A lower bound on the performance of the quadratic discriminant function

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.     

On estimating pressure build-up in severely accelerated,shocked flow

A new approach to the calculation of the high pressures characterizing the flow field in front of a piston undergoing severe acceleration over the short term is presented. In contrast with previous approaches where the computational domain is altered but which stop short of transforming velocities, here the problem is solved in an accelerating non-Euclidean co-ordinate system where the piston is stationary. The method is applied to a study of the problem of premature sabot separation. Through use of Harten's second-order-accurate TVD scheme, flow simulations are performed for both 1D and 3D axisymmetric geometries. The simple 1D model gives pressure profiles surprisingly close to those of the more physical 3D model.     

An investigation of the role of the disparate redox states of the tetrathiafulvalene unit in modulating hydrogen bonding interactions in solution

We have investigated the electrochemically controlled hydrogen bonding interactions between tetrathiafulvalene host 3 and guests 4 or 5. Stabilisation of the 3⁺ state is dependent upon the nature of the guest species, whereas both guests prevent precipitation of the electrochemically generated 3²⁺ species at the working electrode via hydrogen bonded molecular recognition processes.     

Longitudinal relaxation of muonium in Ge and GaAs

Longitudinal-field muon-spin depolarization rates in high-purityGe and semiinsulatingGaAs are reported and compared to similar data for intrinsicSi. Depolarization onset temperatures provide a comparison of charge carrier concentrations leading to rapid charge exchange and a shift in the onset, for n-typeGaAs verifies anelectron process. The temperature dependence of the low-field rate constants imply more complicated dynamics inGe than observed earlier inSi. Features near 750K inGaAsTe appear consistent with dissociation of aMu-Te pair.This work was supported by the US National Science Foundation (DMR-8917639 [TLE, BH]), the Science and Engineering Research Council of the UK (EAD, AS, SFJC), the Robert A. Welch Foundation (D-1053 [RLL], and C-1048 [TLE]), and a NATO Collaborative Research Grant (RLL, SFJC, RCD, CS). We wish to thank D.A. Vanderwater of Hewlett Packard for providing theGaAsTe sample.     

XeAuF

XeAuF has been detected and characterized using microwave rotational spectroscopy. It was prepared by laser ablation of Au in the presence of Xe and SF(6), and stabilized in a supersonic jet of Ar. The spectrum was measured with a cavity pulsed jet Fourier transform microwave spectrometer, in the frequency range 6-26 GHz. Rotational constants, centrifugal distortion constants, and (131)Xe and (197)Au nuclear quadrupole coupling constants have been evaluated. The molecule is linear, with a short XeAu bond (2.54 A), and is rigid. The (131)Xe nuclear quadrupole coupling constant (NQCC) is large (-135 MHz). The (197)Au NQCC differs radically from that of uncomplexed AuF. The results are supported by those of ab initio calculations which have given an XeAu dissociation energy approximately 100 kJ mol(-1), plus Mulliken and natural bond orbital populations, MOLDEN plots of valence orbitals, and an energy density distribution. All evidence is consistent with XeAu covalent bonding in XeAuF.     

Amination and [2,3]-sigmatropic rearrangement of propargylic sulfides using a ketomalonate-derived oxaziridine: synthesis of N-allenylsulfenimides

Amination of propargylic sulfides with a ketomalonate-derived oxaziridine under metal free conditions gives N-Boc-N-allenylsulfenimides via [2,3]-sigmatropic rearrangement.     

Model systems for flavoenzyme activity: a tuneable intramolecularly hydrogen bonded flavin-diamidopyridine complex

We report the electrochemically tuneable intramolecular hydrogen bonding interactions between a covalently linked flavin-diamidopyridine unit.