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Retrieval of cases is one important step within the case-based reasoning paradigm. We propose an improvement of this stage in the process model for finding most similar cases with an average effort of O[log2n], n number of cases. The basic idea of the algorithm is to use the heterogeneity of the search space for a density-based structuring and to employ this precomputed structure, a k-d tree, for efficient case retrieval according to a given similarity measure sim. In addition to illustrating the basic idea, we present the expe- rimental results of a comparison of four different k-d tree generating strategies as well as introduce the notion of virtual bounds as a new one that significantly reduces the retrieval effort from a more pragmatic perspective. The presented approach is fully implemented within the (Patdex) system, a case-based reasoning system for diagnostic applications in engineering domains.

We have presented here a two-dimensional kinetical scheme for equations governing the motion of a compressible flow of an ideal gas (air) based on the Kaniel method. The basic flux functions are computed analytically and have been used in the organization of the flux computation. The algorithm is implemented and tested for the 1D shock and 2D shock-obstacle interaction problems.

Moduli for singularities
(1991)

The aim of this article is to give a survey on recent results about moduli spaces for curve singularities and for modules over the local ring of a fixed curve singularity. We emphasize especially the general concept which lies behind these constructions.
Therefore, the article might be useful to the reader who wishes to have the leading ideas and the main steps of the proofs explained without going into all the details. We also calculate explicit examples (for singularities and for modules) which illustrate
the general theorems.

In this paper we continue the study of p - groups G of square order \(p^{2n}\) and investigate the existence of partial congruence partitions (sets of mutually disjoint subgroups of order \(p^n\)) in G. Partial congruence partitions are used to construct translation nets and partial difference sets, two objects studied extensively in finite geometries and combinatorics. We prove that the maximal number of mutually disjoint subgroups of order \(p^n\) in a group G of order \(p^{2n}\) cannot be more than \((p^{n-1}-1)(p-1)^{-1}\) provided that \(n\ge4\)and that G is not elementary abelian. This improves a result in [6] and as we do not distinguish the cases p=2 and p odd in the present paper, we also have a generalization of D. FROHARDT' s theorem on 2 - groups in [4]. Furthermore we study groups of order \(p^6\). We can show that for each odd prime number, there exist exactly four nonisomorphic groups which contain at least p+2 mutually disjoint subgroups of order \(p^3\). Again, as we do not distinguish between the even and the odd case in advance, we in particular obtain
D. GLUCK' s and A. P. SPRAGUE' s classification of groups of order 64 which contain at least 4 mutually disjoint subgroups of order 8 in [5] and [13] respectively.

In this paper the existence of translation transversal designs which is equivalent to the existence of certain particular partitions in finite groups is studied. All considerations are based on the fact that the particular component of such a partition (the component representing the point classes of the corresponding design) is a normal subgroup of the translation group. With regard to groups admitting an (s,k,\(\lambda\))-partiton, on one hand the already known families of such groups are determined without using R. BAER's, 0.H.KEGEL's and M. SUZUKI' s classification of finite groups with partition and on the other hand some new results on the special structure of p - groups are proved. Furthermore, the existence of a series of nonabelian p - groups of odd order which can be represented as translation groups of certain (s,k,1) - translation transversal designs is shown; moreover, the translation groups are normal subgroups of collineation groups acting regularly on the set of flags of the same designs.