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.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue     

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.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Validation of HPLC Analysis of 2-Phenoxyethanol, 1-Phenoxypropan-2-ol, Methyl, Ethyl, Propyl, Butyl and Benzyl 4-Hydroxybenzoate (Parabens) in Cosmetic Products, with Emphasis on Decision Limit and Detection Capability

The Commission Decision of August 12, 2002 on the performance of analytical methods and the interpretation of results was applied to the HPLC method for the analysis of parabens, 2-phenoxyethanol and 1-phenoxypropan-2-ol in cosmetic products. This method is published in the seventh Directive 96/45/EC of the European Commission. Non-compliant concentrations, taking into account the data distribution (CC) and the probability of false negative values (CC) were determined. The repeatability and reproducibility amount to <4% and <7%, respectively. These values were obtained with blanc samples that were fortified in the laboratory. Calibration linearity was confirmed by absence of lack of fit for all seven preservatives. Matrix effects on the determinations of the preservatives in body milk or shampoo are negligible.     

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