FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Anomalous grazing incidence small-angle x-ray scattering studies of platinum nanoparticles formed by cluster deposition

The size evolution of platinum nanoparticles formed on a SiO2/Si(111) substrate as a function of the level of surface coverage with deposited clusters has been investigated. The anisotropic shapes of sub-nanometer-size nanoparticles are changed to isotropic on the amorphous substrate as their sizes increased. Using anomalous grazing incidence small-angle x-ray scattering (AGISAXS), the scattering from nanoparticles on the surface of a substrate is well separated from that of surface roughness and fluorescence. We show that AGISAXS is a very effective method to subtract the background and can provide unbiased information about particle sizes of less than 1 nm.     

Reactivity of DNA guanyl radicals with phenolate anions

Guanine bases are the most easily oxidized sites in DNA. Electron-deficient guanine species are major intermediates produced in DNA by the direct effect of ionizing radiation (ionization of the DNA itself) because of preferential hole migration within DNA to guanine bases. By using thiocyanate ions to modify the indirect effect (ionization of the solvent), we are able to produce these single-electron-oxidized guanine radical species in dilute aqueous solutions of plasmid DNA where the direct effect is negligible. The guanyl radical species produce stable modified guanine products. They can be detected in the plasmid by converting them to strand breaks after incubation with a DNA repair enzyme. If a phenol is present during irradiation, the yield of modified guanines is decreased. The mechanism is reduction of the guanine radical species by the phenol. It is possible to derive a rate constant for the reaction of the phenol with the guanyl radical. The pH dependence shows that phenolate anions are more reactive than their conjugate acids, although the difference for guanyl radicals is smaller than with other single-electron-oxidizing agents. At physiological pH values, the reduction of a guanyl radical entails the transfer of a proton in addition to the electron. The relatively small dependence of the rate constant on the driving force implies that the electron cannot be transferred before the proton. These results emphasize the potential importance of acidic tyrosine residues and the intimate involvement of protons in DNA repair.     

Dications of fluorenylidenes. The effect of substituent electronegativity and position on the antiaromaticity of substituted tetrabenzo[5.5]fulvalene dications

Oxidation of 3,6-disubstituted tetrabenzo[5.5]fulvalenes by SbF(5) results in the formation of dications that behave like two antiaromatic fluorenyl cations connected by a single bond. Both fluorenyl systems exhibit the paratropic shifts and nucleus independent chemical shifts (NICS) characteristic of antiaromatic species. Comparison with analogous 2,7-disubstituted tetrabenzo[5.5]fulvalenes reveals that the antiaromaticity of the substituted ring system can be altered substantially by changes in the placement of the substituents, possibly due to changes in the delocalization of charge in the system. Substituents in the 3,6-position decrease the antiaromaticity because of the increase in the benzylic resonance compared to 2,7-substituents.     

The ionization of perchloric and hydrofluoric acids in aqueous solution

Cyclical bifurcated hydrogen bonded structures are proposed for aqueous solutions of hydrofluoric acid and for the bifluoride ion which are consistent with the spectral data. The structure proposed for HF is also applicable to solutions in organic solvents. Raman spectra of tetramethylguanidinium perchlorate suggest that the corresponding Raman spectra of perchloric acid solutions may not be interpreted in terms of a completely dissociated acid. Other evidence including activity coefficient, heat capacity and partial molal volume data suggest that there is some association in relatively dilute perchloric acid solutions between the perchlorate ion and the hydrated proton. This association decreases in concentrated aqueous solutions.     

Enhancement of phosphoprotein analysis using a fluorescent affinity tag and mass spectrometry

A fluorescent affinity tag (FAT) was synthesized and was utilized to selectively modify phosphorylated serine and threonine residues via beta-elimination and Michael addition chemistries in a 'one-step' reaction. This labeling technique was used for covalent modification of both phosphoproteins and phosphopeptides, allowing identification of these molecular species by fluorescence imaging after solution- or gel-based separation methods. In addition to the strong fluorescence of the rhodamine tag, a commercially available antibody can be used to enrich low-abundance post-labeled phosphopeptides present in complex mixtures. Application of this methodology to phosphorylation-site mapping has been evaluated for a phosphoprotein standard, bovine beta-casein. Initial results demonstrated low femtomole detection limits after fluorescence image analysis of FAT-labeled proteins or peptides.