The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

Twisted K-theory and finite-dimensional approximation

We provide a finite-dimensional model of the twisted K-group twisted by any degree three integral cohomology class of a CW complex. One key to the model is Furuta's generalized vector bundle, and the other is a finite-dimensional approximation of Fredholm operators.Comment: 26 pages, LaTeX 2e, Xypic; main theorem improve

Inclusion of [H3PW12O40] and [H4SiW12O40] into a silica gel matrix via "sol-gel" methodology

Indexación: Web of Science; Scopus.Here we report the inclusion of two Keggin Polyoxometalates (POMs), [H3PW12O40] and [H4SiW12O40], into silica gels by integrating them during the preparation of the SiO2 matrix via "sol-gel" methods. Aerogels were produced by supercritical drying of the wet gels impregnated with the POMs, and lyogels were obtained by means of a lyophilization process. These materials were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier transformed infrared (FT-IR) spectroscopy and thermoanalytical techniques (TGA-DSC). We found that a large fraction of POMs are lost during the aging time, and solvent exchange for lyophilization. However the thermal stability of the bare matrix is modified by the inclusion of POMs. Some aggregates with a high content of POMs were found via SEM-EDX.http://ref.scielo.org/3fg9t

Twisted K-theory and K-theory of bundle gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on twisted Chern character in non-torsion cas

A 100 pc Elliptical and Twisted Ring of Cold and Dense Molecular Clouds Revealed by Herschel Around the Galactic Center

Thermal images of cold dust in the Central Molecular Zone of the Milky Way, obtained with the far-infrared cameras on board the Herschel satellite, reveal a ~3 × 10^7 M_☉ ring of dense and cold clouds orbiting the Galactic center. Using a simple toy model, an elliptical shape having semi-major axes of 100 and 60 pc is deduced. The major axis of this 100 pc ring is inclined by about 40° with respect to the plane of the sky and is oriented perpendicular to the major axes of the Galactic Bar. The 100 pc ring appears to trace the system of stable x_2 orbits predicted for the barred Galactic potential. Sgr A⋆ is displaced with respect to the geometrical center of symmetry of the ring. The ring is twisted and its morphology suggests a flattening ratio of 2 for the Galactic potential, which is in good agreement with the bulge flattening ratio derived from the 2MASS data

Thermal Effects on the Magnetic Field Dependence of Spin Transfer Induced Magnetization Reversal

We have developed a self-aligned, high-yield process to fabricate CPP (current perpendicular to the plane) magnetic sensors of sub 100 nm dimensions. A pinned synthetic antiferromagnet (SAF) is used as the reference layer which minimizes dipole coupling to the free layer and field induced rotation of the reference layer. We find that the critical currents for spin transfer induced magnetization reversal of the free layer vary dramatically with relatively small changes the in-plane magnetic field, in contrast to theoretical predictions based on stability analysis of the Gilbert equations of magnetization dynamics including Slonczewski-type spin-torque terms. The discrepancy is believed due to thermal fluctuations over the time scale of the measurements. Once thermal fluctuations are taken into account, we find good quantitative agreement between our experimental results and numerical simulations.Comment: 14 pages, 4 figures, Submitted to Appl. Phys. Lett., Comparison of some of these results with a model described by N. Smith in cond-mat/040648

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page