The Well-Posedness Issue in Sobolev Spaces for Hyperbolic Systems with Zygmund-Type Coefficients

In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund type assumptions, and we prove well-posedness in H^∞ respectively without loss and with finite loss of derivatives. The key to obtain the results is the construction of a suitable symmetrizer for our system, which allows us to recover energy estimates (with or without loss) for the hyperbolic operator under consideration. This can be achievied, in contrast with the classical case of systems with smooth (say Lipschitz) coefficients, by adding one step in the diagonalization process, and building the symmetrizer up to the second order.     

Conformational Sensitivity in Photoelectron Circular Dichroism of 3‐Methylcyclopentanone

A study of (R)‐3‐methylcyclopentanone [(R)‐3‐MCP] by photoelectron spectroscopy and photoelectron circular dichroism (PECD) is presented. The synchrotron radiation gas‐phase photoelectron spectra of (R)‐3‐MCP were measured and are discussed on the basis of different theoretical methodologies. The experimental dichroism of (R)‐3‐MCP for selected deconvoluted valence states and for the carbonyl carbon 1s core state are reported and reproduced well by calculated dispersions generated by considering the contributions of two different conformers. The theoretical dichroic parameters are calculated by employing a multicentre basis set of B‐spline functions and a Kohn–Sham Hamiltonian. Temperature‐dependent PECD studies of the HOMO state and the carbonyl carbon 1s core level allowed the separation of the contributions of each conformer by photoelectron dichroism. This new approach clearly shows how the PECD methodology is sensitive to conformational and structural changes of unoriented (R)‐3‐MCP in the gas phase, opening up new perspectives in the characterisation of chiral molecular systems.     

“Green polyethylene” and curauá cellulose nanocrystal based nanocomposites: Effect of vegetable oils as coupling agent and processing technique

Cellulose nanocrystals (CNC) were prepared from curauá fibers via acid hydrolysis, and used as reinforcing phase for high‐density biopolyethylene (HDBPE) or green polyethylene. Castor oil (CO), epoxidized soybean oil (ESO) and epoxidized linseed oil (ELO) were chosen as compatibilizers for this study. Nanocomposites reinforced with CNC (3, 6, and 9 wt %) were processed by extrusion, using CO (3, 6, and 9 wt %) to evaluate its action as CNC dispersing agent in the HDBPE matrix. From the results obtained for these films, the CNC and oil contents were set at 3 wt%. In addition to CO, ELO, and ESO were also used, and besides processing by extrusion, extrusion/hot‐pressing process was also considered, in order to compare the two processing techniques. The nanocomposites were characterized by microscopic, thermal, mechanical, and rheological analyses. The presence of oil leads to less opaque films and improved dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1010–1019     

Rapid Access to 1-Benzyl 2-Substituted Piperazines: Application to the Synthesis of 1-Benzyl-2-difluoromethyl-Piperazine

A rapid and efficient synthesis of 1-benzyl-2-difluoromethyl-piperazine is herein described. The new pathway has the advantage of avoiding orthogonal protection at the two piperazine nitrogen atoms; therefore it is suitable for access to several 1-benzyl 2-substituted piperazines starting from the simple commercially available N,N′-dibenzylethylendiamine.