Fourier-Bohr spectrum of sequences related to continued fractions

Let α be a real irrational number and q₁, q₂, q₃,… the sequence of denominators of the convergents of α. Call σ_α(n)) the sum of the digits of the integer n in basis q₁, q₂, q₃,…. The Fourier-Bohr spectrum of the sequence exp(2πiσ_α(n)) and more generally of sequences exp(2πif(n)) is studied, where f is a completely α-additive real sequence. A sufficient condition is derived for the sequence xn + yσ_α(n) to be uniformly distributed modulo one.     

Synthése totale d'α-disaccharidyles de tridésoxy-2,5,6-streptamine apparentés aux aminosides à partir du maltose et du lactose

Total synthesis of α-disaccharidyl-2,5,6-trideoxy-streptamines related to aminoglycoside antibiotics derived from maltose and lactose The synthesis of the hitherto unknown 4-O-substituted α-linked pseudo-tri-saccharides 1,2 and 3 is described. The key intermediates required in the reaction sequence are the glycals 12, 13 and 14 , prepared from maltose, lactose and the chiral ditosyloxy-cyclohexanol 15 , readily accessible from quinic acid. The pivotal step in the reaction's scheme - a stereospecific α-glycosylution procedure -, is an acid-catalyzed addition of the alcohol 15 to the glycals 12, 13 and 14 leading to the corresponding 2,3-unsaturated trisaccharides. The latter compounds were transformed to the target α-glycosides of 2,5,6-trideoxystreptamine 1, 2 and 3 which were devoid of significant antibacterial activity. These results indicate that the presence of an ether linkage at the position 4′ is probably critical for antibacterial activity.     

Ketene bis(trimethylsilyl) acetals. Cross-aldol type condensation reactions with aldehydes and schiff bases

Condensation of the title acetals with aldehydes and Schiff bases in the presence of titanium tetrachloride is reported for the first time. It leads to β-hydroxyacids and to β-lactams via a cross-aldol type reaction, with good yields.     

Combination of gas chromatography-mass spectrometry and mass spectral deconvolution for structural elucidation of an unusual C29-steroid detected in a complex sedimentary matrix

A complex sedimentary sample from the Monterey Formation (CA, USA) has been submitted to GC-MS analysis followed by mass spectral deconvolution using Automated Mass Spectral Deconvolution and Identification System (AMDIS). Adjusting the parameters of the software allowed for the extraction of the spectrum of an unusual steroidal hydrocarbon coeluting with the major compound of the chromatogram. Following a careful interpretation of the "extracted" mass spectrum, the structure of the unknown has been postulated to be the 4,14-dimethylcholestane (DMC). Possible origins of this rare steroid are briefly discussed. Thus, application of AMDIS appears to be particularly suitable for the GC-MS analysis of natural complex mixtures characterized by a high number of analytes present in low amounts.     

First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory

We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.