Regularizing properties of a class of matrices including the optimal and the superoptimal preconditioners

In this work, given a positive definite matrix A, we introduce a class of matrices related to A, which is obtained by suitably combining projections of its powers onto algebras of matrices simultaneously diagonalized by a unitary transform. After a detailed theoretical study of some spectral properties of the matrices of this class, which suggests their use as regularizing preconditioners, we prove that such matrices can be cheaply computed when the matrix A has a Toeplitz structure. We provide numerical evidence of the advantages coming from the employment of the proposed preconditioners when used in regularizing procedures.     

Leibniz rules and reality conditions

An analysis is made of reality conditions within the context of non-commutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule fixes the reality condition for the covariant derivative itself. We show also that the map which determines the right Leibniz rule must satisfy the braid equation if the extension of the covariant derivative to tensor products is to satisfy the reality condition. Received: 6 June 2000 / Published online: 9 August 2000     

Photoproduction of heavy vector mesons at HERA – a test field for diffraction

Exclusive diffractive photoproduction of heavy vector mesons (V=, and ) at HERA is studied in a model employing a dipole Pomeron exchange (P) with an inelastic vertex. The model is fitted to the data on , B, and for and beyond the threshold region. The elastic cross sections for both and photoproduction show a moderate increase within the HERA energy region. The flattening of the slope B(s) (indicating little or no shrinkage) for is not correlated with the slope of the Pomeron trajectory. Estimates for photoproduction at HERA are given. Received: 11 January 1999 / Published online: 8 September 1999     

Universality of the string picture in lattice gauge systems

We test the conjecture that the infrared behaviour of gauge theories is described by an effective string picture by analyzing the Monte Carlo data of five different three- and four-dimensional lattice gauge systems, SU(2) and SU(3) included. We find that there is a unique string of fermionic type which fits well to the whole set of analyzed data.     

Alpha particle emission from the 198Pb compound nucleus: comparison between the fusion-evaporation and the pre-scission channels

The α-particle emission from the ²⁸Si+¹⁷⁰Er fusion-evaporation reaction at 165 and 185 MeV has been measured and compared with published data relative to the pre-scission emission in the same reaction. The spectra in the two channels exhibit nearly the same shape in the low energy region, whereas in the high energy region the spectrum for the fusion-evaporation case features a larger apparent temperature. The interpretation of the difference in shape between the two decay channels is based on statistical model calculations which account for the effects due to the different length of the decay chain. Statistical model calculations with standard parameters describe well the gross features of the alpha particle spectra in the fusion-evaporation channel and the proton spectra in the pre-scission channel. On the contrary, the model predictions seem to overestimate by ≃2 MeV the emission barrier for the alpha particles in the pre-fission channel. This effect is ascribed to the larger elongation of the nucleus during the fission process. An average axis ratio b/a∼ 2 for the emitter is suggested. Received 29 April 1997 / Revised version 10 September 1997     

Synthesis and mesomorphic properties of new liquid crystalline stilbene derivatives containing vinyloxyalkoxy chains

New liquid crystalline stilbene derivatives containing vinyloxyalkoxy chains 1 (n=5, 7, 9, 11) have been synthesised. Their mesomorphic properties have been studied by polarising optical microscopy and differential scanning calorimetry. It is interesting to note that even their alcohol precursors showed liquid crystalline behaviour. The effect of terminal alkoxy chain length and UV irradiation on the mesomorphic behaviour is discussed.     

Explicit model realizing parton-hadron duality

An explicit model realizing parton-hadron duality and fitting the data is suggested. Complex nonlinear Regge trajectories are important ingredients of the model. The inclusion of Δ and N^* trajectories should account for all resonances in the direct channel. The exotic trajectory is responsible for the smooth background. Received: 7 June 2002 / Accepted: 3 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: fiore@cs.infn.it RID="b" ID="b"e-mail: flachi@ifae.es RID="c" ID="c"e-mail: jenk@gluk.org RID="d" ID="d"e-mail: sasha@len.uzhgorod.ua RID="e" ID="e"e-mail: vladimir@cfif.ist.utl.pt Communicated by V.V. Anisovich     

Color screening,absorption, and σ tot pp at LHC

We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances R _c ? 0.3 fm allows extending the BFKL technique from deep inelastic to hadron-hadron scattering. With the inclusion of the absorption corrections our results are in agreement with the LHC data on σ _tot ^pp .     

Young's type interference for probing the mode symmetry in photonic structures

A revisited realization of the Young's double slit experiment is introduced to directly probe the photonic mode symmetry by photoluminescence experiments. We experimentally measure the far field angular emission pattern of quantum dots embedded in photonic molecules. The experimental data well agree with predictions from Young's interference and numerical simulations. Moreover, the vectorial nature of photonic eigenmodes results in a rather complicated parity property for different polarizations, a feature which has no counterpart in quantum mechanics.