Marking Games and the Oriented Game Chromatic Number of Partial <Emphasis Type="Italic">k</Emphasis>-Trees

 Nešetřil and Sopena introduced the concept of oriented game chromatic number. They asked whether the oriented game chromatic number of partial k-trees was bounded. Here we answer their question positively. Received: January 12, 2001 Final version received: February 25, 2002     

Influence of the sample orientation in Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals on the hydrostatic piezoelectric coefficients

The influence of the sample orientation on the effective value of the hydrostatic piezoelectric coefficients d _h ⁽ⁱ⁾ of Sn₂P₂S₆ crystals has been studied. The hydrostatic piezoelectric coefficients d _h ⁽¹⁾ and d′ _h ⁽³⁾ , were measured, d _h ⁽¹⁾ =(244±3) pC/N and d′ _h ⁽³⁾ =(92±1) pC/N. The hydrostatic piezoelectric coefficient d _h ⁽³⁾ for orthogonal axis system was calculated to be d _h ⁽³⁾ =(87±2) pC/N. The, optimal orientation of the sample has been found as (Xy l)−20°-cut. Maximal value of the effective hydrostatic piezoelectric coefficient d _h ⁽¹⁾ equals 260 pC/N. Double rotated samples were also studied. The orientation of the samples insensitive to the pressure has been found. The theoretical mean value of hydrostatic piezoelectric coefficient (d _h ) _mean corresponding to randomly oriented Sn₂P₂S₆ grains in a poled composite has been calculated to be (d _h ) _mean =136 pC/N.     

Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities

In the ultrasonic diagnostics of small-size neoplasms of biological tissues at the earliest stage of their development, an efficient way to eliminate the distorting influence of high-contrast or large inhomogeneities of the biological medium is to apply the iterative technique. A simple approach is proposed, which makes it possible with only two iteration steps to achieve an efficient focusing of the tomograph array. At the first step, the unknown distribution of the large-scale inhomogeneities of sound velocity and absorption over the scatterer is reconstructed, where the large-scale inhomogeneities are those whose size exceeds several wavelengths. At the second step, the fine structure of the scatterer is reconstructed against the large-scale background, which can be performed with a high accuracy owing to the evaluation of the background at the first step. The possibility of simultaneous reconstruction of the large-scale and fine structures by the noniterative Grinevich-Novikov algorithm is considered as an alternative. This algorithm reconstructs in an explicit form two-dimensional refractive-absorbing acoustic scatterers of almost arbitrary shape and strength. Taking into account the effects of multiple scattering, this algorithm provides resolution of the fine structure almost as good as that achieved in reconstructing the same structure against an undistorting homogeneous background. The results of numerical simulations of both algorithms are presented.     

Homology of Lagrangian submanifolds in cotangent bundles

In this paper we find homological restrictions on Lagrangians in cotangent bundles of spheres and Lens spaces. This research was supported by the Israel Science Foundation (grand No. 205/02).     

Femtochemistry of Guest Molecules Hosted in Colloidal Zeolites

The ultrafast deprotonation of 2‐(2′‐hydroxyphenyl)benzothiazole (HBT) hosted in nanometer‐sized FAU and MFI zeolites is reported. Samples are prepared via in‐situ incorporation of HBT in the precursor colloidal solutions resulting in the formation of nanometer‐sized zeolites under hydrothermal treatment. The diameter of the zeolite particles formed in the crystalline suspensions is determined by dynamic light scattering and high‐resolution transmission microscopy to lie in the range 40–100 nm. It is shown that the HBT loading does not influence the degree of the zeolite crystallinity but does change the size and the morphology of the individual zeolite nanoparticles. Colloidal suspensions containing the crystalline nanoparticles are well suited for optical investigations since they are sufficiently transparent and clear. The photochemical properties of the HBT guest in the zeolite‐host systems are studied with femtosecond transient transmission spectroscopy. Depending on the acid–base properties either the enol or the keto tautomer of HBT is found to be hosted in the internal voids of the zeolites; upon UV excitation, the HBT‐keto tautomer is converted to the enol form in both MFI‐ and FAU‐type hosts. The HBT photoconversion takes place via an ultrafast deprotonation within 1.5 ps as detected by femtosecond transient absorption spectroscopy.     

Gaussian Chaos Laws on Banach Function Spaces

We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ _∞ ⁿ 's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces. __________ Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005.     

Polarization losses in reflector antennas

Various definitions for polarization-loss efficiency of Cassegrainian and front-fed reflectors are compared. The effects of flare angle, feed taper and the feed pattern asymmetry on the polarization-loss efficiency are investigated. The definitions based on aperture fields are shown to be inadequate and far fields must be used for calculating the polarization losses.