Helly-type theorems for hollow axis-aligned boxes

A hollow axis-aligned box is the boundary of the cartesian product of compact intervals in . We show that for , if any of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any of a collection of hollow axis-aligned rectangles in have non-empty intersection, then the whole collection has non-empty intersection. The values for and for are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if were lowered to , and to , respectively.

     

Neutral-pion photoproduction off protons in the energy range 0.3 GeV<E(gamma)<3 GeV

Single pi(0) photoproduction has been studied with the CB-ELSA experiment at Bonn using tagged photon energies between 0.3 and 3.0 GeV. The experimental setup covers a very large solid angle of approximately 98% of 4pi. Differential cross sections dsigma/dOmega have been measured. Complicated structures in the angular distributions indicate a variety of different resonances being produced in the s channel intermediate state gammap-->N(*)(Delta(*))-->ppi(0). A combined analysis including the data presented in this letter along with other data sets reveals contributions from known resonances and evidence for a new resonance N(2070)D15.