Graph Complexes in Deformation Quantization

Kontsevich’s formality theorem and the consequent star-product formula rely on the construction of an L _∞-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley–Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich’s proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich’s star-product is described. Mathematics Subject Classifications (2000): 53D55, secondary 18G55     

A gauge model with confinement in four dimensions

It is shown that the correctly written “1/k⁴” propagator in four space-time dimensions leads to a consistent pertubative expansion of a superrenormalizable (asymptotically free) abelian gauge model. Confinement is found in any order of perturbation theory. A discussion of the physical space is sketched and the violation of asymptotic completeness is pointed out.     

Fine Densities for Excessive Measures and the Revuz Correspondence

Suppose that U is the resolvent of a Borel right process on a Lusin space X. If is a U-excessive measure on X then we show by analytical methods that for every U-excessive measure with the Radon–Nikodym derivative d/d possesses a finely continuous version. (Fitzsimmons and Fitzsimmons and Getoor gave a probabilistic approach for this result.) We extend essentially a technique initiated by Mokobodzki and deepened by Feyel. The result allows us to establish a Revuz type formula involving the fine versions, and to study the Revuz correspondence between the -finite measures charging no set that is both -polar and -negligible (U being the potential component of ) and the strongly supermedian kernels on X. This is an analytic version of a result of Azéma, Fitzsimmons and Dellacherie, Maisonneuve and Meyer, in terms of additive functionals or homogeneous random measures. Finally we give an application to the context of the semi-Dirichlet forms, covering a recent result of Fitzsimmons.     

Stability and robustness properties of a class of discrete–time residual generators

The aim of this paper is to present a design methodology for an observer–based fault detection filter. This approach allows to compute a filter gain such that both fault detection and disturbance attenuation requirements are accomplished. The developments are based on H_∞ optimization in the discrete–time framework. The existence conditions for the observer–based detection filter are expressed in terms of feasibility of a system of matrix inequalities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Excessive kernels and Revuz measures

We consider a proper submarkovian resolvent of kernels on a Lusin measurable space and a given excessive measure ξ. With every quasi bounded excessive function we associate an excessive kernel and the corresponding Revuz measure. Every finite measure charging no ξ–polar set is such a Revuz measure, provided the hypothesis (B) of Hunt holds. Under a weak duality hypothesis, we prove the Revuz formula and characterize the quasi boundedness and the regularity in terms of Revuz measures. We improve results of Azéma [2] and Getoor and Sharpe [20] for the natural additive functionals of a Borel right process. Received: 30 April 1997 / Revised version: 17 September 1999 /?Published online: 11 April 2000     

Self-diffusiophoresis of chemically active colloids

Chemically active colloids locally change the chemical composition of their solvent via catalytic reactions which occur on parts of their surface. They achieve motility by converting the released chemical free energy into mechanical work through various mechanisms, such as phoresis. Here we discuss the theoretical aspects of self-diffusiophoresis, which – despite being one of the simplest motility mechanisms – captures many of the general features characterizing self-phoresis, such as self-generated and maintained hydrodynamic flows “driven” by surface activity induced inhomogeneities in solution. By studying simple examples, which provide physical insight, we highlight the complex phenomenology which can emerge from self-diffusiophoresis.     

Electronic Structure and Magnetic Anisotropy of an Unsaturated Cyclopentadienyl Iron(I) Complex with 15 Valence Electrons

The 15 valence-electron iron(I) complex [Cp^ArFe(IiPr₂Me₂)] ( 1 , Cp^Ar=C₅(C₆H₄-4-Et)₅; IiPr₂Me₂=1,3-diisopropyl-4,5-dimethylimidazolin-2-ylidene) was synthesized in high yield from the Fe^II precursor [Cp^ArFe(μ-Br)]₂. ⁵⁷Fe Mössbauer and EPR spectroscopic data, magnetic measurements, and ab initio ligand-field calculations indicate an S= 3/2 ground state with a large negative zero-field splitting. As a consequence, 1 features magnetic anisotropy with an effective spin-reversal barrier of U_eff=64 cm⁻¹. Moreover, 1 catalyzes the dehydrogenation of N,N-dimethylamine–borane, affording tetramethyl-1,3-diaza-2,4-diboretane under mild conditions.     

Carbon Xerogel Nanostructures with Integrated Bi and Fe Components for Hydrogen Peroxide and Heavy Metal Detection

Multifunctional Bi- and Fe-modified carbon xerogel composites (CXBiFe), with different Fe concentrations, were obtained by a resorcinol–formaldehyde sol–gel method, followed by drying in ambient conditions and pyrolysis treatment. The morphological and structural characterization performed by X-ray diffraction (XRD), Raman spectroscopy, N₂ adsorption/desorption porosimetry, scanning electron microscopy (SEM) and scanning/transmission electron microscopy (STEM) analyses, indicates the formation of carbon-based nanocomposites with integrated Bi and Fe oxide nanoparticles. At higher Fe concentrations, Bi-Fe-O interactions lead to the formation of hybrid nanostructures and off-stoichiometric Bi₂Fe₄O₉ mullite-like structures together with an excess of iron oxide nanoparticles. To examine the effect of the Fe content on the electrochemical performance of the CXBiFe composites, the obtained powders were initially dispersed in a chitosan solution and applied on the surface of glassy carbon electrodes. Then, the multifunctional character of the CXBiFe systems is assessed by involving the obtained modified electrodes for the detection of different analytes, such as biomarkers (hydrogen peroxide) and heavy metal ions (i.e., Pb²⁺). The achieved results indicate a drop in the detection limit for H₂O₂ as Fe content increases. Even though the current results suggest that the surface modifications of the Bi phase with Fe and O impurities lower Pb²⁺ detection efficiencies, Pb²⁺ sensing well below the admitted concentrations for drinkable water is also noticed.     

Phase-difference and spectroscopic imaging for monitoring of human brain temperature during cooling

Decrease of the human brain temperature was induced by intranasal cooling. The main purpose of this study was to compare the two magnetic resonance methods for monitoring brain temperature changes during cooling: phase-difference and magnetic resonance spectroscopic imaging (MRSI) with high spatial resolution. Ten healthy volunteers were measured. Selective brain cooling was performed through nasal cavities using saline-cooled balloon catheters. MRSI was based on a radiofrequency spoiled gradient echo sequence. The spectral information was encoded by incrementing the echo time of the subsequent eight image records. Reconstructed voxel size was 1×1×5 mm³. Relative brain temperature was computed from the positions of water spectral lines. Phase maps were obtained from the first image record of the MRSI sequence. Mild hypothermia was achieved in 15–20 min. Mean brain temperature reduction varied in the interval <−3.0; − 0.6>°C and <−2.7; − 0.7>°C as measured by the MRSI and phase-difference methods, respectively. Very good correlation was found in all locations between the temperatures measured by both techniques except in the frontal lobe. Measurements in the transversal slices were more robust to the movement artifacts than those in the sagittal planes. Good agreement was found between the MRSI and phase-difference techniques.