Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Variational derivation of the adiabatic time-dependent Hartree-Fock formalism and generalized Hamiltonian dynamics

The three-particle collision process 3 → 3 with relative high-energy motion of each pair of particles described by a model with eikonal Hamiltonian is investigated. No additional restrictions on the motion of the particles (such as fixed scattering centre approximation) are imposed. It is shown that the three-particle problem in this case can be solved analytically. An explicit expression for 3 → 3 amplitude off the energy shell is obtained as the result of the exact summation of the multiple scattering series in the considered model. On the energy shell this series breaks off (there are no terms higher than triple). The formula for the mutual cancellation of the higher-order terms of the series is derived.     

Local Observation of Field Polarity Dependent Flux Pinning by Magnetic Dipoles

A scanning Hall probe microscope is used to study flux pinning in a thin superconducting Pb film covering a square array of single-domain Co dots with in-plane magnetization. We show that single flux quanta of opposite sign thread the superconducting film below T(c) at the opposite poles of these dipoles. Depending on the polarity of the applied field, flux lines are attracted to a specific pole of the dipoles, due to the direct interaction with the vortexlike structures induced by the local stray field.     

The arrival time brachistochrones in general relativity

We consider a general relativistic version of the classical brachistochrone problem, whose solutions are causal curves, parameterized by a constant multiple of their proper time and with 4-acceleration perpendicular to a given observer field, that extremize the arrival time measured by an observer at the final endpoint. This kind of brachistochrones presents characteristics different from the travel time brachistochrones, that were studied in [8, 9, 10]. In this article we formulate the variational problem in a general context; moreover, in the case of a stationary metric, we prove two variational principles and we determine the second order differential equation satisfied by the arrival time brachistochrone. Using these variational principles and techniques from Critical Point Theory we establish some results concerning the existence and the multiplicity of travel time brachistochrones with a given energy between an event and an observer.     

An analytical theory for Riemannian cubic polynomials

We establish some global existence and multiplicity resultsfor Riemannian cubic polynomials in a complete Riemannian manifold.