On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.     

Approximation du temps local des surfaces gaussiennes

Summary LetX be a centered stationary Gaussian stochastic process with ad-dimensional parameter (d2),F its spectral measure, (x denotes the Euclidean norm ofx). We consider regularizations of the trajectories ofX by means of convolutions of the formX (t)=( *X)(t) where stands for an approximation of unity (as tends to zero) satisfying certain regularity conditions.The aim of this paper is to recover the local time ofX at a given levelu, as a limit of appropriate normalizations of the geometric measure of theu-level set of the regular approximating processesX . A part of the difficulties comes from the fact that the geometric behavior of the covariance of the Gaussian processX can be a complex one as approaches O.The results are onL ²-convergence and include bounds for the speed of convergence.L ^presults may be obtained in similar ways, but almost sure convergence or simultaneous convergence for the various values ofu do not seem to follow from our methods. In Sect. 3 we have included examples showing a diversity of geometric behaviors, especially in what concerns the dependence on the thickness of the set in which the covariance of the original processX is irregular.Some technical results of analytic nature are included as appendices in Sect. 4.     

An in vitro investigation of human enamel wear by restorative dental materials

A radiometric method was applied to assess enamel wear by another enameland by restorative materials. The radioactive enamel was submitted to wearin a machine which allows sliding motion of an antagonistic surface in contactwith the radioactive enamel. The enamel wear was evaluated by measuring thebeta-activity of ³²P transferred to water from this irradiatedtooth. Results obtained indicated that dental porcelains cause pronouncedenamel wear when compared with that provoked by another natural enamel orby resin materials. Resin materials caused less enamel wear than another naturalenamel. Vickers microhardness data obtained for antagonistic materials showeda correlation with the wear caused to the enamel.     

Construction of functional porphyrin polystyrene nano-architectures by ATRP

A series of mono-functionalized metallo-porphyrin polystyrenes have been synthesized using atom transfer radical polymerization and their self-assembling behavior was studied by electron microscopy showing that the polystyrene tail-length influences the aggregate architecture.     

Spectroelectrochemical characterisation of poly[Ni(saltMe)]-modified electrodes

Electrogenerated polymers based on the nickel(II) complex 2,3-dimethyl-N,N'-bis(salicylidene)butane-2,3-diaminatonickel(II), poly[Ni(saltMe)], were characterised by in situ FTIR and UV/Vis spectroscopy and ex-situ EPR spectroscopy in order to gain insights into film structure, electronic states and charge conduction. The role of the nickel ions during film oxidation was probed by using EPR to study naturally abundant Ni and 61Ni-enriched polymers. The data from all the spectroscopic techniques are consistent, and clearly indicate that polymerisation and redox switching are associated with oxidative ligand based processes; coulometry suggests that one positive charge was delocalised through each monomer unit. EPR provided evidence for the non-direct involvement of the metal in polymer oxidation: the polymer is best described as a polyphenylene-type compound (conducting polymer), rather than an aggregation of nickel complexes (redox polymer), and the main charge carriers are identified as polarons. An explanation for the high electrochemical stability and conductivity of poly[Ni(saltMe)] with respect to that of poly[Ni(salen)] is proposed. based on stereochemical repulsion between monomeric units; this can impose a less compact supramolecular structure on polymers with bulkier substituents.     

g tensor of transition ions in a crystalline matrix: Interstitial V(IV) and Ti(III) in rutile TiO2

In order to check if the parametrized crystal field approach is efficient in the analysis of an EPR powder spectrum we study defects of known geometry as if we did not know it. The g tensor of an interstitial V⁴⁺ ion in a single crystal of rutile TiO₂ can be interpreted without ambiguity, and the optimized parameters compare well with their theoretical values. For an interstitial Ti³⁺ ion, two solutions are found: both of them correspond to interstitial positions, but they differ in the principal axis orientation.     

Development of a screening method for cocaine and cocaine metabolites in urine using solvent microextraction in conjunction with gas chromatography

A simple, quick and inexpensive screening method for cocaine and cocaine metabolites has been developed. Drug extraction was achieved using the relatively new technique of solvent microextraction (SME). Complete analysis is achieved in 13 min, using, a 6-min extraction with a 2-microl drop followed by separation on a gas chromatograph. The developed procedure was tested as a screening method for cocaine and cocaine metabolites in spiked urine samples. Using SME, concentrations as low as 0.125 microg ml(-1) of cocaine, ecgonine methyl ester, cocaethylene and anhydroecgonine methyl ester were measurable with relative standard deviation values averaging 9.0%.     

Comparative study of reflectance cells for PLS-FTIR determination of sugars in soft drinks

A comparative study has been carried out between a horizontal Attenuated Total Reflectance (h-ATR) cell and a Cylindrical Internal Reflection (CIR) cell (CIRCLE cell). Both cells were employed for the determination of glucose, fructose, sucrose and total sugar in soft drinks and fruit juices using absorbance measurements at two resolution values (4 and 8 cm^–1). Data were processed by Partial Least Squares regression (PLS). Using a resolution of 4 cm^–1, mean relative errors of prediction from 0.6% to 1.3% were obtained using the horizontal-ATR and from 0.6% to 2.8% using the CIRCLE cell resulting in a limit of detection from 0.03% in the case of sucrose to 0.21% for total sugar for the h-ATR and from 0.06% for sucrose to 0.13% for glucose using the CIRCLE cell. Both cells provided appropriate figures of merit, but the analytical sensitivity obtained using the h-ATR cell was three times higher than that obtained using the CIRCLE cell.