The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Electron impact mass spectrometry of 2-(2-pyridyl)-2,3-dihydroxy-5-phenyl-4-pentene

The mass spectrometric behaviour of 2-(2-pyridyl)-2,3-dihydroxy-5-phenyl-4-pentene has been studied with the aid of B/E, B²/E linked scans, exact mass measurements, collisionally activated dissociation mass-analysed ion kinetic energy spectra, and labelling experiments. The primary loss of water is proved to involve both hydroxylic hydrogens, thus suggesting the formation of an epoxidic radical ion and the presence of extensive skeletal rearrangements.     

Photochemical substitution reactions of 4-Pyridinecarbonitrile with aliphatic alcohols in neutral and acidified medium

Chemical evidence is given that the title photo-reactions proceed via hydrogen abstraction by the photo-excited base from the alcohol in neutral medium and via electron-transfer process between the photo-excited base and the alcohol in hydrochloric acid acidified medium.     

AB initio calculations of the electronic properties of N4− in KN3

The energies of the ground state and low-lying excited states of the N₄^? defect in KN₃ have been calculated using ab initio techniques. A rectangular equilibrium geometry with dimensions X = 2.76 and Z = 2.47 a.u. and ground state symmetry of Γ₄⁺ was determined by calculating N₄^? as a free radical. For this ground state the unpaired electron is in a π orbital which is consistent with the experimental hyperfine tensor only if one edge of the N₄^? radical is parallel to the c axis in KN₃. These results were used to calculate the X²Γ₄⁺ state of N₄^? in the crystal field of KN₃, yielding an energy of ?217.899 Hartrees. The isotropic hyperfine constant was calculated to be a = 2.1 G and the components of the anisotropic hyperfine tensor as B_xx = ?3.4 G, B_yy = 7.0 G and B_zz = ?3.6 G, in good agreement with experimental and INDO results. Several excited states were calculated for the N₄^? defect in KN₃. When an estimate was made of the correlation energy, the transition energy of the X²Γ₄⁺→A²Γ₃^? transition agreed well with the peak energy of the 780 nm absorption band which has been attributed to N₄^?.     

Regioselective synthesis of trisubstituted 2,3-dihydrofurans from donor-acceptor cyclopropanes or from reaction of the Corey ylide with alpha-sulfenyl-, alpha-sulfinyl-, or alpha-sulfonylenones

[reactions: see text] Regioselective synthesis of 2,4,5- or 3,4,5-trisubstituted 2,3-dihydrofurans has been realized by using donor-acceptor cyclopropanes or by a Corey ylide reaction with alpha-sulfenyl-, alpha-sulfinyl-, or alpha-sulfonylenones. The method allowed a straightforward synthesis of the natural product calyxolane B.     

Complete single-photon counting and timing module in a microchip

A complete module for single-photon counting and timing is demonstrated in a single chip. Features comparable with or better than commercially available macroscopic modules are obtained by integration of an active-quenching and active-reset circuit in complementary metal-oxide semiconductor technology together with a single-photon avalanche diode (SPAD). The integrated SPAD has a 12-microm-diameter sensitive area and operates with an overvoltage above breakdown adjustable up to 20 V. With a 5-V overvoltage the photon detection efficiency peaks above 40% around 500 nm, and the dark-counting rate is lower than 600 counts/s at room temperature. The overall counting dead time is 33 ns.