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.     

Parallel synthesis of PNA-peptide conjugate libraries

An optimized semi-automatic protocol for parallel synthesis of up to 96 peptide nucleic acids (PNA) or PNA-peptide conjugates using Boc-protection strategy has been developed using a robotic system. The approach is illustrated by synthesizing PNA and PNA-peptide libraries varying between 15 and 27 amino acid units. The peptides (NLS (nuclear localization signal) or Tat-peptide) were attached to N-terminus of the PNA. The method was found to be far superior to that based on the SPOT/Fmoc protocol by which PNA oligomers are synthesized on a modified cellulose membrane. On a 0.5 micromole scale the method typically yielded 2 mg product of 90% purity by HPLC/MALDI-TOF analysis. This approach is suitable for screening of a large number of PNA and/or peptide sequences for biochemical and biological studies.     

Formation of oligonucleotide-PNA-chimeras by template-directed ligation

DNA sequences have previously been reported to act as templates for the synthesis of PNA, and vice versa. A continuous evolutionary transition from an informational replicating system based on one polymer to a system based on the other would be facilitated if it were possible to form chimeras, that is molecules that contain monomers of both types. Here we show that ligation to form chimeras proceeds efficiently both on PNA and on DNA templates. The efficiency of ligation is primarily determined by the number of backbone bonds at the ligation site and the relative orientation of template and substrate strands. The most efficient reactions result in the formation of chimeras with ligation junctions resembling the structures of the backbones of PNA and DNA and with antiparallel alignment of both components of the chimera with the template, that is, ligations involving formation of 3'-phosphoramidate and 5'-ester bonds. However, double helices involving PNA are stable both with antiparallel and parallel orientation of the two strands. Ligation on PNA but not on DNA templates is, therefore, sometimes possible on templates with reversed orientation. The relevance of these findings to discussions of possible transitions between genetic systems is discussed.     

Esters of 5-carboxyl-5-methyl-1-pyrroline N-oxide: a family of spin traps for superoxide

Apparent rate constants, at acidic pH and neutral pH for the reaction of a family of ester-containing 5-carboxyl-5-methyl-1-pyrroline N-oxides with superoxide (O2*-) were estimated, using ferricytochrome c as a competitive inhibitor. It was of interest to note that the rate constants were similar among the different nitrones and not that significantly different from that found for 5-(diethoxyphosphoryl)-5-dimethyl-1-pyrroline N-oxide. At acidic pH, the rate constant for spin trapping O2*- was 3-fold greater than that at physiological pH. Subsequent experiments determined the half-life of aminoxyls, derived from the reaction of these nitrones with O2*-. The EPR spectra were modeled by using a global analysis method. The results clearly demonstrated that EPR spectra of all the aminoxyls were inconsistent with a model that included a single gamma-hydrogen splitting. A better interpretation modeled them as two diastereomers with identical nitrogen splittings and slightly different beta-hydrogen splittings. Detailed line width analyses slightly favored an equal line width-unequal population ratio for the two diastereomers.