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F or convex co-compact hyperbolic manifolds of even dimension n + 1 , w e derive a P oisson-type formula for scattering resonances which m a y be regarded as a version of Selberg's trace formula for these manifolds. Using techniques of Guillop e and Zworski we easily obtain an O ; R n+1 lower bound for the counting functionfor scattering resonances together(More)
Suppose that ? 1 and ? 2 are geometrically nite, convex co-compact, discrete groups of isometries of real hyperbolic space H 3 whose domains of discontinuity are diieomorphic. We show that if the respective scattering matrices S 1 (s) and S 2 (s) diier from each other by a trace-class perturbation on the unitary axis Re(s) = 1, then ? 1 and ? 2 are(More)
We investigate the relation between the Korteweg-de Vries and modified Korteweg-de Vries equations (KdV and mKdV), and find a new algebro-analytic mechanism, similar to the Lax L-A pair, which involves a family of first-order operators Q λ depending on a spectral parameter λ, instead of the third-order operator A. In our framework, any generalized(More)
The need for policies to control calls is justified by the changing face of communications. It is argued that call control requires distinctive capabilities in a policy system. A spe-cialised policy language called APPEL (ACCENT Project Policy Environment/Language) has therefore been developed for this purpose. However the policy language is cleanly(More)
We consider the problem of enumerating permutations in the symmetric group on n elements which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on L 2 ([0, 1] m), where the patterns in S(More)
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the Laplacian. In(More)