A basis for the Birman-Wenzl algebra

An explicit isomorphism is constructed between the Birman-Wenzl algebra, defined algebraically by J. Birman and H. Wenzl using generators and relations, and the Kauffman algebra, constructed geometrically by H. R. Morton and P. Traczyk in terms of tangles. The isomorphism is obtained by constructing an explicit basis in the Birman-Wenzl algebra, analogous to a basis previously constructed for the Kauffman algebra using 'Brauer connectors'. The geometric isotopy arguments for the Kauffman algebra are systematically replaced by algebraic versions using the Birman-Wenzl relations.Comment: This is a lightly edited version of an article written in 1989 but never fully completed. It was originally intended as a joint paper with A. J.Wassermann. 33 pages, 20 figure

Mutants and SU(3)_q invariants

Details of quantum knot invariant calculations using a specific SU(3)_q-module are given which distinguish the Conway and Kinoshita-Teresaka pair of mutant knots. Features of Kuperberg's skein-theoretic techniques for SU(3)_q invariants in the context of mutant knots are also discussed.Comment: 17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper18.abs.htm

Report on Mini-conference on Sludge Disposal Alternatives in the Ocean off Southern California, 8 September 1976

The purpose of the conference was to review the status of our capability to predict the environmental effects of the disposal of digested sewage sludge in the ocean off the coast of Southern California. At present, the ocean disposal of sewage sludge is prohibited by State and Federal regulations. Ocean disposal of sludge, however, is a complex of many alternative combinations of what, where and how; and the environmental consequences of all such combinations have not yet been determined. There is, in fact, some evidence that at least one environmentally sound mode of sludge disposal in the ocean off the Southern California coast may exist. This is the trapping of sludge in the sediments of deep, nearshore ocean basins. such as the Santa Monica Basin. Details of this method are given in Section 3.3. p. 12. It is the philosophy of the Environmental Quality Laboratory to study and evaluate policy alternatives but not to be an advocate of one alternative or another. Some of the policies studied may be contrary to existing laws or regulations, but it is believed that there is a better chance for improvement in the laws or regulations if alternatives currently outside them are also studied. The conference was sponsored by the Environmental Quality Laboratory in the belief that sufficient information is now available to begin making reasonable estimates of the environmental consequences of existing or alternative ocean disposal methods in order to compare them to land-based disposal methods. The purpose of this report is not to publish the actual proceedings of the conference. but rather to act as a communications aid. It is intended to publicize the issues that were raised at the conference, to give the names and addresses of people who are involved in these issues, and to present abstracts and literature citations. The schedule of the conference is presented in the next section. It is followed by a section containing abstracts of current research by conference attendees along with reference lists supplied by them. The fourth section is a summary of the afternoon discussion sessions. The final section is a list of conference attendees with their mailing addresses

Complete Separability and Fourier representations of n-qubit states

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and to emphasize its interpretation as a Fourier transform. We then prove a general sufficient condition for complete separability in terms of the spin coefficients and give necessary and sufficient conditions for the complete separability of a class of generalized Werner densities. As a further application of the theory, we give necessary and sufficient conditions for full separability for a particular set of $n$-qubit states whose densities all satisfy the Peres condition

Honeylocust Twig-gall Midge (Diptera: Cecidomyiidae) in Michigan

Emergence and oviposition data were gathered for Neolasioptera brevis, a recently described pest of honeylocust. In 1984 the insects first emerged on 21 May and first oviposited on 4 June; in 1985 they first emerged on 28 April and first oviposited between 5-20 May. Average raceme length at emergence and at oviposition were 2.7 and 4.4 cm in 1984 and 2.6 and 4.8 cm in 1985. Approximate duration of the emergence period was one week. In 1985 observed oviposition wounds averaged 0.5/cm