In this paper we give two results about analytic sets. The rst is a counterexample to a problem of Fremlin. We show that there exists ! 1 compact subsets of a Borel set with the property that no -compact subset of the Borel set covers them. In the second section we prove that for any analytic subset A of the plane either A can be covered by countably many lines or A contains a perfect subset P ...

One of the major limiting factors of the CMOS device, circuit and system simulation in sub 100nm regimes is the statistical variability introduced by the discreteness of charge and granularity of matter. The statistical variability cannot be eliminated by tuning the layout or by tightening fabrication process control. Since the compact models are the key bridge between technology and design, it...

Let M = H/Γ a “convex co-compact” hyperbolic surface consisting of a compact core and, possibly, a finite number of infinite volume funnels. We do not allowM to have cusps. (More formally, Γ is convex co-compact if (convex.hull(LΓ))/Γ is compact, where LΓ is the limit set of Γ.) We exclude the possibility that Γ is elementary (i.e. virtually cyclic). The closed geodesics on M are is one-to-one ...

Motivated by questions in stability theory for hybrid dynamical systems, we establish some fundamental properties of the set of solutions to such systems. Using the notion of a hybrid time domain and general results on set and graphical convergence, we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and “upper semicontinuous” w...

Frequent patterns are useful in many data mining problems including query suggestion. Frequent patterns can be mined through frequent pattern tree (FPtree) data structure which is used to store the compact (or compressed) representation of a transaction database (Han, et al, 2000). In this paper, we propose an algorithm to compress frequent pattern set into a smaller one, and store the set in a...

In this case, a set C ∈ C may be called a cell in X. A compact Hausdorff space with a cellular structure is a cellular space. For example, the usual construction of the Cantor set leads to a natural cellular structure, where the cells are the parts of the Cantor set in the closed intervals generated in the construction. Of course, a Hausdorff topological space with a base for its topology consi...