Experimental and Theoretical Studies on the Rearrangement of 2‐Oxoazepane α,α‐Amino Acids into 2′‐Oxopiperidine β2,3,3‐Amino Acids: An Example of Intramolecular Catalysis

Enantiopure β‐amino acids represent interesting scaffolds for peptidomimetics, foldamers and bioactive compounds. However, the synthesis of highly substituted analogues is still a major challenge. Herein, we describe the spontaneous rearrangement of 4‐carboxy‐2‐oxoazepane α,α‐amino acids to lead to 2′‐oxopiperidine‐containing β^2,3,3‐amino acids, upon basic or acid hydrolysis of the 2‐oxoazepane α,α‐amino acid ester. Under acidic conditions, a totally stereoselective synthetic route has been developed. The reordering process involved the spontaneous breakdown of an amide bond, which typically requires strong conditions, and the formation of a new bond leading to the six‐membered heterocycle. A quantum mechanical study was carried out to obtain insight into the remarkable ease of this rearrangement, which occurs at room temperature, either in solution or upon storage of the 4‐carboxylic acid substituted 2‐oxoazepane derivatives. This theoretical study suggests that the rearrangement process occurs through a concerted mechanism, in which the energy of the transition states can be lowered by the participation of a catalytic water molecule. Interestingly, it also suggested a role for the carboxylic acid at position 4 of the 2‐oxoazepane ring, which facilitates this rearrangement, participating directly in the intramolecular catalysis.     

When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.     

Asymptotic stability of semigroups associated with linear weak dissipative systems with memory

We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given.     

On the polarization of non-paraxial transverse fields

On the basis of a plane-wave spectrum representation, the polarization features of a transverse quasimonochromatic non-paraxial field have been studied. A relationship has been established between the polarization characteristics in the near field and the coherence and symmetry properties of the beam in the far field.     

Conjecture de Franchetta forte

Sans résumé     

Polynomial Stability to Three-Dimensional Magnetoelastic Waves

In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.     

Structure–electrical property study of anisotropic polyaniline films

The relationships of the structure and electrical properties of anisotropic HCl‐doped polyaniline (PANI) films cast from N,N′‐dimethylpropylene urea (DMPU) solutions and stretched to different draw ratios were studied. The anisotropic structure of the stretched PANI films was examined by X‐ray diffraction, near‐infrared wave‐guide coupling, and polarized infrared measurements. The PANI emeraldine base (EB) films cast from DMPU solutions had a single‐phase noncrystalline structure, and stretching of the films did not cause crystallization to occur. The transition moment angles of two weakly absorbing infrared bands were determined, and the Hermans' orientation functions for the PANI EB films were calculated. The PANI films were then doped with HCl, and the electrical properties were determined by impedance spectroscopy. With a specially designed test fixture, the in‐plane and through‐plane impedance was obtained. The conductivity along the stretch direction increased with orientation. The in‐plane conductivity was significantly higher than the through‐plane conductivity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 823–841, 2003