Hyperbolic -spheres with conical singularities, accessory parameters and Kähler metrics on

We show that the real-valued function on the moduli space of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic -sphere with conical singularities of arbitrary orders , generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kähler metrics on parameterized by the set of orders , explicitly relate accessory parameters to these metrics, and prove that the functions are their Kähler potentials.

     

Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples.     

Interpretation of Polarized Absorption and Emission Spectra of Molecules Incorporated in Stretched Polymer Films

Different methods for the interpretation of linear dichroic spectra of molecules incorporated in uniaxial matrices are discussed. A method based on the combination of both polarized absorption and emission measurements is described for the resolution of absorption and emission spectra into their different polarized components, and for the investigation of molecular distributions in the oriented matrix. The distributions of some planar molecules of different shapes incorporated in stretched polyethylene films are presented.     

Universality and self-similarity in the bifurcations of circle maps

The bifurcation structure in a two-parameter family of circle maps is considered. These maps have a (topological) degree that may be different from one. A generalization of the rotation number is given and symmetries of the bifurcations in parameter space are described. Continuity arguments are used to establish the existence of periodic orbits. By plotting the locus of parameter values associated with superstable cycles, self-similar bifurcations are found. These bifurcations are a generalization of the familiar period-doubling cascade in maps with one extrema, to two-parameter maps with two extrema. Finally, a scheme for the global organization of bifurcation in these maps is proposed.     

Middle ear prosthesis: significance in magnetic resonance imaging

The Armstrong model of the Schuknecht gel foam and wire prosthesis was tested in the magnetic field of a 1.5 Tesla magnet. The wire component of the prosthesis was found to be non-magnetic. Patients with this prosthesis can therefore undergo MRI examination safely. Two previous articles from the non radiologic literature concerning the magnetic properties of metallic middle ear prostheses are reviewed.     

μ+ depolarization inAlGd alloys

The ⁺ depolarization rate in diluteAlGd alloys containing 50 and 450 atomic ppm Gd was measured in a transverse field of 80 Oe over the temperature range 6–300 K. For both alloys, A increased dramatically above 200 K, reaching values of 0.69 and 0.93 s^–1, respectively, near room temperature. The results are interpreted as providing evidence for a thermally-activated trapping mechanism.This work was supported by the U.S. Department of Energy.     

Muon diffusion and trapping studies in high purity vanadium

We present the first results of a study of the effects of varying impurity concentration on the temperature dependence of the depolarization rate of positive muons implanted into vanadium. Data are reported for the most highly purified polycrystalline sample yet measured, and the same sample subsequently doped with about 500 ppm oxygen by weight. The data for the pure sample shows a low depolarization rate (<.15 sec^–1) at all temperatures measured, showing a broad minimum centered at 35 K, followed by a sharp peak near 90 K and a rapid drop to negligible values at 200 K. The data is contrasted with previously published data [2] on less pure samples, and calls into question previous interpretations of the behavior of the ⁺ at low temperatures in impure vanadium [1] as one-phonon-assisted tunneling.This work was supported by the U. S. Department of Energy     

Transition from decelerated to accelerated cosmic expansion in braneworld universes

Braneworld theory provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Non-static extra dimensions can generally lead to a variable vacuum energy, which in turn may explain the present accelerated cosmic expansion. We concentrate our attention in models where the vacuum energy decreases as an inverse power law of the scale factor. These models agree with the observed accelerating universe, while fitting simultaneously the observational data for the density and deceleration parameter. The redshift at which the vacuum energy can start to dominate depends on the mass density of ordinary matter. For _m = 0.3, the transition from decelerated to accelerated cosmic expansion occurs at z _T ≈ 0.48 ± 0.20, which is compatible with SNe data. We set a lower bound on the deceleration parameter today, namely > − 1 + 3 _m /2, i.e., > − 0.55 for _m = 0.3. The future evolution of the universe crucially depends on the time when vacuum starts to dominate over ordinary matter. If it dominates only recently, at an epoch z < 0.64, then the universe is accelerating today and will continue that way forever. If vacuum dominates earlier, at z > 0.64, then the deceleration comes back and the universe recollapses at some point in the distant future. In the first case, quintessence and Cardassian expansion can be formally interpreted as the low energy limit of our model, although they are entirely different in philosophy. In the second case there is no correspondence between these models and ours.