Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

Tunneling and EPR linewidths due to dislocations in Mn acetate

We compute the width and shape of the EPR and tunneling resonances due to dislocations in Mn₁₂ acetate crystals. Uncorrelated dislocations produce the Gaussian shape of resonances while dislocations bound in pairs produce the Lorentzian shape. We stress that the uniaxial spin Hamiltonian together with crystal defects can explain the totality of experimental data on Mn₁₂. Received 2 August 2001 / Received in final form 15 March 2002 Published online 17 September 2002     

A new three-flavor oscillation solution of the solar neutrino deficit in <Emphasis Type="Italic">R</Emphasis>-parity violating supersymmetry

We present a solution of the solar neutrino deficit using three flavors of neutrinos and R-parity non-conserving supersymmetry. In this model, in vacuum, the is massless and unmixed, mass and mixing being restricted to the - sector only, which we choose in consistency with the requirements of the atmospheric neutrino anomaly. The flavor changing and flavor diagonal neutral currents present in the model and the three-flavor picture together produce an energy dependent resonance-induced - mixing in the sun. This mixing plays a key role in the new solution to the solar neutrino problem. The best fit to the solar neutrino rates and spectrum (1258-day SK and 241-day SNO data) requires a mass square difference of eV² in vacuum between the two lightest neutrinos. This solution cannot accommodate a significant day-night effect for solar neutrinos nor CP violation in terrestrial neutrino experiments. Received: 26 December 2001 / Revised version: 16 February 2002 / Published online: 26 July 2002     

Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron

The renormalization method of Bogoljubov-Parasiuk-Hepp-Zimmermann (BPHZ) is used in order to derive the renormalized energy shift due to the gauge invariant K?llén-Sabry diagram of the two-photon vacuum polarization (VPVP) as well as the self energy vacuum polarization S(VP)E beyond the Uehling approximation. It is outlined, that no outer renormalization is required for the two-photon vacuum polarization and that only the inner renormalization has to be accomplished. It is shown that the so-called nongauge invariant spurious term is absent for a wide class of vacuum polarization (VP) diagrams if one applies the widely used spherical expansion of bound and free-electron propagator. This simplifies significantly calculations in bound state quantum electrodynamics. As one result of our paper the use of the BPHZ-approach in bound state QED is established. Received 28 September 2001     

A new trigonometric method of summation and its application to the degree of approximation

The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and Fourier effective and determine its status with reference to other methods of summation (see §2-§4) and also give an application of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Holder metric (see §5).     

Spontaneous formation of a system of highly ordered germanium nanoislands upon epitaxial deposition on profiled (111) silicon substrates under electromigration conditions

Atomic-force microscopy was used to study the surface topography of SiGe structures grown by epitaxial deposition of Ge on profiled Si(111) substrates under electromigration conditions. Systems of highly ordered germanium nanosized islands with dimensions of 10–20 nm and a density of 6×10¹⁰ cm^?2 were obtained. It is shown that the geometrical parameters of self-organizing nanoislands can be controlled by a proper choice of the growth and postgrowth annealing conditions for these structures.     

Variant superfield representations

We discuss some variant superfield representations which can arise by the replacement of some of the usual fields in a multiplet with p-form gauge fields.     

Transfructosylation of rebaudioside A (a sweet glycoside of Stevia leaves) with Microbacterium beta-fructofuranosidase.

It was found that a beta-fructofuranosidase produced by Microbacterium sp. H-1 has potent trans-beta-fructofuranosylation activity from sucrose (donor). By means of this enzyme system, rebaudioside A (RA), the second major sweet steviol glycoside of the leaves of Stevia rebaudiana, was subjected to transfructosylation, affording a mono-beta-fructofuranosylated product (RA-F) in a high yield. The structure of RA-F was elucidated as beta-D-fructofuranosyl-(2----6)-beta-D-glucopyranosyl ester of steviol-13-O-[beta-D-glucopyranosyl-(1----2)]- [beta-D-glucopyranosyl-(1----3)]-beta-D-glucopyranoside. Some improvement in the quality of sweetness was observed for RA-F.     

Wave propagation through a high-velocity elastic layer

We consider theoretical seismographs of a wave field passing through an elastic layer with high propagation velocity. We note the presence of a low-frequency part of the seismogram for longitudinal waves. It is shown that the propagation time of low-frequency vibrations is equal to that of longitudinal disturbances screened by the layer.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 173, pp. 134–141, 1988.     

A cochlear model with transversally inhomogeneous cross-section

The transversally inhomogeneous cross-section of the model is constructed from the data obtained by Retzius, Hardesty, Wever, and Miller. On the basis of a three-dimensional linear mechanical WKB model of a cochlea without negative friction we obtain high frequency selectivity and a phase shift in the domain of the peak of the amplitude function comparable with the measurements taken by Sellick and Robles.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 128–138, 1989.