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.     

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.     

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     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

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.     

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°.     

Synthesis and stereochemistry of (3α)-6β,7β-dihydroxy- and 6β-hydroxy-8-alkyl-8-azabicyclo[3.2.1]octane-3-spiro-5′-imidazoline-2′,4′-diones

The synthesis of 6β-hydroxy- and 6β,7β-dihydroxy-8-alkyl-8-azabicyclo[3.2.1]octane-3-spiro-5′-hydantoins was stereoselectively achieved by Bucherer-Bergs reaction of the corresponding ketones. An α configuration on C₃ was proposed for all hydantoins on the basis of spectral data.     

Determination of vanadium by solid-phase spectrophotometry after its preconcentration as an Eriochrome Cyanine R complex on a dextran-type exchanger

A method is described for the determination by solid phase spectrophotometry (SPS) of trace amounts of vanadium in natural water and crude petroleum samples. The procedure is based on fixation on a dextran-type anion exchanger of the complex V(IV)-Eriochrome Cyanine R. The absorbance of the gel, at 563 and 750 nm, packed in a 1 mm cell, is measured directly. Vanadium can be determined in the 0.6-25.0 mug l(-1) range with a relative standard deviation of 2.2%. The comparison of the SPS method and the gallic acid persulphate method shows that the linearity, analytical sensitivity and precision were better for the SPS method, and that the latter method has lower detection and quantification limits than the gallic acid persulphate method.