Extending the Kantorovic̆ inequality to normal matrices

Let A be a normal, strictly accretive matrix. The value of min{(Reχ¹A)χ/|χ| |Aχ| : χ≠0} is found, in terms of the spectrum of A. The result is, in the special case of A self-adjoint, a form of the Kantorovic? inequality.     

Matrix-valued shell of an operator or relation

The point spectrum and numerical range of a Hilbert-space operator are subsets of the complex plane. When in place of the operator one puts an arbitrary linear relation, they are naturally replaced by subsets of, respectively, the Riemann sphere and the ball bounded by the Riemann sphere. In this paper, the matrix-valued analogues are studied. The first two sections trace the analogy; in the final two sections it is shown how new phenomena appearing in the matrix version reflect specific singularities of the linear relation.     

Book Reviews

Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications, by Alexander Weinstein and William Stenger. Academic Press, 1971. ($16.00)

Combinatorics, Proceedings of the British Combinatorial Conference 1973, Edited by T.P. McDnough and V.C. Mavron, London Mathematical Society Lecture Note Series 13, Cambridge University Press, London, New York, 1974. 204pp.($9.95)     

Membrane surface dynamics of DNA-threaded nanopores revealed by simultaneous single-molecule optical and ensemble electrical recording

We describe a method for simultaneous single-molecule optical and electrical characterization of membrane-based sensors that contain ion-channel nanopores. The technique is used to study the specific and nonspecific interactions of streptavidin-capped DNA polymers with lipid bilayers composed of diphytanoyl phosphatidylcholine and diphytanoyl phosphatidylglycerol. Biotinylated DNA that is bound to fluorescently labeled streptavidin is electrophoretically driven into, or away from, the lumen of alpha hemolysin (alphaHL) ion channels by an external electric field. Confocal microscopy simultaneously captures single-molecule fluorescence dynamics from the membrane interface at different applied potentials. Fluorescence correlation analysis is used to determine the surface number density and diffusion constant of membrane-associated complexes. The dual optical and electrical approach can detect membrane-associated species at a surface coverage below 10(-5) monolayers of streptavidin, a sensitivity that surpasses most other in vitro surface analysis techniques. By comparing the change in transmembrane current to the number of fluorescent molecules leaving the bilayer when the electrical potential is reversed, we demonstrate the general utility of the approach within the context of nanopore-based sensing and discuss a mechanism by which DNA-streptavidin complexes can be nonspecifically retained at the membrane interface.     

A plasticity model for powder compaction processes incorporating particle deformation and rearrangement

This paper develops a mechanistic model of granular materials that can be used with a commercial finite element package (ABAQUS). The model draws on the ideas of critical state soil mechanics and combines them with the theory of envelopes to develop an elasto-plastic model with a non-associated flow rule. The model incorporates both local deformation at the granule contacts, and rearrangement of the granules so that jointly they account for any bulk deformation. The mechanics of the model closely reflect the physicality of the material behaviour and the model parameters are closely linked (although not simplistically identical) to the characteristics of the granules. This not only gives an insight into the material behaviour, but also enables the model to be used to facilitate design of the material, its processing properties and, hence, component development. The model is used to simulate drained triaxial tests, settlement of a powder in a bin, and some examples of die pressing. Simulations are compared with experimental data and with predictions obtained using other models.     

Effect of solids concentration in dense suspensions of silica-iron(III) oxide and water

The rheological properties of dense suspensions, of silica, iron (III) oxide and water, were studied over a range of solids concentrations using a viscometer, which was modified so as to prevent settling of the solid components. Over the conditions studied, the material behaved according to power—law flow relationships. As the concentrations of silica and iron(III) oxide were increased, an entropy term in the flow equation was identified which had a silica dependent and an iron (III) oxide dependent component. This was attributed to a tendency to order into some form of structural regularity. A, A, B, C pre-exponential functions (K Pa^–n s^–1) - C _ox volume fraction iron (III) oxide - Q activation energy (kJ mol^–1) - R gas constant (kJ mol^–1 K^–1) - R _v silica/water volume ratio - T temperature (K) - n power-law index - H enthalpy (kJ mol^–1) - S entropy change (kJ mol^–1 K^–1) - shear strain rate (s^–1) - shear stress (Pa)     

A Novel Application of Sodium Borohydride for the Regiospecific and Stereoselective Reduction of Conjugated Alkadiynes

Alkynes, when carrying an α-sulfonyl group, are shown to be stereoselectively reduced to z-alkenes using sodium borohydride under mildly basic conditions.     

Molecular explanation for why talc surfaces can be both hydrophilic and hydrophobic

While individual water molecules adsorb strongly on a talc surface (hydrophilic behavior), a droplet of water beads up on the same surface (hydrophobic behavior). To rationalize this dichotomy, we investigated the influence of the microscopic structure of the surface and the strength of adhesive (surface-water) interactions on surface hydrophobicity. We have shown that at low relative humidity, the competition between adhesion and the favorable entropy of being in the vapor phase determines the surface coverage. However, at saturation, it is the competition between adhesion and cohesion (water-water interactions) that determines the surface hydrophobicity. The adhesive interactions in talc are strong enough to overcome the unfavorable entropy, and water adsorbs strongly on talc surfaces. However, they are too weak to overcome the cohesive interactions, and water thus beads up on talc surfaces. Surprisingly, even talc-like surfaces that are highly adhesive do not fully wet at saturation. Instead, a water droplet forms on top of a strongly adsorbed monolayer of water. Our results imply that the interior of hydrophobic zeolites suspended in water may contain adsorbed water molecules at pressures much lower than the intrusion pressure.