Tau functions for the Dirac operator on the Poincaré disk

In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincaré disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painlevé function of type VI.     

A curve fitting signal processing scheme for a white-light interferometric system with a synthetic source

A white-light interferometric system, which comprises two Michelson interferometers linked by a 100 μm diameter core multimode step index fibre has been investigated, where a signal processing scheme, using curve fitting, has been introduced to suppress the noise induced in the system. The theoretical resolution of such a sensor with the use of an appropriate curve fitting signal processing scheme has been discussed. The experimental results obtained show the short term repeatability (to three standard deviations) to be better than 5 nm after signal processing, under conditions where the fibre is constantly vibrated in a known and reproducible way.     

Assignment of the VUV electronic spectrum of allene

Early assignments of the vacuum UV photoabsorption spectrum of allene (1951-1972) gave a number of Rydberg series, but these series had limiting values for the ionization potential, which are incompatible (by up to 0.4 eV) with more recent adiabatic IPs from molecular beam and high resolution photoelectron spectra (UV-PES). We have performed a re-analysis of the VUV spectrum of allene by a combination of overlay of the VUV and UV-PES spectra which leads to new experimental assignments. Major differences in assignment to the early studies are reported, and these include the lowlying Rydberg states, which are now assigned as follows: 6.55 (3s), 7.2 (3p), 8.15 (3d), and 8.25 eV (4s), respectively, with further assignments up to 6s, 6p, and 6d.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

Rhenium ethoxy- and hydroxycarbene complexes with thiophene substituents

Reaction of mono- and dilithiated thiophene (a), bithiophene (b) and 2,5-dibromothiophene (c) with [Re(2)(CO)(10)] afforded, after subsequent alkylation with triethyloxonium tetrafluoroborate, tetra- and binuclear Fischer carbene complexes, [Re(2)(CO)(9){C(OEt){C(4)H(2)S}(n)X}], n = 1, X = H (1a); n = 2, X = H (1b); n = 1, X = Br (1c); n = 1, X = C(OEt)Re(2)(CO)(9), (2a); n = 2, X = C(OEt)Re(2)(CO)(9) (2b), as major products. The dirhenium acylate intermediates from this reaction not only gave the expected novel ethoxycarbene complexes with alkylation but after rhenium-rhenium bond breaking afforded a number of minor products. The (1)H NMR spectrum of the crude reaction mixture revealed the formation of four metal hydride complexes and aldehydes. Protonation with HBF(4) instead of alkylation with Et(3)OBF(4) significantly increased the yields of the hydride complexes, which enabled the positive identification of three of these complexes. In addition to the known compounds [Re(CO)(5)H] and [Re(3)(CO)(14)H] (3), a unique complex displaying a hydroxycarbene fragment connected to an acyl fragment via an O-H···O hydrogen bond and a Re···H···Re bond linking the two Re centers, [(μ-H){Re(CO)(4)C(OH){C(4)H(2)S}(n)H}{Re(CO)(4)C(O){C(4)H(2)S}(n)H}], n = 1 (4a) or n = 2 (4b), were isolated. The formation of thiophene aldehydes, H{C(O)}(m){C(4)H(2)S}(n)C(O)H (m = 0 or 1 and n = 1 or 2), were observed and the novel monocarbene complexes with terminal aldehyde groups, [Re(2)(CO)(9){C(OEt){C(4)H(2)S}(n)C(O)H}], n = 1 (5a) and n = 2 (5b) could be isolated. A higher yield of 5b was obtained after stirring crystals of 2b in wet THF. The crystal structures of 1a, 2a, 4a and 5b are reported.     

The formal [4+3] cycloaddition between donor-acceptor cyclobutanes and nitrones

The formal [4+3] cycloaddition of 2-alkoxy-1,1-dicarboxylate activated donor-acceptor cyclobutanes with nitrones is disclosed. The reaction forms structurally unique oxazepines in moderate to high yield with a wide scope of nitrones. In most cases either a diastereomeric mixture or a single diastereomer may be formed, depending on the reaction conditions.     

Controlled formation of mass-selected Cu-Au core-shell cluster beams

Synthesis of bimetallic clusters is a topic of accelerated interest; their physical and chemical properties are greatly dependent on their composition, size, and structure. The cluster beam technique is widely used for preparation of clusters. However, creating bimetallic clusters with well-controlled composition, size, and structure, especially for larger clusters (>100 atoms), is still a big challenge. Here we demonstrate that not only size and composition but also the structure of bimetallic clusters can be controlled by tuning aggregation parameters.     

Minimising reversion, using seawater and magnesium chloride, caused by the dissolution of tricalcium aluminate hexahydrate

The increase in pH and aluminium concentration after the neutralisation of bauxite refinery residues is commonly known as reversion. This investigation reports the extent of reversion in synthetic supernatant liquor and possible methods to reduce reversion. This work is based on bauxite refinery residues produced from alumina refineries, where reversion is a real life situation in neutralised refinery residues. Tricalcium aluminate hexahydrate, a common phase in bauxite refinery residues, has been found to cause reversion. It has been established that reductions in both pH and aluminium from the seawater neutralisation process are due to the formation of 'Bayer' hydrotalcite Mg(7)Al(2)(OH)(18)(CO(3)(2-),SO(4)(2-))·xH(2)O. This is the primary mechanism involved in the removal of aluminium from solution. Increasing the volume of seawater used for the neutralisation process minimises the extent of reversion for both synthetic supernatant liquor and red mud slurry. The addition of MgCl(2)·6H(2)O also showed a reduction in reversion and confirmed that the decrease in aluminium and hydroxyl ions is due to the formation of Bayer hydrotalcite and not simply a dilution effect.