Minimal regularity of the solution of some boundary value problems of Signorini's type in polygonal domains

We study the regularity in Sobolev spaces of the solution of transmission problems in a polygonal domain of the plane, with unilateral boundary conditions of Signorini's type in a part of the boundary and Dirichlet or Neumann boundary conditions on the remainder part. We use a penalization method combined with an appropriated lifting argument to get uniform estimates of the approximated solutions in order to obtain some minimal regularity results for the exact solution. The same method allows us to consider problems with thin obstacles. It can be easily extended to 3D problems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular solution to Special Lagrangian Equations

We prove the existence of non-smooth solutions to three-dimensional Special Lagrangian Equations in the non-convex case.     

Über einfache Gruppen

Ohne Zusammenfassung     

Total synthesis,isolation, surfactant properties,and biological evaluation of ananatosides and related macrodilactone-containing rhamnolipids

Rhamnolipids are a specific class of microbial surfactants, which hold great biotechnological and therapeutic potential. However, their exploitation at the industrial level is hampered because they are mainly produced by the opportunistic pathogen Pseudomonas aeruginosa. The non-human pathogenic bacterium Pantoea ananatis is an alternative producer of rhamnolipid-like metabolites containing glucose instead of rhamnose residues. Herein, we present the isolation, structural characterization, and total synthesis of ananatoside A, a 15-membered macrodilactone-containing glucolipid, and ananatoside B, its open-chain congener, from organic extracts of P. ananatis. Ananatoside A was synthesized through three alternative pathways involving either an intramolecular glycosylation, a chemical macrolactonization or a direct enzymatic transformation from ananatoside B. A series of diasteroisomerically pure (1→2), (1→3), and (1→4)-macrolactonized rhamnolipids were also synthesized through intramolecular glycosylation and their anomeric configurations as well as ring conformations were solved using molecular modeling in tandem with NMR studies. We show that ananatoside B is a more potent surfactant than its macrolide counterpart. We present evidence that macrolactonization of rhamnolipids enhances their cytotoxic and hemolytic potential, pointing towards a mechanism involving the formation of pores into the lipidic cell membrane. Lastly, we demonstrate that ananatoside A and ananatoside B as well as synthetic macrolactonized rhamnolipids can be perceived by the plant immune system, and that this sensing is more pronounced for a macrolide featuring a rhamnose moiety in its native ¹C₄ conformation. Altogether our results suggest that macrolactonization of glycolipids can dramatically interfere with their surfactant properties and biological activity.

We show that macrolactonization of gluco- and rhamnolipids dramatically interfere with their surfactant properties and biological activity.     

A study of ACO capabilities for solving the maximum clique problem

This paper investigates the capabilities of the Ant Colony Optimization (ACO) meta-heuristic for solving the maximum clique problem, the goal of which is to find a largest set of pairwise adjacent vertices in a graph. We propose and compare two different instantiations of a generic ACO algorithm for this problem. Basically, the generic ACO algorithm successively generates maximal cliques through the repeated addition of vertices into partial cliques, and uses “pheromone trails” as a greedy heuristic to choose, at each step, the next vertex to enter the clique. The two instantiations differ in the way pheromone trails are laid and exploited, i.e., on edges or on vertices of the graph. We illustrate the behavior of the two ACO instantiations on a representative benchmark instance and we study the impact of pheromone on the solution process. We consider two measures—the re-sampling and the dispersion ratio—for providing an insight into the performance at run time. We also study the benefit of integrating a local search procedure within the proposed ACO algorithm, and we show that this improves the solution process. Finally, we compare ACO performance with that of three other representative heuristic approaches, showing that the former obtains competitive results.     

Synthesis and polymerization of functionalized dendritic macromonomers

The synthesis of dendritic building blocks (dendrons) of the first generation (G1) and the second generation, which carry differently protected amine groups in the periphery, is reported. The dendrons are used for the synthesis of the corresponding acrylic and methacrylic macromonomers. Their polymerization behavior under radical conditions is investigated. The G1 dendronized polymers are decorated at their peripheral amino groups, that is, with the chiral amino acid L -phenylalanine by the attach-to approach. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1940–1954, 2001     

Über einige Sätze der Gruppentheorie

Ohne Zusammenfassung     

Mirror symmetry formulae for the elliptic genus of complete intersections

In this paper, we calculate the elliptic genus of certain completeintersections in products of projective spaces. We show thatit is equal to the elliptic genus of the Landau–Ginzburgmodels that are, according to Hori and Vafa, mirror partnersof these complete intersections. This provides additional evidenceof the validity of their construction. Received July 6, 2007.