Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

Evidence that the major degradation product of glucose-dependent insulinotropic polypeptide, GIP(3-42), is a GIP receptor antagonist in vivo

The incretin hormone glucose-dependent insulinotropic polypeptide (GIP) is rapidly degraded in the circulation by dipeptidyl peptidase IV forming the N-terminally truncated peptide GIP(3-42). The present study examined the biological activity of this abundant circulating fragment peptide to establish its possible role in GIP action. Human GIP and GIP(3-42) were synthesised by Fmoc solid-phase peptide synthesis, purified by HPLC and characterised by electrospray ionisation-mass spectrometry. In GIP receptor-transfected Chinese hamster lung fibroblasts, GIP(3-42) dose dependently inhibited GIP-stimulated (10(-7) M) cAMP production (up to 75.4 +/-5.4%; P

Density-viscosity product of small-volume ionic liquid samples using quartz crystal impedance analysis

Quartz crystal impedance analysis has been developed as a technique to assess whether room-temperature ionic liquids are Newtonian fluids and as a small-volume method for determining the values of their viscosity-density product, rho eta. Changes in the impedance spectrum of a 5-MHz fundamental frequency quartz crystal induced by a water-miscible room-temperature ionic liquid, 1-butyl-3-methylimidazolium. trifluoromethylsulfonate ([C(4)mim][OTf]), were measured. From coupled frequency shift and bandwidth changes as the concentration was varied from 0 to 100% ionic liquid, it was determined that this liquid provided a Newtonian response. A second water-immiscible ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C(4)mim][NTf2], with concentration varied using methanol, was tested and also found to provide a Newtonian response. In both cases, the values of the square root of the viscosity-density product deduced from the small-volume quartz crystal technique were consistent with those measured using a viscometer and density meter. The third harmonic of the crystal was found to provide the closest agreement between the two measurement methods; the pure ionic liquids had the largest difference of similar to 10%. In addition, 18 pure ionic liquids were tested, and for 11 of these, good-quality frequency shift and bandwidth data were obtained; these 12 all had a Newtonian response. The frequency shift of the third harmonic was found to vary linearly with square root of viscosity-density product of the pure ionic liquids up to a value of root(rho eta) approximate to 18 kg m(-2) s(-1/2), but with a slope 10% smaller than that predicted by the Kanazawa and Gordon equation. It is envisaged that the quartz crystal technique could be used in a high-throughput microfluidic system for characterizing ionic liquids.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Small volume laboratory on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids

A microfluidic glass chip system incorporating a quartz crystal microbalance (QCM) to measure the square root of the viscosity-density product of room temperature ionic liquids (RTILs) is presented. The QCM covers a central recess on a glass chip, with a seal formed by tightly clamping from above outside the sensing region. The change in resonant frequency of the QCM allows for the determination of the square root viscosity-density product of RTILs to a limit of similar to 10 kg m(-2) s(-0.5). This method has reduced the sample size needed for characterization from 1.5 ml to only 30 mu l and allows the measurement to be made in an enclosed system.

Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

Normalisers, nest algebras and tensor products

We show that if $\cl A$ is the tensor product of finitely many continuous nest algebras, $\cl B$ is a CDCSL algebra and $\cl A$ and $\cl B$ have the same normaliser semi-group then either $\cl A = \cl B$ or $\cl A^* = \cl B$.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

The advanced glycation end product, Nepsilon-(carboxymethyl)lysine, is a product of both lipid peroxidation and glycoxidation reactions

Nepsilon-(Carboxymethyl)lysine (CML) is an advanced glycation end product formed on protein by combined nonenzymatic glycation and oxidation (glycoxidation) reactions. We now report that CML is also formed during metal-catalyzed oxidation of polyunsaturated fatty acids in the presence of protein. During copper-catalyzed oxidation in vitro, the CML content of low density lipoprotein increased in concert with conjugated dienes but was independent of the presence of the Amadori compound, fructoselysine, on the protein. CML was also formed in a time-dependent manner in RNase incubated under aerobic conditions in phosphate buffer containing arachidonate or linoleate; only trace amounts of CML were formed from oleate. After 6 days of incubation the yield of CML in RNase from arachidonate was approximately 0.7 mmol/mol lysine compared with only 0.03 mmol/mol lysine for protein incubated under the same conditions with glucose. Glyoxal, a known precursor of CML, was also formed during incubation of RNase with arachidonate. These results suggest that lipid peroxidation, as well as glycoxidation, may be an important source of CML in tissue proteins in vivo and that CML may be a general marker of oxidative stress and long term damage to protein in aging, atherosclerosis, and diabetes.