On the chromatic number of set systems

An (r, l)‐system is an r‐uniform hypergraph in which every set of l vertices lies in at most one edge. Let m_k(r, l) be the minimum number of edges in an (r, l)‐system that is not k‐colorable. Using probabilistic techniques, we prove that where b_{r, l} is explicitly defined and a_{r, l} is sufficiently small. We also give a different argument proving (for even k) where a′_{r, l}=(r?l+1)/r(2^r?1re)^?l/(l?1). Our results complement earlier results of Erd?s and Lovász [10] who mainly focused on the case l=2, k fixed, and r large. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 87–98, 2001     

Antivarieties and colour-families of graphs

We suggest an algebraic approach to the study of colour-families of graphs. This approach is based on the notion of a congruence of an arbitrary structure. We prove that every colour-family of graphs is a finitely generated universal Horn class and show that for every colour-family the universal theory is decidable. We study the structure of the lattice of colour-families of graphs and the lattice of antivarieties of graphs. We also consider bases of quasi-identities and bases of anti-identities for colour-families and find certain relations between the existence of bases of a special form and problems in graph theory. Received January 19, 1999; accepted in final form October 25, 1999.     

Progress in tire rating based on soil compaction potential

The general trend in soil protection is to reduce the detrimental soil compaction by loaded wheels of power and transport equipment. This paper reports on the progress in research of soil compaction risk assessment by means of Compaction Capacity (CC) tire rating originally introduced as compaction number (CN) rating [Grečenko A. Tire load rating to reduce soil compaction. J Terramech 2003;40:97–115]. The CC rating evaluates soil dry density along a vertical column 20–50 cm below the ground surface. The unique feature of the CC approach is that it converts laboratory compaction measurements directly to soil compaction profiles under evaluated tires without touching the stresses in the ground. The laboratory soil compaction is done with round pressure plate and similarly the tire contact area is represented by a virtual plate loaded by the same mean contact pressure. This paper describes laboratory testing procedures with fundamentals of data conversion and gives examples of CC rating application.     

Temperature dependence of charge transferred by dislocation in Kcl: Ba crystals

Abstract

The electrical charge assosiated with dislocation motion in KCl:Ba has been studied within the interval from 77 to 292K using on indentation method. The comparison of the potential difference values at 77 and 292K was performed on condition that the impression diagonals were roughly equal. The kinetics of the potential change was studied.     

Synthesis and conformational properties of substituted 1,4,2-oxazasilinanes: low temperature NMR study and quantum chemical calculations

A number of N-substituted 2,2-dimethyl-1,4,2-oxazasilinanes 1 were synthesized and studied by variable temperature dynamic ¹H and ¹³C NMR spectroscopy, room temperature ¹⁵N NMR spectroscopy and theoretical calculations at the DFT and MP2 levels of theory. Both the preferred conformers were assigned and the barrier to the ring inversion of the saturated six-membered ring determined. From 1 the corresponding methyl iodide salts were produced, their structure studied by X-ray analysis and found to be in excellent agreement with the results of the theoretical calculations.     

On Fourier–Haar coefficients of the function from the Marcinkiewicz space

The main objective of the paper is to describe asymptotic behaviour of Fourier–Haar coefficients of functions from Marcinkiewicz spaces. We also discuss the Cesàro summability and the almost convergence of sequences related to Fourier–Haar coefficients and generalise a result from [17]. Some analogues of Mercer's theorem for Fourier coefficients are proved.