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.     

Real Paley-Wiener theorems associated with the weinstein operator

In this paper we use real analysis techniques to establish a new real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Weinstein operator. More precisely we characterize the C ^∞-functions whose image under the Fourier-Bessel transform are functions with compact support through an L ^p growth condition, p ∈ [1, +∞] and we give another version of the real Paley-Wiener theorem for L ²-functions.     

Dynamic response of permalloy/Cu/Co magnetoresistive sandwiches

The dynamic response of trilayer magnetoresistive permalloy/Cu/Co films was studied by high-frequency permeability spectra measurements. The resonance frequency is shown to depend on the interlayer copper thickness. This dependence is related to exchange coupling between permalloy and cobalt and the interaction field is estimated using the Landau–Lifschitz–Gilbert model.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].      

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.     

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.