Infrared Problem for the Nelson Model on Static Space-Times

We consider the Nelson model on some static space-times and investigate the problem of existence of a ground state. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass m(x) tends to 0 at spatial infinity. We show that if m(x) ≥ C |x|⁻¹ at infinity for some C > 0 then the Nelson Hamiltonian has a ground state.     

A New Approach to The Synthesis of Enantiomerically Pure 4-Deoxy Sugars

In a recent paper² we have reported the design and synthesis of 3-C-lithiated 5,6-dihydro-1,4-dithiin-2-yl[(4-methoxybenzyl)oxy]methane (1) which can be utilized as an allylic alcohol anion equivalent and leads to three-carbon elongations of various electrophiles by introduction of a fully protected hydroxypropenyl moiety. The latter contains a double bond, which can be unravelled to the cis configuration by diastereoselective removal³ of the dimethylene-disulfur bridge, as well as a protected primary hydroxyl group that, depending on the deprotection conditions used (DDQ/NaBH₄ or DDQ), may either lead to the free allylic alcohol or to an α,β-unsaturated aldehyde.     

Finite elements for a prefractal transmission problem

In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an approximation error estimate. To cite this article: P. Bagnerini et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Structure and Dynamics of Oligonucleotides in the Gas Phase

By combining ion‐mobility mass spectrometry experiments with sub‐millisecond classical and ab initio molecular dynamics we fully characterized, for the first time, the dynamic ensemble of a model nucleic acid in the gas phase under electrospray ionization conditions. The studied oligonucleotide unfolds upon vaporization, loses memory of the solution structure, and explores true gas‐phase conformational space. Contrary to our original expectations, the oligonucleotide shows very rich dynamics in three different timescales (multi‐picosecond, nanosecond, and sub‐millisecond). The shorter timescale dynamics has a quantum mechanical nature and leads to changes in the covalent structure, whereas the other two are of classical origin. Overall, this study suggests that a re‐evaluation on our view of the physics of nucleic acids upon vaporization is needed.     

Charge mapping in 3(10)-helical peptide chains by oxidation of the terminal ferrocenyl group

Two series of 3(10)-helical peptides of different lengths and rigidity, based on the strongly foldameric α-aminoisobutyric acid and containing a terminal ferrocenyl unit, have been synthesized. Oxidation-state sensitive spectroscopic tags of helical peptides, the N-H groups, allowed mapping of the charge delocalization triggered by oxidation of the terminal ferrocenyl moiety and were monitored by IR spectroelectrochemistry.     

Densely Functionalized 2-Methylideneazetidines: Evaluation as Antibacterials

Twenty-two novel, variously substituted nitroazetidines were designed as both sulfonamide and urethane vinylogs possibly endowed with antimicrobial activity. The compounds under study were obtained following a general procedure recently developed, starting from 4-nitropentadienoates deriving from a common β-nitrothiophenic precursor. While being devoid of any activity against fungi and Gram-negative bacteria, most of the title compounds performed as potent antibacterial agents on Gram-positive bacteria (E. faecalis and three strains of S. aureus), with the most potent congener being the 1-(4-chlorobenzyl)-3-nitro-4-(p-tolyl)azetidine 22, which displayed potency close to that of norfloxacin, the reference antibiotic (minimum inhibitory concentration values 4 and 1–2 μg/mL, respectively). Since 22 combines a relatively efficient activity against Gram-positive bacteria and a cytotoxicity on eucharyotic cells only at 4-times higher concentrations (inhibiting concentration on 50% of the cultured eukaryotic cells: 36 ± 10 μM, MIC: 8.6 μM), it may be considered as a promising hit compound for the development of a new series of antibacterials selectively active on Gram-positive pathogens. The relatively concise synthetic route described herein, based on widely available starting materials, could feed further structure–activity relationship studies, thus allowing for the fine investigation and optimization of the toxico-pharmacological profile.     

Groups with many normal or self-normalizing subgroups

In this paper groups in which the set Σ of the normal or self-normalizing subgroups is large will be studied. In particular it will be characterized locally graded groups satisfying the minimal condition on subgroups which do not belong to Σ and locally finite groups for which the set Σ is dense in the lattice of all subgroups.     

Computing spin networks

We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum information manipulation is based on the (re)coupling theory of SU (2) angular momenta. Such scheme automatically incorporates all the essential features that make quantum information encoding much more efficient than classical: it is fully discrete; it deals with inherently entangled states, naturally endowed with a tensor product structure; it allows for generic encoding patterns. The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes of n + 1 angular momentum variables, as well as Wigner rotations in the eigenspace of the total angular momentum. A crucial role is played by elementary j-gates (6j symbols) which satisfy algebraic identities that make the structure of the model similar to “state sum models” employed in discretizing topological quantum field theories and quantum gravity. The spin network simulator can thus be viewed also as a Combinatorial QFT model for computation. The semiclassical limit (large j) is discussed.