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Let G be a discrete subgroup of SL(2, C)/{• 1}. Then G operates as a discontinuous group of isometrics on hyperbolic 3-space, which we regard as the open unit ball B a in Euclidean 3-space E a. G operates on S 2, the boundary of B a, as a group of conformal homeomorphisms, but it need not be discontinuous there. The set of points of S 2 at which G does not act discontinuously is the limit set A(G).If we fix a point 0 in B a, then the orbit of 0 under G accumulates precisely at A(G).The approximation is, however, not uniform. We distinguish a class of limit points, called points o/aproximation, which are approximated very well by translates of 0. The set of points of approximation includes all loxodromic (including hyperbolic) fixed points, and includes no parabolic fixed points. In w 1 we give several equivalent definitions of point of approximation, and derive some properties. We remark that these points were first discussed by Hedlund [7].Starting with a suitable point 0 in B a, we can construct the Dirichlet fundamental polyhedron P0 for G. It was shown by Greenberg [5] that even if G is finitely generated, P0 need not have finitely many sides. Our next main result, given in w 2, is that if P0 is finite-sided, then every point of A(G) is either a point of approximation or a cusped parabolic fixed point (roughly speaking a parabolic fixed point is cusped if it represents the right number of punctures in (S2-A(G))/G).The above theorem has several applications: one of these is a new proof of the following theorem of Ahlfors [1].I/Po has finitely many sides, then the Euclidean measure o/ A(G) is either 0 or 4~.Our next main result, given in w 3, is that the above necessary condition for P0 to have finitely many sides is also sufficient. In fact, we prove that any convex fundamental polyhedron G has finitely many sides if and only if A(G) consists entirely of points of 1-742908 Acta mathematica 132. Imprim6 1r 18 Mars 1974

No abstract

The referential process is defined in the context of Bucci's multiple code theory as the process by which nonverbal experience is connected to language. The English computerized measures of the referential process, which have been applied in psychotherapy research, include the Weighted Referential Activity Dictionary (WRAD), and measures of Reflection, Affect and Disfluency. This paper presents the development of the Italian version of the IWRAD by modeling Italian texts scored by judges, and shows the application of the IWRAD and other Italian measures in three psychodynamic treatments evaluated for personality change using the Shedler-Westen Assessment Procedure (SWAP-200). Clinical predictions based on applications of the English measures were supported.