Investigation of the La24Fe6Li22O56 compound by Mössbauer spectroscopy

Summary Quadrupole splittings of the M?ssbauer spectrum of the La₂₄Fe₆Li₂₂O₅₆ compound are compared with structural data obtained by XRD single-crystal analysis. Agreement turns out to be rather good, in spite of the crude model utilized for evaluating the electric-field gradient on the resonant nucleus     

Investigation of alumina lattice defects by means of thermoluminescence experiments

Summary Samples of α-alumina prepared at low temperature by means of a special procedure are investigated by recording their thermoluminescent emissionvs. temperature and wavelength. Taking into account the effect of thermal treatments, evidence is obtained for the presence of a distribution of electron traps of different depths. Arguments are advanced for characterizing the nature of the lattice defects originating these traps.     

Products of correlated symmetric matrices and q-Catalan numbers

 The well known convergence of the spectrum of large random symmetric matrices, due to Wigner, holds for products of correlated symmetric matrices with general entries. The limiting moments coincide with weighted enumeration of permutations, or of rooted trees. When the correlations are Markovian, the limiting first moments are closely related to Carlitz-Riordan q-Catalan numbers. As a consequence, these moments asymptotically exhibit a phase transition, with respect to the correlation coefficient. The critical correlations can be computed as the least positive zero of q-hypergeometric functions. Similar methods allow to recover some results due to Logan, Mazo, Odlyzko and Shepp. Received: 15 February 2002 / Revised version: 25 May 2002 / Published online: 24 October 2002 Mathematics Subject Classification (2000): Primary: 15A52; Secondary: 05A30, 15A18, 60F05, 82B44     

Schur Functors and Motives

In this article we study the class of Schur-finite motives, that is, motives which are annihilated by a schur functor. We compare this notion to a similar one due to Kimura. In particular, we show that the motive of any curve is Kimura-finite. This last result has also been obtained by V. Guletski. We conclude with an example by OSullivan of a non-Kimura-finite motive which is Schur-finite.Partially supported by INdAM Borse Di Studio Per LEstero.     

Thiophenes as traps for benzyne. 3. Diaryl sulfides and the role of dipolar intermediates

The reactions of seven thiophenes with benzyne generated from diphenyliodonium-2-carboxylate (DPIC) under a standard set of conditions led among other products to the formation of alpha- and beta-naphthyl phenyl sulfides 2a and 2b from thiophene (1a) and of 2c and 2d from 2-methylthiophene (1b). Dithienyl sulfides 4a-f were produced from the halothiophenes 1c-g. The structures of the naphthyl sulfides were proven by comparison with authentic samples of 2a-f, thus eliminating one of two possible mechanisms of formation. The remaining mechanism involves [4+2]-cycloaddition of benzyne to thiophene or to an S-phenylthiophenium ylide 10 to give the dipolar 2:1 benzyne/thiophene adduct 8 followed by ring-opening. Stevens-like rearrangements of 11, formed from 10 by proton transfer, may also explain the origin of arylated thiophenes such as 12 and 3 found in some reactions of benzynes with thiophene.     

On the Mean Pair Correlation Function of ±J Ising Spin Glasses

We provide a formula and an upper bound for the average over the disorder of the pair correlation function of ±J Ising spin glasses by using the symmetries of the system, We show the decay of the mean spin pair correlation function when the proportion of antiferromagnetic bonds is larger than the critical parameter associated with the pair dissociation phase transition.     

sp hybridization in free carbon nanoparticles--presence and stability observed by near edge X-ray absorption fine structure spectroscopy

The presence and stability of sp hybridized atoms in free carbon nanoparticles was investigated by NEXAFS spectroscopy. The experiments show that a predominant fraction of carbon atoms is found in linear sp-chains and that conversion into sp(2) structures proceeds already at low temperature and in the gas phase.     

On the matrices in B-spline collocation methods for Riesz fractional equations and their spectral properties

In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B-spline collocation method. For an arbitrary polynomial degree $p$, we show that the resulting coefficient matrices possess a Toeplitz-like structure. We investigate their spectral properties via their symbol and we prove that, like for second order differential problems, the given matrices are ill-conditioned both in the low and high frequencies for large $p$. More precisely, in the fractional scenario the symbol vanishes at 0 with order $\alpha$, the fractional derivative order that ranges from 1 to 2, and it decays exponentially to zero at $\pi$ for increasing $p$ at a rate that becomes faster as $\alpha$ approaches 1. This translates into a mitigated conditioning in the low frequencies and into a deterioration in the high frequencies when compared to second order problems. Furthermore, the derivation of the symbol reveals another similarity of our problem with a classical diffusion problem. Since the entries of the coefficient matrices are defined as evaluations of fractional derivatives of the B-spline basis at the collocation points, we are able to express the central entries of the coefficient matrix as inner products of two fractional derivatives of cardinal B-splines. Finally, we perform a numerical study of the approximation behavior of polynomial B-spline collocation. This study suggests that, in line with nonfractional diffusion problems, the approximation order for smooth solutions in the fractional case is $p+2-\alpha$ for even $p$, and $p+1-\alpha$ for odd $p$.