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     

A Study of Evaporation of Complex Oxide Systems Based on Chromium(III) Oxide

Evaporation of chromium ore and concentrates was studied using high-temperature differential mass-spectrometry. The data obtained, concerning the component vapor pressures in evaporation of complex oxide systems in the range 1700-2100 K, can be used to calculate the evaporation loss in melting and to assess the possibility of utilization of the sublimates formed.     

Single-electron charging spectra: from natural to artificial atoms

We present a theoretical study of the charging spectra in natural and artificial atoms. We apply a model electrostatic potential created by a homogenously charged sphere. This model potential allows for a continuous passage from the Coulomb potential of the nucleus to parabolic confinement potential of quantum dots. We consider electron systems with N=1,…,10 electrons with the use of the Hartree–Fock method. We discuss the qualitative similarities and differences between the chemical potential spectrum of electron systems bound to nucleus and confined in quantum dots.     

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.     

Local adsorption sites and bondlength changes in Ni(1 0 0)/H/CO and Ni(1 0 0)/CO

The local adsorption geometry of CO adsorbed in different states on Ni(1 0 0) and on Ni(1 0 0) precovered with atomic hydrogen has been determined by C 1s (and O 1s) scanned-energy mode photoelectron diffraction, using the photoelectron binding energy changes to characterise the different states. The results confirm previous spectroscopic assignments of local atop and bridge sites both with and without coadsorbed hydrogen. The measured Ni–C bondlengths for the Ni(1 0 0)/CO states show an increase of 0.16 ± 0.04 Å in going from atop to bridge sites, while comparison with similar results for Ni(1 1 1)/CO for threefold coordinated adsorption sites show a further lengthening of the bond by 0.05 ± 0.04 Å. These changes in the Ni–CO chemisorption bondlength with bond order (for approximately constant adsorption energy) are consistent with the standard Pauling rules. However, comparison of CO adsorbed in the atop geometry with and without coadsorbed hydrogen shows that the coadsorption increases the Ni–C bondlength by only 0.06 ± 0.04 Å, despite the decrease in adsorption energy of a factor of 2 or more. This result is also reproduced by density functional theory slab calculations. The results of both the experiments and the density functional theory calculations show that CO adsorption onto the Ni(1 0 0)/H surface is accompanied by significant structural modification; the low desorption energy may then be attributed to the energy cost of this restructuring rather than weak local bonding.     

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.     

Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004