The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space

Annals of Global Analysis and Geometry - In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.     

Synthesis of β -Cyperone via Fungal Hydroxylation of thujone-derived tricyclic cyclopropanes

Synthesis of optically active sesquiterpenes with a eudesmane C-skeleton from the chiral starting material thujone involves transformation of a tricyclic intermediate (1R,2R,4S)-1,7-dimethyl-4-(1-methylethyl)tricyclo[4.4.0.0^2,4]dec-6-en-8-one ( 2 ) into the bicyclic compound β -cyperone ( 5 ). Hydroxylation of 2 at C(5) or C(11) permits subsequent opening of the cyclopropane ring and rearrangement to β -cyperone. In this publication, studies involving hydroxylation of 2 by fungal cultures are presented. The resultant products are useful intermediates in efficient synthesis of eudesmane sesquiterpenes. Of five fungi tested, Rhizopus oryzae ATCC 11145 proved most versatile. It hydroxylates at the exocyclic C(11) position in high yield (70%) and, to a lesser extent, at C(5) (5%). Enzymatic activity appears at the end of growth phase and at least 2.2 g of 2 per liter can be metabolized without significant loss of product yield. A second fungus, Cunninghamella echinulata ATCC 9244, proved most useful for hydroxylation of derivatives of 2 for the preparation of derivatives of β -cyperone, although product yields were low (2–20%), some derivatives were nonreactive, and hydroxylation at C(9) occurred. The relationship between precursor structure and enzyme affinity is discussed.     

Conceptual continuity as a mode of understanding complex systems: Applications to the dynamics sociopolitical systems

In complex biological systems, entities that are conceptually distinct but empirically related—such as sunlight and plant growth or antigene and immune response—are being explicitly linked through the identification of highly specific uninterrupted interaction sequences that take place between their macromolecular system components. These uninterrupted sequences of causation include common elements that are shared by the empirically related but conceptually distinct entities. Through the identification of specific shared elements, “conceptual continuity” is established between these entities. Examples are introduced to suggest that in sociopolitical systems, an analogous conceptual continuity can be established between distinct sociopolitical entities. The identification of specific shared elements, essential for the well being of each of the entities, can play a significant role in resolving conflicts between those separated by seemingly insurmountable obstacles such as race or religion or ideology. © 2006 Wiley Periodicals, Inc. Complexity 11:20–24, 2006     

Approximation of multi-scale elliptic problems using patches of finite elements

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439–456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1–21). However it is of much more flexible use in comparison to the latter. To cite this article: R. Glowinski et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

The rational design of modified Cinchona alkaloid catalysts. Application to a new asymmetric synthesis of chiral chromanes

A new asymmetric synthesis of 2-substituted chiral chromanes has been achieved. The key step is the intramolecular conjugate addition of a phenolic nucleophile on a α,β-unsaturated ester catalyzed by Cinchona alkaloids. The high ee’s obtained with cinchonine and its derivatives have been rationalized by ab initio quantum chemistry calculations of transition state structures.     

Ueber einige Ozonwirkungen

Ohne Zusammenfassung     

Selective double Suzuki cross-coupling reactions. Synthesis of unsymmetrical diaryl (or heteroaryl) methanes

Using a double Suzuki cross-coupling reaction ortho- or para-bromobenzyl bromides are easily transformed into unsymmetrical diaryl (or heteroaryl) methanes     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.