Constant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs

In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (Proceedings of the eighteenth annual ACM–SIAM symposium on discrete algorithms (SODA 2007), pp. 512–521, 2007) and Bǎdoiu et al. (Proceedings of the 11th international workshop on approximation algorithms for combinatorial optimization problems (APPROX 2008), Springer, Berlin, pp. 21–34, 2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding a graph metric into an outerplanar metric. For this, we introduce a general notion of a metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥α. Then, for H=K _2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.     

Efficient, chemoenzymatic process for manufacture of the Boceprevir bicyclic [3.1.0]proline intermediate based on amine oxidase-catalyzed desymmetrization

The key structural feature in Boceprevir, Merck's new drug treatment for hepatitis C, is the bicyclic [3.1.0]proline moiety "P2". During the discovery and development stages, the P2 fragment was produced by a classical resolution approach. As the drug candidate advanced through clinical trials and approached regulatory approval and commercialization, Codexis and Schering-Plough (now Merck) jointly developed a chemoenzymatic asymmetric synthesis of P2 where the net reaction was an oxidative Strecker reaction. The key part of this reaction sequence is an enzymatic oxidative desymmetrization of the prochiral amine substrate.     

Fourier magnitude of the field incident on a random scattering medium from spatial speckle intensity correlations

Spatial speckle intensity correlations are used to determine the spatial Fourier magnitude of a field incident on a random scattering medium. The patterned beam is scanned across the scattering medium, and the speckle pattern on the opposite side is imaged at each beam position. A theory based on a Green's function representation is used to reconstruct the spatial Fourier magnitude of the patterned incident field.     

Spinning disk for compressive imaging

We report the first, to the best of our knowledge, experimental implementation of a spinning-disk configuration for high-speed compressive image acquisition. A single rotating mask (i.e., the spinning disk) with random binary patterns was utilized to spatially modulate a collimated terahertz (THz) or IR beam. After propagating through the sample, the THz or IR beam was measured using a single detector, and THz and IR images were subsequently reconstructed using compressive sensing. We demonstrate that a 32-by-32 pixel image could be obtained from 160 to 240 measurements in both the IR and THz ranges. This spinning-disk configuration allows the use of an electric motor to rotate the spinning disk, thus enabling the experiment to be performed automatically and continuously. This, together with its compact design and computational efficiency, makes it promising for real-time imaging applications.     

First use of millicurie levels of172Hf−172Lu in the industrial sector

The first use of the¹⁷²Hf–¹⁷²Lu generator system in industry is reported. Millicurie quantities of¹⁷²Lu have been utilized for radiotracer studies of oil pipeline flow rates, refinery column residence times, and the performance of a coal liquefaction pilot plant.     

Complex free energies and metastable lifetimes

For two simple models we consider the analytic continuation of the free energy across a first-order phase transition. For each system we also study an associated stochastic dynamics and decay rates for passage to the stable equilibrium. We then investigate the relation between the imaginary part of the free energy and the decay rate per unit volume.Supported in part by U.S.-Israel Binational Science Foundation and by National Science Foundation Grant MCS 77-20683.Alfred P. Sloan Research Fellow. On leave from Indiana University, Bloomington, Indiana.     

Silicon-29 NMR studies of aqueous silicate solutions part 7: Exchange rates between anions

Silicon-29 NMR evidence is presented regarding the linewidths and the rates of chemical exchange between the smaller silicate anions in alkaline aqueous solutions of sodium and potassium silicates. It is found that the linewidths of different species vary, being relatively large for the dimer under most conditions. Moreover, as well as decreasing with increasing temperature, linewidths also appear to decrease with increasing pH. Some semi-quantitative values for lifetimes in particular solutions under given conditions are presented, but it is emphasized that these are minimum values, since there may be other origins for line-broadening.     

Inequalities for Ising models and field theories which obey the Lee-Yang Theorem

A series of inequalities for partition, correlation, and Ursell functions are derived as consequences of the Lee-Yang Theorem. In particular, then-point Schwinger functions ofeven φ⁴ models are bounded in terms of the 2-point function as strongly as is the case for Gaussian fields; this strengthens recent results of Glimm and Jaffe and shows that renormalizability of the 2-point function by fourth degree counter-terms implies existence of a φ⁴ field theory with a moment generating function which is entire of exponential order at most two. It is also noted that ifany (even) truncated Schwinger function vanishes identically, the resulting field theory is a generalized free field.     

Peak suppression in Fourier transform n.m.r.: Application of the selective excitation technique to the problem of 13C satellites in 31P resonance

Selective pulsed excitation was used in a technique to suppress the resonance due to a per-¹²C-isotopomer so as to overcome dynamic range problems when observing ‘¹³C satellite’ lines. The technique was used to obtain nuclear spin parameters from the ¹³C satellites in ³¹P resonance for the racemic isomer of P,P′-dimethyl-P,P′-diphenyldiphosphine disulphide, [MePhP(:S)]₂.     

Muonium in ice

Muonium has been studied in single crystals of H₂O and D₂O. Two-frequency precession in low transverse fields and a single zero-field oscillation indicate a small anisotropy of axial symmetry in the muonium hyperfine interaction. The anisotropy is shown to be the cause of the hitherto unexplained temperature independent contribution to muonium spin relaxation in polycrystalline samples. Relaxation rates for 99 K–263 K are reported for muonium in a single crystal of H₂O. Relaxation is attributed to electron-nuclear dipolar coupling of muonium to lattice protons, modulated by translational diffusion of muonium alongc-axis channels of the ice lattice. A simple model for H and Mu diffusion in ice is investigated.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.