Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

Solution of large configuration mixing matrices arising in partitioning technique and applications to the generalized eigenvalue problem

A method is presented that can be used (a) to determine the several lowest eigenvalues and eigenvectors of large symmetric matrices, (b) to solve the generalized eigenvalue problem associated with energy-dependent operators, that arises in computations involving energy-dependent many-body Green's functions and in the evaluation of the true parameters of the effective valence shell hamiltonian, and (c) to directly evaluate the matrices associated with resolvent operators. The applicability to large configuration mixing calculations arises when the N-electron basis functions can be easily broken down to a few dominant configurations (the primary block) and their complement. Using the partitioning technique, the effective hamiltonian within the primary block is directly evaluated. The method is extended to evaluation of the dynamical polarizability tensor, which effectively contains the contributions from all of the eigenstates of a hamiltonian matrix, without the necessity of explicitly calculating its eigenvalues and eigenvectors.     

First structural characterization of binary AsIII and SbIII azides

The highly explosive molecules As(N(3))(3) and Sb(N(3))(3) were obtained in pure form by the reactions of the corresponding fluorides with (CH(3))(3)SiN(3) in SO(2) and purification by sublimation. The crystal structures and (14)N NMR, infrared, and Raman spectra were determined, and the results compared to ab initio second-order perturbation theory calculations. Whereas Sb(N(3))(3) possesses a propeller-shaped, pyramidal structure with perfect C(3) symmetry, the As(N(3))(3) molecule is significantly distorted from C(3) symmetry due to crystal packing effects.     

Palladium-catalyzed Heck reactions of styrene derivatives and 2-iodo-p-carborane

p-Carborane has been vinylated on the 2-B-atom in high yields using the Heck reaction. Thus, the reaction between 2-iodo-p-carborane and various styrenes [4-H-, 4-C(6)H(4)-, 4-Cl-, 4-Br-, 4-NO(2)-, 4-CH(3)O-, and 4-CH(3)-] resulted in the production of the corresponding trans-beta-(2-B-p-carboranyl)styrene in DMF solution when reacted in the presence of silver phosphate and the palladacycle Herrmann's catalyst.