The internal space of a N = 4 supersymmetric model with WessZumino term has a connection with totally skew-symmetric torsion and holonomy in SP(<i>n</i>). We study the mathematical background of this type of connection. In particular, we relate it to classical Hermitian geometry, construct homogeneous as well as inhomogeneous examples, characterize it in terms of holomorphic data, develop its potential theory and reduction theory.

Heegaard diagrams on the boundary of a handlebody are studied from the dynamics systems point of view. A relationship between the strongly irreducible condition of CassonGordan and the Masur's domain of discontinuity for the action of the handlebody group is established.

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The main object of this paper is to find a criterion for comparison of two tests for non-parametric hypotheses, taking advantage of the qualitative information that may exist. After a detailed analysis of the problem and some earlier suggestins for its solution (sections 2–4), a criterion is suggested in section 5. In order to apply it to a concrete case, a location problem is specified in section 6. The rank tests to be compared are analyzed in section 7, and the comparison by way of the criterion is carried out in section 8. It turns out that sign tests, sometimes slightly modified, are very often optimal according to the criterion used.