Maximizing Free Entropy

Maximization problems are solved for Voiculescu's free entropy of probability measures supported in R, R+, and [-1, 1], respectively, under constraint of the pth moment for any p > 0 and implications of these results for multivariate free entropy are discussed in the setting of noncommutative random variables. Similar extremum problems are treated for probability measures on C and Tunder certain constraints. The elliptic law and a distribution found earlier in quantum physics are encountered. These results are in the setting of potential theory and can be viewed independently from Voiculescu's work. The machinery of weighted potentials is exploited.     

Spectral Based Estimation of Optical Path Difference of Interference Colors

A spectral intensity distribution of interference colors which is a function of optical path difference (OPD) is represented as a pattern vector on a subspace. A new algorithm to design a color scale on the subspace to estimate OPD values is proposed. In experiments, interference colors generated by a differential interference microscope (DIM) were examined. A subspace spanned by four orthogonal bases was constructed to make a color scale to determine OPD values in the range between 0 nm and 1000 nm. Estimated OPD values almost coincided with these expected. In an experiment on two-dimensional interference colors obtained by a spherical surface of a ballbearing observed by DIM, the resultant OPD distribution coincided well with that expected within a standard deviation of 12.8 nm.     

McMillan type convergence for quantum Gibbs states

Partially supported by the Hungarian National Foundation of Scientific Research, grant No. 1900.     

Molecular structures and hypochromism of two purinophanes

The structures of purinophane 1 and its higher homolog 2 were determined by X-ray crystallographic analysis. Hypochroism of 1 and 2 in various media reported.     

Synthesis of visible-light reactive TiO2−xNy photocatalyst by mechanochemical doping

Yellowish TiO_2−xN_y was prepared by a novel mechanochemical nitrogen-doping method. The samples were prepared by a high-energy ball milling of P25 titania with different nitrogen sources such as hexamethylenetetramine, urea or ammonium carbonate, followed by calcination in air at 400 °C. The high mechanical energy accelerated the phase transformation of anatase to rutile, while the existence of the nitrogen reagents tended to block the transformation. The calcination treatment slightly increased the crystallinity of the prepared titania. The prepared powders possessed two absorption edges at around 400 and 540 nm and showed an excellent photocatalytic ability for the oxidation of nitrogen monoxide under visible light irradiation. Under the irradiation of visible light with wavelengths of >510 nm, nitrogen monoxide could be continuously removed by the nitrogen doped titania prepared from the P25 titania-hexamethylenetetramine mixture, while the powders prepared using urea and ammonium carbonate as nitrogen sources showed lower activities. This mechanochemical technique might be widely useful for doping oxides with nonmetallic elements.     

Maximal subbundles of vector bundles on a curve

For a rank 2 vector bundle E on a non-singular projective curve of genus g, the theorem of Nagata tells us that deg E-2 max deg Fg where the maximum is taken over all sub line bundles F of E. We generalize this result to vector bundles of arbitrary rank.     

A novel synthesis of 8-arylaminotheophyllines

A novel synthesis of 8-arylaminotheophyllines ( 8a-e ) by the reaction of 5-arylazo-6-ethoxy-methyleneamino-1,3-dimethyluracils ( 2a-e ) or 5-arylazo-1,3-dimethyl-6-dimethylaminomethylene-aminouracils ( 3a-e ) with sodium dithionite in formic acid is described.     

A new synthesis of fervenulin 4-oxide

The reaction of 1,3-dimethyl-6-hydrazino-5-nitrosouracil (1) with Vilsmeier reagent (dimethylformamide-phosphorus oxychloride) afforded fervenulin 4-oxide (II) in good yield.