Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space R2n up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.     

Application of exact occupation statistics to surface coverage effect on heat of adsorption

Using an exact expression for the number of nearest-neighbor pairs, the exact relations for the change in heat of adsorption of single particles with surface coverage have been calculated within the framework of random distribution taking into account the first, second and third nearestneighbor interactions. It is shown that (1) when the total number of sites is less than about 30, the influence of the corners and edges of a lattice on the heat of adsorption cannot be neglected, and that (2) when the third nearest-neighbor interactions are taken into account for a rectangular or a hexagonal lattice, the heat of adsorption varies with coverage obeying a quadratic equation.     

Indirect determination of sub-ng ml-1 levels of phosphorus in waters by di-isobutyl ketone extraction of reduced molybdoantimonylphosphoric acid an

Reduced molybdoantimonylphosphoric acid is extracted into di-isobutyl ketone (DIBK) and phosphorus in the extract is indirectly determined by inductively-coupled plasma emission spectrometric measurement of the Mo II 202.03-nm or Sb I 206.83-nm line. Washing of the extract with acid is unnecessary because of the low solubility of DIBK in water. Arsenic(III), Si, Ge, Fe(III) and most anions do not cause serious interference but arsenic(V) must be absent. The detection limits are 5.2 and 45 pg P ml^-1, and the relative standard deviations for 1 μg of phosphorus are 2.0% and 2.5%, for molybdenum and antimony measurements, respectively. The method is applied in the analysis of river and seawater.