A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Some remarks on the operator of Foias and Williams

In this paper we study the Foias-Williams operator

where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol .

     

Stability of rarefaction waves in viscous media

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, Burgers rarefaction wave, for initial perturbations w ₀ with small mass and localized as w ₀(x)= The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error.This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass (log (t)). These diffusion waves have amplitude (t ^-1/2logt) in linear degenerate transversal fields and (t ^-1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.     

Thermoelectric power of superionic conductors

A technique for the calculation of the thermoelectric power in many-particle systems exhibiting hopping conduction is presented. It is shown that the combination of thermopower and conductivity data provides very useful information about the microscopic nature of the ion hopping process in solid electrolytes. There are two main qualitative features of the transport data. In most systems the heat of transport (determined from the thermopower) and the activation energy for conduction are nearly equal, and in systems exhibiting lattice gas order-disorder transitions, these parameters may change across the phase boundary. An extended polaron lattice gas model is presented which is consistent with these features of the data and which allows a determination of the relative strengths of static barrier and polaron effects on the hopping. The results of the model suggest that polaron coupling is relatively small in most materials except for those based on organic halides.     

N2 activation by iron-sulfur complexes

Inspired by the determination of the structure of the nitrogenase enzyme cofactor by Rees et al., the binding of an N₂ molecule to some model iron-sulfur compounds was investigated usingab initio calculations. Side-on and end-on coordination to one two and four iron centers were investigated. In most cases, the N₂ is loosely bound and retains its internal triple bond, but a few examples are found where the N₂ is “activated” and has a longer N-N bond length.     

Gallium cluster "magic melters"

Calorimetry measurements (using a method based on multicollision induced dissociation) have been performed for unsupported gallium clusters, Gan+ (n = 30-50 and 55). Melting transitions have been identified from spikes in the heat capacities recorded as a function of temperature. There are enormous fluctuations in the melting temperatures and the heats of fusion with cluster size. Clusters with n = 31, 33, 37, and 45-47 are "magic melters" with particularly well-defined melting transitions. There is a strong correlation between the heats of fusion, entropies of fusion, and the stabilities of the clusters. However, these quantities are not strongly correlated with the melting temperatures.     

Simultaneous multichannel mass-specific detection for high-performance liquid chromatography using an array detector sector-field mass spectrometer

The use of a separation step, such as liquid chromatography, prior to inductively coupled plasma mass spectrometry (ICP–MS) has become a common tool for highly selective and sensitive analyses. This type of coupling has several benefits including the ability to perform speciation analysis or to remove isobaric interferences. Several limitations of conventional instruments result from the necessity to scan or pulse the mass spectrometer to obtain a complete mass spectrum. When the instrument is operated in such a non-continuous manner, duty cycle is reduced, resulting in poorer absolute limits of detection. Additionally, with scanning instruments, spectral skew can be introduced into the measurement, limiting quantitation accuracy. To address these shortcomings, a high-performance liquid chromatograph has been coupled to an ICP–MS capable of continuous sample introduction and simultaneous multimass detection. These features have been realized with a novel detector array, the focal plane camera. Instrument performance has been tested for both speciation analysis and for the elimination of isobaric interferences. Absolute limits of detection in the sub picogram to tens of picograms regime are obtainable, while the added mass dimension introduced by simultaneous detection dramatically increases chromatographic peak capacity.     

Free radical-mediated vinyl amination: access to N,N-dialkyl enamines and their beta-stannyl and beta-thio derivatives

[reaction: see text] The first examples of free radical-mediated vinyl amination are described by nonconventional vinyl radical addition to azomethine nitrogen. This new vinyl amination protocol is mild and provides convenient synthetic access to nonstabilized N,N-dialkyl enamines and tandem bond-forming processes.     

Enhanced post-source decay and cross-ring fragmentation of oligosaccharides facilitated by conversion to amino derivatives

Post-source decay (PSD) fragmentation of chemically or enzymatically produced aminoglycans has been evaluated through matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry. Conversion of native glycans to their respective aminoglycan derivatives improved detection sensitivity of the usual fragments and promoted cross-ring fragmentation of linear oligosaccharides, facilitating linkage recognition. The cross-ring fragmentations for both dextrin and dextran oligosaccharides were not limited to the reducing-end glucose moiety, as they were extended throughout the entire molecule. When the amino group was generated for N-glycans derived from three different glycoproteins, an enhancement of PSD was observed, without a significant extent of cross-ring fragmentation.     

New approach to Ru(II) pincer ligand chemistry. Bis(tert-butylaminomethyl)pyridine coordinated to ruthenium(II)

Reaction of 2,6-bis-(tBuNHCH2)2NC5H3 ("N2py") with RuCl2(PPh3)3 gives two isomers of Ru(N2py)Cl2(PPh3), 5, while reaction with RuCl2(DMSO)4 (DMSO = Me2SO) gives isomerically pure Ru(N2py)Cl2(DMSO), whose structure is reported. The PPh3 of 5 can be replaced by CO, P(OPh)3, or pyridine. The chlorides in Ru(N2py)Cl2(CO) can both be replaced by F3CSO3-. Isomer structure preferences are discussed, and the reaction of Ru(N2py)Cl2(pyridine) with O2 gives apparent oxidation of N2py to give the diimine.