Duality for Finite Hopf Algebras Explained by Corings

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements. This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.     

Electrochemical Recovery of Silver from Lead Alloys in Chloride Melts

Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

A STUDY OF VARIOUS BARRIERS IN ENCLOSED SOUND FIELD BY USING THE COMPUTER PROGRAM—SOFIS

In the study of the behaviors of barriers in an enclosed field, one should take into account such phenomena as sound energy reflection, absorption, scattering and diffraction. Therefore, the study is much more difficult than that in free field. In this paper, sound barriers are classified into four kinds according to their size, number and shape. Each kind of barriers is modelled by a corresponding method based on a computer program—SOFIS. The program combines the ray-tracing technique and statistical method. The impulse response and some acoustical parameters such as sound pressure level at different positions can be calculated by the program, no matter there are a certain kind of barriers in the field or the field is empty. The ray-tracing program and the algorithms for various barriers are validated by the comparison between measurement and prediction of the reverberation room and the anechoic room of the Northwestern Polytechnic University.     

Characteristics of propagation of light beams in gyrotropic crystals

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 815–819, May, 1991.     

Kaplansky conjecture in the theory of quadratic forms

This article considers the splitting properties of finite-dimensional division rings over universal splitting fields of quadratic forms. An example of a field with u-invariant equal to 6 is constructed, which contradicts Kaplansky's conjecture concerning u-invariants.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 75–89, 1989.     

Inverse Process with Independent Positive Increments: Finite-Dimensional Distributions

An inverse process with independent positive increments is considered. For such a process, the first hitting time τ_x of level x as a function of x ≥ 0 is a proper process with independent positive increments. In terms of first hitting times and their Levy measures, multidemensional distribution densities and Laplace transformations are derived. Stationary distributions of increments of the process are investigated. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 286–297.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.