The general three-vertex,BRS identities and renormalizability of the light-cone gauge

The general one-loop three-vertexГ _μeλ ^abc (p, q, r) in the four-component formulation of the Yang-Mills theory is calculated in the light-cone gauge. The nonvanishing counter Lagrangian constructed from this three-vertex and the self-energy is proportional to the original Lagrangian, the single renormalization constant being -11g² C _YM Г(2?ω)/48π². Gauge dependent and nonlocal counterterms do not contribute to the renormalization constant, but are needed to verify the appropriate Slavnov-Taylor (ST) and Becchi-Rouet-Stora (BRS) identities.     

Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Comment on a paper of Rao et al., an entry of Ramanujan and a new 3F2(1)

A hypergeometric transformation formula is developed that simultaneously simplifies and generalizes arguments and identities in a previous paper of Rao et al. [An entry of Ramanujan on hypergeometric series in his notebooks, J. Comput. Appl. Math. 173(2) (2005) 239–246].     

The nonadditivity of the genus

A class of cubic graphs is introduced for which the genus is a nonadditive function of the genus of subgraphs. This provides a small (28 node) counterexample to Duke’s conjecture concerning the relation of the Betti number to the genus of a graph.     

Catalytic conjugate additions of carbonyl anions under neutral aqueous conditions

The conjugate addition of carbonyl anions catalyzed by thiazolium salts that is fully operative under neutral aqueous conditions has been accomplished. The combination of alpha-keto carboxylates and thiazolium-derived zwitterions produces reactive carbonyl anions in a buffered protic environment that readily undergo conjugate additions to substituted alpha,beta-unsaturated 2-acyl imidazoles. The scope of the reaction has been examined and found to accommodate various alpha-keto carboxylates and beta-aryl substituted unsaturated 2-acyl imidazoles. The optimal precatalyst for this process is the commercially available thiazolium salt 5, a simple analogue of thiamin diphosphate. In this process, no benzoin products from carbonyl anion dimerization are observed. The corresponding 1,4-dicarbonyl compounds can be efficiently converted into esters and amides by way of activation of the N-methylimidazole ring via alkylation.     

The homotopy type of rational functions

During the preparation of this work each of the authors was supported by an NSF grant, the second author by an NSF-PYI award, and the first and fourth authors by the S.F.B. 170 in G?ttingen