Illumination of the shadow zone in a two-channel oceanic waveguide with a fine structure of sound speed inhomogeneities

The experimental data on the sound field structure, which were obtained by emitting a continuous pseudonoise signal (a midfrequency of 3.2 kHz) in a two-channel oceanic waveguide, are compared with the calculations performed by the wave program with allowance for the fine structure of the sound speed inhomogeneities. A considerable increase in the intensity of the sound field with a definite angular spectrum is observed in the upper channel in the first shadow zone, and, in the experiment, the increase begins nearer to the sound source than predicted by the wave and ray calculations for a smooth sound speed profile. These features of the field structure are explained by the illumination of the shadow zone by the regular scattering of signals from highly anisotropic fine-structure inhomogeneities of the sound speed profile, which are clearly pronounced in the region of the given oceanic experiment.     

On the Finite Base Property for Semigroup Varieties

No algorithm determines from an arbitrary recursive system of semigroup identities whether the variety defined by this system is finitely based.     

Effect of Gd-Mn exchange on phase transitions in GdMn<Subscript>2</Subscript>O<Subscript>5</Subscript> induced by a strong magnetic field

Complex studies of the magnetic, magnetoelectric, and magnetoelastic properties of GdMn₂O₅ single crystals in strong pulsed magnetic fields are carried out in order to obtain additional indirect information on the character of the rare-earth and manganese spin ordering. It is shown that magnetic ordering of Gd³⁺ spins affects the manganese sublattice spin orientation and initiates new magnetic phase transitions. The observed magnetoelectric properties of the GdMn₂O₅ system are interpreted in terms of the theory of phase transitions.     

The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.