On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Site segregation in size-mismatched nanoalloys: Application to Cu-Ag

In order to determine the energetic driving forces for surface segregation in bimetallic clusters, we use a combined approach coupling numerical simulations within an N-body interatomic potential and a lattice-gas model. This approach, which has been used successfully to study both the superficial segregation in semi-infinite alloys and the intergranular segregation, allows us to determine the relative contributions of the three elementary driving forces for the different sites of the cluster surface (vertices, edges and facets) in both dilute limits for the Cu-Ag system. We show that the segregation hierarchy based on broken-bond arguments (preferential segregation to the vertex sites, less to edge sites, and least to facet sites) is not at all universal. In particular, unusual hierarchies are predicted when the sizes of the constituents are strongly different. Furthermore, we compare the segregation driving forces for cubo-octahedral and icosahedral clusters. They are similar for the vertex sites and edge sites, whereas they differ significantly for the sites of the triangular facets. The segregation of the species with the largest atomic radius (Ag) is indeed largely enhanced in the icosahedral structure due to dilations of the orthoradial distances.     

Direct conversion of tert-butyl 2-hydroxyalkyl sulfides to 1,3-oxathiolanes

tert-Butyl 2-hydroxyalkyl sulfides, prepared by reaction of epoxides with 2-methylpropane-2-thiol, are converted directly to 1,3-oxathiolanes upon treatment with pivalaldehyde and boron trifluoride diethyl etherate in the presence of thioanisole.     

Total Synthesis of Cyclothialidine

A total synthesis of cyclothialidine ( 1 ), a new DNA gyrase inhibitor isolated from Streptomyces filipinensis, is described. The synthetic concept was tested by preparing the lactone 13 (Scheme 2) which contains the characteristic bicyclic core entity of 1 . Key features of the synthesis of 1 are: preparation of 3,5-dihydroxy-2,6-dimethylbenzoic acid ( 23 ) from 3,5-dihydroxybenzoic acid ( 19 ) by two consecutive Mannich aminomethylation/hydrogenation sequences; benzylic N-bromosuccinimide bromination of an ester derivative 25 thereof and its subsequent coupling with Boc-Ser-Cys-OMe ( 11 ); cyclization of the ω-hydroxy acid 29 29 to the 12-membered lactone 30 using preferably Mitsunobu conditions; completion of the peptidic side chains of 1 using Boc strategy (Scheme 4). Optically pure cis-N-(tert-butoxycarbonyl)-3-hydroxy-L -proline ((–)- 14 ) was obtained by resolution of the racemate via an efficient reaction sequence containing a lipase-catalyzed enantiospecific acetate hydrolysis (Scheme 3). The structure of natural 1 was confirmed by comparison with the synthetic material. The synthetic route described provides also easy access to analogues of 1 , e.g., via the intermediate 30 .     

The chemistry of fluorine containing phosphaalkenes, arsaalkenes and selenocarbonyls

This review covers our extensive research activities in the area of fluorine containing phospha- and arsaalkenes as well as selenocarbonyls, which differ considerably in their properties and reactivities from their alkyl and aryl counterparts and thus contribute in a gratifying manner to the still growing field of unsaturated element-carbon compounds of 3rd and 4th row main group elements E. Of particular interest is the influence of the fluorine substituents and other small groups (OR, NR₂) with either inductive and/or mesomeric effects on the polarity and reactivity of the EC bond. Addition reactions of proton acidic and hydridic polar HX reactants as well as [2+2], [3+2] and [4+2] cycloadditions have been thoroughly studied. The results obtained allow a classification of the EC systems within five different types, A to E, and prove a change from “normal” to “inverse” heteroalkenes in this sequence. The ligand properties of some derivatives have also been investigated in some detail.     

Kinetics of radical telomerization of vinylidene fluoride in the presence of CCl3Z chain transfer agents

The kinetics of radical telomerization of VDF at 141 °C, initiated by ditertbutylperoxide, in the presence of three chain transfer agents (CTAs), HCCl₃, CCl₄ and CCl₃Br, are presented. The values of the chain transfer constants were assessed as 35, 0.25 and 0.06 at 141 °C for CCl₃Br, CCl₄ and HCCl₃, respectively. The values of the degree of polymerization (DP_n) were obtained for each CTA and were compared for the same CTA concentration. Hence, CCl₃Br behaved as an efficient CTA towards VDF and usually afforded the monoadduct selectively, but in certain conditions the VDF diadduct can also be produced. In contrast, HCCl₃ was not so efficient since a polymeric structure was identified as the major product.     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.