Approximation by harmonic functions on closed subsets of Riemann surfaces

Given continuous functionsu and ∈ on a closed subsetF of a Riemann surface, we seek a harmonic functionv on the surface (possibly with logarithmic singularities) such that |u−v|<∈ onF. Research supported in part by NSERC—Canada and FCAR—Quebec.     

On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I

Let A be an n × n complex matrix, and write A = H + iK, where i² = ?1 and H and K are Hermitian matrices. The characteristic polynomial of the pencil xH + yK is f(x, y, z) = det(zI ? xH ? yK). Suppose f(x, y, z) is factored into a product of irreducible polynomials. Kippenhahn [5, p. 212] conjectured that if there is a repeated factor, then there is a unitary matrix U such that U^?1AU is block diagonal. We prove that if f(x, y, z) has a linear factor of multiplicity greater than n?3, then H and K have a common eigenvector. This may be viewed as a special case of Kippenhahn’s conjecture.     

Aziridines N-Non substituées. Détermination des Paramètres Thermodynamiques ΔG°, ΔH°, ΔS° Liés à l'Equilibre Conformationnel à partir de Mesures RMN 1H à Haut Champ

Although nitrogen inversion in unsubstituted aziridines has been shown by ¹H NMR, it was only possible to study quantitatively the distribution of both invertomers and determine the thermodynamic parameters by a systematic high field NMR study (CAMECA 250 MHz). Thermodynamic parameters have been determined for 32 compounds. In C-aryl aziridines, the steric hindrance of the aromatic group and its variation with other aziridine ring substituents can be studied. These observations are in agreement with a conjugation phenomenon between the aromatic system and the aziridine ring.     

Tests of resonance recognition criteria in coupled channel problems with separable potentials

Exactly soluble two-body two-channel problems are set up with separable potentials. Resonance is defined theoretically then the empirical resonance recognition criteria used in two-body data analyses are tested. Results are summarized in the last section of the paper.     

Monophotonically UV excited delayed luminescence in rigid solutions of aromatic amines

During a study of neutralization luminescence following photoionization of aromatic solutes in rigid organic glasses, a new type of long-lived luminescence has been observed simultaneously with the well-known neutralization luminescence following biphotonic ionization. It has been extensively studied for tetramethyl-p-phenylenediamine in methylcyclohexane or ethanol: it is one-photon excited but differs from the ordinary luminescence by the emission spectrum (λ_max 430 nm compared to λ_{max f.} 395 nm and λ_{max ph.} 490 nm in ethanol) and by the excitation spectrum, the present luminescence being observed only for short wavelength excitation. Finally the lifetime (of the order of seconds) depends on experimental conditions. Other solid and liquid phase studies suggest that the precursor of this new luminescence is a solute-solvent charge transfer state.     

TE mode coupling between end separated buried waveguides: expressions and calculations

In this paper the power coupling expression between two identical axially aligned and spatially separated waveguides is presented. Calculations using the coupling expression for a Gaussian mode profile in the input waveguide produce results that are in excellent agreement with experimental observations.     

Q-band EPR and ENDOR of low temperature X-irradiated beta-D-fructose single crystals

Beta-D-fructose single crystals were in situ X-irradiated at 80 K and measured using electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR) and ENDOR-induced EPR (EIE) techniques at Q-band (34 GHz) microwave frequencies. The measurements revealed the presence of at least four carbon-centered radicals stable at 80 K. By means of ENDOR angular variations in the three principal crystallographic planes, six proton hyperfine coupling tensors could be determined and were assigned to four different radicals by the aid of EIE. Two of the radicals exhibit only beta-proton hyperfine couplings and reveal almost identical EIE spectra. For the other two radicals, the major hyperfine splitting originates from a single alpha-proton hyperfine coupling and their EIE spectra were also quite similar. The similarity of the EIE spectra and hyperfine tensors led to the assumption that there are only two essentially different radical structures. The radical exhibiting only beta-proton hyperfine couplings was assigned to a C3 centered radical arising from H3 abstraction and the other radical suggested to be an open-ring species with a disrupted C2-C3 bond and a double C2-O2 bond. A possible formation mechanism for the latter open-ring radical is presented. By means of cluster density functional theory (DFT) calculations, the structures of the two radicals were determined and a fairly good agreement between the calculated and experimental hyperfine tensors was found.