Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators

We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators.     

Jacobi matrices with absolutely continuous spectrum

Let be a Jacobi matrix defined in as , where is a unilateral weighted shift with nonzero weights such that Define the seqences: If and , then has an absolutely continuous spectrum covering . Moreover, the asymptotics of the solution is also given.

     

Inverse gas chromatography in the study of polymer degradation. Part 4: A study of model systems for reinforced vulcanizates

Summary Inverse gas chromatography with olefinic stationary phases, impregnated with silica gel or carbon black, and air as carrier gas has been found to yield characteristic shifts of retention data and concomitant changes in peak shape. The plots of retention index versus oxygen flow obtained indicate carbon black to have significant antioxidant properties, which are not altogether lost on solvent extraction. On the other hand, silica gel yields results consistence with the existence of a novel chain scission repair process.     

High pressure transport behaviour of AgI-Ag2O-MoO3 glasses and the cluster model

The effect of pressure on the conductivity of fast ion conducting AgI-Ag₂O-MoO₃ glasses has been investigated down to 150 K. The observed variation of conductivities appears to support the application of cluster model to the ionic glasses. Contribution No. 258 from the Solid State and Structural Chemistry Unit.     

The non-isothermal rheological behaviour of molten polymers: Shear and elongational stress growth of polyisobutylene under heating

Summary Data of stress growth under both shear and elongational kinematics have been taken in presence of heating temperature ramps on a commerical polyisobutylene.The experimental results have been analysed on the basis of a generalized Maxwell model already proved to be very accurate in predicting the isothermal behaviour. A good agreement is observed between the theoretical predictions and the experimental results.Also the features usually observed in volume-temperature curves by effect of cooling acrossT _g are qualitatively reproduced by the model.With 6 figures     

Thermal behaviour of complexes of antipyrine derivatives II

Parent and mixed ligand complexes of cobalt(II) and copper(II) ions with N,N-bis-(4-antipyrylmethyl)piperazine or N,N-tetra(4-antipyryl-methyl)-1,2-diaminoethane or/and imidazole as ligand and ClO ₄ ^– or SCN^– as counterion were synthesised and their thermal behaviour was investigated.This work was performed in the framework of cooperation between the Hungarian Academy of Sciences and Romanian Academy and was supported financially, in part, by the Hungarian Scientific Research Foundation (OTKA T 029554).     

Polyacid gels under a uniaxial load

Swelling and shrinking of polyacid gels is accompanied by forming and breaking of hydrogen bonds yielding additional crosslinks of the polymer network. Continuous forming and breaking of hydrogen bonds even in equilibrium gives rise to viscoelastic behaviour. Based on molecular considerations a two-network model has been developed to describe microstructural changes under a uniaxial load. A phenomenological theory is presented which describes the temporal evolution of viscoelastic processes. By this approach the number of adjustable parameters can be reduced considerably compared to the Kelvin or Maxwell model.Received: 11 November 2002, Accepted: 10 February 2003, Published online: 27 June 2003     

Combustion Behaviour of Nitrocellulose and its Complexes with Copper Oxide. Hot stage microscopic studies

Complexes of nitrocellulose (NC – low and high nitrogen content) with copper oxide (CuO) have been synthesized and studied for morphological behaviour on heating from room temperature to 500°C with the help of hot stage microscopy (HSM). During decomposition, NC:CuO complexes show contraction of fibrous boundaries followed by mass movement of matrix, with the evolution of brown yellow colour gas at higher temperatures as compared to NC alone. This revised version was published online in July 2006 with corrections to the Cover Date.