Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes

We completely classify all the twistor holomorphic Lagrangian immersions in the complex projective plane ², i.e. those Lagrangian immersions such that their twistor lifts to the twistor space over ² are holomorphic. This classification provides a one-parameter family of examples of Lagrangian spheres in ².Research partially supported by a DGICYT grant No. PB91-0731.     

Balancing domain decomposition for problems with large jumps in coefficients

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size . Computational experiments for two- and three-dimensional problems confirm the theory.

     

Sur les metriques admettant les plans comme surfaces minimales

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.

     

The role of radicals in metal-assisted oxygenation reactions

The oxo-functionalization of organic substrates with the aid of metal oxo moieties is of fundamental importance not only in nature but also in academic and industrial research. Nevertheless the corresponding reaction mechanisms remain among the most enigmatic in chemistry and few of them are understood in detail. Recent research efforts have resulted in significantly improved information: in the cases of many oxygenation reactions evidence has been provided for the occurrence radical intermediates, even though the high selectivity observed suggests to a different mechanism. Examples stem from various areas of chemistry and include processes involving molecular metal oxo complexes, gas-phase and matrix-isolated species, metalloenzymes, and solid-state oxide surfaces. This review treats this seemingly wide variety of systems with the aim of providing an overview of common reactivity patterns and principles, as well as open problems.     

Corrugated single-layer graphite sheet as a model of stepped surface of a crystal

Electronic structure calculations have been performed for flat graphite sheets and periodically distorted sheets with different values of deformation angle and hydrogen adsorption. These characteristics do not all behave monotonically with increasing deformation angle. At small deformation angles, the electrons pass from the atoms of terraces to those of edges, while at larger angles the reverse pattern is observed. The position of the Fermi level also varies nonmonotonically. The binding energy of hydrogen depends significantly on the adsorption site, and the difference can be doubled. Based on the ata obtained, it was concluded that a priori statements derived from the “general concepts” on the difference in the physicochemical properties of, for example, terrace and edge atoms on high-index facets are unreliable.     

Covalent-ionic nature of the potential energy surface of the Li-CO2 complex

Unrestricted Hartree-Fock calculations with large basis sets, including d-functions, and the estimation of the correlation energy, show that the potential energy surface for the Li-CO₂ complex is built from the crossing of two states, each of them corresponding to a different electron arrangement. One has a strong ionic character and the other is of van der Waals type. Each portion of the energy surface presents a minimum, which is stable in respect to the dissociation limit.     

Hydrogel networks of poly(ethylene oxide) star-molecules supported by expanded polytetrafluoroethylene membranes: characterization, biocompatibility evaluation and glucose diffusion characteristics

The present work discusses the grafting by electron beam irradiation of poly(ethylene oxide) (PEO) star-shaped polymers onto porous expanded polytetrafluoroethylene (EXPTFE) surfaces. The resulting materials are intended to combine the good biocompatible properties of PEO with the outstanding mechanical properties of PTFE. The star-shaped PEOs were synthesized via anionic polymerization. 3 Mev electron beam irradiation was applied to graft these PEO stars onto porous EXPTFE surfaces. The hydrophobic EXPTFE surface had to be pre-modified with N-vinylpyrrolidone. ESCA was used to quantify the amount of grafted star-shaped PEO. Unmodified EXPTFE surfaces are well known, when implanted in a body, to be rapidly covered by a layer of cells and fibrin. The EXPTFE coated with PEO were implanted in the peritoneal cavity of rats (or under the back skin). This implantation did not induce any inflammation reactions and SEM analysis had attested the absence of adsorbed cells and fibrin. The glucose diffusion properties of these membranes were studied by a lag time analysis method and compared to those of pure PEO hydrogels. As expected, glucose diffuses through the hydrogel coated membrane and diffusion is not affected by the presence of the EXPTFE membrane.     

Conformational changes of the amyloid beta-peptide (1-40) adsorbed on solid surfaces

The conformational change of the 39-43 residues of the amyloid beta-peptide (Abeta) toward a beta-sheet enriched state promotes self-aggregation of the peptide molecules and constitutes the major peptide component of the amyloid plaques in Alzheimer patients. The crucial question behind the self-aggregation of Abeta is related to the different pathways the peptide may take after cleavage from the amyloid precursor proteins at cellular membranes. This work is aiming at determining the conformation of the Abeta (1-40) adsorbed on hydrophobic Teflon and hydrophilic silica particles, as model sorbent surfaces mimicking the apolar transmembrane environment and the polar, charged membrane surface, respectively. The mechanism by which the Abeta interacts with solid surfaces strongly depends on the hydrophobic/hydrophilic character of the particles. Hydrophobic and electrostatic interactions contribute differently in each case, causing a completely different conformational change of the adsorbed molecules on the two surfaces. When hydrophobic interactions between the peptide and the sorbent prevail, the adsorbed Abeta (1-40) mainly adopts an alpha-helix conformation due to H-bonding in the apolar part of the peptide that is oriented towards the surface. On the other hand, when the peptide adsorbs by electrostatic interactions beta-sheet formation is promoted due to intermolecular association between the apolar parts of the adsorbed peptide. Irrespective of the characteristics of the solid sorbent, crowding the surface results in intermolecular association between adsorbed molecules leading to a strong aggregation tendency of the Abeta (1-40). [Diagram: see text] CD spectra of Abeta (1-40) at pH 7: A) in solution ([Abeta]=0.2 mg.ml(-1)) freshly prepared (line) and after overnight incubation (symbols);B) on Teflon (Gamma=0.5 mg.m(-2)).     

Controlled-rate thermal analysis

Controlled-rate thermal analysis (CRTA) and differential scanning calorimetry (DSC) were used to investigate the adsorbed water layers and the surface properties of different commercial activated carbons. A simple method is proposed to obtain information on the properties of the adsorbed water film and the surface heterogeneity of the materials studied. This method utilizes TG mass loss and the first derivative of the DTG mass loss curves with respect to temperature and time, obtained during programmed liquid thermodesorption. The obtained TG mass loss curves, which reflect the energetic heterogeneity, consisted of steps and inflections which were associated with the mechanism of wetting of the solid surfaces. The heights of these steps and inflections depend on the adsorption capacity, the adsorption potential and the nature and number of the active centers of the carbon samples studied. The values of the total porosity and the surface phase capacity obtained by this method are in good agreement with those estimated on the basis of independent methods. The behaviour of water/carbon samples was studied by means of DSC at subambient and elevated temperatures. The experimental results provided novel data on the structural heterogeneity, the thermal stability of the water/carbon interface and its phase and structural transitions.Support from the Research Council of Kent State University (Ohio, USA) is acknowledged. The author is pleased to thank Drs M. Jaroniec, R. K. Gilpin, J. Choma and R. Dobrowolski for fruitful discussions and the active carbon samples.     

Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.