Invertibility of the biharmonic single layer potential operator

The 2×2 system of integral equations corresponding to the biharmonic single layer potential in ² is known to be strongly elliptic. It is also known to be positive definite on a space of functions orthogonal to polynomials of degree one. We study the question of its unique solvability without this orthogonality condition. To each curve , we associate a 4×4 matrixB such that this problem for the family of all curves obtained from by scale transformations is equivalent to the eigenvalue problem forB . We present numerical approximations for this eigenvalue problem for several classes of curves.     

Synergistic Interaction of Photodynamic Treatment with the Sensitizer Aluminum Phthalocyanine and Hyperthermia on Loss of Clonogenicity of CHO Cells

Abstract— When CHO cells were exposed to hyperthermia and subsequently to photodynamic treatment, the combined effects were additive but in the reverse sequence the interaction was synergistic. The synergistic interaction comprised two quite different components: (1) photodynam-ically induced sensitization of cellular proteins and/or supramolecular structures for thermal inactivation and (2) a photodynamically induced inhibition of the cellular repair system for sublethal thermal damage. The first component of the synergistic interaction was reflected by a change of the Arrhenius parameters of thermal cell killing. A lowering of the activation energy of this process was responsible for the synergistic interactions, whereas a concomitant decrease of the frequency factor, opposing this effect, actually caused a much lower degree of synergism at higher temperatures. This component of the synergistic interaction did not respond to the insertion of an intermediate incubation period between the two treatments. The second component of the synergistic interaction, viz. the interference with the ability of cells to survive sublethal thermal damage, was reversible, as an intermediate incubation between photodynamic treatment and hyperthermia resulted in its repair. The photodynamically induced inhibition of the ability of cells to survive sublethal thermal damage was not related to ATP or glutathione depletion, inhibition of de novo protein synthesis or impairment of degradation of damaged protein molecules. Restoration of the repair system for sublethal damage depended on a metabolic process and required free intracellular Ca²⁺, suggesting that a cell signaling pathway may be involved. Thus, in a practical sense the magnitude of the synergistic interaction between photodynamic treatment and hyperthermia depends on the length of the interval between the two treatments and on the temperature and duration of the subsequent thermal treatment. This may have significant consequences for the development of clinical protocols.     

Spectres de vibration de composes organiques des elements de la colonne IVB : VIII. Derives organometalliques a liaison germanium—azote: Trialkylgermyl-et bis(trialkylgermyl)-amines

We have examined in the 3600–100 cm^?1 region the IR and Raman spectra of three bis(trialkylgermyl)amines (R₃Ge)₂NR′ (R = Me, Et; R′ = H, C₆H₅), of three dialkyl(trialkylgermyl)amines R₃GeNR′₂ (R = Me, Et; R′ = Me, n-Bu) and of two triethylgermylpyrazoles:

Assignments are discussed for the characteristic vibrations of these derivatives.     

Spheriodal multipolar expansions for intermolecular energy in crystal theory .: II. Lattice energy of the orthorhombic structure of actylene crystal

The spheroidal formalism for the interaction energy between two non-overlapping ellipsoidal charge distributions is applied to the determination of the lattice energy of the orthorhombic structure of the acetylene crystal. The molecules are assimilated to quadrupolar prolate ellipsoids and the pair potential is assumed to be a sum of two terms: a Kihara corepotential extended to prolate ellipsoids and the spheroidal quadrupolar interaction. The value so obtained for the lattice energy is ?25.01 kJ mole^? while an evaluation of the corresponding observed value is ?23.81 kJmole^?.     

On the geometric structure of independence systems

A bouquet of matroids is a combinatorial structure that generalizes the properties of matroids. Given an independence system, there exist several bouquets of matroids having the same family of independent sets. We show that the collection of these geometries forms in general a meet semi-lattice and, in some cases, a lattice (for instance, when is the family of the stable sets in a graph). Moreover, one of the bouquets that correspond to the highest elements in the meet semi-lattice provides the smallest decomposition of into matroidal families, such that the rank functions of the different matroids have the same values for common sets. In the last section, we give sharp bounds on the performance of the greedy algorithm, using parameters of some special bouquets in the semi-lattice.     

Reactivite des carbanions benzyliques : II. Stereochimie d'alcoylation des ethyl et isopropyl-9 lithio-10 dihydro-9,10 anthracenes

A detailed study of the stereochemistry of alkylation of 9-ethyl- and 9-isopropyl-10-lithio-9,10-dihydroanthracenes by alkyl halides (R′ = Me, Et, i-Pr) is reported. The reaction is under kinetic control. cis-9-Ethyl-10-isopropyl-9,10-dihydroanthracene has been found more stable than the trans isomer. If we take into account the stereoelectronic factor, which favors axial attack, and the main steric interactions in the transition state, stereochemistry seems to be mainly controlled by the competition between axial-axial and peri interactions.     

Three body asymptotic completeness forP(Φ)2 models

We consider weakly coupled even P()₂ models that do not have a two-body bound state, and prove asymptotic completeness on the subspace of states with mass between 3m+a() and 4m–b(), wherea andb are positive functions tending to zero with . The analytic structure of the six point function, integrated over the three incoming momenta, shows only two Landau singular manifolds (plus normal thresholds) associated to three particle processes.Laboratoire associé au Centre National de la Recherche ScientifiqueGroupe de Recherche du C.N.R.S. No. 48     

Stereochemical and mechanistic aspects of the nickel complex catalysed formation of olefins from allylic alcohols and Grignard reagents

The reaction of (+)-S-but-1-en-3-ol with phenylmagnesium bromide in the presence of bis(triphenylphosphine)nickel dichloride has been shown to proceed with inversion of configuration to yield (?)-R-3-phenylbut-1-ene.     

Deuterium effects on radiationless electronic transitions of xanthene dyes in aqueous and alcoholic solutions

Solvent deuteration effects on internal conversion (S₁ ～→ S₀) and intersystem crossing (S₁ ～→ T₁) in 6-hydroxy-9-phenylfluoron and fluorescein were determined from fluorescence and triplet quantum yield measurements in alkaline solutions of H₂O, D₂O, CH₃OH, CH₃OD, C₂H₅OH, and C₂D₅OD. Deuterium substitution of the oxygen-bonded hydrogens of these solvenis reduces both the internal conversion (by approximately 1.6) and the intersystem crossing (by approximately 1.2) rate constants; the additional deuteration of the alkyl groups of the alcohols does not produce any further effect. The effect of solvent deuteration was negligible for fluorescein. Deuteration of the xanthene groups of the dyes does not influence the radiationless transition probabilities to any significant extent.