Variational representations of Varadhan functionals

Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational ``rate function" representation.

     

Positive and negative 3-K-contact structures

The aim of this paper is to give a characterization of 3-K-contact and quasi 3-K-contact manifolds.

     

Epitaxial graphene perfection vs. SiC substrate quality

Polytype instability of SiC epitaxial films was the main focus of attention in the experiment performed since this factor has a decisive influence on graphene growth, which was the second stage of the experiment. Layers deposited in various initial C/Si ratios were analyzed.     

A practical guide for the setup of a 1H-31P-13C double cross-polarization (DCP) experiment

O-phospho-L-threonine is a convenient sample to setup a (1)H-(31)P-(13)C double cross-polarization (DCP) Hartmann-Hahn match. The (1)H-(31)P-(13)C technique is extremely sensitive to the rate of the sample spinning. Both zero-quantum (ZQ) and double-quantum (DQ) cross-polarization operate at an average spinning rate (6-7 kHz). At higher spinning rates (10 kHz), the DQCP mechanism dominates and leads to a reduction of signal intensity, in particular for lower (31)P RF field strength. The application of two shape pulses during the second cross-polarization greatly improves the signal to noise ratio allowing the recording of better quality spectra. (31)P-(13)C spectrally induced filtering in combination with cross-polarization (SPECIFIC-CP) experiments can be carried out under ZQCP and DQCP conditions if careful attention is paid to the choice of RF field amplitudes and carriers Ω. Application of 1D and 2D (1)H-(31)P-(13)C experiments is demonstrated on model samples; disodium ATP hydrate and O-phospho-L-tyrosine.     

A note on total colourings of digraphs

In the paper two different arc-colourings and two associated with the total colourings of digraphs are considered. In one of these colourings we show that the problem of calculating the total chromatic index reduces to that of calculating the chromatic number of the underlying graph. In the other colouring we find the total chromatic indices of complete symmetric digraphs and tournaments.     

Ultrafast experiments on intermolecular electron transfer in the benzene - bromine atom charge transfer complex

Ultrafast pump - probe measurements have been made on the benzene - bromine atom charge transfer (CT) complex in CCl₄ and cyclohexane solutions. Ultrafast optical excitation of the CT band of the complex yields an ion pair, which is comprised of a benzene cation and a bromide anion. The rate of charge recombination between the bromide and the benzene cation in the ion pair has been observed to be much faster than the rate of diffusion apart. The charge recombination rate is accelerated at high benzene concentrations as a result of the formation of a benzene dimer cation - bromide ion pair which undergoes much faster charge recombination than the benzene cation - bromide ion pair.     

Clustered flow shop models

This paper deals with flow-shop models where n items are grouped in fixed sequences, called clusters. The clusters are to be processed on m machines in the same technological order. Each machine handles the clusters in the same order. Each completed item is available for processing on the next machine. The question is how to arrange the clusters to minimize the completion time. Models that include setup times for clusters with identical items are also examined. Approximate solutions along with new lower bounds are presented. Those solutions are optimal for the two machine case.     

A symplectic framework of linear field theories

Summary A framework for linear field theories based on the geometry of Lagrangian subspaces of symplectic spaces is formulated. Fields defined on finite compact domains and infinitesimal limits are treated in terms of de Rham currents. Field sources are included in the formulation. No distinction between elliptic and hyperbolic field equations is made.     

Multilinear forms and measures of dependence between random variables

Based on an idea of Rosenblatt, the methods of interpolation theory are used to establish moment inequalities and equivalence relations for measures of dependence between two or more families of random variables. A couple of “interpolation” theorems proved here appear to be new.