RuO4-promoted oxidative polycyclization of isoprenoid polyenes. A further insight into the stereochemistry of the process

Further studies on the RuO₄-catalyzed oxidative polycyclization of isoprenoid polyenes have been carried out. The configuration of the tris-THF product from the oxidation of geranylgeranyl acetate has been determined by a combination of spectral and chemical correlation methods. The oxidation of (E,Z)-farnesyl acetate, synthesized from nerol, has been carried out. This process stops at the first cyclization indicating that an E configuration of the Δ⁶ double bond is needed for the second cyclization to occur. The results are discussed in comparison with previous knowledge on the related Re(VII) polycyclization of polyenic bis-homoallylic alcohols.     

Conformational studies by dynamic NMR spectroscopy. Part 96: Stereomutations of highly hindered naphthylphenyl atropisomers in solution and in the solids

When a benzene ring bears two 2-methyl-1-naphthyl moieties in the para, meta or ortho positions as in 1,4-bis(2-methyl-1-naphthyl)benzene, 1, 1,3-bis(2-methyl-1-naphthyl)benzene, 2 and 1,2-bis(2-methyl-1-naphthyl)benzene 3, two rotational isomers (atropisomers) are generated, with the two naphthyl substituents in a syn or anti relationship. In the case of the para and meta derivatives (1 and 2, respectively) these atropisomers could not be separated but were detected by NMR spectroscopy, that also allowed the determination of their syn-anti interconversion barriers in solution (19.5 and 20.4 kcal mol⁻¹, respectively) and, in the case of 2, also in the solid state (26.7 kcal mol⁻¹). In the more hindered ortho derivative 3, the syn (meso) and anti (racemic) atropisomers interconvert in solution with a barrier (31.2 kcal mol⁻¹) sufficiently high to allow their physical separation. The racemic form could also be separated (by enantioselective HPLC) into the PP and MM enantiomers. Analysis of the corresponding CD spectra allowed the assignment of the absolute configuration. When three such naphthyl substituents are bonded to the phenyl in a meta relationship, two atropisomers in statistical proportions were observed: the anti (C_s symmetry) and the syn (C_3v symmetry) display a 3:1 ratio at the equilibrium in solution. This ratio is different in the solid state, as is the interconversion barrier (22.1 and 32.1 kcal mol⁻¹ in solution and in the solid, respectively).     

A constructive proof by elementary transformations of Roth's removal theorems in the theory of matrix equations

W. E. Roth gave necessary and sufficient conditions for the existence of solution(s) of certain types of linear matrix equations. Proofs were based on invariant factors and were long and complicated. Other shorter but non-constructive proofs have since been provided by later authors. We present here very brief constructive proofs based on the simplest of mathematical techniques, namely row- and column-reduction of a matrix.     

Absolute configurations of C34 and C35 of antibiotic niphimycin A

The relative configurations of four stereogenic centers of the C33‐C42 fragment of niphimycin A were assigned as 2S*, 3R*, 4S* and 6S*, based upon ¹H NMR analysis with double‐quantum filtered COSY and nuclear Overhauser spectroscopy experiments. These data were then correlated with absolute configurations at C36 and C38 of niphimycin A, which were declared previously as 36S and 38S [3]. This allowed for the assignment of the absolute configurations at C34 and C35 of niphimycin A as 34S and 35R. Copyright © 2012 John Wiley & Sons, Ltd.     

A Kochen-Specker inequality from a SIC

Yu and Oh (eprint) [1] have given a state-independent proof of the Kochen-Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute a SIC (symmetric informationally-complete positive operator-valued measure) and a complete set of MUB (mutually unbiased bases). A theory-independent inequality is also presented using the same 21 rays, as required for experimental tests of contextuality.     

Hjelmslev quadrilateral central configurations

A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. Using mutual distances as coordinates, we show that any four-body central configuration forming a Hjelmslev quadrilateral must be a right kite configuration.     

悬链线竖向集中力作用下的构形分析和张力计算

目前,悬链线在竖向集中力和均布荷载共同作用下的构形分析和受力计算的理论仍不完善。针对这一问题,通过引入悬链线的几何约束方程、力平衡方程和超越方程,建立了竖向集中力与均布荷载共同作用下的非线性方程组。采用牛顿迭代法求解方程组,得到了悬链线的构形和受力情况。为了验证理论计算的正确性,进行了算例和试验验证。结果表明,算例的计算结果与文献结论保持一致,试验测得的构形和水平张力大小与理论计算的构形和水平张力大小吻合较好。本文的理论计算可以更加简单精确地计算出悬链线在竖向集中力和均布荷载共同作用下的构形和受力情况,为实际工程提供重要的理论指导。