Monotone norms and tensor products

Various refinements of orthant monotonicity for norms are studied. A partial order is induced in the tensor product of two partially ordered vector spaces. The induced norm in the tensor product is shown to be orthant monotone in certain cases.     

Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

Study of Anderson localization by a continued-fraction method

The electron localization is studied for Anderson's tight-binding model of a disordered two-dimensional square lattice. For a large system of 10⁴ sites the averaged squared modulus $\text{| G}{}_{00}\text{|}{}^2$ of the Green's function is evaluated by a continued-fraction method. From this quantity, following Anderson's criterion, the energy of the mobility edge is found as a function of the degree of disorder. Also the Anderson transition is recognized.     

Optimization of the irradiation power in chemical exchange dependent saturation transfer experiments

In chemical exchange dependent saturation transfer imaging experiments, exchangeable solute protons are saturated and the transfer of saturation to water is subsequently detected. When the applied irradiation power is comparable to the resonance frequency difference between the water protons and saturated solute protons, the proton transfer (PT) efficiency is reduced due to concomitant direct saturation effects. In this study, the PT process is modeled using a two-pool system. An empirical general proton transfer ratio (PTR) equation for arbitrary RF irradiation power is derived, and its optimal power to maximize the PTR is analyzed. The results are confirmed experimentally on 4.7 T using a poly-L-lysine solution. The theory provides a useful tool for optimizing the irradiation power of the PT sequences in the presence of direct saturation effects.     

Molecular dynamics studies of the stability of water/n-heptane interfaces with adsorbed naphthenic acids

The mechanism by which naphthenic acids stabilize water/oil interfaces has received extensive attention because of its industrial relevancy. In this work, we employed a molecular dynamics simulation to study its molecular origin. Two models were adopted, wherein naphthenic acid coverage of water/n-heptane interfaces, both spherical and flat, was hypothesized, respectively. It was found that the coalescence of two water clusters is entirely attributed to the diffusional motion of the components involved which requires the initial departure of the naphthenic acid molecules from the interface so that a water bridge can form. The naphthenic acids not only act as a steric barrier but also reduce the mobility of the water and n-heptane molecules making the formation of the water bridge rather difficult. In fact, our results show that the coalescence of two water clusters fully covered by naphthenic acid molecules is a low-probability event even at evaluated temperatures. In addition, the results from the flat interface models suggest that the emulsion stability is weakly dependent on the molecular weight of the naphthenic acids utilized. Order parameter calculations reveal liquid-crystal-like ordering of naphthenic acids at the water/n-heptane interfaces. All these observations are consistent with the corresponding experimental observations. The present work also suggests that the mobility of naphthenic acids is considerably enhanced with more n-heptane molecules present outside a water droplet. However, in such a case, coalescence could not occur as the water clusters are far apart from each other.     

Oxabicyclo[3.2.1]octane derivatives as highly reactive dienophiles: synthesis of bicyclo[5.n.0] systems

[reaction: see text] We have developed highly versatile, homochiral oxabicyclo[3.2.1]octadiene building blocks for the synthesis of natural products. We have found that these bridged alkenes undergo exceptionally facile Diels-Alder reactions and react faster than several well studied bicyclo[2.2.1]heptene dienophiles. The reaction proceeds with high levels of stereochemical control and in very good to excellent yields, providing access to bicyclo[5.4.0]undecane and bicyclo[5.3.0]decane systems. This reactivity is attributed to strain and homoconjugation effects.     

Lipopeptides incorporated into supported phospholipid monolayers have high specific activity at low incorporation levels

The ability to present cell adhesion molecule (CAM) ligands in controlled amounts on a culture surface would greatly facilitate the control of cell growth and differentiation. Supported lipid monolayer/bilayer systems have previously been developed that allow for presentation of CAM ligands for cell interaction; however, these systems have employed peptide loadings much higher than those used in poly(ethylene glycol) (PEG)-based immobilization systems. We report the development of synthetic methods that can be used for the efficient and versatile creation of many linear and cyclic lipid-linked peptide moieties. Using RGD-based peptides for the alpha5beta1 integrin as a model system, we have demonstrated that these lipopeptides support efficient cell binding and spreading at CAM ligand loadings as low as 0.1 mol %, which is well below that previously reported for supported lipid systems. Engineered lipopeptide-based surfaces offer unique presentation options not possible with other immobilization systems, and the high activity at low loadings we have shown here may be extremely useful in presenting multiple CAM ligands for studying cell growth, differentiation, and signaling.     

The synthesis of symmetrical bis-1,2,5-thiadiazole ligands

We have been engaged in a search for coordination catalysts for the copolymerization of polar monomers (such as vinyl chloride and vinyl acetate) with ethylene. We have been investigating complexes of late transition metals with heterocyclic ligands. In this report we describe the synthesis of a symmetrical bis-thiadiazole. We have characterized one of the intermediates using single crystal X-ray diffraction. Several unsuccessful approaches toward 1 are also described, which shed light on some of the unique chemistry of thiadiazoles.     

Hodge Theory and Geometry

Hodge theory for a smooth algebraic curve includes both theHodge structure (period matrix) on cohomology and the use ofthat Hodge structure to study the geometry of the curve, viathe Jacobian variety. Hodge extended the theory of the periodmatrix to smooth algebraic varieties of any dimension, definingin general a Hodge structure on the cohomology of the variety.He gave a few applications to the geometry of the variety, butthese did not attain the richness of the Jacobian variety. Inrecent years, Hodge theory has been successfully extended toarbitrary varieties, and to families of varieties. In this expositorypaper, some of these developments are reviewed, with specialemphasis on instances where these extensions can be used tostudy the geometry – especially the algebraic cycles –on the variety. 2000 Mathematics Subject Classification 14CDFJ.     

Quantum capping potentials with point charges: a simple QM/MM approach for the calculation of large-molecule NMR shielding tensors

A simple quantum-mechanics/molecular-mechanics (QM/MM) approach for calculating NMR shielding tensors (sigma) is presented. The method involves capping the QM region with quantum capping potentials (QCPs) and representing the MM region with point charges. Test calculations on simple systems without MM charges show that calculated sigma values improve relative to the full QM results with increasing distance between the capped bond and chromophore. Calculations on the histidine amino acid and cytosine monophosphate (CMP) nucleic acid show that the use of QCPs with point charges result in mean errors in the isotropic component of sigma that are less than 1.6 ppm. The results also reveal that, contrary to previous work, the explicit effect of point charges on sigma through coupling with gauge factors, as in the gauge including atomic orbital approach, is minimal for the CMP molecule. The present QM/MM approach for calculating sigma is easy to apply and requires no code modification.