The representation of terminological knowledge may naturally lead to terminological cycles. In addition to descriptive semantics , the meaning of cyclic terminologies can also be captured by xed-point semantics, namely, greatest and least xed-point semantics. To gain a more profound understanding of these semantics and to obtain inference algorithms as well as complexity results for inconsisten...

This paper consists of three independent but related parts. In the ̄rst part (xx1{ 6) we give a combinatorial formula for the constants appearing in the \numerators" of characters of stable discrete series representations of real groups (see x3) as well as an analogous formula for individual discrete series representations (see x6). Moreover we give an explicit formula (Theorem 5.1) for certain ...

We give examples of classes of rigid structures which are of unbounded rigidity but Least xed point (Partial xed point) logic can express all Boolean PTIME (PSPACE) queries on these classes. This shows that deenability of linear order in FO+LFP although suucient for it to capture Boolean PTIME queries, is not necessary even on the classes of rigid structures. The situation however appears very ...

This paper nishes the series 12, 16, 17] of papers that aim to show the existence of non-trivial group actions (\symmetries") on certain classes of manifolds. More speciically, we ask whether there is a semifree smooth action of the circle group T = S 1 { resp., a non-trivial action of a cyclic group Z=p; p a prime { on a given manifold X with a xed point set of a given rational homotopy type F...

The geometrical and dynamical properties of area preserving maps in the neighborhood of an elliptic xed point are analyzed in the framework of resonant normal forms. The interpolating ow is not obtained from a map tangent to the identity, but from the normal form of the given map and a time independent interpolating hamiltonian H is introduced. On this hamiltonian the local stability properties...

We prove that the only possible biaccessible points in the Julia set of a Cremer quadraticpolynomialare the Cremer xed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.

{ In this note we present a general mountain pass principle dropping any smoothness or even continuity assumptions on the functional. As a corollary, we prove existence of a point with an arbitrarily xed small slope if the "low" part of the "barrier" is suuciently far from the "boundary", obtaining in addition estimates for the location of the point.

Suucient conditions for controllability of semilinear integrodif-ferential systems in a Banach space are established. The results are obtained using the asymptotic xed-point theorem for k-set contractions .

The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...

We prove a generalization of Brouwer's famous xed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X one can always nd a point x 2 X such that kx ? f(x)k is less than a certain measure of discontinuity. Applications to artiicial neural nets, economic equilibria, and analysis are given.