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.     

Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate

A new mechanism is proposed for the energy relaxation of hot carriers in single-wall carbon nanotubes: scattering with the emission of surface optical phonons into the semiconductor substrate. The theory involves intrasubband and intersubband forward and backward scattering. The analytical result and numerical data indicate that intrasubband forward scattering is the main process: the corresponding lifetime comprises several femtoseconds for a quartz substrate, which allows this mechanism of energy relaxation to be considered dominating for a nanotube on the surface of a polar semiconductor or a dielectric.     

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.     

Simulation of a High Harmonic Gyrotron with Axis-Encircling Electron Beam and Permanent Magnet

A computer code for simulation of beam-field interaction in a resonant cavity of a gyrotron has been developed. It is based on a self-consistent, time-independent, single-mode physical model. The code has been applied to the analysis of the electrodynamical system of a novel high-harmonic gyrotron with axis-encircling beam and a permanent magnet. In this paper both the physical model and numerical techniques used are outlined. Some results of the numerical experiments are presented and discussed.     

Frequency resolution as a function of hearing threshold level and age

Frequency resolution ability was measured using a psychoacoustical tuning curve (PTC) or a notch-noise technique in two population samples. The first sample incorporated 1764 subjects with various degrees of sensorineural hearing impairment and ranging in age from 17-80 years. The second sample included 240 subjects aged between 50 and 75 years, carefully balanced in terms of impairment and age to avoid confounding between these two variables. In both samples, frequency resolution ability declined with increasing hearing threshold level (HTL), as measured by either method. In a subsample tested with both methods, the correlation between the two was only modest. After accounting for HTL, there was a minor dependence of frequency resolution on age, older subjects having poorer frequency resolution once HTL had been accounted for. No addition to the explained variance was achieved by taking sex, occupational group, or audiogram slope into account. Despite the documented reproducibility of the measures, much of the variance in the frequency resolution measurements remained unrelated to HTL or age.     

Characteristics of propagation of light beams in gyrotropic crystals

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

Inverse and saturation theorems for linear combination of modified Baskakov operators

In this paper, we consider linear combinations of modified Baskakov operators. By use of several lemmas, we obtain the inverse theorem (Theorem 1.1) and the saturation (Theorem 1.2) for those linear combinations.