Unsteady axisymmetric stagnation flow on a circular cylinder

Unsteady, axisymmetric stagnation flow about a circular cylinderis examined when the far-field flow is a periodic function oftime with a fixed time average and an oscillatory part of prescribedamplitude and frequency. Solutions are computed for arbitraryvalues of the Reynolds number, quantifying the effects of surfacecurvature, and a frequency parameter based on the period ofthe far-field flow. It is found that solutions remain regularand periodic provided that the far-field amplitude lies belowa critical value. Above this value, solutions terminate in afinite-time singularity. The blow-up time is delayed by increasingthe curvature of the surface. These results are corroboratedby asymptotic predictions valid in the limits of small and largeamplitude and frequency. For large Reynolds number, the problemreduces to the two-dimensional stagnation-point flow againsta plane wall studied by previous authors.     

A two-dimensional Minkowski ?(x) function

A function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is shown there exists a natural class of pairs of cubic irrational numbers in the same cubic number field that are mapped to pairs of rational numbers, in analog to ?(x) mapping quadratic irrationals on the unit interval to rational numbers on the unit interval. It is also shown that this new function satisfies an analog to the fact that ?(x), while increasing and continuous, has derivative zero almost everywhere.     

Identification of Error Types in Preservice Teachers' Attempts to Create Fraction Story Problems for Specified Operations

The purpose of this research was to determine if recognizable error types exist in the work of preservice teachers required to create story problems for specific fraction operations. Students were given a particular single‐operation fraction expression and asked to do the calculation and then create a story problem that would require the use of both the expression and calculation to answer the story problem. Distinct error types, determined by mathematical and grammatical characteristics, were identified by the researchers. These error types were then used to analyze an additional set of work samples to determine frequency rates of error types. Future research will involve evaluating the efficacy of specific instructional methods with the goal of reducing the frequency of certain error types.     

Polyethylene glycol matrix reduces the rates of photochemical and thermal release of nitric oxide from S-nitroso-N-acetylcysteine

S -nitrosothiols have many biological activities and may act as nitric oxide (NO) carriers and donors, prolonging NO half-life in vivo. In spite of their great potential as therapeutic agents, most S -nitrosothiols are too unstable to isolate. We have shown that the S -nitroso adduct of N -acetylcysteine (SNAC) can be synthesized directly in aqueous and polyethylene glycol (PEG) 400 matrix by using a reactive gaseous (NO/O₂) mixture. Spectral monitoring of the S–N bond cleavage showed that SNAC, synthesized by this method, is relatively stable in nonbuf-fered aqueous solution at 25°C in the dark and that its stability is greatly increased in PEG matrix, resulting in a 28-fold decrease in its initial rate of thermal decomposition. Irradiation with UV light (λ= 333 nm) accelerated the rate of decomposition of SNAC to NO in both matrices, indicating that SNAC may find use for the photogeneration of NO. The quantum yield for SNAC decomposition decreased from 0.65 ± 0.15 in aqueous solution to 0.047 ± 0.005 in PEG 400 matrix. This increased stability in PEG matrix was assigned to a cage effect promoted by the PEG microenvironment that increases the rate of geminated radical pair recombination in the homolytic S–N bond cleavage process. This effect allowed for the storage of SNAC in PEG at −20°C in the dark for more than 10 weeks with negligible decomposition. Such stabilization may represent a viable option for the synthesis, storage and handling of S -nitrosothiol solutions for biomedical applications.     

Reversible chemisorption of carbon dioxide: simultaneous production of fuel-cell grade H2 and compressed CO2 from synthesis gas

One vision of clean energy for the future is to produce hydrogen from coal in an ultra-clean plant. The conventional route consists of reacting the coal gasification product (after removal of trace impurities) with steam in a water gas shift (WGS) reactor to convert CO to CO₂ and H₂, followed by purification of the effluent gas in a pressure swing adsorption (PSA) unit to produce a high purity hydrogen product. PSA processes can also be designed to produce a CO₂ by-product at ambient pressure. This work proposes a novel concept called “Thermal Swing Sorption Enhanced Reaction (TSSER)” which simultaneously carries out the WGS reaction and the removal of CO₂ from the reaction zone by using a CO₂ chemisorbent in a single unit operation. The concept directly produces a fuel-cell grade H₂ and compressed CO₂ as a by-product gas. Removal of CO₂ from the reaction zone circumvents the equilibrium limitations of the reversible WGS reaction and enhances its forward rate of reaction. Recently measured sorption-desorption characteristics of two novel, reversible CO₂ chemisorbents (K₂CO₃ promoted hydrotalcite and Na₂O promoted alumina) are reviewed and the simulated performance of the proposed TSSER concept using the promoted hydrotalcite as the chemisorbent is reported.     

C-glycosylation reactions of sulfur-substituted glycosyl donors: evidence against the role of neighboring-group participation

Nucleophilic substitution reactions of C-4 sulfur-substituted tetrahydropyran acetals revealed that neighboring-group participation does not control product formation. Spectroscopic evidence for the formation of an intermediate sulfonium ion is provided, as are data from nucleophilic substitution reactions demonstrating that products are formed from oxocarbenium ion intermediates. The selectivity was not sensitive to solvent or to which Lewis acid was employed. The identity of the heteroatom at the C-4 position also did not significantly impact diastereoselectivity. Consequently, neighboring-group participation was not responsible for the formation of either the major or the minor products. These studies implicate a Curtin-Hammett kinetic scenario in which the formation of a low-energy intermediate does not necessitate its involvement in the product-forming pathway.     

Structural effects on the reactivity of substituted arylphosphines as potential oxygen-scavenging additives for future jet fuels

Efforts to develop oxygen-scavenging additives for future jet fuels (JP-900) are presented. Results from radiolytic experiments are used to develop structure-reactivity relationships for electron-transfer-initiated oxygenation (ETIO) of variously substituted arylphosphines. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:133–138, 1998