On the group extension of the transformation associated to non-archimedean continued fractions

Summary Let F_q be a finite field with q elements. We consider formal Laurent series of F_q -coefficients with their continued fraction expansions by F_q -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors.     

Dynamics of acoustoelectromagnetic solitons as a manifestation of higher nonlinearity

The acoustoelectromagnetic interaction is examined in a regime where three mechanisms must be taken into account simultaneously: photoelasticity, quadratic photoelasticity, and elastic nonlinearity. It is shown that beyond the critical conditions, acoustic solitary waves are formed at harmonic and subharmonic frequencies in a crystal. Including damping and nonideal reflection at the boundaries does not lead to the establishment of any sort of stationary state: a soliton spatial-temporal dynamic develops. Fiz. Tverd. Tela (St. Petersburg) 39, 1101–1104 (June 1997)     

Energetics of an adiabatically-loaded excited anharmonic oscillator

The dependence of the energy characteristics on an adiabatically slowly increasing external force is determined analytically for an anharmonic oscillator. The analytical results are confirmed by a numerical calculation. The nature of the force dependences of the energy characteristics are determined and discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 153–157 (January 1997)     

Propagation of magnetostatic waves in unsaturated ferrite films with a strip domain structure

The propagation of surface and volume magnetostatic waves in unsaturated films of yttrium iron garnet is studied experimentally for the case when the wavelength greatly exceeds the domain width, while the domain width is comparable to the film thickness. The characteristics of these waves are examined for symmetric linear, asymmetric linear, and symmetric zigzag strip domain structures in the films. These characteristics cannot be explained by a theory based on averaging the magnetization over all the domains. Zh. éksp. Teor. Fiz. 111, 1016–1031 (March 1997)     

On edge states in superconductors with time inversion symmetry breaking

The efficiency of conversion of the heat flux into hard x radiation (HXR) is analyzed, via time-dependent two-temperature one-dimensional non-LTE-radiation-hydrodynamic numerical modeling, for a heat-to-radiation flux converter linked to the edge of a low-atomic-number hot Z-pinch. The domain of parameters in this scheme is found where about the same HXR yield can be achieved at values of input energy which are an order of magnitude lower than in the conventional scheme of a radially imploding plasma. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 502–506 (10 April 1997) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

Excitation of metal spectra in combined glow discharge

Consideration is given to the special features of the excitation of spectra of metals (Ag, Au, Fe, Hg, Pt, and Sb) that manifest themselves in investigating spectral sources with combined glow discharge (glow discharge and capillary discharge). It is established that the proposed method for introducing a substance into a plasma makes it possible to realize two fundamentally different regimes: without evaporation and with complete evaporation and matrix atomization. It is shown that a spectral source of combined glow discharge with a nonequilibrium plasma has significant advantages for the most important analytical characteristics over quasi-equilibrium combined discharge at atmospheric pressure. The gold and platinum sensitivity in combined glow discharge is 10⁻⁷%, and the reproducibility of spectral determinations is 0.001–0.100, depending on the measurement range. A fractional separation of elements that makes it possible to analyze the phase composition of substances, particularly metals, with high sensitivity is revealed in glow discharge. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 143–147, March–April, 1997.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

Generation of mesoscopic magnetic structures by local laser action

New effects are observed wherein the internal structure of the domain walls in a thin magnetic iron garnet film are modified by the action of focused laser radiation. A single laser pulse with increasing power gives rise to the following: 1) displacement of vertical Bloch lines in a domain wall; 2) generation of a pair of vertical Bloch lines on initially line-free walls; and, 3) an irreversible change in shape of a domain wall and the domain structure as a whole. The mechanism leading to the generation and displacement of Bloch lines is connected with the motion of domain walls which is induced by a local change in the distribution of demagnetizing fields as a result of a heating-induced decrease of the magnetization in the focal spot of the laser radiation. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 398–402 (25 September 1997)