Stereoselective Epoxidation of Cyclic Dienes and Trienes by Dioxiranes

Epoxides are essential building blocks in organic chemistry. The epoxidation of unsubstituted cyclic dienes 2 , 3 , 4 and triene 5 using dimethyldioxirane ( 1a ) and its trifluoro analog 1b methyl(trifluoromethyl)dioxirane has been investigated. The excellent yields obtained (90–98%) are accompanied by outstandingly high diastereoselectivities (90–98%). Interpretation of results based upon the early idea that polar groups can direct the dioxirane attack by dipole–dipole interaction provides a likely rationale, along with a more generalized mechanistic view.     

Exponential self-similar mixing and loss of regularity for continuity equations

We consider the mixing behavior of the solutions to the continuity equation associated with a divergence-free velocity field. In this Note, we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity fields, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity field exhibiting instantaneous loss of any fractional Sobolev regularity.     

Observational effects from quantum cosmology

The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler–DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the more recent loop quantum cosmology can generate potentially detectable departures from the standard cosmic spectrum. Thus, present observations constrain the parameter space of the model, which could be made falsifiable by near‐future experiments.     

Ethylene/hindered phenol substituted norbornene copolymers: Synthesis and NMR structural determination

A new family of ethylene‐based copolymers with controlled amounts of a norbornene comonomer (N_ArOH) bearing a stabilizing antioxidant functionality (2,6‐di‐tert‐butyl phenol) was prepared. Due to unavoidable exo/endo equilibrium operative in N_ArOH comonomer, a complete and detailed NMR assignment of the structure of the prepared ethylene/N_ArOH copolymers was carried out for the determination of the exo/endo ratio inside the polymer. These novel functionalized comonomers can be considered suitable starting material for preparing ethylene‐based copolymers, with tunable comonomer content, as non‐releasing macromolecular antioxidant additives for specific application in safe food and/or drug packaging © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Polymerization of (E)‐1,3‐Pentadiene and (E)‐2‐methyl‐1,3‐pentadiene with neodymium catalysts: Examination of the factors that affect the stereoselectivity

(E)‐1,3‐Pentadiene (EP) and (E)‐2‐methyl‐1,3‐pentadiene (2MP) were polymerized to cis‐1,4 polymers with homogeneous and heterogeneous neodymium catalysts to examine the influence of the physical state of the catalyst on the polymerization stereoselectivity. Data on the polymerization of (E)‐1,3‐hexadiene (EH) are also reported. EP and EH gave cis‐1,4 isotactic polymers both with the homogeneous and with the heterogeneous system, whereas 2MP gave an isotactic cis‐1,4 polymer with the heterogeneous catalyst and a syndiotactic cis‐1,4 polymer, never reported earlier, with the homogeneous one. For comparison, the results obtained with the soluble CpTiCl₃‐based catalyst (Cp = cyclopentadienyl), which gives cis‐1,4 isotactic poly(2MP), are examined. A tentative interpretation is given for the mechanism of the formation of the stereoregular polymers obtained and a complete NMR characterization of the cis‐1,4‐syndiotactic poly(2MP) is reported. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3227–3232     

Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

In this work, we prove the existence and the uniqueness of the strong solution of a low‐Mach model, for which the dynamic viscosity of the fluid is a given function of its temperature. The method is based on the convergence study of a sequence towards the solution, for which the rates are also given. The originality of the approach is to consider the system in terms of the temperature and the velocity, leading to a nonlinear temperature equation and the development of some specific tools and results.