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 Organization of Interaction Between Oil Refineries

The paper deals with the appropriate form of interaction between two refineries with different demand patterns. This problem can be formulated as finding a decentralized solution of linear programming problems linked by buying and selling activities. The complete problem is first solved for central values of product demands and costs and revenues. The structure of the basis then determines the organization of the interaction in terms of which unit sets quantities and which prices, or whether centralized decisions should be made. If, for expected values of product demand and costs, the structure of the basis is the same then the related organization of trading can be used for day-to-day transactions. For a well-known oil refinery model it is found that, for fairly large demand variations, decentralized interaction is effective, but that the structure of the basis changes easily with crude price variations, and that simulations did not converge for these variations.     

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.     

Scattering theory relevant to the linear transport of particle swarms

The long-time behavior of the velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D.C. electric field is studied within the framework of scattering theory. We prove the existence of wave and scattering operators for a simplified one-dimensional model of the linearized Boltzmann equation. The theory is applied to the study of the long-term behavior of electrons and the occurrence of traveling waves in runaway processes.     

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.     

2'-chloro-2',3'-dideoxy-3'-fluoro-d-ribonucleosides: synthesis,stereospecificity, some chemical transformations,and conformational analysis

The synthesis of methyl 5-O-benzoyl-2-chloro-2,3-dideoxy-3-fluoro-beta-d-ribofuranoside (5) and its use as a glycosylating agent for persilylated thymine, N(6)-benzoyladenine, and N(4)-benzoylcytosine are described (Scheme 1). The 2'-chloro-2',3'-dideoxy-3'-fluoro-d-ribonucleosides 10-12 synthesized were transformed to 2',3'-dideoxy-3'-fluoro-alpha- and -beta-d-erythro-pentofuranoside nucleosides of thymine (13a,b), adenine (14a,b), and cytidine (15a,b) by treatment with tributyltin hydride in the presence of alpha,alpha'-azobisisobutyronitrile (Scheme 2). Treatment of 2'-chloro-2',3'-dideoxy-3'-fluoro-d-ribonucleosides with 1 M MeONa/MeOH under reflux for 1-5 h afforded 2',3'-didehydro-2',3'-dideoxy-2'-chloro-d-pentofuranosyl nucleosides as the principal products (47-81%) of the reaction, along with recovered starting nucleoside (11-33%) (Scheme 3). Easy HF elimination was also observed in the case of the 2'-azido-2',3'-dideoxy-3'-fluoro-beta-d-ribofuranosides of thymine (17) and adenine (20) (Scheme 3). The role of conformational peculiarities of 2'-chloro-2',3'-dideoxy-3'-fluoro-d-ribonucleosides as well as of 17 and 20 in the observed exclusive elimination of HF is discussed. The conformational analysis of a rather broad palette of 2,3-dideoxy-3-fluoro-2-(X-substituted)-d-ribofuranosides was performed with the aid of the PSEUROT (version 6.3) program, using (i) the recently reparametrized Karplus-type relation (Chattopadhyaya and co-workers. J. Org. Chem. 1998, 63, 4967) and (ii) empirical bond angle correction terms suggested by us. The predictive power of the Brunck and Weinhold model (J. Am. Chem. Soc. 1979, 101, 1700) of the gauche effect between atoms and groups as a conformational driving force acting upon the pentofuranose ring is explored. Their model invokes maximum antiperiplanar sigma <--> sigma stabilization when the donating bond is the least polar one and the acceptor orbital is at the most polarized bond and is found at least as satisfactory, and in various specific cases more so than, as rationalizations on the basis of the preference of the gauche vs the trans conformation of two vicinal electronegative substituents (Wolfe. Acc. Chem. Res. 1972, 5, 102).     

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.