Let (X, z) be a topological space, and (Y, d) a metric space. A mapping F: X -+ 2’ which associates with every x E X a non-empty subset F(x) OF Y is said to be lower semi-continuous (I.s.c.) (respectively, upper semi-continuous (u.s.c.)) if, for each open set % in Y, the set (X E X: F(x) n %f # @ > (respectively, the set (X E X: F(x) c @ )) is open in X A mapping f: X-a Y is a selection for F i...

Let Sλ(1−b) (b 6= 0, complex) denote the class of functions f(z) = z+a2z 2+· · · analytic in the open unit disc D = {z ∈ C||z| < 1} which satisfy for z = reiθ ∈ D, f(z) z 6= 0 and Re [

The discrete dynamics generated by a continuous map can be represented combinatorially by an appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. In this paper we provide explicit algorithms and computational complexity bounds for computing dynamical structures for the resulting combinatorial multivalued maps. Specifically we focus on the c...

We show that there is a Bore1 measurable selection of Paretian utilities in ‘markets with a continuum of traders’. Theorem: Let T and X be Polish spaces, R a Bore1 subset of T x X xX, and B={(t,x): (t,x,x)ER}. Suppose that for each t, R,={(x,y): (t,x,y)ER} is a preference order on B, = {x: (t,x) EB). Then there is a Bore1 measurable function f: B-$0, l] such that for all t E IT; f,: B,+[O, I] i...

This paper presents two new functional decomposition partitioning algorithms that use multivalued decision diagrams (MDDs). MDDs are an exceptionally good representation for generalized decomposition because they are canonical and they can represent very large functions. Algorithms developed in this paper are for Boolean/multivalued input and output, completely/incompletely specified functions ...