Set systems without a 3-simplex

A 3-simplex is a collection of four sets A_1,...,A_4 with empty intersection such that any three of them have nonempty intersection. We show that the maximum size of a set system on n elements without a 3-simplex is $2^{n-1} + \binom{n-1}{0} + \binom{n-1}{1} + \binom{n-1}{2}$ for all $n \ge 1$, with equality only achieved by the family of sets either containing a given element or of size at most 2. This extends a result of Keevash and Mubayi, who showed the conclusion for n sufficiently large.Comment: 5 page

A-3 scientific results

The scanning modulation collimator experiment designed to identify the optical counterparts of celestial X-ray sources is described. Identification of galactic sources is discussed. Results concerning active galaxies are presented

Valence Quark Distribution in A=3 Nuclei

We calculate the quark distribution function for 3He/3H in a relativistic quark model of nuclear structure which adequately reproduces the nucleon approximation, nuclear binding energies, and nuclear sizes for small nuclei. The results show a clear distortion from the quark distribution function for individual nucleons (EMC effect) arising dominantly from a combination of recoil and quark tunneling effects. Antisymmetrization (Pauli) effects are found to be small due to limited spatial overlaps. We compare our predictions with a published parameterization of the nuclear valence quark distributions and find significant agreement.Comment: 18pp., revtex4, 4 fig

Electromagnetic transitions for A=3 nuclear systems

Recent advances in the study of pd radiative capture in a wide range of center-of-mass energy below and above deuteron breakup threshold are presented and discussed.Comment: Invited lead talk at the 19th European Conference on Few-Body Problems in Physics, Groningen, The Netherlands, 8/23 - 8/27 2004, 5 pages, 4 figure