Conversion of n,n-dimethylhydrazones to carbonyl compounds by clay-supported ferric nitrate

Cleavage of N,N-dimethylhydrazones is cleanly effected with good yield in dichloromethane using the extremely inexpensive clay-supported ferric nitrate.     

Uniform catalytic site in Sn-beta-zeolite determined using X-ray absorption fine structure

The Sn silicate zeolite, Sn-beta, has been shown to be an efficient, selective heterogeneous catalyst for Baeyer-Villiger oxidations. Using primarily a multishell fit to extended X-ray absorption fine structure (EXAFS) data, we show that the Sn does not randomly insert into the beta-zeolite structure but rather occupies identical, specific, crystallographic sites. These sites are the T5/T6 sites in the six-membered rings. Moreover, the Sn is substituted in pairs on opposite sides of these six-membered rings. We believe that it is the specific, uniform crystallographic location of the Sn in the beta crystal structure that leads to sites with uniform catalytic activity, and consequently to the high chemical selectivity demonstrated for this catalyst. This manifests itself in the almost enzyme-like selectivity of this catalyst in Baeyer-Villiger oxidations. This uniform site distribution of the Sn suggests that there is likely a symbiotic relationship between the structure-directing agent in the zeolite synthesis and the Sn heteroatoms during the framework formation.     

Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves

Consider a marketplace operated by a buyer who wishes to procure large quantities of several heterogeneous products. Suppliers submit price curves for each of the commodities indicating the price charged as a function of the supplied quantity. The total amount paid to a supplier is the sum of the prices charged for the individual commodities. It is assumed that the submitted supply curves are piecewise linear as they often are in practice. The bid evaluation problem faced by the procurer is to determine how much of each commodity to buy from each of the suppliers so as to minimize the total purchase price. In addition to meeting the demand, the buyer may impose additional business requirements that restrict which contracts suppliers may be awarded. These requirements may result in interdependencies between the commodities which lead to suboptimal results if the commodities are traded in independent auctions rather than simultaneously. Even without the additional business constraints the bid evaluation problem is NP-hard. The main contribution of our study is a flexible column generation based heuristics that provides near-optimal solutions to the procurer’s bid evaluation problem. Our method scales very well due to the Branch-and-Price technology it is built on. We employ sophisticated rounding and local improvement heuristics to obtain quality solutions. We also developed a test data generator that produces realistic problems and allows control over the difficulty level of the problems using parameters.     

Preferential Solvation of the Sodium Cation in Binary Mixtures of Tetrahydrofuran with Unidentate Nitrogen Ligands

²³Na-chemical shifts for the NaClO₄ solute depend markedly upon the composition of binary solvent mixtures of THF with amines (pyridine, piperidine, pyrrolidine, aniline, propylamine, and isopropylamine). These changes, analyzed in a novel application of the Hill formalism, show equality of the intrinsic equilibrium constant K for the successive steps, upon displacement of THF from sodium coordination by one of these amines. The results, which are entirely consistent with tetracoordination of the sodium cation by these solvents, also indicate proportionality of the K values to the amine chemical shifts.     

Strongly interacting low-viscosity matter created in relativistic nuclear collisions

Substantial collective flow is observed in collisions between large nuclei at BNL RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity eta to entropy density s by Kovtun, Son, and Starinets within anti-de Sitter space/conformal field theory yields eta/s=variant Planck's over 2pi/4pikB, which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio eta/s. We suggest that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD.