Bel-Robinson Energy and Constant Mean Curvature Foliations

An energy estimate is proved for the Bel-Robinson energy along a constant mean curvature foliation in a spatially compact vacuum spacetime, assuming an bound on the second fundamental form, and a bound on a spacetime version of Bel-Robinson energy. Communicated by Sergiu KlainermanSubmitted 25/07/03, accepted 27/01/04     

A model for the economic evaluation of master city plans: a pilot study of Västerås,Sweden

The paper introduces the framework, problems addressed, objective function, types of variables and so on for a model designed to facilitate the economic evaluation of master city plans. The model presented here has been used in a pilot study of the city of Västerås, Sweden. It consists of three main parts, data, results and method. Some conclusions are drawn.     

Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

Comparison of the efficiency of different GLC multi-residue methods on crops containing pesticide residues

Summary The efficiency of the extraction methods with acetone and with ethyl acetate are compared with regard to the multi-pesticide residue determination in fruits and vegetables. The ethyl acetate-method gave higher recoveries for polar pesticides and seems somewhat easier, quicker and cheaper in handling but some co-extractives in the GC-extract are observed. In general, both methods gave acceptable and equivalent recoveries for the pesticides tested.     

REMPI as a tool for studies of OH radicals in catalytic reactions

2 +? O₂→H₂O on polycrystalline Pt foils has been studied by detection of desorbing OH radicals using the Resonance Enhanced Multiphoton Ionization, REMPI, technique. The measurements were performed at catalyst temperatures of 1000–1400 K and a total pressure below 10^-4 mbar. The studies of OH desorption by REMPI were achieved using a two-photon excitation D²Σ^-–X²Π (1–0), followed by one-photon ionization. The ions were detected in a time-of-flight mass spectrometer, TOF-MS, in order to avoid interference from non-resonantly ionized molecules. By applying TOF-MS, a simultaneous non-resonant ionization and detection of H₂, O₂ and H₂O was achieved. Recorded REMPI spectra were compared with spectra simulated using known molecular constants. The kinetics of the reaction derived from the measurements were compared with what was obtained in earlier LIF detection of OH, performed at higher total reactant pressure using the A–X transition. REMPI TOF-MS is shown to be a complement to LIF for reaction studies below 5×10^-4 mbar total pressure, where LIF is too insensitive for quantification. The reaction kinetics was found to be in agreement with a theoretic model and previous LIF studies. Received: 8 March 1996/Revised version: 4 October 1996     

The use of uncertainty estimates of test results in comparisons with acceptance limits

When a test is performed in order to qualify a material or a product for a certain use, the result is generally compared with an acceptance limit. The test result has an uncertainty which should be estimated and stated (e.g. in accordance with GUM). Very often this is not the case. Further, discussions often arise on the issue of how the uncertainty shall be considered in relationship to the acceptance limit. The intention of this note is to describe, in simple terms, the statistical background and to give some recommendations. In short, there are two clean-cut, extreme situations. The first case is when the uncertainty of the testing procedure is the dominating factor. Here it is found that the estimates of single laboratories cannot, generally, be used for comparisons with acceptance limits. One should have standardised, well-verified estimates based on comprehensive investigations of the method. It can also be concluded that comparisons between test results and acceptance limits have to be made with regard to the actual circumstances, as, e.g. how the acceptance limit is related to the risk. In the second case, the variation in the property of the material or product dominates and the uncertainty of the testing procedure is negligible. When the results are non-quantitative (go – no go), statistical methods can be used to estimate the risk taken with a certain sampling and acceptance strategy that a certain proportion of the batch to be delivered does not qualify. This should be considered more often in standardisation of product test methods. When the results are quantitative, a statistical analysis should be performed and the uncertainty should be compared with the acceptance limit as before, from the actual circumstances. When effects of testing uncertainty and product variation are comparable a sound treatment requires extensive experimental work. No short cuts can be made without loss of confidence! Received: 17 August 2001 Accepted: 21 March 2002     

Pionic Fusion Study of the halo analogue state6Li

The isobaric analogue state of the ground state of the halo nucleus⁶He,⁶Li* has been studied in a pionic fusion experiment at the CELSIUS storage ring facility in Uppsala, Sweden. This was the first of two proposed experiments with the aim to study the high momentum part of the wave functions of the halo nuclei⁶He and⁶Li (0⁺, T=1). The Li nuclei were produced in inverse kinematics reactions with alpha particles incident on a deuterium cluster jet target. The⁶Li ions were detected in a zero-degree spectrometer situated in the fourth quadrant of the CELSIUS ring. The measurement was done for three different beam energies corresponding to 5.4, 2.2 and 1.5 MeV above threshold in the c.m. The cross-sections slowly increase with beam energy from 95 nb at the lowest energy to about 250 nb at 5.4 MeV above threshold.