Gamma radiation from the celestial X-ray source sco X-1

Gamma radiation from the X-ray sources Sco X-1 due to Comptonsynchrotron process is calculated. Comparison with the upper limits set by an experimental survey for sources of gamma-rays with energy greater than 100 MeV has been made and constraints on the size of the source and its magnetic field are discussed. The flux predicted in the energy range 10¹¹–10¹² eV is above the observable lower limit of presentday detectors. An observation of this flux will serve as a test of the synchrotron origin of the X-radiation.     

Energy flux of elastic waves

The energy fluxes of complex fields in inhomogeneous media are considered.     

Energy density and flux in nonrelativistic quantum mechanics

A number of mathematical consequences of the Schroedinger equation are given and interpreted as local energy and momentum conservation laws. Several Hamiltonians are treated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1090–1095, August, 1992.     

Evolution of X-ray spectrum in down-Comptonization process

The extended Kompaneets equation is reviewed. This equation can be applied not only to the up-Comptonization process but also to the down-Comptonization which is important in X-ray and γ-ray astronomy. Based on this equation, the variation of some typical X-ray spectrum in astrophysics due to the down-Comptonization is down-Cumptonimation, spectrum shape, diffusion approximation, extended Kompanects equation. Project supported by the National Natural Science Foundation of China (Grant No. x x x) and the Climbing Program of China.     

On absolute continuity of the spectrum of random polynomials orthogonal on the circle and their continual versions

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 170–173, 1992.     

Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers

For totally positive algebraic integers of degree , we consider the set of values of , where is the Mahler measure of . C. J. Smyth has found the four smallest values of and conjectured that the fifth point is . We prove that this is so and, moreover, we give the sixth point of .

     

A calculation of the flux and energy spectrum of secondary electrons at high altitudes in the atmosphere

Calculations are carried out to determine the flux and energy spectra of secondary electrons which are produced by the cosmic radiation in the upper layers of the atmosphere. The calculations are valid to an atmospheric depth of about 10 g./cm.² Electron spectra are presented for different depths and locations where measurements of the electron flux have been carried out: Ft. Churchill, Manitoba; Sioux Falls, South Dakota; Palestine, Texas; and Hyderabad, India. The calculations are compared with observed electron fluxes during the ascents of balloon flights.     

Energy spectrum in the force field of an electrostatic image

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 1, pp. 109–115, January, 1989.     

On the Lyapunov theory of equilibrium figures of celestial bodies

The work of A. M. Lyapunov on the theory of equilibrium figures of celestial bodies is analyzed. The main results are mentioned, such as sufficient conditions for the existence and uniqueness of solutions to the complicated integral and integro-differential equations of the problem; the solution of the stability problem for the MacLaurin and Jacobi ellipsoids; the solution of the existence and stability problem for figures branching from the ellipsoids; the solution of the problem for slowly rotating inhomogeneous bodies in terms of series (called now the Lyapunov series) in powers of a small parameter, which is equal in the first approximation to the centrifugal-to-gravitational force ratio; and the estimation of the convergence radius of the Lyapunov series. Further development of Lyapunov’s ideas and unsolved problems is discussed.     

Comparison results for the volume of geodesic celestial spheres in Lorentzian manifolds

Volume comparison results are obtained for the volume of geodesic celestial spheres in Lorentzian manifolds and the corresponding objects in Lorentzian space forms. Also, as a rigidity result it is shown that the volume of geodesic celestial spheres is independent of the instantaneous observer if and only if the spacetime has constant curvature.     

Relations between the Taylor spectrum and the Xia spectrum

Let be a doubly commuting -tuple of -hyponormal operators with unitary operators from the polar decompositions . Let and . In this paper, we will show relations between the Taylor spectrum and the Xia spectrum .