Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.     

Oxygen inhibition in thiol–acrylate photopolymerizations

The overall effects of oxygen on thiol–acrylate photopolymerizations were characterized. Specially, the choice of thiol monomer chemistry, functionality, and concentration on the extent of oxygen inhibition were considered. As thiol concentration was increased, the degree of oxygen inhibition was greatly reduced because of chain transfer from the peroxy radical to the thiol. When comparing the copolymerization of 1,6‐hexanediol diacrylate with the alkane‐based thiol (1,6‐hexane dithiol) to the copolymerization with the propionate thiol (glycol dimercaptopropionate), it was found that the propionate system was much more reactive and polymerized to a greater extent in the presence of oxygen. In addition, the functionality was considered where the glycol dimercaptopropionate was compared to a tetrafunctional propionate of similar chemistry (pentaerythritol tetrakis(mercaptopropionate)). Given the same thiol concentration, the higher functionality thiol imparted a faster polymerization rate, due to the increased polymer system viscosity, which limited oxygen diffusion and decreased the extent of overall oxygen inhibition. Thus, preliminary insight is provided into how thiol monomer choice affects the extent of oxygen inhibition in thiol–acrylate photopolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2007–2014, 2006     

Truncation error bounds for modified continued fractions with applications to special functions

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a _n , 1;x ₁), with andnth approximant

Conversion of clavulanic acid into thiadeoxa nuclear analogues

1,4-Addition of sulphur nucleophiles to the diene ($\text{12}$) derived $\text{via}$ the pen-2-em ($\text{5}$) from clavulanic acid provides the thiadeoxa analogues ($\text{14}$–$\text{15}$). X-ray analysis of the ester ($\text{14}$) shows the thermodynamically stable isomers to have the same relative stereochemistry as clavulanic acid.     

CHEMISTRY OF SINGLET OXYGEN—XXVI. PHOTOOXYGENATION OF PHENOLSy†

Abstract— The aerobic dye-sensitized photooxygenation of monohydric phenols proceeds by way of singlet oxygen under the conditions studied. Various phenols give different proportions of reaction with and quenching of singlet oxygen. Para-substituted 2,6-di-t-butylphenols show a linear correlation between the log of the total rate of singlet oxygen removal and their halfwave oxidation potentials; the same correlation is given for certain phenol methyl ethers. A Hammett plot using s?⁺ gives ρ - 1.72 ± 0.12, consistent with development of some charge in the quenching step. Reaction of photo-chemically generated singlet oxygen with 2,4,6-triphenylphenol gives 2,4,6-triphenylphenoxy radical as an intermediate in singlet oxygen quenching, although no overall reaction occurs. Kinetic analysis indicates that the radical is derived exclusively from the interaction of 2,4,6-triphenylphenol with singlet oxygen. A charge-transfer mechanism for quenching of singlet oxygen by phenols is proposed.     

A ferrocene based palladacyclic precatalyst for the Suzuki cross-coupling of aryl chlorides

Addition of palladium acetate to 2-(dicyclohexylphosphino)-phenylferrocene gave palladacycle 16 that is a very effective precatalyst for the Suzuki cross-coupling of aryl chlorides at room temperature (1 mol% 16) or 60 degrees C (> or = 0.01 mol% 16).     

Syntheses of seven-membered rings: ruthenium-catalyzed intramolecular [5+2] cycloadditions

The Ru-catalyzed intramolecular [5+2] cycloaddition of cyclopropylenynes is investigated with respect to the regio- and diastereoselectivity as well as the functional group compatibility of the reaction. Evidence for the mechanism as occurring through a ruthenacyclopentene intermediate is elucidated from 1) the study of the diastereoselectivity of the cycloaddition; 2) the effect of variation of substituents on the regioselectivity of cyclopropyl bond cleavage in 1,2-trans- and 1,2-cis-disubstituted cyclopropanes and 3) examples that clearly do not involve ruthenacyclohexene as intermediates as products still incorporate the cyclopropyl moiety. The scope and limitations of the Ru-catalyzed cycloaddition are discussed and compared with the Rh-catalyzed reaction. The potential power of this methodology towards natural product total synthesis is demonstrated by the formation of several polycyclic systems with the chosen reaction conditions and readily available cyclopropylenyne substrates.     

An explicit description of the fundamental unitary for SU(2) q

In this paper we study the Cauchy problem for the generalized equation of finite-depth fluids

Classification of Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks

This paper describes and classifies a family of invertible discrete-time signal transforms, referred to assymmetric extension transforms(SET's), for finite-length signals. SET's are algorithms for applying perfect reconstruction multirate filter banks to symmetric extensions of finite-length signals, thereby avoiding the boundary artifacts introduced by simple periodic extension. A key point is when such symmetric decompositions can be formed with no increase in data storage requirements (“nonexpansive decompositions”). Transforms based on three types of symmetric extension and four classes of linear phase filters are analyzed in terms of their memory requirements for generalM-channel perfect reconstruction filter banks. The classification is shown to be complete in the sense that it contains all possible nonexpansive SET's. Completeness is then used to deduce design constraints on the construction of nonexpansiveM-channel SET's, including new obstructions to the existence of certain classes of filter banks. This paper also forms the principal technical reference on the SET algorithms incorporated in the Federal Bureau of Investigation's digital fingerprint image coding standard.