Natural Representations of the Multiplicity of an Analytic Operator-valued Function at an Isolated Point of the Spectrum

Representations are given for the multiplicity of an analytic operator-valued function A at an isolated point z₀ of the spectrum in the form of kernels and ranges of Hankel and Toeplitz matrices whose entries are derived from the Taylor coefficients of A and the Laurent coefficients of A⁻¹ about z₀. In two special cases the results can be expressed in terms of finite matrices: when A is a polynomial and when A⁻¹ has a pole at z₀. The latter case leads to the theory of Jordan chains.     

Lipopolysaccharide removal by a peptide-functionalized surface

Five peptides: BPI(85-109); CAP18(106-137); endotoxin inhibitor (EI); GQ33 and GQ33C, derived from lipopolysaccharide (LPS)-binding molecules were investigated for LPS-binding ability with a view to a potential use in extracorporeal therapy. The surface plasmon resonance technique (SPR) was used to monitor the interaction between LPS in solution and the surface-immobilized peptides. The peptides were covalently bound to a model dextran surface via inherent amino groups or via terminally introduced cysteine residues. The results showed that the binding efficacy and binding stability of the peptides varied greatly. The CAP18(106-137) peptide, which exhibited the highest binding efficacy and binding stability, was also immobilized on a poly(ethylene imine)-poly(ethylene glycol) (PEI-PEG) surface through maleimide-terminal PEG. The binding efficacy of the CAP18(106-137) peptide was not significantly affected by the different immobilization methods used in the attachment to a dextran or a PEI-PEG surface. LPS bound selectively to CAP18(106-137) and showed very low unspecific binding to the PEI-PEG surface layer. The EI peptide proved to have a reasonably good binding capacity but a less stable interaction with LPS. The other peptides exhibited much poorer binding efficacy. We believe that the results presented in this work can be of practical value for the development of extracorporeal treatment of patients suffering from septic shock.     

Neuroscience and accelerator mass spectrometry

Accelerator mass spectrometry (AMS) is a mass spectrometric method for quantifying rare isotopes. It has had a great impact in geochronology and archaeology and is now being applied in biomedicine. AMS measures radioisotopes such as 3H, 14C, 26Al, 36Cl and 41Ca, with zepto- or attomole sensitivity and high precision and throughput, allowing safe human pharmacokinetic studies involving microgram doses, agents having low bioavailability or toxicology studies where administered doses must be kept low (<1 microg kg(-1)). It is used to study long-term pharmacokinetics, to identify biomolecular interactions, to determine chronic and low-dose effects or molecular targets of neurotoxic substances, to quantify transport across the blood-brain barrier and to resolve molecular turnover rates in the human brain on the time-scale of decades. We review here how AMS is applied in neurotoxicology and neuroscience.     

Ghost fields in classical gauge theories

It is shown that ghost fields, characterized as unphysical entities, are a valuable tool in finding numerical solutions of the Euler-Lagrange equations of gauge field theories.     

Beta-depsipeptides--the effect of a missing and a weakened hydrogen bond on the stability of the beta-peptidic 3(14)-helix

The importance of hydrogen bonding in beta-peptide 3(14)-helices is demonstrated by an NMR analysis of three beta-heptadepsipeptides containing a 3-hydroxybutanoic residue in position 2, 4 or 6.     

Probability density functions for hyperbolic and isodiachronic locations

Animal locations are sometimes estimated with hyperbolic techniques by estimating the difference in distances of their sounds between pairs of receivers. Each pair specifies the animal's location to a hyperboloid because the speed of sound is assumed to be spatially homogeneous. Sufficient numbers of intersecting hyperboloids specify the location. A nonlinear method is developed for computing probability density functions for location. The method incorporates a priori probability density functions for the receiver locations, the speed of sound, winds, and the errors in the differences in travel time. The traditional linear approximation method overestimates bounds for probability density functions by one or two orders of magnitude compared with the more accurate nonlinear method. The nonlinear method incorporates a generalization of hyperbolic methods because the average speed of sound is allowed to vary between different receivers and the source. The resulting "isodiachronic" surface is the locus of points on which the difference in travel time is constant. Isodiachronic locations yield correct location errors in situations where hyperbolic methods yield incorrect results, particularly when the speed of propagation varies significantly between a source and different receivers.     

Pressure-induced colossal magnetocaloric effect in MnAs

To present day, the maximum magnetocaloric effect (MCE) at room temperature for a magnetic field change of 5 T is 40 J/(kg K) for MnAs. In this Letter we present colossal MCE measurements on MnAs under pressure, reaching values up to 267 J/(kg K), far greater than the magnetic limit arising from the assumption of magnetic field independence of the lattice and electronic entropy contributions. The origin of the effect is the contribution to the entropy variation coming from the lattice through the magnetoelastic coupling.