An approximation algorithm for cutting out convex polygons

We provide an O(logn)-approximation algorithm for the following problem. Given a convex n-gon P, drawn on a convex piece of paper, cut P out of the piece of paper in the cheapest possible way. No polynomial-time approximation algorithm was known for this problem posed in 1985.     

Une caractérisation des variétés complexes compactes parallélisables admettant des structures affines

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections. To cite this article: S. Dumitrescu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Preparation,physicochemical characterization and biological activity evaluation of some inclusion complexes containing artesunate

Journal of Thermal Analysis and Calorimetry - The use of cyclodextrins as carrier molecules is currently highly researched since they can improve not only the apparent water solubility and...     

7,8,9,10-Tetrahydropyrrolo[2,1-a]isoquinolines in the search for new indolizine derivatives

7,8,9,10-Tetrahydropyrrolo[2,1-a]isoquinolines were obtained by 1,3-dipolar cycloaddition reactions of their corresponding N-ylides with olefinic (acrylonitrile) and symmetrical or non-symmetrical acetylenic dipolarophiles (methyl/ethyl propiolate, dimethyl acetylenedicarboxylate). Also, stable 5,6,7,8-tetrahydroisoquinolinium dicyanomethylide was isolated and characterized by X-ray diffraction analysis.     

Dual Protection of Sulfur by Carbon Nanospheres and Graphene Sheets for Lithium–Sulfur Batteries

Well‐confined elemental sulfur was implanted into a stacked block of carbon nanospheres and graphene sheets through a simple solution process to create a new type of composite cathode material for lithium–sulfur batteries. Transmission electron microscopy and elemental mapping analysis confirm that the as‐prepared composite material consists of graphene‐wrapped carbon nanospheres with sulfur uniformly distributed in between, where the carbon nanospheres act as the sulfur carriers. With this structural design, the graphene contributes to direct coverage of sulfur to inhibit the mobility of polysulfides, whereas the carbon nanospheres undertake the role of carrying the sulfur into the carbon network. This composite achieves a high loading of sulfur (64.2 wt %) and gives a stable electrochemical performance with a maximum discharge capacity of 1394 mAh g^?1 at a current rate of 0.1 C as well as excellent rate capability at 1 C and 2 C. The improved electrochemical properties of this composite material are attributed to the dual functions of the carbon components, which effectively restrain the sulfur inside the carbon nano‐network for use in lithium–sulfur rechargeable batteries.     

On the compression process in a free-piston shock-tunnel

Preliminary results in the Marseille free-piston shock-tunnel facility are presented. The compression of the driver gas by the piston is studied experimentally for two different geometries of the end of the compression tube. Peak pressures obtained with the end of the compression tube closed, and with bursting of the diaphragm separating the high pressure from the low pressure chamber, are compared with calculated values in the cases of N₂ and He as driver gases. A phenomenon of accoustic resonance has been uncovered, generating strong pressure oscillations which, if not properly dealt with, could impair the quality of the useful flow in such a facility.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.