Approximation of Solutions of Nonlinear Equations of Monotone and Hammerstein Type

Let X be a real uniformly smooth and uniformly convex Banach space with dual X ^*. Let A: X → X ^* be a bounded uniformly submonotone map. It is proved that a Mann-type approximation sequence converges strongly to Jx ^* where x ^* ∈ N(A). Furthermore, as an application of this result an iterative sequence which converges strongly to a solution of the Hammerstein equation u+KFu = 0 is constructed where, F:X→X^* and K:X^*→X are monotone-type mappings. No invertibility assumption is imposed on K. Moreover, neither K nor F need be compact. Finally, our method is of independent interest.     

Conditions for secondary particle formation in emulsion polymerization systems

A simple means is deduced for determining conditions for secondary particle formation in emulsion polymerization systems in systems where the amount of added surfactant is below the cmc. A new radical formed from initiator in the aqueous phase will undergo some polymerization with aqueous-phase monomer, but must have three possible eventual fates: aqueous-phase termination, entry into a preexisting particle, or creation of a new particle. The means for determining the onset and extent of secondary nucleation is to modify HUFT theory to take into account a successful model for entry [ Macromolecules, 24, 1629 (1991)] which states that entry occurs if and only if the aqueous-phase radical has achieved a critical degree of polymerization z. Particle formation below the cmc is by homogeneous/coagulative nucleation which (if coagulation is ignored) gives an upper bound to the rate of formation of precursor particles; these are of a degree of polymerization J_crit > z. The resulting equations are readily solved, and require only a knowledge of the aqueous-phase propagation and termination rate coefficients (the latter is very high: ca. 10⁹ dm³ mol⁻¹ s⁻¹ for termination between the very small radicals), z and j_crit. Easily applied means are given for estimating all these quantities. The treatment gives good accord with experimentally observed conditions for the onset of secondary nucleation in low-surfactant systems (including taking in situ micellization into account).     

Determination of fumonisins B1 and B2 in corn by liquid chromatography/mass spectrometry with immunoaffinity column cleanup: single-laboratory method validation

A single-laboratory method validation was conducted to establish the effectiveness of an immunoaffinity column cleanup procedure followed by liquid chromatography/mass spectrometry (LCIMS) for the determination of fumonisins B1 and B2 (FBI + FB2) in corn. The test portion is extracted with acetonitrile-methanol-water (25 + 25 + 50). The extract is filtered, diluted with phosphate-buffered saline solution, and applied to an immunoaffinity column. FB1 + FB2 are removed with methanol and directly determined by reversed-phase LC with MS detection using selected-ion monitoring of 2 characteristic ions in each case. Test portions of blank corn samples were spiked with a mixture of FB1 + FB2 to give total levels of 200 and 500 ng/g, respectively. Recoveries of both FB1 and FB2 from spiked samples averaged 90.4-101%. Based on results for spiked raw corn (triplicates at 2 levels), the relative standard deviation for repeatability ranged from 2.8 to 7.1%. The accuracy of the method was demonstrated by analysis of Food Analysis Performance Assessment Scheme (FAPAS) test material. The method was also applied to a small survey of processed corn products such as corn chips, cornflakes, and popcorn.     

alpha- and beta-FOX-7, polymorphs of a high energy density material, studied by X-ray single crystal and powder investigations in the temperature range from 200 to 423 K

The alpha-beta phase transition in the novel energetic material 1,1-diamino-2,2-dinitroethylene, C2H4N4O4 (FOX-7), has been studied by single-crystal X-ray investigations at five different temperatures over the 200-393 K range. In these investigations, the positions of the hydrogen atoms were experimentally determined without any geometric constraints. In addition, X-ray powder investigations using the Guinier technique have been performed to characterize the beta-phase up to 423 K. The alpha-beta phase transition at 389 K is first order, shows a discontinuous increase of the molar volume and entropy (DeltaV = 1.75 cm3/mol, X-ray investigation; DeltaS = 1.5 cal/K mol, DSC analysis), and can be classified as displacive. The hitherto unknown structure of beta-FOX-7 was solved at 393 K and showed simple structural relations to the alpha-polymorph. The characteristic bonding in wave-shaped layers is now found for beta-FOX-7 (P2(1)2(1)2(1), z = 4, a= 6.9738(7) A, b = 6.635(1) A, c = 11.648(2) A, 393 K), as well as for alpha-FOX-7 (P2(1)/n, z = 4, a = 6.9467(7) A, b = 6.6887(9) A, c = 11.350(1) A, beta = 90.143(13) degrees , 373 K). Interestingly, whereas the intramolecular C-C, C-N, N-O, and N-H bond distances remain nearly unchanged for both polymorphs over the whole temperature range from 200 to 393 K, the two nitro groups deviate strongly from the molecular plane formed by the two carbon and two amino nitrogen atoms. In alpha-FOX-7 at 373 K, the nitro groups are twisted -47 and +6 degrees with respect to the carbon-carbon bond, but in beta-FOX-7 at 393 K, these twist angles are changed to -36 and +20 degrees . Within the layers, the FOX-7 molecules show strong pi-conjugation and extensive intra- and intermolecular hydrogen bonding. In this investigation, we have been able to show that alpha- and beta-FOX-7 build up different nets of intermolecular hydrogen bonds. In alpha-FOX-7, each oxygen atom of the nitro groups is involved in two hydrogen bonds resulting in two intramolecular and six intermolecular hydrogen bonds. But in beta-FOX-7 this coordination changes, and half of the oxygen atoms build up two and the other half build up three hydrogen bonds leading to two intramolecular and eight intermolecular hydrogen bonds. The average intermolecular hydrogen bond distance increases slightly from 2.31 A in alpha-FOX-7 to 2.52 A in beta-FOX-7. The C-NO2 bonds are of particular interest because they are referred to as the detonation trigger. It has been suggested that these bonds could be strengthened by the extensive intermolecular hydrogen bonding within the layers in both polymorphs. Such bond strengthening via cooperative effects was proposed in earlier DFT calculations on FOX-7 and may be one key to understanding its low sensitivity and high activation energy to impact.     

Pulsed‐laser polymerization‐gel permeation chromatographic determination of the propagation‐rate coefficient for the methyl acrylate dimer: A sterically hindered monomer

The methyl acrylate dimer (MAD) is a sterically hindered macromonomer, and the propagating radical can fragment to an unsaturated end group. The propagation‐rate coefficient (k_p) for MAD was obtained by pulsed‐laser polymerization (PLP). The Mark–Houwink–Sakaruda parameters required for the analysis of the molecular weight distributions (MWDs) were obtained by multiple‐detector gel permeation chromatography (GPC) with on‐line viscometry. The small radical created by the fragmentation results in a short‐chain polymer that means the MWD may no longer be given by that expected for “ideal” PLP conditions; simulations suggest that the degree of polymerization required for “ideal” PLP conditions can be obtained from the primary point of inflection provided the GPC traces also show a clear secondary inflection point (radicals terminated by the second, rather than the first, pulse subsequent to initiation). Over the temperature range of 40–75 °C, the data can be best fitted by k_p/dm³ mol^?1 s^?1 = 10^6.1 exp(?29.5 kJ mol^?1), with a moderately large joint confidence interval for the Arrhenius parameters. The data are consistent with an increased activation energy and reduced frequency factor as compared with acrylate or methacrylate; both of these changes can be ascribed to hindrance. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3902–3915, 2001     

Surfactant control of gas uptake: effect of butanol films on HCl and HBr entry into supercooled sulfuric acid

The entry of HCl into 60-68 wt % D(2)SO(4) and HBr into 68 wt % acid containing 0-0.18 M 1-butanol was monitored by measuring the fractions of impinging HCl and HBr molecules that desorb as DCl and DBr after undergoing H --> D exchange within the deuterated acid. The addition of 0.18 M butanol to the acid creates butyl films that reach approximately 80% surface coverage at 213 K. Surprisingly, this butyl film does not impede exchange but instead enhances it: the HCl --> DCl exchange fractions increase from 0.52 to 0.74 for 60 wt % D(2)SO(4) and from 0.14 to 0.27 for 68 wt % D(2)SO(4). HBr --> DBr exchange increases even more sharply, rising from 0.22 to 0.65 for 68 wt % D(2)SO(4). We demonstrate that this enhanced exchange corresponds to enhanced uptake into the butyl-coated acid for HBr and infer this equivalence for HCl. In contrast, the entry probability of the basic molecule CF(3)CH(2)OH exceeds 0.85 at all acid concentrations and is only slightly diminished by the butyl film. The OD groups of surface butanol molecules may assist entry by providing extra interfacial protonation sites for HCl and HBr dissociation. The experiments suggest that short-chain surfactants in sulfuric acid aerosols do not hinder heterogeneous reactions of HCl or HBr with other solute species.     

Synthesis of l,l-puromycin

l,l-Puromycin, a diastereomer of the natural peptidyl nucleoside antibiotic puromycin, has been synthesized from l-xylose in 13 steps.     

One-pot synthesis of new tetrasubstituted thiophenes and selenophenes

In this work, we described the synthesis of new tetrasubstituted thiophenes and selenophenes achieved by an easy one-pot four-step procedure. Expected compounds were obtained in good yield from ketene dithioacetals.     

Structural studies of the allelic wheat glutenin subunits 1Bx7 and 1Bx20 by matrix-assisted laser desorption/ionization mass spectrometry and high-performance liquid chromatography/electrospray ionization mass spectrometry

Structural studies of the high molecular mass (HMM) glutenin subunits 1Bx7 (from cvs Hereward and Galatea) and 1Bx20 (from cv. Bidi17) of bread wheat were conducted using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) and reversed-phase high-performance liquid chromatography/electrospray ionization mass spectrometry (RP-HPLC/ESI-MS). For all three proteins, MALDI-TOFMS analysis showed that the isolated fractions contained a second component with a mass about 650 Da lower than the major component. The testing and correction of the gene-derived amino acid sequences of the three proteins were performed by direct MALDI-TOFMS analysis of their tryptic peptide mixture. Analysis of the digest was performed by recording several MALDI mass spectra of the mixture at low, medium and high mass ranges, optimizing the matrix and the acquisition parameters for each mass range. Complementary data were obtained by RP-HPLC/ESI-MS analysis of the tryptic digest. This resulted in coverage of about 98% of the sequences. In contrast to the gene-derived data, the results obtained demonstrate the insertion of the sequence QPGQGQ between Trp716 and Gln717 of subunit 1Bx7 (cv. Galatea) and a possible single amino acid substitution within the T20 peptide of subunit 1Bx20. Moreover, the mass spectrometric data demonstrated that the lower mass components present in all the fractions correspond to the major components but lack about six amino acid residues, which are probably lost from the protein C-terminus. Finally, the results obtained provide evidence for the lack of glycosylation or other post-translational modifications of these subunits.     

Site-specific C content by quantitative isotopic C Nuclear Magnetic Resonance spectrometry: A pilot inter-laboratory study

Isotopic ¹³C NMR spectrometry, which is able to measure intra-molecular ¹³C composition, is of emerging demand because of the new information provided by the ¹³C site-specific content of a given molecule. A systematic evaluation of instrumental behaviour is of importance to envisage isotopic ¹³C NMR as a routine tool. This paper describes the first collaborative study of intra-molecular ¹³C composition by NMR. The main goals of the ring test were to establish intra- and inter-variability of the spectrometer response. Eight instruments with different configuration were retained for the exercise on the basis of a qualification test. Reproducibility at the natural abundance of isotopic ¹³C NMR was then assessed on vanillin from three different origins associated with specific δ¹³C_i profiles. The standard deviation was, on average, between 0.9 and 1.2‰ for intra-variability. The highest standard deviation for inter-variability was 2.1‰. This is significantly higher than the internal precision but could be considered good in respect of a first ring test on a new analytical method. The standard deviation of δ¹³C_i in vanillin was not homogeneous over the eight carbons, with no trend either for the carbon position or for the configuration of the spectrometer. However, since the repeatability for each instrument was satisfactory, correction factors for each carbon in vanillin could be calculated to harmonize the results.