Monoid of self-equivalences and free loop spaces

Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .

     

A universal constant for the convergence of Newton's method and an application to the classical homotopy method

We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth ₀=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method.     

Separation of nonstationary sound fields in the time-wavenumber domain

A number of sound field separation techniques have been proposed for different purposes. However, these techniques just consider the separation of sound fields in the space domain and are restricted to stationary sound fields. When the sound fields are nonstationary, it is also necessary to perform the separation in the time domain. Therefore, on the basis of the propagation principle of sound pressure in the time-wavenumber domain, a nonstationary sound field separation technique with two closely spaced parallel measurement surfaces is proposed. It can separate the nonstationary signals generated by the primary sources in both time and space domains when the disturbing sources exist on the other side of the measurement plane. The signals in time and space domains are separated by using the spatial Fourier transform method and the time domain deconvolution method. A simulation involving two monopoles driven by nonstationary signals demonstrates that the method proposed can remove the influence of disturbing sources in both time and space domains. The feasibility of this method is also demonstrated by an experiment with two loudspeakers located on two sides of measurement planes. Additionally, to comment more objectively on the separation results, some indicators are computed in both the simulation and experiment.     

Diagram,valence-to-core,and hypersatellite Kβ X-ray transitions in metallic chromium

We report on measurements of the Kβ diagram, valence-to-core (VtC), and hypersatellite X-ray spectra induced in metallic Cr by photon single and double K-shell ionization. The experiment was carried out at the Stanford Synchrotron Radiation Lightsource using the seven-crystal Johann-type hard X-ray spectrometer of the beamline 6-2. For the Kβ diagram and VtC transitions, the present study confirms the line shape features observed in previous works, whereas the K^hβ hypersatellite transition was found to exhibit a complex spectral line shape and a characteristic low-energy shoulder. The energy shift of the hypersatellite relative to the parent diagram line was deduced from the measurements and compared with the result of extensive multiconfiguration Dirac–Fock (MCDF) calculations. A very good agreement between experiment and theory was found. The MCDF calculations were also used to compute the theoretical line shape of the hypersatellite. A satisfactory agreement was obtained between the overall shapes of the experimental and theoretical spectra, but deviations were observed on the low- and high-energy flanks of the hypersatellite line. The discrepancies were explained by chemical effects, which were not considered in the MCDF calculations performed for isolated atoms.     

Isokinetic Relationships in Alcohol Oxidation with Chromic Acid

The activation parameters for the oxidation of 13 secondary alcohols with chromic acid have been determined. Application of a statistical treatment of Exner [9] shows that the reactions are isoentropic with an average entropy of activation (ΔS^≠) of ?24.0 e. u.