Generic Rigidity Matroids with Dilworth Truncations

We prove that the linear matroid that defines generic rigidity of $d$-dimensional body-rod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of ${d+1 \choose 2}$ graphic matroids by applying variants of Dilworth truncation $n_r$ times, where $n_r$ denotes the number of rods. This leads to an alternative proof of Tay's combinatorial characterizations of generic rigidity of rod-bar frameworks and that of identified body-hinge frameworks

Constructing Effective Pair Wave Function from Relativistic Mean Field Theory with a Cutoff

We propose a simple method to reproduce the ^1S_0 pairing properties of nuclear matter, which are obtained using a sophisticated model, by introducing a density-independent cutoff into the relativistic mean field model. This can be applied successfully to the physically relevant density range.Comment: 9 pages, 4 figure