An expansion in the exponent for compound binomial approximations

The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise bounds in the compound Poisson approximation. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006.     

The excited states of pyrazine: A basis set study

Summary Multiconfigurational second order perturbation theory (CASSCF/CASPT2) has been used to investigate the dependence of computed valence excitation energies and transition moments on the basis sets. Pyrazine has been selected as the test molecule. Atomic normal orbital (ANO) type basis sets are used throughout. Contractions of the structure (4s3p1d/2s) are found to be an optimal compromise between the quality and the size of the calculations and are capable of yielding results virtually identical to more extended basis sets.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Curium isotopes in Chernobyl fallout

In nuclear reactors plutonium and transplutonium isotopes are produced by multiple neutron capture of uranium and plutonium and are important for the energy production and their composition reflects the core burnout. Under normal operation these elements are not released to the environment in significant amounts. There are accordingly very few areas or source terms where exotic transplutonium elements, such as curium isotopes, can be studied in the environment. The Chernobyl accident provided a complex spectrum of fission and activation products in fallout while the relative amounts, compared to the core inventory, of refractory elements such as transuranium and transplutonium elements were small. The major alpha-activity consisted of ²⁴²Cm (T _1/2 = 163 d) that would have decayed after a few years. In this study we have demonstrated the presence of so called supported ²⁴²Cm from the long-lived ²⁴²Am^m (T _1/2 = 141 a) in environmental samples, following fallout from the Chernobyl accident. It has also been possible to assess the core burn up by using the data obtained for the Cm isotopes. The curium isotopes ²⁴³Cm (T _1/2 = 29.1 a) and ²⁴⁴Cm (T _1/2 = 18.1 a) cannot be resolved by conventional alpha-spectrometry. The assessment of these isotopes in environmental samples contaminated from the Chernobyl accident has been made by studying the effective half-life of the mixture of the isotopes. The data are compared with those previously obtained by high-resolution alpha-spectrometry and spectral deconvolution.     

Compound Poisson approximation for unbounded functions on a group,with application to large deviations

Summary A second order error bound is obtained for approximating h d by h d , where is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.Research of the second author was supported by Schweizerischer Nationalfonds     

On the theoretical determination of the electron affinity of ozone

Summary Multiconfigurational electron correlation methods have been analyzed in order to theoretically compute the electron affinity (EA) of ozone. The near-degeneracy correlation effects, which are so important in O₃ and O ₃ ^– , have been described using complete active space (CAS) SCF wave functions. Remaining dynamic correlation effects are computed using second-order perturbation theory (the CASPT2 method). The best calculated adiabatic value (including zero-point energy corrections), 2.19 eV, is about 0.09 eV larger than the experimental value. Comparative studies using size-consistent coupled pair functional approaches (CPF and ACPF) have also been performed. The harmonic frequencies in O ₃ ^– have been determined to be: ₁=992, ₂=572, and ₃=879 cm^–1, which gives a zero-point energy of 0.151 eV.     

Thermal analysis,state transitions and food quality

Thermal properties of food systems are important in understanding relationships between food properties and changes in food quality. Concentrated food systems (low-moisture and frozen foods) are seldom in an equilibrium state and they tend to form amorphous, non-crystalline structures. Several glass transition-related changes in such foods affect stability, e.g., stickiness and caking of powders, crispness of snack foods and breakfast cereals, crystallisation of amorphous sugars, recrystallisation of gelatinised starch, ice formation and recrystallisation in frozen foods and rates of non-enzymatic browning and enzymatic reactions. Relationships between glass transition, water plasticisation and relaxation times can be shown in state diagrams. State diagrams are useful as stability or quality maps and in the control of rates of changes in food processing and storage.This revised version was published online in November 2005 with corrections to the Cover Date.