Logarithmic Sobolev trace inequality

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.

     

A microspectroscopic study of the electronic homogeneity of ordered and disordered Sr2FeMoO6

Disordered Sr₂FeMoO₆ shows a drastic reduction in saturation magnetization compared to highly ordered samples, moreover magnetization as a function of the temperature for different disordered samples shows qualitatively different behaviours. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that e_xtensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples, is responsible for the observed magnetic inhomogeneity. It is further pointed out that these inhomogeneities are connected with composition fluctuations of the type Sr₂Fe_1+x Mo_1-x O₆ with Fe-rich (x > 0) and Mo-rich (x < 0) regions. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

Positive Schatten(-Herz) Class Toeplitz Operators on the Half-space

On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided to show that various results are sharp. This research was supported by KOSEF(R01-2003-000-10243-0).     

THE FIRST EXPERIMENT OF A THz GYROTRON WITH A PULSE MAGNET

A THz gyrotron with a pulse magnet has been designed, constructed and operated in FIR FU. It is developed as one of high frequency gyrotrons included in Gyrotron FU Series. The gyrotron has already achieved the first experimental result for high frequency operations whose radiation frequency exceeds 1 THz. In this paper, the design detail and the operation test results for sub-terahertz to terahertz range are described. The second harmonic operation is confirmed experimentally at the expected frequency of 1.005 THz due to TE_6,11 cavity mode at the magnetic field intensity of 19.0 T.     

Nusselt number correlations for heat transfer to small spheres in thermal plasma flows

Seven different equations predicting heat transfer rates to small spheres in plasma flows are examined considering argon and nitrogan as plasma gases from 300 to 21,000 K at 1 atm. For argon there is a general consensus up to 9000 K, beyond which wide deviations in behavior occur. For nitrogen, the seven correlations are in good agreement up to 4000 K, but show substantial deviations beyond this value. Comparisons with the sparsely available experimental data are made for argon from 300 to 17,000 K and for nitrogen up to 5500 K. Disagreement between the various correlations and experiment can exceed one order of magnitude.     

INFLUENCE OF MAGNETIC FIELD INHOMOGENEITY ON OPERATION OF THE THz GYROTRON WITH A PULSE MAGNET

Influence of magnetic field tapering on operation of a gyrotron working in the TE _4,12 mode at the second harmonic frequency 1013.67 GHz is investigated. It is found that the existing inhomogeneity of the magnetic field of the order of 0.25%–0.50% in the cavity allows one to achieve higher efficiencies. It improves also mode competition scenario by suppressing oscillations of the two parasitic TE _3,6⁺ and TE _5,5⁻ modes at the fundamental frequencies 513.35 GHz and 503.64 GHz, respectively.