Some observations on uncertainty propagation through a simple nonlinear system

This paper discusses a number of issues relating to the analysis of uncertain systems or data in the context of (low-frequency) structural dynamics. In order to illustrate potential problems in applying ‘classical’ uncertainty analysis methods to nonlinear systems, a simple nonlinear system is simulated and the breakdown of two standard approaches is demonstrated on data from the system. By relaxing the requirements of the analysis, it is shown that an alternative uncertainty theory gives useful qualitative information about the system. This motivates a discussion of how uncertainty frameworks should be chosen to suit the problem in hand and leads to a clustering of uncertainty problems in structural dynamics into three types: quantification, fusion and propagation.     

Additions of enantiopure alpha-sulfinyl carbanions to (S)-N-sulfinimines: asymmetric synthesis of beta-amino sulfoxides and beta-alphamino alcohols

The addition of the lithium anions derived from (R)- and (S)-methyl and -ethyl p-tolyl sulfoxides to (S)-N-benzylidene-p-toluenesulfinamide provides an easy access route to enantiomerically pure beta-(N-sulfinyl)amino sulfoxides. Stereoselectivity can be achieved when the configurations at the sulfur atoms of the two reagents are opposite (matched pair), thus resulting in only one diastereoisomer, even for the case in which two new chiral centers are created. The N-sulfinyl group primarily controls the configuration of the carbon bonded to the nitrogen, whereas the configuration of the alpha-sulfinyl carbanion seems to be responsible for the level of asymmetric induction, as well as for the configuration of the new stereogenic C-SO carbon in the reactions with ethyl p-tolyl sulfoxides. An efficient method for transforming the obtained beta-(N-sulfinyl)amino sulfoxides into optically pure beta-amino alcohols, based on the stereoselective non-oxidative Pummerer reaction, is also reported.     

Structural and magnetic behavior of the kinked chain Cu(hfac)2(tan) and its relevance to Cu(NO3)2(tan) (hfac = hexafluoroacetylacetonate; tan = 1,4,5-triazanaphthalene)

When stoichiometric amounts of Cu(hfac)(2).H(2)O and 1,4,5-triazanaphthalene (tan) were combined in methanol, green crystals of Cu(hfac)(2)(tan) were formed. Its structure was determined at low temperature (P2(1)/c; a = 8.3308(4) A, b = 14.8945(7) A, c = 18.3046(10) A, beta = 99.298(2) degrees, V = 2241.5(3) A(3)) and found to consist of a novel kinked-chain arrangement where N atoms on opposite sides of the tan ligand bridge Cu(hfac)(2) moieties together. Long axial Cu-N bonds lead to rather weak (J/k(B) = -0.06(5) K) antiferromagnetic interactions according to a Bonner-Fisher fit of the magnetic susceptibility data. The magnetic behavior demonstrated by Cu(hfac)(2)(tan) contrasts markedly with that of Cu(NO(3))(2)(tan), as reported by Hatfield and co-workers, and is attributed to the differing orientations of the Cu d(x)2(-)(y)2 magnetic orbital.