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.     

Temperature coefficient of NH chemical shifts of thioamides and amides in relation to structure

NH chemical shift temperature coefficients have been measured in a large series of N-substituted-3-piperidinethiopropionamides in which the NN distances are short but of varied length, as well as in a couple of the corresponding amides and in some simpler amides and thioamides. Geometries are calculated by means of ab initio DFT methods. The N-substituted-3-piperidinethiopropionamides show in most cases strong intramolecular N–HN hydrogen bonds according to IR spectra and ab initio calculations. For compounds with rather short NN distances the S=C–N–H moiety is non-planar. Dihedral angles as small as 160° are found. The NH chemical shift coefficients measured in non-polar solvents in all the N-substituted-3-piperidinethiopropionamides are more negative (−8 to −17 ppb/K) than in non-hydrogen bonded thioamides. For the latter in non-polar solvents like CDCl₃ and toluene the temperature coefficients are as small as −1 to −4 ppb/K. The large negative effects can be related not only to the non-planarity of the thioamide group in a way that the more pronounced the non-planarity the more negative the temperature coefficients, but also to strong hydrogen bonding and the fact that the acceptor is a nitrogen. For similar amides with non-planar amide groups and nitrogen acceptor large negative temperature coefficients are likewise seen. In polar solvents like DMF the effects in simple thioamides are uniform and close to −6 ppb/K, whereas in the more complex compound like 4p(t) the temperature coefficient is close to 0. An essential feature of measuring temperature coefficients of compounds without strong intramolecular hydrogen bonds in non-polar solvents and at low temperatures is to keep the concentration low enough to avoid dimerisation.     

Optical Diffractive Memories: Angular Selectivity and Diffraction Efficiency in Dichromated Gelatin

Two thousand images of resolution 512×512 pixels as a regular matrix pattern of 10×10 elements are stored, where each element is angularly multiplexed 20 times in a 25 μm thickness of dichromated gelatin emulsion without cross-talk effect. The surface area of the matrix is 1 cm². We show good concordance of the angular selectivity between the experimental result and theory. The diffraction efficiency of each 20 multiplexed images is measured and has nearly the same value. Examples of reconstructed images for multiple applications are given, for example, storage of 160,000 images on a 3′1/2 floppy disc format, which is about 100 min of black and white film. Application can be made to automobile cartography and storage of X-ray images as well as weather forecast images. Colored diffractive images are also possible and are illustrated.     

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.     

Methane activation on Ni(1 1 1): Effects of poisons and step defects

We have, theoretically and experimentally, investigated the dissociation of methane on the terraces and steps of a Ni(1 1 1) surface. Using Density Functional Theory (DFT) total energy calculations combined with Ultra High Vacuum (UHV) experiments, we find that the steps exhibit a higher activity than the terraces. We have, furthermore, investigated how carbon and sulfur present on the surface will deactivate the steps, leaving only the terraces active. We find the intrinsic sticking probabilities of methane on the steps and terraces at 500 K to be 2.8 × 10⁻⁷ for the steps and 2.1 × 10⁻⁹ for the terraces, in complete agreement with our calculated difference in activation energy of 17 kJ/mol.