A note on the extension of BV functions in metric measure spaces

In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 1969 (translated from Russian)] is generalized to the abstract setting of doubling metric measure spaces endowed with a differentiation structure called D-structure.     

New phosphorylating reagents for deoxyribonucleosides and oligonucleotides

New phosphorylating reagents 1 and 2 were prepared in three steps from 4-hydroxybenzaldehyde. They showed good efficiency in the solid phase synthesis of 5′-phosphate monoester nucleosides. End-phosphate DNA sequence synthesis demonstrated the efficiency of the new reagents (1 and 2) according to the general procedure of automated DNA synthesis. The oxidation of P(III) to P(V) and the removal of benzyl protecting groups were achieved in a single step by treatment with a 0.02 M I₂/pyridine/H₂O solution. Due to this one-pot treatment, it is possible to use the phosphorylating reagents (1 and 2) for the synthesis of base-sensitive ODNs. The reagents 1 and 2 are unique among phosphorylating reagents.     

The Relevance of the Collaborative Effect in Determining the Performances of Photorefractive Polymer Materials

A derivative of 2‐methylindole, 3‐[2‐(4‐nitrophenyl)ethenyl]‐1‐allyl‐2‐methylindole, NPEMI‐A, is studied for its photoconductivity and photorefractivity behaviour. Its blends with the organic polymer poly‐(2,3‐dimethyl‐N‐vinylindole), PVDMI, are also investigated. Due to the expected and devised mutual solubility of the two components of the blends, it is possible to carry out measurements with the weight percent of the chromophore NPEMI‐A changing from zero to 100. Films were produced by a squeezing process between two ITO‐covered glass sheets. No opacity phenomena, that are so common for many other organic blends due to the segregation of the dissolved chromophore, are observed. The photorefractive optical gain Γ₂ is obtained as a function of the chromophore content. Differential scanning calorimetry measurements (DSC) are also carried out to obtain the whole change of the glass transition temperature T_g as a function of the amount of chromophore contained in the blends. From the experimental trend of T_g a meaningful quantitative estimate of the value of the electrostatic interactions acting in the studied blends, is obtained. The importance of the value of T_g, and of the electrostatic interactions, in determining the extent of the photorefractivity is clearly evident. The results are compared for NPEMI‐A (Γ₂=210 cm^?1) and for NPEMI‐E (Γ₂ ≈ 2000 cm^?1) that has a N‐2‐ethylhexyl group instead of a N‐allyl group. The Pockels and Kerr contributions and—for the first time—a “collaborative effect” of the photorefractivity of NPEMI‐A are distinguished and quantitatively evaluated.     

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.