Axion dark matter and cosmological parameters

We observe that photon cooling after big bang nucleosynthesis but before recombination can remove the conflict between the observed and theoretically predicted value of the primordial abundance of ^{7}Li. Such cooling is ordinarily difficult to achieve. However, the recent realization that dark matter axions form a Bose-Einstein condensate provides a possible mechanism because the much colder axions may reach thermal contact with the photons. This proposal predicts a high effective number of neutrinos as measured by the cosmic microwave anisotropy spectrum.     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

A geometric Gordan-Stiemke theorem

Let C and K be closed cones in Rⁿ. Denote by φ (K∩C) the face of C generated by K ∩ C, by φ(K ∩ D)^D the dual face of φ(K ∩ C) in C¹, and by φ(-K¹ ∩ C¹) the face of C¹ generated by -K¹ ∩ C¹. It is proved that φ(K ∩ C¹) if and only if -C¹ ∩ [span(K ∩ C)] ⊥ ? C¹ + K¹. In particular, the closedness of C¹ + K¹ is a sufficient condition. Our result contains a generalization of the Gordon-Stiemke theorem which appeared in a recent paper of Saunders and Schneider.     

Proof of a conjecture of V. Nikiforov

Using analytical tools, we prove that for any simple graph G on n vertices and its complement [`(G)]\bar G the inequality $\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4} {3}n - 1$\mu \left( G \right) + \mu \left( {\bar G} \right) \leqslant \tfrac{4} {3}n - 1 holds, where μ(G) and m( [`(G)] )\mu \left( {\bar G} \right) denote the greatest eigenvalue of adjacency matrix of the graphs G and [`(G)]\bar G respectively.     

Symmetry classes of tensors associated with certain groups

We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with certain subgroups of the full symmetric group The dimensions of these symmetry classes of tensors are also given     

Perceptual recalibration in human sound localization: learning to remediate front-back reversals

The efficacy of a sound localization training procedure that provided listeners with auditory, visual, and proprioceptive/vestibular feedback as to the correct sound-source position was evaluated using a virtual auditory display that used nonindividualized head-related transfer functions (HRTFs). Under these degraded stimulus conditions, in which the monaural spectral cues to sound-source direction were inappropriate, localization accuracy was initially poor with frequent front-back reversals (source localized to the incorrect front-back hemifield) for five of six listeners. Short periods of training (two 30-min sessions) were found to significantly reduce the rate of front-back reversal responses for four of five listeners that showed high initial reversal rates. Reversal rates remained unchanged for all listeners in a control group that did not participate in the training procedure. Because analyses of the HRTFs used in the display demonstrated a simple and robust front-back cue related to energy in the 3-7-kHz bandwidth, it is suggested that the reductions observed in reversal rates following the training procedure resulted from improved processing of this front-back cue, which is perhaps a form of rapid perceptual recalibration. Reversal rate reductions were found to generalize to untrained source locations, and persisted at least 4 months following the training procedure.     

Electron impact spectra of some alkyl derivatives of water and related compounds

Electron impact energy loss spectra at impact energies of 100 eV and 50 eV and a scattering angle of 2 degrees are presented for alkyl derivatives of H₂O and related compounds. Spectra of H₂O, CH₃OH, CH₃OCH₃, ethylene oxide, CH₃CH₂OH, (CH₃)₂CHOH, (CH₃)₃C C₂H₅OC₂H₅ and tetrahydrofuran are tentatively assigned using derived term values and ionization potentials from photoelectron spectrosc Substituent effects on Rydberg orbital energies are discussed using Taft σ* values.     

Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations

We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model of the so-called regenerative machine toolvibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the specialalgebraic structure of the delayed terms in the nonlinear part of the equation,the computation results in simple analytical formulas. Numerical simulationsgave excellent agreement with the results.