Fano direct products as rationally connected fibrations

Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 183–206, 2004.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

Structure and properties of the Ti-Si-N nanocrystalline coatings synthesized in vacuum by the electroarc method

Phase composition, defect substructure, and mechanical properties of the Ti-Si-N coating deposited on metal and ceramic-metal substrates by electroarc sputtering of the Ti-Si composite cathode in an ionized nitrogen atmosphere are investigated by the methods of modern materials science. It is established that coatings so formed with a thickness of ∼1–3 μm are superhard (H_v ∼ 50 GPa), and have the nanocrystalline structure (with crystalline sizes D = 7 nm) based on titanium nitride δ-TiN. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–51, February, 2007.     

Squeezed states and uncertainty relations since 1991

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.     

Electrodynamic properties of nanoporous silicon in the range from terahertz to infrared frequencies

The dielectric response (conductivity and permittivity) spectra of a series of nanoporous silicon samples prepared by anodization of low-resistivity single-crystal silicon are measured, for the first time, using terahertz and IR spectroscopy in the frequency range 7–4000 cm^?1 at room temperature. The spectra obtained are analyzed in terms of the effective medium theory with a size-dependent dielectric response function of nanoinclusions and averaged dielectric characteristics of the surrounding medium. The geometric and dielectric characteristics of silicon nanoinclusions are determined. The dielectric properties of inclusions are found to be affected by nanosize effects, namely, carrier scattering at crystallite boundaries and a broadening of the band gap due to quantum confinement. The spectra of the samples prepared by adding iodine to the electrolyte exhibit a resonance at frequencies of 150–300 cm^?1. The nature of the resonance can be associated with the presence of chemisorbed iodine on the surface of porous silicon. Possible mechanisms responsible for the changes in broadband conductivity and permittivity spectra of single-crystal silicon upon transformation into a nanoporous structure are discussed.     

Activation of cells in a cavitation flow

A cavitation flow in an expanding nozzle is numerically simulated. The cavitation activation of cells is studied experimentally.     

Scattering of a Rayleigh wave by monopole-dipole resonators

The problem of scattering of a Rayleigh wave by a chain of identical closely spaced monopole-dipole resonators with friction is considered. The values of resonator parameters that provide the rejection of the Rayleigh wave are found. The conditions under which the Rayleigh wave is much more efficiently reflected by the dipole resonators than by the monopole ones are determined.     

Change in the magnetic state of a surface upon formation of hydrogen bonds during adsorption

It is established that reversible adsorption of water and methyl alcohol molecules, occurring via formation of hydrogen bonds, changes the dynamic properties of domain walls in the surface region of soft ferromagnets, as well as their initial static magnetic susceptibility. A mechanism is proposed for the effects revealed.     

Light scattering by aggregates of magnetite nanoparticles in a magnetic field

The effect of variation of the scattered light intensity in a magnetic fluid with aggregates of magnetite particles several microns in size under the action of a magnetic field is studied. The effect relaxation times are determined when the magnetic field is turned on and off. This effect is found to be caused by the orientation of anisotropically magnetized aggregates. Experimental data are used to calculate the average anisotropy of the magnetic susceptibility of the aggregate and estimate its magnetic permeability.