The Cartan,Choquet and Kellogg properties for the fine topology on metric spaces

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We apply these key tools to establish a fine version of the Kellogg property, characterize finely continuous functions by means of quasicontinuous functions, and show that capacitary measures associated with Cheeger supersolutions are supported by the fine boundary of the set.     

A variational principle for adaptive approximation of ordinary differential equations

Summary A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=local errorweight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms. Mathematics Subject Classification (2000):65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK).     

Moser iteration for (quasi)minimizers on metric spaces

We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces.     

Multicriteria Semi-Obnoxious Network Location Problems (MSNLP) with Sum and Center Objectives

Locating a facility is often modeled as either the maxisum or the minisum problem, reflecting whether the facility is undesirable (obnoxious) or desirable. But many facilities are both desirable and undesirable at the same time, e.g., an airport. This can be modeled as a multicriteria network location problem, where some of the sum-objectives are maximized (push effect) and some of the sum-objectives are minimized (pull effect).We present a polynomial time algorithm for this model along with some basic theoretical results, and generalize the results also to incorporate maximin and minimax objectives. In fact, the method works for any piecewise linear objective functions. Finally, we present some computational results.     

Algorithms for suppressing ultrasonic backscattering from material structure

In pulse-echo ultrasonic inspection the backscattering from the material structure appears in the received ultrasonic images as clutter, often referred to as grain noise, which impairs the inspection results. A toolbox including algorithms for suppressing ultrasonic clutter is presented in the paper. Several processing algorithms capable of suppressing grain noise have been proposed, of which the split spectrum processing (SSP) probably is the most renowned. The classical SSP technique applies a filter bank to some frequency band that has to be precisely known in advance, to obtain a set of narrow-band signals that are tested for mutual correlation using some statistical operation. A number of SSP algorithms with different statistical operations are included in the toolbox. A completely different approach is to use explicit statistical models of grain noise and defects and to design an optimal filter based on those models. A simple such algorithm, based on noncoherent detection (NCD) known from communications, is also included in the toolbox. The toolbox, implemented in Matlab, is provided with a user-friendly graphical interface facilitating comparison of the algorithms.     

Bier Spheres and Posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bier’s construction: the Bier posets Bier(P, I) of an arbitrary bounded poset P of finite length. In the case of face posets of PL spheres this yields cellular “generalized Bier spheres.” In the case of Eulerian or Cohen–Macaulay posets P we show that the Bier posets Bier(P, I) inherit these properties. In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields “many shellable spheres,” most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.     

CRYRING at the LSR at FLAIR

FLAIR will be the next-generation facility for physics with low-energy antiprotons, providing antiprotons at energies from tens of MeV down to rest. It will also offer unique possibilities for physics with highly charged ions at very low energies. The FLAIR facility will have two deceleration rings, the LSR which will decelerate antiprotons to 300 keV and the USR which will bring them down further to 20 keV. The LSR will consist of the present CRYRING at the Manne Siegbahn Laboratory. During the next few years, CRYRING will be modified with respect to injection and extraction, to allow injection of 30 MeV antiprotons and to provide it with both fast (single-turn) and slow (resonant) extraction at a variable energy. We here describe plans and preparations for the transfer of CRYRING to FLAIR, giving, in particular, an overview of new components for injection and extraction.     

New methods for calculating \alpha BB-type underestimators

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another.     

Acoustic characteristics of a heavy duty vehicle cooling module

Studies dedicated to the determination of acoustic characteristics of an automotive cooling package are presented. A shrouded subsonic axial fan is mounted in a wall separating an anechoic- and a reverberation room. This enables a unique separation of the up- and downstream sound fields. Microphone measurements were acquired of the radiated sound as a function of rotational speed, fan type and components included in the cooling module. The aim of the present work is to investigate the effect of a closely mounted radiator upstream of the impeller on the SPL spectral distribution. Upon examination of the SPL spectral shape, features linked specifically to the source and system are revealed. The properties of a reverberant sound field combined with the method of spectral decomposition permit an estimation of the source spectral distribution and the acoustic transfer response, respectively. Additionally, purely intrinsic acoustic properties of the radiator are scrutinized by standardized ISO methods. A new methodology comprising a dipole sound source is adopted to circumvent limitation of transmission loss measurement in the low frequency range. The sound attenuation caused by the radiator alone was found to be negligible.