Counterexamples on L_p-maximal regularity

We establish a transference result for -maximal regularity for the abstract Cauchy problem on Banach space. From this result we deduce counterexamples to -maximal regularity In particular we obtain an operator B without any -maximal regularity although it admits bounded imaginary powers with for all . We also derive an operator which satisfies -maximal regularity on bounded intervals [0, T[ but not on the half line Received March 5, 1997; in final form October 10, 1997     

Infrared investigation of benzene to 30 GPa transformation to a polymer

Abstract

After a pressure cycle to 30 GPa, benzene transforms to a white solid which can be recovered at ambient. Results obtained from infrared spectroscopy and other physico-chemical methods show that the recovered solid is a highly cross-linked polymer. The molecular structure of benzene is very likely completely altered by the transformation.     

Synthetic studies towards diazepanone scaffolds

The synthesis of new enantiopure polyfunctionalised diazepanone scaffolds is described. The key steps involve the opening of an azido-epoxide C4 building block derived from l-ascorbic or d-isoascorbic acid by a l-serine derivative followed by a lactonisation–lactamisation two-step sequence.     

Strange particles production and absorption in nuclei at high energies

The absorption of the secondary hadrons in nuclear matter is studied as a function of their flavour dependent inelastic cross section on nucleons. In particular the ratiosK ⁺/π⁺ andK ^?/π^? of particles produced in the proton-nucleus high energy interactions are examined and described in the very simple phenomenological model. The enhanced production ofK ⁺ mesons is explained by their relatively small interaction. The presence of the initial particle absorption is clearly demonstrated forx _F>0.5.     

Simultaneous reversible addition fragmentation chain transfer and ring‐opening polymerization

The simultaneous ring‐opening polymerization (ROP) of ε‐caprolactone (ε‐CL) and 2‐hydroxyethyl methacrylate (HEMA) polymerization via reversible addition fragmentation chain transfer (RAFT) chemistry and the possible access to graft copolymers with degradable and nondegradable segments is investigated. HEMA and ε‐CL are reacted in the presence of cyanoisopropyl dithiobenzoate (CPDB) and tin(II) 2‐ethylhexanoate (Sn(Oct)₂) under typical ROP conditions (T > 100 °C) using toluene as the solvent in order to lead to the graft copolymer PHEMA‐g‐PCL. Graft copolymer formation is evidenced by a combination of size‐exclusion chromatography (SEC) and NMR analyses as well as confirmed by the hydrolysis of the PCL segments of the copolymer. With targeted copolymers containing at least 10% weight of PHEMA and relatively small PHEMA backbones (ca. 5,000–10,000 g mol^?1) the copolymer grafting density is higher than 90%. The ratio of free HEMA‐PCL homopolymer produced during the “one‐step” process was found to depend on the HEMA concentration, as well as the half‐life time of the radical initiator used. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3058–3067, 2008     

Stochastic optimal control and algorithm of the trajectory of horizontal wells

This paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke–Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm.