Nonabelian orbifolds and the boson-fermion correspondence

For a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) associated to the spin lattice _l . For a broad class of finite groupsG of automorphisms of we prove the existence and uniqueness of irreducibleg-twisted -modules and establish the modular-invariance of the partition functionsZ(g, h, ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between and a certain fermionic construction, and which extends work of Frenkel and others.Supported by NSA grant MDA904-92-H-3099.Supported by NSF grant DMS-9122030.     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Time variations in environmental pollution

Two programmes of work are described involving the measurement of environmental pollution over periods from two hours to many years. The long period measurements are deduced from neutron activation analysis of whole wood samples taken from individual tree rings for trees grown in various locations, and some results for cadmium, antimony and germanium levels are reported. In a second series of experiments the concentration of airborne particulate matter is being measured using a moving filter (streak sampler) technique to give a continuous record with two hour resolution. The filter samples are being analysed by proton induced X-ray emission (PIXE) and preliminary data is presented.     

Synthesis of tridimensional polymers by the copolymerization of phenylglycidylether with aromatic diglycidylethers

Copolymers from phenylglycidylether and several aromatic diglycidylethers are prepared using different ratios of difunctional comonomers and the AIP/ZnCl₂ initiator system. It is found that the percentage of incorporated comonomer depends on the nature of the aromatic moiety introduced. The copolymers are characterized by ¹³C-NMR spectroscopy and turn out to be completely regular and with a high degree of isotacticity (about 80%) that confirms the high degree of regio- and stereoselectivity of the initiator system used. The thermal characteristics of copolymer networks are investigated using differential scanning calorimetry and thermogravimetry. Two fusion endotherms are observed which vary with the degree of crosslinking. By thermogravimetric analyses the thermal stability is found to increase when the crosslinking degree does. © 1994 John Wiley & Sons, Inc.     

Enantioselective synthesis of 1-deoxy-d-gulonojirimycin from a phenylglycinol-derived lactam

Cyclocondensation of (R)-phenylglycinol with appropriately γ-substituted δ-oxo acid derivatives provides bicyclic lactams from which the enantioselective synthesis of 1-deoxy-d-gulonojirimycin has been reported.     

Comparison of micro- and mesoporous inorganic materials in the uptake and release of the drug model fluorescein and its analogues

The uptake of the three species of the drug model fluorescein (fluorescein sodium salt (FNa), fluorescein free acid (F), and fluorescein diacetate (FDA)) by zeolite NaX and the mesoporous zeotype MCM-41 was investigated as well as their release rates into solutions at pH 7 and pH 4.5. UV/Vis analysis was carried out at a wavelength of 490 nm. Uptakes of the sodium salt of 9 % for zeolite X and 14 % for MCM suggest little penetration of the pores. The use of ethanol as the loading solvent for F resulted in little uptake for both zeolitic materials due to the successful competition of the ethanol for binding sites. Use of acetone (weaker proton acceptor) as loading solvent significantly improved the uptake of F to 17 % and 12 % for zeolite X and MCM, respectively, whilst the uptake of FDA in acetone increased still further to 22 % and 17 % for zeolite X and MCM, respectively. Generally there was a large initial release of the fluorescein analogues from the surface of the zeolites with very little further increase over time. The prescence of an esterase enzyme in the release medium of FDA tripled the release from MCM to 15 % but left the release from zeolite X unaffected at 6 %. The results obtained show that uptake of fluorescein and its analogues is dependent on the loading solvent used, the amount released is influenced by not only the solvent but the pH and the presence of enzymes in the release medium.     

Efficient combination of task-specific ionic liquid and microwave dielectric heating applied to one-pot three component synthesis of a small library of 4-thiazolidinones

The first report of the use of task-specific ionic liquid as synthetic equivalent of ionic liquid-phase matrice for the preparation of a small library of 4-thiazolidinones is reported in this paper. The starting (ethyleneglycol)ionic liquid-phase is functionalized in good yields with 4-(formylphenoxy)butyric acid by using usual esterification reaction conditions (DCC/DMAP as catalyst). The synthesis of the ionic liquid-phase bound 4-thiazolidinones was performed by a one-pot three-component condensation under microwave dielectric heating. The final cleavage under microwave/catalysis strategy provides the expected 4-thiazolidinones in high purity after flash-chromatography purification. According to the ionic liquid-phase organic synthesis (IoLiPOS) methodology, it was found that optimized reaction conditions were performed by standard analytical methods (NMR, TLC). The ¹H, ¹³C NMR spectrum of some representative 4-thiazolidinones and ionic liquid-phase bound benzaldehyde are also reported.     

The temperature dependence of the d-electron dipole strengths of cobalt(II) tetrahalides

The dipole strengths of the ⁴A₂ → ⁴T₁(F), ⁴T₁(P), d-electron transitions of the cobalt(II) tetrahalides are found to decrease with an increase in temperature, in agreement with a dynamic ligand-polarisation model for the absorption mechanism. The reduction in dipole strength is accounted for by a decrease in the coulombic coupling between the quadrupole moment of the d-electron transition of the metal ion and the transient electric dipole moment induced in the ligands, due to the anharmonic increase in the mean bond length and the progressively larger mean-square amplitudes of the bending modes of the complex ion in its ground electronic state as the temperature is raised.