Sur les hypersurfaces minimales dans un espace elliptique à quatre et à cinq dimensions

Résumé On étude des hypersurfaces minimales dans un espace elliptique à quatre et à cinq dimensions. L’introduction de certaines notions qui ont trait à des relations d’invariance entre champs de vecteurs et r-formes permet de traduire quelques propriétés de ces variétés liées à ces relations d’invariance. Ce travail a été réalisé dans le cadre de l’accord culturel entre la Belgique et la Roumanie. Entrata in Redazione il 5 novembre 1971.     

On totally real surfaces of the nearly Kaehler 6-sphere

Let M be a minimal totally real surface of the nearly Kaehler 6-sphere. We prove that if M is homeomorphic to a sphere, then M is totally geodesic. Consequently, if M is compact and has non-negative Gaussian curvature K, then eithe K=0 or K=1. Finally, we derive from these results that if M has constant Gaussian curvature K, then either K=0 or K=1.Aspirant Navorser N.F.W.O. (Belgium).     

Intrinsic characterizations for complex hypercylinders and complex hyperspheres

In terms of conditions on the curvature tensors of Riemann-Christoffel, Ricci, Weyl and Bochner we obtain several new characterizations of complex hyperspheres in complex projective spaces, of complex hypercylinders in complex Euclidean spaces and of complex hyperlanes in complex space forms.Aspirant N.F.W.O. (België).     

Einstein, conformally flat and semi-symmetric submanifolds satisfying chen’s equality

In a recent paper, B. Y. Chen proved a basic inequality between the intrinsic scalar invariants infK andτ ofM ⁿ , and the extrinsic scalar invariant |H|, being the length of the mean curvature vector fieldH ofM ⁿ in . In the present paper we classify the submanifoldsM ⁿ of for which the basic inequality actually is an equality, under the additional assumption thatM ⁿ satisfies some of the most primitive Riemannian curvature conditions, such as to be Einstein, conformally flat or semi-symmetric. The first author is Senior Research Assistant of the National Fund for Scientific Research (Belgium). The second author was supported by the Research Council of the Katholieke Universiteit Leuven when this work was finished.     

STRUCTURAL AND FUNCTIONAL INTEGRITY OF THE PHOTOSYSTEM II REACTION CENTER ON SILVER ELECTRODES: FLUORESCENCE AND REDOX PROBES

Two simple and sensitive methods have been developed to assess the structural and functional integrity of isolated photosystem II reaction centers deposited on a roughened Ag electrode. Surface-enhanced resonance Raman scattering (SERRS) spectra useful for ascertaining structural information can be obtained from biological materials with this technique. The first method presented is based on observing differences in the fluorescence emission properties of reaction centers; these depend on the activity of the material. The second is based on the observation of changes in Raman bands that are sensitive to the redox state of cytochrome b₅₅₉ present in the reaction center complex. It is concluded that the conditions used here to obtain SERRS spectra do not affect the structural or functional integrity of the isolated photosystem II reaction center complex. In principle these approaches also could be used with other chromoproteins.     

The compact cyclides of Dupin and a conjecture of B.-Y. Chen

We show that the compact cyclides of Dupin are of infinite type; this result provides further support for a conjecture of Chen.Supported by a post-doctoral fellowship of the Research Council of the Katholieke Universiteit Leuven     

Heterogeneous nucleation of nitric acid trihydrate on clay minerals: relevance to type ia polar stratospheric clouds

Although critical to atmospheric modeling of stratospheric ozone depletion, selective heterogeneous nuclei that promote the formation of Type Ia polar stratospheric clouds (PSCs) are largely unknown. While mineral particles are known to be good ice nuclei, it is currently not clear whether they are also good nuclei for PSCs. In the present study, a high-vacuum chamber equipped with transmission Fourier transform infrared spectroscopy and a quadrupole mass spectrometer was used to study heterogeneous nucleation of nitric acid trihydrate (NAT) on two clay minerals-Na-montmorillonite and kaolinite-as analogs of atmospheric terrestrial and extraterrestrial minerals. The minerals are first coated with a 3:1 supercooled H2O/HNO3 solution prior to the observed nucleation of crystalline NAT. At 220 K, NAT formation was observed at low SNAT values of 12 and 7 on kaolinite and montmorillonite clays, respectively. These are the lowest SNAT values reported in the literature on any substrate. However, NAT nucleation exhibited significant temperature dependence. At lower temperatures, representative of typical polar stratospheric conditions, much higher supersaturations were required before nucleation was observed. Our results suggest that NAT nucleation on mineral particles, not previously treated with sulfuric acid, may not be an important nucleation platform for Type Ia PSCs under normal polar stratospheric conditions.     

Exploring the substrate selectivity of human sEH and M. tuberculosis EHB using QM/MM

The mechanisms of human soluble epoxide hydrolase (sEH) and the corresponding epoxide hydrolase enzyme from Mycobacterium tuberculosis (EHB) are studied computationally, using the quantum mechanics/molecular mechanics (QM/MM) method. To do this, we modeled the alkylation and the hydrolysis steps of three substrates: trans-1,3-diphenylpropene oxide, trans-stilbene oxide and cis-stilbene oxide. Studying the regioselectivity for trans-1,3-diphenylpropene oxide, we determined that both enzymes prefer ring opening via attack on the benzylic carbon. In agreement with experimental studies, our computations show that the rate-limiting step is hydrolysis of the ester intermediate, with reaction barriers of approximately 13 to 18 kcal/mol. Using the barrier energies of this rate-limiting step, the three epoxides were ranked in order of reactivity. Though the reactivity order was correctly predicted for sEH, the predicted order for EHB did not correspond to experimental observations. Next, the electrostatic contributions of individual residues on the barrier height of the rate-limiting step were also studied. This revealed several residues important for catalysis. The secondary tritium kinetic isotope effect for the alkylation step was determined using a cluster model for the active site of sEH. The calculated value was 1.27, suggesting a late transition state for the rate-limiting step. Finally, we analyzed the reactivity trends using reactivity indicators from conceptual density functional theory, allowing us to identify ease of electron transfer as the primary driving force for the reaction.