Extremal Rational Functions on Symmetric Discrete Sets and Superlinear Convergence of the ADI Method

There is a very fruitful interaction between numerical linear algebra and logarithmic potential theory. For instance, we may describe weak asympotics for a polynomial extremal problem occurring in the convergence analysis of conjugate gradients (CG) or of Ritz values; here the link with a constrained minimal energy problem allows to quantify the effect of superlinear convergence.     

The Orthogonal (e,e,e)‐Tris‐Adduct of 9,10‐Dimethylanthracene with C60‐Fullerene: A Hidden Cornerstone of Fullerene Chemistry. Preliminary Communication

Tris(9′,10′‐dimethyl[9,10]ethanoanthracene[11′,12′: 1,9;11″,12″: 16,17;11′′′,12′′′: 30,31])[5,6]fullerene C₆₀, the orthogonal (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene, was obtained from [4+2]‐cycloaddition (Diels–Alder reaction) at room temperature. The thermally unstable orange red (e,e,e)‐tris‐adduct was purified by chromatography and was isolated in the form of red monoclinic crystals. Its C₃‐symmetric addition pattern was established spectroscopically. Its structure could be further investigated by single crystal X‐ray diffraction. The (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene has earlier been suggested as intermediate and reversibly formed critical component in ‘template directed’ addition reactions of C₆₀. This previously elusive compound has now been isolated and structurally characterized.     

Organoalkoxochlorogallane

Organoalkoxochlorogallanes Me₂GaCl was treated with ⁿBuOH and ⁱBuOH in a molar ration of 1:2, respectively. However, only one equivalent of the alcohol reacted with MeGaCl₂ to give [MeGa(Cl)OⁿBu]₃ ( 1 ) or [MeGa(Cl)OⁱBu]₃ ( 2 ). 1 and 2 were characterized by NMR and IR techniques as well as by X‐ray structure determinations. According to that 1 and 2 form trimers in solution and the solid state. In solution both isomers C_s and C_3v were observed while the trimers exist only as C_s isomers in the solid state which exhibit strongly distorted boat conformations with a disorder of the Cl/Me position at one of the gallium atoms.     

Convenient multigram synthesis of monodisperse oligo(ethylene glycols): effective reaction monitoring by infrared spectroscopy using an attenuated total reflection fibre optic probe

A convenient approach for the synthesis of monodisperse oligo(ethylene glycols) up to 12 units is described. A novel cleavage protocol replacing laborious hydrogenolysis is introduced to achieve a fast, inexpensive and widely applicable procedure. In addition to the synthetic part, Fourier transform infrared (FTIR) spectroscopy using a fibre optic attenuated total reflection (ATR) sensor was applied to monitor the formation of sensitive key intermediates, resulting in optimized reaction times. By applying this in-line technique, the possibility of real-time analysis under inert conditions was impressively demonstrated.