner algebras and the basic structure theory. One of the applications of these observations is the classi-cation of the association schemes with a non-symmetric relation of valency 2 if the cardinality of the point set is a product of two primes, and another is the proof of Li’...

We summarize recent developments on the computation of discrete logarithms in general groups as well as in some specialized settings. More specifically , we consider the following abelian groups: the multiplicative group of nite elds, the group of points of an elliptic curve over a nite eld, and the class group of quadratic number elds.

ABSTRACT High order nite di erence WENO methods have the advantage of simpler coding and smaller computational cost for multi-dimensional problems, compared with nite volume WENO methods of the same order of accuracy. However a main restriction is that conservative nite di erence methods of third and higher order of accuracy can only be used on uniform rectangular or smooth curvilinear meshes. ...