Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Heterogeneous nuclear ribonucleoprotein A3, a novel RNA trafficking response element-binding protein

The cis-acting response element, A2RE, which is sufficient for cytoplasmic mRNA trafficking in oligodendrocytes, binds a small group of rat brain proteins. Predominant among these is heterogeneous nuclear ribonucleoprotein (hnRNP) A2, a trans-acting factor for cytoplasmic trafficking of RNAs bearing A2RE-like sequences. We have now identified the other A2RE-binding proteins as hnRNP A1/A1(B), hnRNP B1, and four isoforms of hnRNP A3. The rat and human hnRNP A3 cDNAs have been sequenced, revealing the existence of alternatively spliced mRNAs. In Western blotting, 38-, 39-, 41 -, and 41.5-kDa components were all recognized by antibodies against a peptide in the glycine-rich region of hnRNP A3, but only the 41- and 41.5-kDa bands bound antibodies to a 15-residue N-terminal peptide encoded by an alternatively spliced part of exon 1. The identities of these four proteins were verified by Edman sequencing and mass spectral analysis of tryptic fragments generated from electrophoretically separated bands. Sequence-specific binding of bacterially expressed hnRNP A3 to A2RE has been demonstrated by biosensor and UV cross-linking electrophoretic mobility shift assays. Mutational analysis and confocal microscopy data support the hypothesis that the hnRNP A3 isoforms have a role in cytoplasmic trafficking of RNA.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

Tenuous threads, small miracles

With the new Noosa Youth Centre, Deborah Fisher Architects has woven a small yet sophisticated building out of highly constrained and complex circumstances. Douglas Neale explores a project that convinces through its modesty.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.