A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

Identification and quantification of major species of arsenic in rice

A study was undertaken to develop a method for the chemical speciation of As in rice on the basis of current knowledge in this field for use in preparing a certified reference material (CRM). Samples of the Arborio rice variety were ground to a fine powder, which was extracted under sonication with a water-methanol mixture (1 + 1, v/v). The resulting solutions were injected into a high-performance liquid chromatograph combined on-line with a quadrupole inductively coupled plasma-mass spectrometer. This hyphenated system allowed for the quantification of As species in one analytical step. Four forms of As were detected: inorganic As (III), dimethylarsinic acid (DMA), monomethylarsonic acid (MMA), and inorganic As (V) at concentrations of 88.2 +/- 7.1, 50.8 +/- 5.0, 15.2 +/- 1.7, and 51.2 +/- 3.5 ng/g, respectively. The concentration of total As was 211 +/- 7 ng/g. The limits of detection (3sigma criterion) and the quantitation (10sigma criterion) were, respectively, as follows (in ng/g): As (III), 0.095 and 0.320; As (V), 0.082 and 0.273; MMA, 0.110 and 0.367; and DMA, 0.145 and 0.480. Ten hours were needed for the extraction procedure, 6 h for the evaporation, and 30 min for quantification of the analytes. This investigation was performed in the frame of a European Commission Project on the feasibility of CRMs for As and Se species.     

C2-symmetric diphosphinite ligands derived from carbohydrates. The strong influence of remote stereocenters on asymmetric rhodium-catalyzed hydrogenation

Modular ligands of C(2) symmetry (13a-e, 14a,b,d, and ent-9), systematically modified at positions 2 and 5, were easily prepared from d-glucosamine, D-glucitol, and tartaric acid, respectively. The application of these ligands in the rhodium-catalyzed hydrogenation of methyl acetamidoacrylate, methyl acetamidocinnamate, and dimethyl itaconate shows that both the configuration and the substituents at positions 2 and 5 of the tetrahydrofuran backbone have a strong influence on the enantioselectivty of the processes.     

Structure of ionic liquids of 1-alkyl-3-methylimidazolium cations: a systematic computer simulation study

Molecular dynamics simulations of room temperature molten salts (ionic liquids) containing imidazolium cations have been performed. Ten different systems were simulated at 323 K by using united atom force fields, in which the anion size (F-, Cl-, Br-, and PF6-) and the length of the alkyl chain of 1-alkyl-3-methylimidazolium cations (1-methyl-, 1-ethyl-, 1-butyl-, and 1-octyl-) were systematically varied. It is shown that the resulting equilibrium structures account for the observed features of experimental static structure factors when available. A detailed analysis of the simultaneous effect of changing the anion and the alkyl chain on the preferential location of nearest-neighbor anions around the cations is provided. It is shown that regions above and below the imidazolium ring are the preferential ones in case of large anions. By increasing the length of the alkyl chain, nearest-neighbor anions are pushed away from the volume occupied by the flexible alkyl chain. Partial structure factors of 1-butyl- and 1-octyl- derivatives display a peak at a wave vector smaller than the main peak, indicating the occurrence of an intermediate range order in these ionic liquids due to the presence of long alkyl chains.     

Vibrational Stark Effects on Carbonyl, Nitrile, and Nitrosyl Compounds Including Heme Ligands, CO, CN, and NO, Studied with Density Functional Theory

Changes in the matrix electric field in a protein, due for example to mutations or structural fluctuations, can be correlated with changes in the vibrational transition frequencies of suitable chromophores measured by IR spectroscopy through the Stark tuning rate. To make this correlation, the Stark tuning rate must be known from experiment or theory. In this paper, density functional theory at the B3LYP/TZV level of theory is used to compute the Stark tuning rate of adducts of heme porphyrin, namely, -CO, -CN, and -NO+ compounds. The results are compared with the corresponding vibrational frequencies-field dependencies from vibrational Stark spectroscopy of heme-proteins. The zero-field computed Stark tuning rate of 1.3 cm-1/MV/cm for heme-CO is in agreement with experiment, where typically the rate is 2.4/f cm-1/MV/cm for myoglobin, where f is a local field correction between 1.1 and 1.4. Several small nitrile, carbonyl, and dinitrile molecules were studied to rationalize the findings for the heme-adducted models. Here, the higher B3LYP/6-311++G(2d,2p) level of theory could be used so the agreement with recent experimental results is even better than for heme-adducted groups.     

Efficient synthesis of enantiomerically pure alpha-alkyl cyclopropanecarbonitrile derivatives from pyrazolines

[reaction: see text] Thermolysis of enantiopure sulfonyl pyrazolines 4 and 5, easily obtained from (Z)-3-p-tolylsulfinylacrylonitriles (1), afforded sulfonyl cyclopropanes (6, 7) in a completely stereoselective manner in almost quantitative yields. Both cyclopropanes and alkylidenecyclopropanes, containing one or two chiral carbon atoms, one of them being quaternary, were obtained by hydrogenolysis of the C-S bonding and under the conditions reported by Julia, respectively. The highly stereoselective extrusion of nitrogen suggests a concerted mechanism.     

N-(phenylthio)-epsilon-caprolactam: a new promoter for the activation of thioglycosides

N-(phenylthio)-epsilon-caprolactam (1) has been applied as a new promoter for the activation of thioglycosides. This proceeds by the reaction of 1 with trifluoromethansulfonic anhydride, which subsequently activates the thioglycoside for glycosidic bond formation. Notably, the reaction proceeds efficiently at room temperature and is adaptable to our reactivity-based one-pot oligosaccharide synthesis. [reaction: see text]     

On the Almost Intersections of Transient Brownian Motions

Let {B ₁ ^d (t)} and {B ^d ₂(t)} be independent Brownian motions in R ^d starting from 0 and nx respectively, and let w ^d _i (a,b) ={xR ^d : B ^d _i (t)=x for some t(a,b)}, i=1,2. Asymptotic expressions as n for the probability of dist(w ^d ₁(n ² t ₁, n ² t ₂), w ₂ ^d (0,n ² t ₃))1 with d4, respectively for the probability of dist(w ₁ ⁴(n ² t ₁,n ² t ₂),w ₂ ⁴(0,n ² t ₃))1 are obtained. As an application, an improvement of a result due to M. Aizenman concerning the intersections of Wiener sausages in R ⁴ is presented.     

Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

Does the Schulman's titration of microemulsions really provide meaningful parameters?

In 1955, Bowcott and Schulman coined the term microemulsions and, in passing, proposed a cosurfactant titration of interfaces tailored for water-in-oil systems (Bowcott, J. E.; Schulman, J. H. Z. Elektrochem. 1955, 59, 283). This procedure, elegant and inexpensive, is accomplished by dilution with both oil and cosurfactant up to the onset of microemulsion formation. The rationale they proposed for this method should furnish, with high accuracy, the composition of reverse micelles and continuous bulk in the presence of cosurfactant partition. The present paper demonstrates, by means of pulsed gradient spin-echo NMR, that the Schulman's titration quantitatively describes the cosurfactant partition and that the titration path really corresponds to a dilution path for reverse micelles (at constant composition) dispersed in a continuous bulk (at constant composition).