A note on the Newton radius

The Newton radius of a code is the largest weight of a uniquely correctable error. We establish a lower bound for the Newton radius in terms of the rate. In particular we show that in any family of linear codes of rate below one half, the Newton radius increases linearly with the codeword length.     

The effect of clay on the morphology of multiphase latex particles

The effect of montmorrilonite clay (MMT) platelets on the morphology of polystyrene/poly(methyl methacrylate) (PMMA) composite latex particles prepared via PMMA-seeded (semi-) batch emulsion polymerization of styrene was studied. It was found that the particle morphology obtained greatly depended on the ability of the clay platelets to diffuse through the polymer particle. Indeed, when the reactions were strictly under kinetic control, i.e., where the clay platelets were unable to diffuse during polymerization, anisotropic core-shell-like morphologies with split core were observed. A better mobility of the clay platelets could more or less restrict the diffusion of the second-stage polymers within the host polymer, leading to original kinetically controlled morphologies. In the case of a full migration of the clay platelets to the particle surface, the penetration of the second-stage polymer species in the seed latex was found to be more limited, enhancing the formation of secondary particles.     

Highly Enantioselective,Organocatalytic, and Scalable Synthesis of a Rare cis,cis-Tricyclic Diterpenoid

A highly enantioselective, organocatalytic, and scalable synthesis of a very unusual cis-decalin-cis-hydrindane tricyclic diterpenoid system has been achieved. Despite the prevalent pharmacological space that the related trans,trans and trans,cis-systems occupy, there have been no reports of an asymmetric synthesis of the cis,cis systems in the literature until now. We demonstrate the flexibility of our approach not only through access to a diverse range of products, all of which are attained in exceptionally high selectivities, but also by showing their easy conversion to the corresponding trans,cis-system and other derivatives.     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Ultrasound promoted synthesis of thioesters from 2-mercaptobenzoxa(thia)zoles

An ultrasound-enhanced method has been developed for the synthesis of a variety of thioesters from benzoyl chlorides and 2-mercaptobenzoxa(thia)zoles. Applying this methodology, 14 compounds were synthesized in excellent yields.