Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

Towards Treating Correlations in Bose Condensates

 We use the adiabatic hyperspheric expansion and the Faddeev decomposition of the wave function with only s-waves. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. The correlations lower the interaction energy for N = 20 by about a factor of 5. Received October 22, 2001; accepted for publication November 5, 2001     

Amplifiers and Lasers in PCF Configurations

In this paper we will present an overview of the use of photonic crystal fibers as fiber amplifiers. We will describe the basic concepts of optical amplification, and how to do numerical modelling of such components. We will then identify advantages and disadvantages of amplifiers based on PCF technology compared to conventional fibers, and then go into greater detail on some of these specific applications, such as low pump power amplifiers, and high-power double-clad amplifiers and lasers.     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004     

On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002     

Group-valued measures on coarse-grained quantum logics

In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.     

Fluoride effect on the palladium–phenanthroline catalyzed carbonylation of nitroarenes to carbamates

Fluorides promote the palladium–phenanthroline catalyzed carbonylation of nitroarenes to carbamates. The effect is more evident on the rate of the reaction at short reaction times, but a positive effect on selectivity is also observed under certain conditions. The effect is observed even under conditions under which chloride inhibits the reaction. Tetraethylammonium is a better countercation than sodium. Copyright © 2007 John Wiley & Sons, Ltd.