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-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

Vibrational dynamics of fullerene molecules adsorbed on metal surfaces studied with synchrotron infrared radiation

Infrared (IR) spectroscopy of chemisorbed C₆₀ on Ag (111), Au (110) and Cu (100) reveals that a non-IR-active mode becomes active upon adsorption, and that its frequency shifts proportionally with the charge transferred from the metal to the molecule by about 5 cm^-1 per electron. The temperature dependence of the frequency and the width of this IR feature have also been followed for C₆₀/Cu (100) and were found to agree well with a weak anharmonic coupling (dephasing) to a low-frequency mode, which we suggest to be the frustrated translational mode of the adsorbed molecules. Additionally, the adsorption is accompanied by a broadband reflectance change, which is interpreted as due to the scattering of conduction electrons of the metal surface by the adsorbate. The reflectance change allows determination of the friction coefficient of the C₆₀ molecules, which results in rather small values (∼2×10⁹ s^-1 for Ag and Au, and ∼1.6×10⁹ s^-1for Cu), consistent with a marked metallic character of the adsorbed molecules. Pre-dosing of alkali atoms onto the metal substrates drastically changes the IR spectra recorded during subsequent C₆₀ deposition: anti-absorption bands, as well as an increase of the broadband reflectance, occur and are interpreted as due to strong electron–phonon coupling with induced surface states. Received: 6 June 2001 / Accepted: 23 October 2001 / Published online: 3 April 2002     

Konvergente und asymptotische Darstellungen für die Lösungen linearer Differentialgleichungen,deren Koeffizienten Dirichletsche Reihen oder Exponentialpolynome mit komplexen Exponenten sind

Ohne ZusammenfassungDie vorliegende Arbeit wurde von der Mathematisch-naturwissenschaftlichen Fakultät der Universität Jena als Dissertation (D 27) angenommen. nachdem sie vorher einen Fakultätspreis erhalten hatte. Referent war Herr Prof. Hermann Schmidt. Ich möchte ihm auch hier meinen Dank für die Förderung aussprechen, die er mir durch seine vielfachen persönlichen Anregungen zuteil werden ließ.     

On Congruence of Complex Matrices

For each of a standard set of normal forms for (n × n) complex matrices under the relation of congruence, explicit matrices are exhibited which transform, via congruence, the normal form to its transpose.