A class of time-machine solutions with a compact vacuum core

We present a class of curved-spacetime vacuum solutions which develop closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically flat, and topologically trivial. Stability remains the main open question.     

Extended Hückel calculations of the ionization potentials of some conjugated hydrocarbons

The prediction of ionization potentials of conjugated hydrocarbons using extended Hückel theory is reevaluated. Consequently, two major modifications to the theory are proposed and then tested on five sample molecules. Allowance for distinct sigma and pi orbital parameters as well as for diagonal and off-diagonal parameters constitute the changes examined and are shown to arise naturally from the theory. Subsequent testing of the reproduction of photoelectron spectra indicates significant improvements over previous usage of extended Hückel theory.     

New bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem

Data assimilation algorithms combine prior and observational information, weighted by their respective uncertainties, to obtain the most likely posterior of a dynamical system. In variational data assimilation the posterior is computed by solving a nonlinear least squares problem. Many numerical weather prediction (NWP) centers use full observation error covariance (OEC) weighting matrices, which can slow convergence of the data assimilation procedure. Previous work revealed the importance of the minimum eigenvalue of the OEC matrix for conditioning and convergence of the unpreconditioned data assimilation problem. In this article we examine the use of correlated OEC matrices in the preconditioned data assimilation problem for the first time. We consider the case where there are more state variables than observations, which is typical for applications with sparse measurements, for example, NWP and remote sensing. We find that similarly to the unpreconditioned problem, the minimum eigenvalue of the OEC matrix appears in new bounds on the condition number of the Hessian of the preconditioned objective function. Numerical experiments reveal that the condition number of the Hessian is minimized when the background and observation lengthscales are equal. This contrasts with the unpreconditioned case, where decreasing the observation error lengthscale always improves conditioning. Conjugate gradient experiments show that in this framework the condition number of the Hessian is a good proxy for convergence. Eigenvalue clustering explains cases where convergence is faster than expected.     

On multivariate polynomial interpolation

We provide a map which associates each finite set in complexs-space with a polynomial space from which interpolation to arbitrary data given at the points in is possible and uniquely so. Among all polynomial spacesQ from which interpolation at is uniquely possible, our is of smallest degree. It is alsoD- and scale-invariant. Our map is monotone, thus providing a Newton form for the resulting interpolant. Our map is also continuous within reason, allowing us to interpret certain cases of coalescence as Hermite interpolation. In fact, our map can be extended to the case where, with eachgq, there is associated a polynomial space P, and, for given smoothf, a polynomialqQ is sought for which

Bis-β,β′-conjugate addition

Addition of organocuprates to α,β-enones which possess on the β′-carbon a heteroatom substituent leads in good to excellent yield to β,β′-dialkylated ketones. This process is termed bis-β,β′-conjugate addition.     

Synthesis and assignment of absolute configuration of (-)-oleocanthal: a potent, naturally occurring non-steroidal anti-inflammatory and anti-oxidant agent derived from extra virgin olive oils

[structure: see text] Effective total syntheses and the assignment of absolute configurations of both the (+)- and (-)-enantiomers of oleocanthal 1 (a.k.a. deacetoxy ligstroside aglycon), the latter derived from extra virgin olive oils and known to be responsible for the back of the throat irritant properties of olive oils, have been achieved. The absolute and relative stereochemistry of the naturally occurring enantiomer (-)-1 proved to be 3S,4E. Both syntheses begin with d-(-)-ribose, proceed in 12 steps, and are achieved with an overall yield of 7%. Both enantiomers proved to be non-steroidal anti-inflammatory and anti-oxidant agents.     

Nickel ferrocyanide modified electrodes as active cation-exchange matrices: real time XRD evaluation of overlayer structure and electrochemical behavior

The dynamic variations in the structure of nickel ferrocyanide modified electrodes was determined using in situ diffractoelectrochemical techniques. X-ray powder diffraction peaks from the nickel ferrocyanide modified electrode were recorded during electrochemical oxidation/reduction of the surface overlayer and reversible changes in the unit cell lattice parameter observed. The electrochemical changes that occur during oxidation/reduction in various alkali cation electrolytes are correlated with changes in the lattice parameter. It is postulated that micro-domains form when two cations having markedly different radii such as cesium and potassium are intercalated into the nickel ferrocyanide structure so that distinct regions of the nickel ferrocyanide layer containing cesium exist separated from regions with the lighter alkali cations.     

An asymmetric synthesis of (+)-kjellmanianone

Racemic and asymmetric syntheses of kjellmanianone, a novel cyclopentenoid antibiotic, are described.     

Acyl radical addition to benzene and related systems—a computational study

The addition of the acetyl radical to benzene, aniline, trifluoromethylbenzene and naphthalene has been investigated using DFT calculations. Addition to benzene is calculated to have an energy barrier of 63.6 kJ mol⁻¹ at the BHandHLYP/6-311G(d,p)+ZPE level of theory. This reaction is associated with simultaneous SOMO→π^∗ and π→SOMO interactions with the latter interaction dominating, suggesting that acetyl reacts predominantly as an electrophilic radical in its interaction with benzene. Addition to the ortho and para positions of aniline is calculated to be slightly less favourable, while attack at the meta position is predicted to be unaffected in relation to the chemistry involving benzene. Inclusion of the electron-withdrawing substituent, trifluoromethyl, is predicted to accelerate reactions slightly at the ortho and para positions, while attack at the C1 position of naphthalene is calculated to involve a barrier of 50.3 kJ mol⁻¹ (BHandHLYP/6-311G(d,p)+ZPE).