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.     

X-ray structures and homolysis of some alkylcobalt(III) phthalocyanine complexes

The first crystallographic data for sigma-bonded alkylcobalt(III) phthalocyanine complexes are reported. A single-crystal X-ray structure of CH(3)CH(2)Co(III)Pc (Pc = dianion of phthalocyanine) reveals that the solid consists of centrosymmetric face-to-face dimers in which the CH(3)CH(2)Co(III)Pc units retain their square pyramidal geometry. The structure appears to be the first one reported for a five-coordinate RCo(III)(chelate) complex with an electron-deficient equatorial system. The Co-C bond in CH(3)CH(2)Co(III)Pc (2.031(5) A) is the longest found in five-coordinate RCo(III)(chel) complexes (R = simple primary alkyl group). Another X-ray study demonstrates that CH(3)Co(III)Pc(py) has a distorted octahedral geometry with axial bonds of very similar length to those in methylcobalamin. The axial bonds are shorter than those in its octaethylporphyrin analogue, in accordance with a weaker trans axial influence in six-coordinate complexes containing an electron-deficient phthalocyanine equatorial ligand. A different trend has been observed for five-coordinate RCo(III)(chel) complexes: electron-rich equatorial systems seem to make the Co-C axial bond shorter. Kinetic data for the homolysis of RCo(III)Pc complexes (R = Me, Et) in dimethylacetamide are also reported. Homolysis of ethyl derivatives is faster. The Co-C bond dissociation energies (BDEs) for the pyridine adducts of the methyl and the ethyl derivative are 30 +/- 1 and 29 +/- 1 kcal/mol, respectively. The BDE for CH(3)CoPc(py) is considerably lower than that for MeCbl despite the very similar lengths of the axial bonds in the two complexes. The results of this work do not support any correlation between the Co-C bond length and the bond strength as defined by BDE.     

Strong mixing coefficients for non-commutative Gaussian processes

Bounds for non-commutative versions of two classical strong mixing coefficients for -Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a -mixing -Gaussian stationary sequence with growth conditions on variances of partial sums. If classical processes with analogous properties were to exist, they would provide a counter-example to the Ibragimov conjecture.

     

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.

     

Immobilization and electrochemical redox behavior of cytochrome c on fullerene film-modified electrodes

Two different fullerene film-modified electrodes were prepared and used for surface immobilization and electrochemical property investigation of horse heart cytochrome c (cyt c). Both a pristine fullerene film and fullerene-palladium (C(60)-Pd) polymer film-modified platinum, glassy carbon and indium-tin-oxide (ITO) electrodes were used. The immobilized cyt c was characterized by piezoelectric microgravimetry at a quartz crystal microbalance (QCM), UV-visible absorption, and X-ray photoelectron spectroscopy (XPS), as well as cyclic voltammetry (CV) techniques. The UV-visible spectral studies revealed a small blue shift of both the Soret and Q band of the heme moiety of cyt c, immobilized on the C(60)-Pd polymer film-modified ITO electrode, as compared to the bands of cyt c in solution suggesting that molecules of cyt c are densely packed onto the surface of the modified electrode. The CV studies revealed a quasi-reversible electrode behavior of the heme moiety indicating the occurrence of kinetically hindered electron transfer. A good agreement was found between the values of cyt c electrode surface coverage determined by piezoelectric microgravimetry and cyclic voltammetry. For piezoelectric microgravimetry, these values ranged from 0.5 x 10(-10) to 2.5 x 10(-10) mol cm(-2), depending upon the amount of cyt c present in solution and the time allowed for immobilization, which compared with a value of 3.6+/-0.4 x 10(-10) mol cm(-2) determined by CV. The possible mechanisms of cyt c immobilization on the C(60) film and C(60)-Pd film-modified electrodes are also discussed.     

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.     

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 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.