Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities

Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up to the four exceptional cases in low dimensional stratum, any stratum of meromorphic quadratic differentials is either connected, or has exactly two connected components. In this last case, one component is hyperelliptic, the other not.     

A simple method for crack growth in mixed mode with X-FEM

In this paper, a new method for level set update is proposed, in the context of crack propagation modeling with the extended finite element method (X-FEM) and level sets. Compared with the existing methods, such as the resolution of the Hamilton–Jacobi equations, this new method is much simpler because it does not required complex manipulations of the level sets. This method, called the “projection” method, uses both a classical discretization of the surface of the crack (segments for 2d cracks and triangles for 3d cracks) and a level set representation of the crack. This discretization is updated with respect to the position of the new crack front. Then the level sets are re-computed using the true distance to the new crack, by an orthogonal projection of each node of the structure onto the new crack surface. Then, numerical illustrations are given on 2d and 3d academic examples. Finally, three illustrations are given on 3d industrial applications.     

Questions about the structures of nitraraine and nitraraidine

Investigations have been carried out in order to give new insights into the real structure of two alkaloids isolated from the Nitraria genus namely nitraraine and nitraraidine. Closely related tangutorine is put forward as a plausible alternative to the structure proposed so far for nitraraine.     

Spontaneous Formation of Nitrarine and Polycyclic Skeletons Related to Nitraria Indolic Alkaloids under Non‐Enzymic Conditions

Mixtures of tryptamine and reactive C₅ units, presumably derived from lysine in nature, were studied to ascertain the spontaneous formation of the complex polycyclic alkaloid nitrarine. Several indolic compounds tracing the unified metabolism within the Nitraria genus were also characterized.     

Active Mamyshev regenerator

In this contribution, we numerically and experimentally investigate the extension of the so-called Mamyshev regenerator with the implementation of an additional Raman gain. We evaluate the potential efficiency and advantages of this new active Mamyshev regenerator at 40 Gbps and we highlight a strong reduction of the working power as well as a large improvement of the available output power.     

Synthesis of poly(vinyl laurate)‐b‐poly(vinyl stearate) diblock copolymers by cobalt‐mediated radical polymerization in solution

Poly(vinyl laurate) (PVL) and poly(vinyl stearate) (PVS) were synthesized by means of cobalt‐mediated radical polymerization (CMRP). Cobalt(II) diacetylacetonate (Co(acac)₂) was demonstrated to control the radical polymerization of these monomers in solution. Molecular weights up to 15,000 g·mol^?1 were obtained with reasonably low polydispersity indices (PDI < 1.3). The efficiency of the redox initiator [lauroyle peroxide (LPO)/citric acid (CA)] was found to be low (around 10%) as already reported for vinyl acetate. The solvent and temperature were found to have a very weak influence on the initiator efficiency. It appeared that CA played no role in the initiation process that only involved a redox reaction between LPO and Co(acac)₂. PVL‐b‐PVS diblock copolymers could be synthesized using two strategies: (1) Sequential addition, that is, addition of the second monomer (VS) at high conversion of the first one (VL). (2) Macroinitiator technique, that is, isolation of a PVL macroinitiator then polymerization of VS from this cobalt functionalized macroinitiator. Both techniques allowed the synthesis of diblock copolymers with molar masses around 25,000 g·mol^?1 and PDI lower than 1.4. The resulting materials were characterized by DSC, revealing that both blocks exhibit side‐chain crystallinity and phase segregate in the bulk. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of double hydrophilic poly(ethylene oxide)‐b‐poly(2‐hydroxyethyl acrylate) by single‐electron transfer–living radical polymerization

In this study, the polymerization of (2‐hydroxyethyl) acrylate (HEA), in polar media, using Cu(0)‐mediated radical polymerization also called single‐electron transfer–living radical polymerization (SET‐LRP) is reported. The kinetics aspects of both the homopolymerization and the copolymerization from a poly(ethylene oxide) (PEO) macroinitiator were analyzed by ¹H NMR. The effects of both the ligand and the solvent were studied. The polymerization was shown to reach very high monomer conversions and to proceed in a well‐controlled fashion in the presence of tris[2‐(dimethylamino)ethyl]amine Me6‐TREN and N, N,N′, N″, N″‐pentamethyldiethylenetriamine (PMDETA) in dimethylsulfoxide (DMSO). SET‐LRP of HEA was also led in water, and it was shown to be faster than in DMSO. In pure water, Me₆‐TREN allowed a better control over the molar masses and polydispersity indices than PMDETA and TREN. Double hydrophilic PEO‐b‐PHEA block copolymers, exhibiting various PHEA block lengths up to 100 HEA units, were synthesized, in the same manner, from a bromide‐terminated PEO macroinitiator. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A direct and rapid route to α,α-difluoroacylsilanes from trifluoroethanol

α,α-Difluoroacylsilanes were synthesised directly from a range of allyl ethers of trifluoroethanol via dehydrofluorination/metallation procedures, followed by thermal [3,3]-sigmatropic rearrangement of the intermediate vinylmetals. The scope and limitations of ether synthesis and dehydrofluorination/metallation are described.     

Long-time averaging for integrable Hamiltonian dynamics

Summary. Given a Hamiltonian dynamical system, we address the question of computing the limit of the time-average of an observable. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that this limit coincides with the space-average over an invariant manifold. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a symplectic numerical scheme is applied to the system, up to the order of the integrator.