Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

The calculation of neutron self-shielding factors of a group of isolated resonances

The resonance neutron self-shielding factor, G _res, is required in neutron metrology and activation data analysis. In a previous paper, the authors have shown that a dimensionless variable can be introduced which converts the dependence of G _res on the physical and nuclear properties of the material samples into an universal curve, valid for the isolated resonances of any nuclide. This work presents a methodology based on the universal curve, which enables to calculate G _res for a group of isolated resonances by weighting its individual contributions. A good agreement was reached with results calculated by the MCNP code and with experimental values for Mo foils and wires. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

Infrared and Raman spectroscopic investigation of Eu3+-doped mono and Di-urethanesil hybrid siliceous materials

The general features of two series of sol-gel derived materials, designatedurethanesils (Ut), have been investigated by infrared and Raman spectroscopies with the goal of elucidating the chemical environment of the Eu³⁺ cations. The host frameworks of the two families of ormolytes studied have been represented by m-Ut(350) and d-Ut(300), where m stands for mono, d stands for di, 350 and 300 are the average molecular weights of the organic precursors (poly(ethylene glycol) methyl ether, PEGME, and poly(ethylene glycol), PEG, respectively). The hybrid matrix of the mono-xerogels is composed by a siliceous backbone bonded by means of urethane linkages (-NHC (=O)O-) to pendant methyl end capped oligopolymer chains with approximately 7 oxyethylene units, whereas that of the di-xerogels is based on a siliceous network grafted through urethane groups to both ends of poly(oxyethylene) segments containing about 6 (OCH₂CH₂) repeat units. Both classes of materials have been doped with europium triflate (Eu(CF₃SO₃)₃). The doped samples have been identified by m-Ut(350)_nEu(CF₃SO₃)₃ and d-Ut(300)_nEu(CF₃SO₃), where n is the molar ratio of (OCH₂CH₂) repeat units per Eu³⁺ ion. Materials with n ranging from ∞ to 5 have been analyzed. The spectral data obtained provide evidence that the cations begin to coordinate to the ether oxygen atoms of the oligopolymer chains at n=40 in the mono-urethanesils and at n=10 in the di-urethanesils. In mono-urethanesils samples with n>40 and in di-urethanesils materials with n>10, the Eu³⁺ coordinate exclusively to the carbonyl oxygen atoms of the urethane linkages. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

Polarized light and X-ray precession study of the ferroelastic domains of YBa2Cu3O7-δ

The ferroelastic domains of the orthorhombic phase of YBa₂Cu₃O_7- have been observed in polarized light on ceramics and single crystals. By combining polarized light microscopy with the X-ray precession technique, the correlation of the orientation of the orthorhombica- andb-axes with that of thea-b-plane bireflectance, reflection dichroism, transmission dichroism (at a thickness of about 1m), reflection tints generated with compensators and upon uncrossing of polars, as well as the orientation of etch pits has been realized on ferroelastic single domains, bi-domains and more complicated domain patterns. Four ferroelastic orthorhombic domain states have been identified, at variance with former group theoretical considerations, predicting only two states. Ensembles of lamellar domains beyond optical resolution generate strong bireflectance with principal axes rotated by 45° relative to the truea, b-directions.     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.