Sur le groupe des homographies et des antihomographies d'une variable complexe

Sans résumé     

Symmetric presentations of Abelian groups

We characterise the abelianisation of a group that has a presentation for which the set of relations is invariant under the full symmetric group acting on the set of generators. This improves a result of Emerson.

     

Influence of spectral and angular sensitivity on the readout of biological dosimeters

Biological systems used as biological dosimeters can possess different angular sensitivities from the detectors usually used in physical devices. A simple experimental setup has been developed and used to measure the angular sensitivity of uracil thin-layer biological dosimeters. Results of angular sensitivity measurements for uracil thin-layer dosimeters are presented using a Xe arc lamp as the UV source. According to the experiments described here, uracil thin-layer dosimeters show a cosine-type angular dependence. In several indoor experiments broadband UV meters are used to control the applied dose rate from a given artificial UV source. The experimental setup has been designed and used to verify experimentally the importance of spectral and angular sensitivity differences of biological and physical UV meters applied in biological experiments. Model calculations for two different irradiation systems, using different geometrical arrangements of artificial UV sources, are also presented. For these arrangements relative dose rates that could be measured with dosimeters of arbitrary spectral, but different angular sensitivity have been calculated.     

On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

Synthesis of Fully O-Benzylated N-Linked Core Pentasaccharide Glycosyl Azide

The fully O-benzylated pentasaccharide glycosyl azide representing the common core structure of N-glycans was synthesized. The β-mannosidic linkage was created by C-2 epimerization of the initially introduced β-d- gluco-unit via DMSO/Ac₂O oxidation followed by stereoselective reduction with tetrabutylammonium borohydride.     

New Heterocyclic Analogues of Anthracycline Antibiotics

ABSTRACT

Synthetic approaches to anthracycline antibiotic analogues in which the nitrogen atom of the carbohydrate portion is incorporated into a 1, 2, 3-triazolyl moiety were investigated. By using methyl 6-azido-2, 6-dideoxy-β-D--arabino-hexopyranoside and methyl 6-azido-2, 3, 6-tricdeoxy--α-L-arabino-hexopyranoside, the corresponding glycosides (16 a, b - 18 a, b) of carminomycinone and daunomycinone were prepared. The desired heterocyclic system was developed directly with the C-3′ and C-6′ azido anthracyclines by means of a cycloaddition process to give 7-0-[6′-(4, 5--dicarboethoxy-l, 2, 3-triazolyl)-2′, 6′-dideoxy-β-D-arabino--hexopyranosyl]-carminomycinone (23) and -daunomycinone (22), and 3′-(4, 5-dicarboethoxy - l, 2, 3-triazolyl)-4′ -epi-daunomycin (24).     

A Versatile Long‐Wavelength‐Absorbing Scaffold for Eu‐Based Responsive Probes

Coumarin‐sensitized, long‐wavelength‐absorbing luminescent Eu^III‐complexes have been synthesized and characterized. The lanthanide binding site consists of a cyclen‐based chelating framework that is attached through a short linker to a 7‐hydroxycoumarin, a 7‐B(OH)₂‐coumarin, a 7‐O‐(4‐pinacolatoboronbenzyl)‐coumarin or a 7‐O‐(4‐methoxybenzyl)‐coumarin. The syntheses are straightforward, use readily available building blocks, and proceed through a small number of high‐yielding steps. The sensitivity of coumarin photophysics to the 7‐substituent enables modulation of the antenna‐absorption properties, and thus the lanthanide excitation spectrum. Reactions of the boronate‐based functionalities (cages) with H₂O₂ yielded the corresponding 7‐hydroxycoumarin species. The same species was produced with peroxynitrite in a ×10⁶–10⁷‐fold faster reaction. Both reactions resulted in the emergence of a strong ≈407 nm excitation band, with concomitant decrease of the 366 nm band of the caged probe. In aqueous solution the methoxybenzyl caged Eu‐complex was quenched by ONOO^?. We have shown that preliminary screening of simple coumarin‐based antennae through UV/Vis absorption spectroscopy is possible as the changes in absorption profile translate with good fidelity to changes in Eu^III‐excitation profile in the fully elaborated complex. Taken together, our results show that the 7‐hydroxycoumarin antenna is a viable scaffold for the construction of turn‐on and ratiometric luminescent probes.     

Exploring the Reactivity of B-Connected Carboranylphosphines in Frustrated Lewis Pair Chemistry: A New Frame for a Classic System

The primary phosphines MesPH₂ and tBuPH₂ react with 9-iodo-m-carborane yielding B9-connected secondary carboranylphosphines 1,7-H₂C₂B₁₀H₉-9-PHR (R=2,4,6-Me₃C₆H₂ (Mes; 1 a ), tBu ( 1 b )). Addition of tris(pentafluorophenyl)borane (BCF) to 1 a , b resulted in the zwitterionic compounds 1,7-H₂C₂B₁₀H₉-9-PHR(p-C₆F₄)BF(C₆F₅)₂ ( 2 a , b ) through nucleophilic para substitution of a C₆F₅ ring followed by fluoride transfer to boron. Further reaction with Me₂SiHCl prompted a H−F exchange yielding the zwitterionic compounds 1,7-H₂C₂B₁₀H₉-9-PHR(p-C₆F₄)BH(C₆F₅)₂ ( 3 a , b ). The reaction of 2 a , b with one equivalent of R'MgBr (R’=Me, Ph) gave the extremely water-sensitive frustrated Lewis pairs 1,7-H₂C₂B₁₀H₉-9-PR(p-C₆F₄)B(C₆F₅)₂ ( 4 a , b ). Hydrolysis of the B−C₆F₄ bond in 4 a , b gave the first tertiary B-carboranyl phosphines with three distinct substituents, 1,7-H₂C₂B₁₀H₉-9-PR(p-C₆F₄H) ( 5 a , b ). Deprotonation of the zwitterionic compounds 2 a , b and 3 a , b formed anionic phosphines [1,7-H₂C₂B₁₀H₉-9-PR(p-C₆F₄)BX(C₆F₅)₂]⁻[DMSOH]⁺ (R=Mes, X=F ( 6 a ), R=tBu, X=F ( 6 b ); R=Mes, X=H ( 7 a ), R=tBu, X=H ( 7 b )). Reaction of 2 a , b with an excess of Grignard reagents resulted in the addition of R’ at the boron atom yielding the anions [1,7-H₂C₂B₁₀H₉-9-PR(p-C₆F₄)BR’(C₆F₅)₂]⁻ (R=Mes, R’=Me ( 8 a ), R=tBu, R’=Me ( 8 b ); R=Mes, R’=Ph ( 9 a ), R=tBu, R’=Ph ( 9 b )) with [MgBr(Et₂O)_n]⁺ as counterion. The ability of the zwitterionic compounds 3 a , b to hydrogenate imines as well as the Brønsted acidity of 3 a were investigated.     

Bis(4-benzhydryl-benzoxazol-2-yl)methane – from a Bulky NacNac Alternative to a Trianion in Alkali Metal Complexes

A novel sterically demanding bis(4-benzhydryl-benzoxazol-2-yl)methane ligand 6 (^4−BzhH2BoxCH₂) was gained in a straightforward six-step synthesis. Starting from this ligand monomeric [M(^4-BzhH2BoxCH)] (M=Na ( 7 ), K ( 8₁ )) and dimeric [{M(^4-BzhH2BoxCH)}₂] (M=K ( 8₂ ), Rb ( 9 ), Cs ( 10 )) alkali metal complexes were synthesised by deprotonation. Abstraction of the potassium ion of 8 by reaction with 18-crown-6 resulted in the solvent separated ion pair [{(THF)₂K@(18-crown-6)}{bis(4-benzhydryl-benzoxazol-2-yl)methanide}] ( 11 ), including the energetically favoured monoanionic (E,E)-(^4-BzhH2BoxCH) ligand. Further reaction of ^4−BzhH2BoxCH₂ with three equivalents KH and two equivalents 18-crown-6 yielded polymeric [{(THF)₂K@(18-crown-6)}{K@(18-crown-6)K(^4-BzhBoxCH)}]_n (n→∞) ( 12 ) containing a trianionic ligand. The neutral ligand and herein reported alkali complexes were characterised by single X-ray analyses identifying the latter as a promising precursor for low-valent main group complexes.