Guy Bonneau has kindly pointed out two errors in [1]. The first is that the manifolds M (k) and M (k)/Z2 do not admit U (2)-invariant Einstein-Weyl structures for k 2; thus the last four entries in Table 4 (page 422) do not occur. The error is on pages 429430. The analysis there is correct, except that the critical line to consider in Lemma 7.5 and the subsequent calculation is = , instead of = 2/k, because of the constraint (D, ](equivalently, > ) occurring in the definition of . On this line, one has

We present the recent work on the noncommutative Fourier transform for subfactors and locally compact quantum groups, a Survey.We give a short introduction to subfactors and locally compact quantum groups and their properties;the Hausdorff-Young inequality and its extremal functions;Young's inequality and its extremal pairs;uncertainty principles and its minimizers;a noncommutative sum set theorem.

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In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.

Given a compact orientable surface with finitely many punctures \Sigma , let $\Cal S (\Sigma) $ be the set of isotopy classes of essential unoriented simple closed curves in \Sigma . We determine a complete set of relations for a function from $\Cal S (\Sigma) $ to $\bold R $ to be the geodesic length function of a hyperbolic metric with geodesic boundary and cusp ends on \Sigma . As a conse quence, the Teichmller space of hyperbolic metrics with geodesic boundary and cusp ends on \Sigma is reconstructed from an intrinsic $(\bold QP^ 1, PSL (2,\bold Z)) $ structure on $\Cal S (\Sigma) $.