Hard noncommutative loops resummation

The noncommutative version of the Euclidean g2phi4 theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector cannot be treated perturbatively and requires a resummation of the leading divergences in the two-point function. This is analogous to what is done in the hard thermal loops resummation of finite temperature field theory. Next-to-leading order corrections to the self-energy are computed, resulting in O(g3) contributions in the massless case, and O(g6logg2) in the massive one.     

Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition

We present exact diagonalization results on a modified Peierls-Hubbard model for the neutral-ionic phase transition. The ground state potential energy surface and the infrared intensity of the Peierls mode point to a strong, nonlinear electron-phonon coupling, with effects that are dominated by the proximity to the electronic instability rather than by electronic correlations. The huge infrared intensity of the Peierls mode at the ferroelectric transition is related to the temperature dependence of the dielectric constant of mixed-stack organic crystals.     

Ultrarapid capillary electrophoresis method for the determination of reduced and oxidized glutathione in red blood cells

We describe a very rapid high-performance capillary electrophoresis method for the separation and quantification of reduced (GSH) and oxidized (GSSG) glutathione in red blood cells. Two procedures for sample preparation have been compared, Microcon-10 membrane filtration and acid precipitation. The separation is obtained in an uncoated capillary using a high ionic strength borate buffer at pH 7.8. The intra-assay coefficients of variation (CVs%) are 1.53 and 1.66 for GSH and GSSG, respectively. The run is shorter than 90 s and the migration time is highly reproducible both for GSH (CV% 0.22) and GSSG (CV% 0.17). When the filtration step is used only GSH is found, whereas both GSH and GSSG are detectable after acid precipitation, suggesting that GSSG revealed after acid treatment may be an artefact due to GSH oxidation. Because of its good analytical performance this method could be used for routine red blood cell glutathione measurement in healthy or pathological conditions.     

Analytic Discs and Extension of CR Functions

Let M be a manifold of X = C ⁿ , A a small analytic disc attached to M, z ^o a point of A where A is tangent to M, z ¹ another point of A where M extends to a germ of manifold M ₁ with boundary M. We prove that CR functions on M which extend to M ₁ at z ¹ also extend at z ^o to a new manifold M ₂. The directions M ₁ and M ₂ point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.     

Conditioning of the Exponential of a Block Triangular Matrix

We propose a new measure of conditioning for the exponential of a block triangular matrix. We also show that different condition numbers must be used to assess the accuracy of different algorithms which implement diagonal Padé with scaling and squaring.     

The Chaboche nonlinear kinematic hardening model: calibration methodology and validation

This work studies how a nonlinear kinematic model aimed for cyclic plasticity could be put into effect and used within a FEM code. A correct modeling of cyclic elasto-plastic behavior can be exploited in low-cycle fatigue life investigation as well as in manufacturing problems related to springback prediction. The chosen formulation has been proposed by Chaboche, and it is implemented in most of the commercial codes used for nonlinear FEM simulations. At first, a procedure for the proper identification of unknown material model parameters has been put forward. This calibration, based on the data collected from experimental low-cycle fatigue tests, has been performed by means of an inverse method. Laboratory tests differ according to the type of material under investigation. A classification can be operated distinguishing between specimens obtained from bulk materials or from sheet metals. For the former, standard tension-compression tests have been performed, while for the latter, a dedicated testing equipment for three-point bend cyclic tests has been devised. Then, further experimental tests have been run to check model transferability: different strain per cycle amplitudes, asymmetric strain cycling and different stress triaxiality levels have been investigated. For each of these tests, experimental vs. FEM results have been analyzed to show the level of agreement that has been reached.     

Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations

Summary. By providing a matrix version of Koenig's theorem we reduce the problem of evaluating the coefficients of a monic factor r(z) of degree h of a power series f(z) to that of approximating the first h entries in the first column of the inverse of an Toeplitz matrix in block Hessenberg form for sufficiently large values of n. This matrix is reduced to a band matrix if f(z) is a polynomial. We prove that the factorization problem can be also reduced to solving a matrix equation for an matrix X, where is a matrix power series whose coefficients are Toeplitz matrices. The function is reduced to a matrix polynomial of degree 2 if f(z) is a polynomial of degreeN and . These reductions allow us to devise a suitable algorithm, based on cyclic reduction and on the concept of displacement rank, for generating a sequence of vectors that quadratically converges to the vector having as components the coefficients of the factor r(z). In the case of a polynomial f(z) of degree N, the cost of computing the entries of given is arithmetic operations, where is the cost of solving an Toeplitz-like system. In the case of analytic functions the cost depends on the numerical degree of the power series involved in the computation. From the numerical experiments performed with several test polynomials and power series, the algorithm has shown good numerical properties and promises to be a good candidate for implementing polynomial root-finders based on recursive splitting strategies. Applications to solving spectral factorization problems and Markov chains are also shown. Received September 9, 1998 / Revised version received November 14, 1999 / Published online February 5, 2001     

Organic Ion Exchangers. Synthesis and Their Behaviour in the Retention of Some Metal Ions

Summary: Three pyridine strong base anion exchangers as beads were obtained by quaternization reactions of a 4-vinylpyridine : 8% divinylbenzene copolymer of gel type. These resins possess methyl / ethyl / butyl radicals as substituents on N⁺ atoms and have exchange capacities of 4.80 mEq/g and 2.10 mEq/mL. For pyridine strong base anion exchangers, the behaviours in the retention processes of Cr(VI) as oxyanions and Ga(III) as [GaCl₄]⁻ complex anion were evaluated with the bath method. All the resins exhibited retention properties, but the retained amounts of the metal cations are different as a function of the alkyl length as substituent on N⁺ atoms and the complex anion nature. Thus, Cr(VI) oxyanions are best retained by the resin with  CH₃ as substituent on N⁺ atoms while [GaCl₄]⁻ complex anion by the resin with  C₄H₉ as substituent on N⁺ atoms. By aminolysis reaction of an ethylacrylate : acrylonitrile : divinylbenzene copolymer as beads of macroporous type with NH₂OH · HCl in the presence of C₂H₅OH a new chelating ion exchanger was performed which contains both amidoxime and hydroxamic acid functional groups. This ion exchanger has the retention property for different metal cations but its retention capacities values are strongly dependent of the nature of metal cation and the counterion as well as pH of the solution. Thus, in the static conditions Zn(II) cation with NOequation/tex2gif-stack-1.gif anion as counterion is retained with the best result at pH = 5. As an example, for the aqueous metal cation solution of 10⁻² M concentration for Zn(NO₃)₂ the resin possess at equilibrium a retention capacity of 6.70 mmol Zn/g dry resin and for Cu(II) from Cu(NO₃)₂ solution of same concentration, the retention capacity is 0.22 mmol Cu/g dry resin and Fe(III) from Fe(NO₃)₃ solution is not retained.