Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

Novel acrylic macromonomer with amphiphilic character derived from Triton X‐100: Radical copolymerization with methyl methacrylate and thermal properties

This article explores the synthesis of a novel methacrylic macromonomer with an amphiphilic character derived from poly(ethylene glycol) tert‐octylphenyl ether (MT) and its respective homopolymer. To know their reactivity in radical copolymerization reactions with methyl methacrylate (MMA), a model monomer (MTm) was synthesized to determine the reactivity ratios and compare them with the low molar fractions of copolymers of MT with MMA because they were difficult to isolate. They were r_MTm = 0.97 and r_MMA = 0.95. The compositional diagrams when representing the weight fraction of MT and MTm in the feed and the copolymer suggested that a clear correlation exists between the experimental points of the model monomer MTm and the macromonomer MT ones, suggesting that the length of the side poly(ethylene oxide) chain does not affect the reactivity of the methacrylic double bond in the prepared monomers for this type of polymerization reaction. The reactivity ratios of the copolymers have a tendency for the formation of random or Bernoullian copolymers. The glass‐transition temperatures (T_g's) of the prepared copolymers were determined by differential scanning calorimetry, deviated from the Fox equation, and discussed on the basis of treatments that consider the influence of the monomeric units along the copolymer chains, determining the T_g of the corresponding alternating dyads. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1641–1649, 2003     

Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Hydrophilic and hydrophobic copolymer systems based on acrylic derivatives of pyrrolidone and pyrrolidine

This article deals with the synthesis of hydrophilic methacrylic monomers derived from ethyl pyrrolidone [2‐ethyl‐(2‐pyrrolidone) methacrylate (EPM)] and ethyl pyrrolidine [2‐ethyl‐(2‐pyrrolidine) methacrylate (EPyM)] and their respective homopolymers. For the determination of their reactivity in radical copolymerization reactions, both monomers were copolymerized with methyl methacrylate (MMA), the reactivity ratios being calculated by the application of linear and nonlinear mathematical methods. EPM and MMA had ratios of r_EPM = 1.11 and r_MMA = 0.76, and this indicated that EPM with MMA had a higher reactivity in radical copolymerization processes than vinyl pyrrolidone (VP; r_VP = 0.005 and r_MMA = 4.7). EPyM and MMA had reactivity ratios of r_EPyM = 1.31 and r_MMA = 0.92, and this implied, as for the EPM–MMA copolymers, a tendency to form random or Bernoullian copolymers. The glass‐transition temperatures of the prepared copolymers were determined by differential scanning calorimetry (DSC) and were found to adjust to the Fox equation. Total‐conversion copolymers were prepared, and their behavior in aqueous media was found to be dependent on the copolymer composition. The swelling kinetics of the copolymers followed water transport mechanism case II, which is the most desirable kinetic behavior for a swelling controlled‐release material. Finally, the different states of water in the hydrogels—nonfreezing water, freezing bound water, and unbound freezing water—were determined by DSC and found to be dependent on the hydrophilic and hydrophobic units of the copolymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 395–407, 2003     

Interpretation of the polyelectrolyte and antipolyelectrolyte effects of poly(N‐vinylimidazole‐co‐sodium styrenesulfonate) hydrogels

Hydrogels of N‐vinylimidazole (VI) and sodium styrenesulfonate (SSS) were synthesized in aqueous solution by radical crosslinking copolymerization with N,N′‐methylene‐bis(acrylamide) as crosslinker. Swelling in several saline solutions was measured for hydrogel samples synthesized with different comonomer concentrations (C_T = 10, 25, or 40%) and with SSS mole fractions covering a broad range (f_SSS = 0–0.7), while the crosslinker ratio was 2 wt % in all cases. The degree of swelling in aqueous solution with a specific ionic strength (μ), plotted versus the SSS composition of the feed, shows a minimum for any set of samples synthesized with a fixed C_T. The dependence of swelling on μ shows both polyelectrolyte (f_SSS beyond the minimum) and antipolyelectrolyte behaviors (in the low f_SSS limit). It was found that the nonGaussian factor of the crosslinking density and the polymer‐solvent interaction parameter increase with f_SSS for any C_T. Moreover, in the low f_SSS limit, the osmotic swelling pressure is governed not only by the ionic contribution, but also by the polymer‐solvent mixing and, the concentration of mobile counterions inside the gel is not proportional to the net fixed charge but to the addition of cationic and anionic side groups, what discards the formation of ionic pairs. The antipolyelectrolyte effect is interpreted as due to the increasing protonation of VI as μ goes up. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1683–1693, 2007     

Radiation heterogeneous processes of14C-acetic acid adsorbed in Na-Montmorillonite

This research addresses itself to the study of the mechanism of the acetic acid decarboxylation in Na-Montmorillonite exposed to ionizing radiation. The results obtained indicated that the decarboxylation reaction is enhanced several times by the irradiation. This behavior is probably due to an oxidation reaction at the edges of the clay. Also it is by energy transfer from the clay to adsorbed molecules by an interaction of non-equilibrium charge carriers with the adsorbed molecules.