Asymmetric total synthesis of rollicosin

[structure: see text] The first total synthesis of rollicosin, a member of a rare subgroup of Annonaceous acetogenins containing two terminal gamma-lactones, is reported. The approach features a highly regio- and stereoselective tandem ring-closing/cross-metathesis reaction for construction of the east-wing lactone and incorporation of the alkyl spacer. Establishment of the C4 stereocenter and addition of the west-wing lactone were achieved by Sharpless asymmetric dihydroxylation and enolate alkylation.     

Optimal design of an uncoupled six degree of freedom dynamometer

A design analysis of a class of six degree of freedom strain-gage dynamometers which are virtually uncoupled in each force and moment component is presented. The method of design is detailed and an optimal design algorithm is implemented. The dynamometer is made of six or more T-sections with thin webs and flanges called shear panel elements (SPE). Complete stress and buckling analyses are carried out for the SPE, and experiments confirm the predictions of the analyses. The optimal design method is illustrated with several case studies. A dynamometer has been built and used in laboratory and field experiments.     

Transition to escape in a system of coupled oscillators

We study a Hamiltonian system of coupled oscillators derived from two forced pendulums, connected with a torsional spring. The uncoupled limit is described by two identical oscillators, each possessing a homoclinic orbit separating bounded from unbounded motion. We focus on intermediate energy levels which lead to detained motions, defined as trajectories that, though unbounded as t → ∞, oscillate within the region defined by the homoclinic orbit of the unperturbed system for a long but finite time. We analyze the existence and behavior of these motions in terms of equipotential surfaces. These curves provide bounds on the motion of the system and are shown to be closed for low energies. However, above some critical energy level the equipotential curves become open. The detained trajectories are shown to arise from the region of phase space that was, for appropriate energies, stochastic. These motions remain within this region for long times before finally “leaking out” of the opening in the equipotential curves and proceeding to infinity.     

A Mössbauer spectroscopy and neutron diffraction study of magnetostrictive,melt-spun Fe–Ga alloy ribbons

Ribbons of Fe_100−xGa_x (x=15, 17.5, 19.5 and 22.5) were prepared by rapid solidification from the melt. ⁵⁷Fe Mössbauer spectroscopy and high resolution neutron diffraction have revealed that Fe_100−xGa_x alloys with x=15 and 17.5 have the disordered bcc (A2) structure even after annealing, but the alloy with x=19.5 developed the short-range ordered D0₃ phase when annealed. The x=22.5 alloys showed mainly D0₃ phase with a fraction of bcc phase. A fraction of the bcc phase transformed into D0₃ phase and the long-range ordering of D0₃ phase was improved after annealing. ⁵⁷Fe Mössbauer spectra showed no observable L1₂ phase in any samples even though less than 1% volume of L1₂ phases has been found in the annealed samples by neutron diffraction. The additional absorption at hyperfine field of 25 T in x=22.5 samples was regarded as a result of imperfect D0₃ structure, rather than L1₂ phase.     

Measuring modulated luminescence using non-modulated stimulation: ramping the sample period

Conventional methods of recording linearly modulated (LM) optically stimulated luminescence (OSL) require control over either the exciting light intensity, or the ability to pulse the source. For many light sources (e.g. constant-power CW lasers, arc lamps and synchrotrons) this can be problematic. Directly analogous results to LM-OSL can, however, be achieved with non-modulated excitation sources, by ramping the sample period (RSP) of luminescence detection. RSP-OSL has the distinct advantage over LM-OSL in that, since the excitation remains at full power, data accumulation times (that can be considerable) can be reduced by typically 50%. RSP methods are universally applicable and can be employed, for example, where the excitation source is constant heat, rather than light: here, iso-thermal decay of phosphorescence becomes recorded as a sequence of peaks, corresponding to de-trapping of charge from different defect levels, and is particularly useful for analysing shallow-trap effects. RSP methods are also useful in providing significant compaction of data sets, where signal analysis is required of overlapping systems having a wide range of decay kinetics.     

A symmetrized Hückel analysis of carbon cages of Ih point group symmetry

Some new aspects of qualitative molecular-orbital theory are developed within the context of group theory and a symmetrized Hückel approximation. Conclusions concerning the eigenvalue sums for sets of eigenfunctions of the same symmetries, the occurrence of repetitions of symmetry-adapted projections and the relations between eigenvalues of Γ_g and Γ_u symmetries are exemplified using the ₁₂₀ cage structure of I_h point symmetry. The implications of the orbit-by-orbit approach are outlined for larger clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

The André/Bruck and Bose representation of conics in Baer subplanes of PG(2,q 2)

The André/Bruck and Bose representation ([1], [5,6]) of PG(2,q ²) in PG(4,q) is a tool used by many authors in the proof of recent results. In this paper the André/Bruck and Bose representation of conics in Baer subplanes of PG(2,q ²) is determined. It is proved that a non-degenerate conic in a Baer subplane of PG(2,q ²) is a normal rational curve of order 2, 3, or 4 in the André/Bruck and Bose representation. Moreover the three possibilities (classes) are examined and we classify the conics in each class. Received 1 September 1999; revised 17 July 2000.