On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

Level-spacing distributions and the Airy kernel

Scaling level-spacing distribution functions in the bulk of the spectrum in random matrix models ofN×N hermitian matrices and then going to the limitN leads to the Fredholm determinant of thesine kernel sin(x–y)/(x–y). Similarly a scaling limit at the edge of the spectrum leads to theAiry kernel [Ai(x)Ai(y)–Ai(x)Ai(y)]/(x–y). In this paper we derive analogues for this Airy kernel of the following properties of the sine kernel: the completely integrable system of P.D.E.'s found by Jimbo, Miwa, Môri, and Sato; the expression, in the case of a single interval, of the Fredholm determinant in terms of a Painlevé transcendent; the existence of a commuting differential operator; and the fact that this operator can be used in the derivation of asymptotics, for generaln, of the probability that an interval contains preciselyn eigenvalues.     

On orthogonal and symplectic matrix ensembles

The focus of this paper is on the probability,E (O;J), that a setJ consisting of a finite union of intervals contains no eigenvalues for the finiteN Gaussian Orthogonal (=1) and Gaussian Symplectic (=4) Ensembles and their respective scaling limits both in the bulk and at the edge of the spectrum. We show how these probabilities can be expressed in terms of quantities arising in the corresponding unitary (=2) ensembles. Our most explicit new results concern the distribution of the largest eigenvalue in each of these ensembles. In the edge scaling limit we show that these largest eigenvalue distributions are given in terms of a particular Painlevé II function.     

Quantum-chaotic scattering effects in semiconductor microstructures

We show that classical chaotic scattering has experimentally measurable consequences for the quantum conductance of semiconductor microstructures. These include the existence of conductance fluctuations-a sensitivity of the conductance to either Fermi energy or magnetic field-and weak-localization-a change in the average conductance upon applying a magnetic field. We develop a semiclassical theory and present numerical results for these two effects in which we model the microstructures by billiards attached to leads. We find that the difference between chaotic and regular classical scattering produces a qualitative difference in the fluctuation spectrum and weak-localization lineshape of chaotic and nonchaotic structures. While the semiclassical theory within the diagonal approximation accounts well for the weak-localization lineshape and for the spectrum of the fluctuations, we uncover a surprising failure of the semiclassical diagonal-approximation theory in describing the magnitude of these quantum transport effects.     

Relativistic effective potential SCF calculations of AgH and AuH

Relativistic effective potentials (REP) are now widely used in molecular electronic structure calculations. Tests of these REP are needed to assess their accuracy. This can now be done for AgH and AuH since Lee and McLean have published Dirac-Fock calculations for these molecules. Comparative SCF calculations have been performed for two types of effective potential. Satisfactory agreement between the effective potential results and Dirac-Fock values is found for spectroscopic constants and dipole moments, which supports the use of these potentials for heavy atom containing molecules.     

Adduct formation in electrospray ionization mass spectrometry II. Benzoic acid derivatives

This work serves as a follow-up to Part I of experiments designed to determine the underlying principles in the formation of pseudomolecular, or adduct, ions during electrospray ionization. Aromatic acids were studied by flow injection analysis in the negative ionization mode of electrospray ionization mass spectrometry. Part I dealt with common acidic anti-inflammatory pharmaceuticals. such as ibuprofen and related analogues. Part II deals with functionally less complex molecules, namely benzoic acid (BA) and substituted benzoic acids. Halide-substituted molecules are investigated to deduce the effect of electron-withdrawing substituents (bromo-, chloro-, and fluoro-) and ring position (ortho-, meta- and para-) on the response of a traditional deprotonated molecular ion ([M-H]-) and a sodium-bridged dimer ion ([2M-2 H+Na]-). Amino-substituted benzoic acids are also analyzed in order to study the effect of an additional ionizable group on the molecule, and para-tert.-butyl-BA is analyzed to study the effect of increased hydrophobicity, as they relate to the formation of pseudomolecular ions. This study shows that solution character [octanol-water partition coefficient (or log P) and pKa] of the model compounds controls the relative efficiency of formation of [M-H]- and [2M-2H+Na]- ions. However the relative gas phase character (gas phase basicity and proton affinity) also has a significant effect on the formation of the sodium-bridged dimer ion. For the halide-substituted species, placement of the electron-withdrawing atom at the meta-position gives the greatest enhancement in sensitivity. Observations also show that as the structural complexity of the model compound increases, predictions relating analyte acidity to sodium-bridged dimer ion formation give way to a stronger dependence between log P values and ionization efficiency. Supporting this hypothesis is the nearly ten-fold enhancement in signal for tert.-butyl BA relative to BA. due to the greater hydrophobicity, and consequently, increased surface activity in an electrosprayed droplet of the analyte molecule.     

Nonpeptide inhibitors of cathepsin G: optimization of a novel beta-ketophosphonic acid lead by structure-based drug design

The serine protease cathepsin G (EC 3.4.21.20; Cat G), which is stored in the azurophilic granules of neutrophils (polymorphonuclear leukocytes) and released on degranulation, has been implicated in various pathological conditions associated with inflammation. By employing high-throughput screening, we identified beta-ketophosphonic acid 1 as a moderate inhibitor of Cat G (IC(50) = 4.1 microM). We were fortunate to obtain a cocrystal of 1 with Cat G and solve its structure by X-ray crystallography (3.5 A). Structural details from the X-ray analysis of 1.Cat G served as a platform for optimization of this lead compound by structure-based drug design. With the aid of molecular modeling, substituents were attached to the 3-position of the 2-naphthyl ring of 1, which occupies the S1 pocket of Cat G, to provide an extension into the hydrophobic S3 region. Thus, we arrived at analogue 7 with an 80-fold potency improvement over 1 (IC(50) = 53 nM). From these results, it is evident that the beta-ketophosphonic acid unit can form the basis for a novel class of serine protease inhibitors.     

Pharmacokinetics of the nitroxide PCA measured by in vivo EPR

PCA (2,2,5,5-tetramethylpiperidine-1-oxyl-3-carboxylic acid) is a relatively stable free radical which has been shown to be useful as a contrast agent for nuclear magnetic resonance imaging and as an imaging/spectroscopy agent for EPR. In an effort to determine the role of the liver and kidney in the pharmacokinetics of PCA, using low frequency in vivo EPR spectroscopy, we followed the clearance of PCA after intravenous injection in mice: under normal conditions, with a restricted blood supply to the kidneys, after exposure to an acute hepatotoxin CCl₄, and after exposure to lipopolysaccharide (endotoxin). The observed pharmacokinetics fit a two-component model. The fast component was dramatically affected when the renal vessels were restricted, while CCl₄ and endotoxin had a smaller but significant effect. The half times of the slow components were not significantly different (p>0.05) in the groups treated by renal blood flow occlusion, CCl₄, or LPS, compared with the control group. In conclusion, we find that the pharmacokinetics of PCA need to be completely described in term of a two component model: the fast component of the decay is mainly due to the elimination by the kidneys and also is affected by the time for the initial distribution; the slow component is related to the bioreduction of the nitroxide. In addition to the liver other tissues can also effectively metabolize PCA. The effect of oxygen on the rate of metabolism is modest at most.