Kaplansky conjecture in the theory of quadratic forms

This article considers the splitting properties of finite-dimensional division rings over universal splitting fields of quadratic forms. An example of a field with u-invariant equal to 6 is constructed, which contradicts Kaplansky's conjecture concerning u-invariants.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 75–89, 1989.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.     

Application of rainbow schlieren deflectometry to measure temperature and oxygen concentration in a laminar gas-jet diffusion flame

The quantitative rainbow schlieren deflectometry (RSD) technique was applied to measure temperature and oxygen concentration in an axisymmetric hydrogen gas-jet diffusion flame burning in quiescent air at fuel jet exit Reynolds number of 70. Schlieren measurements were compared with conventional measurements using a thermocouple and a gas-sampling probe. Good agreement between the two measurement techniques was achieved on the fuel-lean side of the flame.     

Velocity measurements in liquid sodium by means of ultrasound Doppler velocimetry

A successful application of ultrasound Doppler velocimetry in liquid sodium flows is described. To obtain sufficient Doppler signals, different problems had to be solved: the transmission of the ultrasonic beam through the channel wall made of stainless steel, the acoustic coupling between the transducer and the channel wall, and the wetting of the inner surface of the wall by the liquid metal, respectively. A sodium flow in a square duct exposed to a transverse magnetic field is investigated. In accordance with the existing knowledge about MHD channel flows, we found that the velocity profiles modified to a M-shape owing to the effect of an inhomogeneous magnetic field. Received: 12 June 2001/Accepted: 27 October 2001     

Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002