On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

Supercritical CO2 as a superior solvent for the cyclization of diallylmalonate catalyzed by palladium-containing zeolites

Palladium-containing zeolites catalyze the cycloisomerization of diethyl diallylmalonate to dimethylcyclopentenes. When the reaction is carried out in toluene, the performance of the palladium catalyst depends on the pore size of the zeolites. At 60 °C, palladium adsorbed on large pore size Beta zeolite (pore size ∼7.4 Å) is more active than medium pore size ZSM-5 (pore size ∼5.4 Å). This lower activity of ZSM-5 compared to Beta is attributable to the restricted diffusion of reagent and products through the ZSM-5 channels as compared to Beta zeolite. However, due to the gas-like diffusion characteristic of the supercritical state, the activity of ZSM-5 increases and becomes identical to that of Beta zeolite using supercritical CO₂ as medium.     

Block copolymer nanoparticles of controlled sizes via ring‐opening metathesis polymerization

This article describes the formation and characterization of self‐assembled nanoparticles of controlled sizes based on amphiphilic block copolymers synthesized by ring‐opening metathesis polymerization. We synthesized a novel hydrophobic derivative of norbornene; this monomer could be polymerized using Grubbs' catalyst [Cl₂Ru(CHPh)(PCy₃)₂] forming polymers of controlled molecular weight. We synthesized amphiphilic block copolymers of controlled composition and showed that they assemble into nanoparticles of controlled size. The nanoparticles were characterized using dynamic light scattering and transmission electron microscopy. Tuning the composition of the block copolymer enables the tuning of the diameters of the nanoparticles in the 30‐ to 80‐nm range. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3352–3359, 2004     

On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

Incubation period in the 2,2,4,4‐tetramethyl‐1‐piperidinyloxy‐mediated thermal autopolymerization of styrene: Kinetics and simulations

Mechanisms and simulations of the induction period and the initial polymerization stages in the nitroxide‐mediated autopolymerization of styrene are discussed. At 120–125 °C and moderate 2,2,4,4‐tetramethyl‐1‐piperidinyloxy (TEMPO) concentrations (0.02–0.08 M), the main source of radicals is the hydrogen abstraction of the Mayo dimer by TEMPO [with the kinetic constant of hydrogen abstraction (k_h)]. At higher TEMPO concentrations ([N?] > 0.1 M), this reaction is still dominant, but radical generation by the direct attack against styrene by TEMPO, with kinetic constant of addition k_ad, also becomes relevant. From previous experimental data and simulations, initial estimates of k_h ≈ 1 and k_ad ≈ 6 × 10^?7 L mol^?1 s^?1 are obtained at 125 °C. From the induction period to the polymerization regime, there is an abrupt change in the dominant mechanism generating radicals because of the sudden decrease in the nitroxide radicals. Under induction‐period conditions, the simulations confirm the validity of the quasi‐steady‐state assumption (QSSA) for the Mayo dimer in this regime; however, after the induction period, the QSSA for the dimer is not valid, and this brings into question the scientific basis of the well‐known expression k_th[M]³ (where [M] is the monomer concentration and k_th is the kinetic constant of autoinitiation) for the autoinitiation rate in styrene polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6962‐6979, 2006     

QSAR modeling with the electrotopological state indices: Corticosteroids

A structure-activity analysis of a series of steroids binding to corticosteroid-binding globulin was made using the electrotopological state index for each atom in the molecule. Two indices were found to correlate well with the binding affinity. The indices encode structural characteristics in the A and the D rings of the steroids in the study. One of the indices was formulated as the difference between two indices in the A ring. The two were not intercorrelated, suggesting that the composite index signals the influence of structure changes in or near the A ring that can be monitored by the composite index. This is a new observation using this structure-activity method. It is suggested that this model makes some contributions towards detection of the pharmacophore.     

A finitely convergent “row-action” method for the convex feasibility problem

We present a modification of the Cyclic Subgradient Projection (CSP) method by Censor and Lent, which solves the convex feasibility problem in a finite number of steps when a Slater type condition holds, while preserving its row-action properties. A linear rate of convergence for the CSP method is established assuming the same hypothesis.Research partially supported by CNPq, under Grant No. 301699/81.     

Inductively coupled plasma compared with direct current arc spectrometry for analysis of minor elements in aluminium baths

A validation study was carried out in order to evaluate the efficiency of inductively coupled plasma-optical emission spectrometry (ICP-OES) for the analysis of minor elements (manganese, chromium, copper, iron, and titanium) in aluminium alloys. Aluminium casting samples were obtained by adding compressed powder compacts of each alloying element and aluminium (minitablets) to aluminum baths in a laboratory crucible furnace. Digestion of solid samples was performed using concentrated HCI and H202 35% (v/v) previous to analysis by ICP-OES without any matrix separation. This solution-based method was validated considering direct current arc spectrometry as the reference method based on direct analysis without any pretreatment of the solid samples considered. Univariate statistical procedures were carried out, for which precision <3% and trueness of the analytical results were taken into account.     

Organonickel(II) Complexes with Anionic N-Donor Ligands. Hydration of coordinated nitriles at a nickel(II) site

The hydroxo complex (Bu₄N)₂[Ni₂(C₆F₅)₄(μ-OH)₂]reacts with 2,3,4,5,6-pentafluoro benzenamine (C₆F₅-NH₂), 1,3-diaryltriaz-1-enes (ArNH? N=N? Ar, Ar = Ph, 4-MeC₆H₄, 4-MeOC₆H₄), 7-aza-1H-indole (= 1H-pyrrolo[2.3-b]pyridine; Hazind), N-phenylpyridin-2-amine(pyNHPh), and N-phenylpyridine-2-carboxamide (py-CONHPh) at room temperature in acetone to give the binuclear complexes (Bu₄N)₂[Ni₂(C₆F₅)₄(μ-C₆F₅NH)₂] ( 1 ) and (Bu₄N)₂[{Ni(C₆F₅)₂} 2(μ-OH)(μ-azind)] ( 2 ) and the mononuclear complexes Bu₄N[Ni(C₆F₅)2(ArN₃Ar)] ( 3 – 5 ), Bu₄N[Ni(C₆F₅)₂(pyNPh)] ( 6 ), and Bu₄N[Ni(C₆F₅)₂(pyCONPh)] ( 7 ). The hydroxo.complex (Bu₄N)₂[{Ni(C₆F₅)2-(μ-OH)}₂] promotes the nucleophilic addition of water to pyridine-2-carbonitrile, 2-aminoacetonitrile, and 2-(dimethylamino)acetonitrile, and complexes 8 – 10 containing pyridine-2-carboxamidato, 2-aminoacetamidato and 2-(dimethylamino)acetamidato ligands are formed. Analytical (C, H, N) and spectroscopic (IR, ¹H and ¹⁹F-NMR, and FAB-MS) data were used for structural assignments. A single-crystal X-ray diffraction study of (Bu₄N)₂[{Ni(C₆F₅)₂}₂(μ-OH)(μ-azind)] ( 2 ) established the binuclear nature of the anion; the two Ni-atoms are bridged by an OH group and a 7-aza-7H-indol-7-yl group, but the central Ni? O? Ni? N? C? N ring is not planar, the dihedral angle between the Ni? O? Ni and Ni? N? C? N? Ni planes being 84.4°.