Unbounded Soboleff Regions.

Graph Based Hybrid Clustering With Unbounded Regions

An extension of the hybrid clustering approach is proposed for partitioning data with possibly unbounded polygon regions. Clustering or partitioning data into relatively homogeneous and coherent subpopulations can be an effective pre-processing method to achieve data analysis tasks such as pattern recognition and classification. Our method uses a graph to model the initial manual partition of t...

Unbounded Regions of Infinitely Logconcave Sequences

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Moll and Boros in [1] that the binomial coefficients are ∞-logconcave.

Sto hasti Methods for Multiple Integrals over Unbounded Regions

The Hadwiger Number of Jordan Regions is Unbounded

We show that for every n > 0 there is a planar topological disk A0 and n translates A1, A2, . . . , An of A0 such that the interiors of A0, . . . An are pairwise disjoint, but with each Ai touching A0 for 1 6 i 6 n.

Unbounded Regions in an Arrangement of Lines in the Plane

We take a set Ω of n points and an arrangement Σ of m lines in the plane which avoid these points but separate any two of them. We suppose these satisfy the following unboundedness property: for each point x ∈ Ω there is a homotopy from Σ to Σ′ avoiding Ω so that x is in an unbounded component of the complement of Σ′. It is proved that then n ≤ 2m. This result is required to partially solve a p...