Representation of elements of a sequence by sumsets

In this note the method of [5] and a result from [3] are combined to treat the following classical problem: Given a finite setA and an infinite sequenceS (both inZ), what is the minimal number of elements ofA whose sum lies inS? We obtain an upper bound depending only on the densities ofA andS (but not on their arithmetic nature).     

Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

Four-dimensional BF theory as a topological quantum field theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4,) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds.     

A noncommutative geometric approach to left-right symmetric weak interactions

By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models of the form SU(2) _L SU(2) _R U(1). We see that within this formalism maximal use can be made of the gauge connection associated with the noncommutative graded algebra.     

Harmonic analysis in infinite dimension

We study the Hermite transform onL ²() where is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space () of analytic functions onE which is also a natural range for the Laplace transform. LetB be a convenient Hilbert-Schmidt operator on the Cameron-Martin spaceH of . There exists a natural sequence Cap _n of capacities onE associated toB. This implies the Kondratev-Yokoi theorem about positive linear forms on the Hida test-functions space.     

Correlations of13C chemical shifts and geometry modifications

The effect of geometry modifications of¹³C chemical shifts has been investigated in a small subset of molecules using both LO-INDO and Gaussian 70 (4 13;31) calculations. The Gaussian calculations, while known to give poor absolute shifts, compare well to the reparameterized semi-empirical INDO determinations in calculated shift changes. In virtually all cases the signs of the shift changes were found to be opposite to that of the changes in the calculated electronic energy.     

Evidence of a phase transition of RbHCO3 from high-resolution solid-state 13C and 87Rb NMR by comparison with KHCO3

A variable-temperature high-resolution 13C and 87Rb solid-state NMR study of powder rubidium hydrogencarbonate, RbHCO3, is presented for the first time. At ambient temperature, RbHCO3 is formed by centrosymmetric dimers linked by hydrogen bonds, but almost no information is available on this compound concerning proton disorder and the low-temperature phase. However, potassium hydrogencarbonate, KHCO3, which has an isomorphic structure for the high temperature phase, was well studied: it undergoes a non-ferroic, non-ferroelectric phase transition at Tc = 318 K between two monoclinic structures. The protons are disordered in an asymmetric double-well potential in the low-temperature phase, and the double-well potential becomes symmetric in the high-temperature phase. By comparison with recent solid-state NMR experimental results on KHCO3, we show that RbHCO3 undergoes a phase transition at Tc approximately 245 K, and give evidence that the proton dynamic disorder in both compounds is very similar.     

19F and 1H NMR spectra of halocarbons

19F NMR chemical shifts and coupling constants are reported for 215 compounds. For 77 of these compounds, 1H NMR spectral data are also given. Long-range couplings, including 8J(F,F) and 5J(F,H), are reported. The complexity of halocarbon spectra owing to the presence of rotational isomers, asymmetric centers, long-range couplings, and chlorine isotope effects are illustrated, and the methods used for analyzing such complex spectra are briefly discussed.     

New far infrared laser lines obtained by optically pumping13CD3OD

We have obtained laser action on 34 far infrared lines for the first time in fully deuterated methyl alcohol with the¹³C isotope (¹³CD₃OD), and we have measured the frequency of 13 lines. The molecule was pumped by a cw CO₂ laser. We have measured the wavelength, the relative polarization, the relative intensity of most lines, the frequency, and the CO₂ pump frequency offset of the strongest lines. The new lines are distributed in the wavelength region from 75.27 m to 464.7 m.Supported in part by a joint grant with the U.S. National Science Foundation grant # INT 80-19014 and the Brazilian Conselho Nacional de Pesquisas (CNPq).     

Glucomannan from Narcissus poeticus Studied by PMR and 13C NMR Spectroscopy

Native acetylated glucomannan of molecular weight (MW) 32000 with a glucose:mannose ratio 1:30 was isolated from bulbs of Narcissus poeticus. Glucomannan was depolymerized to a fragment of MW 15000 with an unchanged primary structure and was studied using PMR and ¹³C NMR spectroscopy. It was found that the linear chain of the biopolymer consists of 1-4-bound D-gluco- and D-mannopyranose units and the O-Ac groups are localized on C-2, C-3, and C-6 hydroxyls in certain anhydromannose units.