1 Let P be a set of n points in the plane in general position. A 2 subset H of P consisting of k elements that are the vertices of a convex 3 polygon is called a k-hole of P , if there is no element of P in the interior 4 of its convex hull. A set B of points in the plane blocks the k-holes of 5 P if any k-hole of P contains at least one element of B in the interior 6 of its convex hull. In thi...

In this paper, a common generalization of the Rogers-Ramanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsP-polynomials. In turn, the BsP-polynomials provide simultaneously a proof of the Rogers-Ramanujan identities and a new, more rapidly converging series expansion for the basis partition generating function....

Our first main objective here is to unify two important theories in finite geometries, namely, the theories of k-arcs and blocking sets. This has a number of consequences, which we develop elsewhere. However,one consequence that we do discuss here is an improvement of Bruck’s bound [ l] concerning the possibility of embedment of finite nets of order II, in the controversial case when n = 10. Th...

1 SUMMARY As part of a study of almost-everywhere complex sets, we i n vestigate sets that are immune to AC 0 ; that is, sets with no innnite subset in AC 0. W e show that such sets exist in P PP and in DSPACElog n log n. Our main result is an oracle construction indicating that any improvement in these immunity results will represent a signiicant advance, in that we show that any answer to the...

We describe a closed-form technique for mapping the output of a trained backpropagation network int.o input activity space. The mapping is an inverse mapping in the sense that, when the image of the mapping in input activity space is propagat.ed forward through the normal network dynamics, it reproduces the output used to generate that image. When more than one such inverse mappings exist, our ...

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an underlying logical knowledge base. This conflicting information often allows for the presence of more than one possible reasonable position (extension/labelling) which one can take. A relevant question, therefore, is how much these positions differ from each other. In the current paper, w...

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M .

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...

In the early fties L. Schwartz posed the problem to characterize those linear partial differential operators P(D) that admit a (continuous linear) right inverse on the Fr echet space E(() of all innnitely diierentiable functions on an open set in IR n respectively on the space D 0 (() of all distributions on. This problem was solved in 6], 7]. Its solution was extended to diierential complexes ...

The notion of a first order topological structure was introduced by Pillay [1] as a generalization of the notion of an o-minimal structure. The idea is to provide a general framework in which model theory can be used to analyze a topological structure whose topology isn’t necessarily induced by a definable order. In the o-minimal case, the topology is generated from a basis where each basis set...