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In this paper we study real linear dynamical systems $$\dot x = Fx + Gu,y = Hx,x \in R^n $$ = state space,u ∈ R m = input space,y ∈ R p = output space, under the equivalence relation induced by base change in state space; or in other words we study triples of matrices with real coefficients (F, G, H) of sizesn × n, n × m, p × n respectively, under the… (More)
The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian groupG. ForG = R ,H is the usual Heisenberg group. For the case when G is the finite cyclic group Zn, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction… (More)
The subject of this discussion paper is information storage and, especially, information retrieval from large and very large collections of objects. The focus is on scientific objects such as papers, tables, programs, handbooks, manuals, ... . All of these will be referred to here and below as documents. They can be quite heterogeneous in form and content… (More)
In this lecture I discuss some aspects of MKM, Mathematical Knowledge Management, with particuar emphasis on information storage and information retrieval.
This is partly an introductory survey paper to clustering and classification problems with particular emphasis on the classification of lists of key words and phrases from a given scientific domain such as mathematics. In addition the paper contains a number of new concepts and results; a number of open questions, and some as yet untried embryo clustering… (More)
Let A be a reduced incidence relation between n lines and m points. Suppose that (a) Through each two points there pass λ lines (b) Each two lines intersect in µ points. If λ µ = = 1 assume, moreover, that there are four points no three of which are on one line. Then n m = , λ µ = , and there is a number r such that all lines have r points and through each… (More)
Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification)… (More)
. This paper is concerned with information retrieval from large scientific data bases of scientific literature. The central idea is to define metrics on the information space of terms (key phrases) and the information space of documents. This leads naturally to the idea of a weak enriched thesaurus and the semiautomatic generation of such tools. Quite a… (More)
Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it.… (More)
Using methods from the geometric theory of quiver representations, moduli spaces of linear control systems are described as vector bundles over Grassmannians. Inspired by ideas from non-commutative geometry, unions of such moduli spaces are identified as open subsets of infinite Grassmannians.