We construct normal forms for Levi degenerate hypersurfaces of finite type in C. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the dimension of the stability group of the hypersurface.

Several protocols have been specified in the Routing Area of the IETF using a common variant of the Backus-Naur Form (BNF) of representing message syntax. However, there is no formal definition of this version of BNF. There is value in using the same variant of BNF for the set of protocols that are commonly used together. This reduces confusion and simplifies implementation. Updating existing d...

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Article history: Received 19 November 2010 Revised 10 September 2011 Available online 19 October 2011 MSC: 34C20 34A34 16W5 68U99

We consider the use of random CNF formulas in evaluating the performance of SAT testing algorithms, and in particular the role that the phase transition phenomenon plays in this use. Examples from the literature illustrate the importance of understanding the properties of formula distributions prior to designing an experiment. We expect this to be of increasing importance in the eld.

Bundy. Silver and Plummet (1985) provide an analysis of the Focussing algori thm and the Classification algorithm in the case where the description space consists of a set of relation trees. This paper discusses an extension to their analysis in which the description space is construed as a geometric space. Under this construal the behaviour of both the Focussing algori thm and the Classificati...

Group testing algorithms are very useful tools for DNA library screening. Building on recent work by Levenshtein (2003) and Tonchev (2008), we construct in this paper new infinite classes of combinatorial structures, the existence of which are essential for attaining the minimum number of individual tests at the second stage of a two-stage disjunctive testing algorithm.

We introduce a method of decomposing a p-player normal form game into 2p simultaneously-played component games, each distinguished by the set of “active” players whose choices influence payoffs. We then prove that a normal form game is a potential game if and only if in each of the component games, all active players have identical payoff functions, and that in this case, the sum of these share...

We follow 8] in asking when a set of ordinals X is a countable union of sets in K, the core model. We show that, analogously to L, an X closed under the canonical 1 Skolem function for K can be so decomposed, provided K is such that no !-closed lters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erd} os type property.