Compact High-Order Finite Differences for Interface Problems in One Dimension

This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem –(pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h²) O(h³) and O(h⁴) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

Solvent accessibility of protein surfaces by amide H/2H exchange MALDI-TOF mass spectrometry

One advantage of detecting amide H/2H exchange by mass spectrometry instead of NMR is that the more rapidly exchanging surface amides are still detectable. In this study, we present quench-flow amide H/2H exchange experiments to probe how rapidly the surfaces of two different proteins exchange. We compared the amide H/2H exchange behavior of thrombin, a globular protein, and IkappaBalpha, a nonglobular protein, to explore any differences in the determinants of amide H/2H exchange rates for each class of protein. The rates of exchange of only a few of the surface amides were as rapid as the "intrinsic" exchange rates measured for amides in unstructured peptides. Most of the surface amides exchanged at a slower rate, despite the fact that they were not seen to be hydrogen bonded to another protein group in the crystal structure. To elucidate the influence of the surface environment on amide H/2H exchange, we compared exchange data with the number of amides participating in hydrogen bonds with other protein groups and with the solvent accessible surface area. The best correlation with amide H/2H exchange was found with the total solvent accessible surface area, including side chains. In the case of the globular protein, the correlation was modest, whereas it was well correlated for the nonglobular protein. The nonglobular protein also showed a correlation between amide exchange and hydrogen bonding. These data suggest that other factors, such as complex dynamic behavior and surface burial, may alter the expected exchange rates in globular proteins more than in nonglobular proteins where all of the residues are near the surface.     

Formal hydride transfer mechanism for photoreduction of 3-phenylquinoxalin-2-ones by amines. Association Of 3-phenylquinoxalin-2-one with aliphatic amines

The photophysical and photochemical behavior of 1-methyl-3-phenylquinoxalin-2-one (MeNQ) and 3-phenylquinoxalin-2-one (HNQ) in the presence of amines is reported. While HNQ fluorescence shows an auxochromic effect and a bathochromic shift with added amines, explained by association of HNQ with amine in the ground state and emission from both excited species HNQ and [HNQ-amine], both MeNQ and HNQ are photoreduced efficiently on irradiation in the presence of amines, leading to the semireduced quinoxalin-2-ones, MeNQH(-) and HNQH(-), respectively, via an electron-proton-electron transfer, with unit quantum yields at high amine concentrations. The semireduced quinoxalin-2-ones XNQH(-) (X = H, Me) revert almost quantitatively to the parent XNQ in a dark thermal reaction with an activation free energy for MeNQH(-) of 17.4 and 25.9 kcal/mol in acetonitrile and benzene, respectively. Kinetic and spectroscopic (UV and NMR) evidence supports the proposed reaction mechanism for the reversible photoreduction.     

ABSORPTION AND EMISSION STUDIES OF ELECTRONIC STATES OF N-ARYLBENZAMIDES

Abstract— Absorption and emission spectra of several N-arylbenzamides have been measured. The quantum yields for their fluorescence were found to be dependent on matrix viscosity and temperature. Singlet-triplet splittings for these compounds were determined from their emission spectra and found to be abnormally small for π. π* states (˜ 1500 cm^-1). Indeed, the phosphorescence maxima of N-arylbenzamides occur slightly to the blue relative to their fluorescence maxima. Intersystem crossing efficiencies were determined for several of these compounds and are consistent with S₁→ S ₀ radiationless decay.     

In situ coarsening study of inverse micelle-prepared Pt nanoparticles supported on γ-Al2O3: pretreatment and environmental effects

The thermal stability of inverse micelle prepared Pt nanoparticles (NPs) supported on nanocrystalline γ-Al(2)O(3) was monitored in situ under different chemical environments (H(2), O(2), H(2)O) via extended X-ray absorption fine-structure spectroscopy (EXAFS) and ex situ via scanning transmission electron microscopy (STEM). Drastic differences in the stability of identically synthesized NP samples were observed upon exposure to two different pre-treatments. In particular, exposure to O(2) at 400 °C before high temperature annealing in H(2) (800 °C) was found to result in the stabilization of the inverse micelle prepared Pt NPs, reaching a maximum overall size after moderate coarsening of ～1 nm. Interestingly, when an analogous sample was pre-treated in H(2) at ～400 °C, a final size of ～5 nm was reached at 800 °C. The beneficial role of oxygen in the stabilization of small Pt NPs was also observed in situ during annealing treatments in O(2) at 450 °C for several hours. In particular, while NPs of 0.5 ± 0.1 nm initial average size did not display any significant sintering (0.6 ± 0.2 nm final size), an analogous thermal treatment in hydrogen leads to NP coarsening (1.2 ± 0.3 nm). The same sample pre-dosed and annealed in an atmosphere containing water only displayed moderate sintering (0.8 ± 0.3 nm). Our data suggest that PtO(x) species, possibly modifying the NP/support interface, play a role in the stabilization of small Pt NPs. Our study reveals the enhanced thermal stability of inverse micelle prepared Pt NPs and the importance of the sample pre-treatment and annealing environment in the minimization of undesired sintering processes affecting the catalytic performance of nanosized particles.     

Organometallic Polymers. XXVII. Radical-Initiated Polymerization and Copolymerization of π-(2, 4-Hexadien-1-yl Acrylate) tricarbonyliron

The novel monomer, π-(2, 4-hexadiene- l-yl acrylate) tricarbonyliron (HATI), has been prepared by two routes. It was homopolymerized and copolymerized with acrylonitrile, vinyl acetate, styrene, and methyl acrylate in benzene solutions. In all cases azobisisobutyronitrile was the initiator. The relative reactivity ratios, where HATI is defined as M₁, were determined: r₁ = 0.34, r₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = vinyl acetate; r₁ = 0.26, r₂ = 1.81, M₂ = styrene; and r₁ = 0.30, r₂ = 0.74, M₂ = methyl acrylate. The homo-and copolymers had high values of T_g. When polymerizations are carried out at high concentrations, a very high molecular weight tail is observed in HATI hompolymerizations and in HATI-methyl acrylate copolymerizations. The polymers were characterized by IR, gel permeation chromatography, viscosity, and differential scanning calorimetry studies. Finally, thermal decompositions carried out in air resulted in decomposition of the Fe(CO)₃ group, producing Fe₂O₃ as a fine powder. Thermal decomposition under nitrogen (in solution and on solids ground into KBr pellets) resulted in slow destruction of the Fe(CO)₃ groups but the resulting polymer mass was insoluble, and the question of what form the iron exists in (Fe metal, oxides, carbides, etc.) has not been answered.     

Polymerization of Methane and Olefin Mixtures over Fluosulfonic Acid and Antimony Pentafluoride

Mixtures of methane and olefins (ethylene, propylene, butenes, butadiene, and styrene) have been polymerized over HSO₃ F-SbF₃ to yield an oily oligomer with a molecular weight ranging from 100 to 700. The NMR spectra of each polymer showed a sharp peak at or near 1.25 &, suggesting the presence of block methylene in the polymer. The formation of block methylene is surprising considering the fact that the polymerization reaction is carbonium ion in nature. A primary cation has been invoked to explain the results. The formation of this primary cation must involve some extraordinary stabilization by some component in the acid.     

Graft Copolymerizations of Polysaccharides. II. Acrylamide Grafting to Yellow Dextrin

Graft copolymers of acrylamide and yellow dextrin were prepared using cerium(IV) as initiator. The yellow dextrin had a very broad molecular weight distribution but was fractionated utilizing dialysis and ultrafiltration membranes. Initiator efficiencies were determined using size exclusion chromatography and were found to be between 2.4 and 34%. Initiator efficiency increased with acrylamide concentration at constant cerium (IV) and yellow dextrin concentrations, and decreased with increasing cerium(IV) concentration at constant acrylamide and yellow dextrin concentrations. Plots of acrylamide conversion and intrinsic viscosity vs initial acrylamide concentration at constant yellow dextrin and ceric ion concentrations showed a maximum at about 2.0 M.