A thermodynamic formulation of the equations of motion and buoyancy frequency for Earth's fluid outer core

This work presents a precise formulation of the balance and constitutive relations appropriate to the modeling of the motion of the fluid outer core, including a full thermodynamic analysis and derivation of the buoyancy frequency, its role in the equations of motion for the fluid outer core, and the dependence of this equation on the thermodynamic state of the outer core. It is shown that the equation of motion is controlled by a single parameter, the buoyancy frequency. Its definition is general, so as to include also thermodynamic effects in various forms. The dependence on concentration or entropy-gradients is of importance for motions on longer time scales but also influences core undertones, the oscillations of the Earth's outer core, in regions of strong concentration gradients. By appropriate scaling a variety of different approximations arise from this formulation using the thermodynamic definiton of the buoyancy frequency. Special interest is put on the scaling for the outer core eigenmodes yielding consistent formulations for the Boussinesq- and the subseismic approximation.     

A remark on the uniqueness of embeddings of linear spaces into desarguesian projective planes

Suppose that q ? 2 is a prime power. We show that a linear space with a(q + 1)² + (q + 1) points, where a ? 0.763, can be embedded in at most one way in a desarguesian projective plane of order q. © 1995 John Wiley & Sons, Inc.     

A remark on tilting theory and DG algebras

Techniques of homological algebra over DG algebras [2, VI, 10] provide an alternative approach to ‘Morita theory for derived categories’ [5]. Supported by a grant of the Swiss National Foundation     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

A long-wavelength biolabeling reagent based on the oxonol fluorophore

A red fluorescent dye of the oxonol class, bis-[1-(carboxymethyl)barbituric acid-(5)]-pentamethinoxonol, has been synthesized and, in the form of the succinimidyl active ester, has been applied to antibody labeling for application to flow cytometry and to imaging of tissue sections. The new dye, named CMOX (for carboxymethyloxonol), shows maximum excitation at 583 nm and emission at 611 nm, with a quantum yield of 0.2 in aqueous buffer and methanol. Antibodies labeled with the new dye show favorable brightness, photostability, and low levels of nonspecific binding.     

Strategy-proofness, solidarity, and consistency for multiple assignment problems

We consider a problem of allocating indivisible objects when agents may desire to consume more than one object and no monetary transfers are allowed. We are interested in allocation rules that satisfy desirable properties from an economic and social point of view. In addition to strategy-proofness and Pareto efficiency, we consider consistency and two solidarity properties (replacement-domination and population-monotonicity). In most of the cases, these properties are satisfied only by serially dictatorial rules. Received: November 1999/Final version: December 2001     

Gas chromatographic determination of aromatic amines in water samples after solid-phase extraction and derivatization with iodine: I. Derivatization

A new method for the selective determination of aromatic amines is presented, which is based on the solid-phase extraction at pH 9 and subsequent derivatization of the analytes to the corresponding iodobenzenes. These can selectively and sensitively be determined with gas chromatography and electron-capture detection. Separation of at least 30 compounds in a single chromatographic run in 30 min is possible. With this method, 56 aromatic amines were investigated, and only in six cases no derivatives were obtained. Limits of quantitation were between 0.5 and 8 μg l⁻¹, but may still be lowered with higher sample volumes or different injection techniques. The application to water samples revealed the suitability for the investigation of ground, leachate and wastewater.     

Thin-Film Flow Influenced by Thermal Noise

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely on a long-wave-approximation and Fokker–Planck-type arguments. We formulate a discretization method and give first numerical evidence for our conjecture that thermal fluctuations are capable of accelerating film rupture and that discrepancies with respect to time-scales between physical experiments and deterministic numerical simulations can be resolved by taking noise effects into account.