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.     

Space-Time Topology (II)—Causality, the Fourth Stiefel–Whitney Class and Space-Time as a Boundary

We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition.     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

New synthesis of 2',3'-didehydro-2',3'-dideoxynucleosides.

The 3'-iodonucleoside 4 and the 3'-O-methylsulfonylthymidine 9 have been synthesized by condensation of silylated uracils 2 with methyl 5-O-tert-butyldiphensilyl-2,3-dideoxy-3-iodo-D-threo-pentofuran oside (3) and methyl 5-O-tert-butyldiphenylsilyl-2-deoxy-3-methylsulfonyl-D-erythro- pentofuranoside (8), respectively. The nucleoside 4 and 9 produced the corresponding 2',3'-didehydro-2',3'-dideoxynucleosides 5 in an elimination reaction on treatment with sodium methoxide. The compounds 5b showed no antiviral activity against HIV-1.     

Excess partial molar enthalpies,entropies, Gibbs energies,and volumes in aqueous dimethylsulfoxide

The excess partial molar enthalpies, the vapor pressures, and the densities of dimethylsulfoxide (DMSO)–H₂O mixtures were measured and the excess partial molar Gibbs energies and the partial molar volumes were calculated for DMSO and for H₂O. The values of the excess partial molar Gibbs energies for both DMSO and H₂O are negative over the entire composition range. The results for the water-rich region indicated that the presence of DMSO enhances the hydrogen bond network of H₂O. Unlike monohydric alcohols, however, the solute-solute interaction is repulsive in terms of the Gibbs energy. This was a result of the fact that the repulsion among solutes in terms of enthalpy surpassed the attraction in terms of entropy. The data in the DMSO-rich region suggest that DMSO molecules form clusters which protect H₂O molecules from exposure to the nonpolar alkyl groups of DMSO.     

Stabilisation of a nucleic acid three-way junction by an oligonucleotide containing a single 2'-C to 3'-O-phosphate butylene linkage prepared by a tandem RCM-hydrogenation method

A cyclic dinucleotide with a butylene linker between the upper 2'-C position and the 3'-O-phosphate linkage was synthesised from simple nucleoside building blocks via a tandem ring-closing metathesis and hydrogenation procedure. The major of two phosphorus epimers was incorporated into an oligodeoxynucleotide, as well as into an LNA-DNA mixmer oligonucleotide. These were evaluated as parts in three different secondary structures, a duplex, a bulged duplex and a three-way junction, with both DNA and RNA complements. In the DNA:RNA hybrid molecule, the oligodeoxynucleotide containing this single 2'-C to 3'-O-phosphate butylene linkage was found to stabilise a three-way junction.