Realization of 2-solvable nilpotent groups as groups of classes of homotopy self-equivalences

Let X be a 1-connected CW-complex of finite type and ε_?(X) be the group of homotopy classes of self-equivalences of X which induce the identity on homotopy groups. In this paper, we prove that every finitely generated 2-solvable rational nilpotent group is realizable as ε_?(X) where X is the rationalization of a 1-connected CW-complex of finite type.     

Determination of microtacticity of poly(vinylketones) and their derivatives by NMR spectroscopies of carbon-13 and proton

Sequence distribution of atactic poly(phenylvinylketone) (PPVK) has been determined by [¹³C]-[¹H]NMR spectroscopy. Quantitative analysis of the carbonyl pattern allows resolution into pentads with intensities fitting a first order Markov process. The carbonyl pattern of highly isotactic PPVK, initiated by diethylzinc, deviates strongly from Bernoullian statistics, as in the case of highly isotactic polymethylvinylketone (PMVK). For n-butyl-lithium initiated poly(isopropenylphenylvinylketone) (PIPK), the carbonyl pattern practically agrees with a Bernoullian distribution. Atactic PMVK, analyzed from the methylene and the carbonyl pattern in [¹³C] or [¹H]NMR, shows that the polymerization process is purely Bernoullian and quite different from that for poly(isopropenylmethylketone). Except for poly(methylallylalcohol) for which the tacticity can be determined, the resolution is too poor to allow a quantitative sequence distribution of poly(allylalcohols) or poly(allyltrifluoroacetates). [¹H] and [¹⁹F]NMR spectroscopies of these compounds do not give better results.     

Regularization procedures of mixed finite element approximations of the stokes problem

We propose a theoretical framework for the study of regularization of the Stokes problem. This enables us to perform a general error analysis and to apply it to known schemes as well as to a new one pertaining to the use of the P1-P1 element. Finally we show that in the P1-case the theory can also be used to get convergence results for elements obtained by addition of bubble functions, without using the usual mixed finite element machinery.     

Synthesis of new 7-aminosterol squalamine analogues with high antimicrobial activities through a stereoselective titanium reductive amination reaction

A series of 7-amino- and polyaminosterol analogues of squalamine and trodusquemine were synthesized involving a new stereoselective titanium reductive amination reaction in high chemical yields of up to 95% in numerous cases. These derivatives were evaluated for their in vitro antimicrobial properties against human pathogens. All the compounds present excellent activities against Gram-positive bacteria exhibiting similar results against Staphylococcus aureus and Streptococcus faecalis with minimum inhibitory concentrations (MICs) varying from 2.5 to 10 μg/mL. Numerous derivatives possess also MICs against Gram-negative Escherichia coli bacteria (MICs varying from 2.5 to 10 μg/mL) suggesting that nature of the amino group attached to the sterol moiety plays an important role on the activities of such products.     

Polygermoxanes suitable for biochemical purposes. Part I. Digermoxanes (low-viscosity oils)

In order to replace silicones in some of their biomedical applications, e.g. syringe lubrication, implants ets., a series of digermoxanes (R¹R²R³Ge)₂O (R = n–alkyl, aryl) were synthesized. These compounds are thermally stable oils; their viscosities, depending on the nature of substituents, lie in the range 1–72 cPo (mPa s) at 20°C.     

LA RECONSTRUCTION DES TOURNOIS SANS DIAMANT

We prove that if T is a tournament of order n > 6 in which any 4-sub-tournament is hamiltonian or transitive, then T is reconstructible in the sense of Ulam.