Expressive equivalence of least and inflationary fixed-point logic

We study the relationship between least and inflationary fixed-point logic. In 1986, Gurevich and Shelah proved that in the restriction to finite structures, the two logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFP-formula was left open.

In this paper, we answer the question negatively, i.e. we show that the two logics are equally expressive on arbitrary structures. We give a syntactic translation of IFP-formulae to LFP-formulae such that the two formulae are equivalent on all structures.

As a consequence of the proof we establish a close correspondence between the LFP-alternation hierarchy and the IFP-nesting depth hierarchy. We also show that the alternation hierarchy for IFP collapses to the first level, i.e. the complement of any inflationary fixed point is itself an inflationary fixed point.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.     

Primes in quadratic progressions on average

In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.     

Isotopic production cross sections of residues in reactions induced by relativistic heavy ions with protons and deuterons

The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets.     

Non-destructive analysis of archeological samples by energy-dispersive X-ray fluorescence

Summary A non-destructive method is described for the determination of major and minor constituents in archeological specimens by energy-dispersive X-ray fluorescence. Homogeneity tests are made by measuring at various sites of the specimen. In the same way, mean values are obtained for inhomogeneous specimen without taking samples. For calibration, powder standards are used. In case of the determination of elements with numbers up to 14 (Si) a vacuum chamber is used and the dimensions of the specimens are limited by the dimensions of that vacuum chamber, whereas for the determination of elements from K up to U specimens of any size, form or weight are suitable.

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Zerstörungsfreie Analyse von archäologischen Proben mit Hilfe der Energie-dispersiven Röntgenfluorescenzanalyse

Zusammenfassung Eine zerstörungsfreie Methode für die Bestimmung von Haupt- und Nebenbestandteilen in archäologischen Proben mit Hilfe der Energie-dispersiven Röntgenfluorescenzanalyse wird beschrieben. Für Homogenitätstests wird an mehreren Stellen der Probe gemessen. In der gleichen Weise werden für inhomogene Proben Mittelwerte erhalten ohne Probenahme. Für die Eichung werden Pulverstandards verwendet. Im Falle der Bestimmung von Elementen mit Ordnungszahlen bis 14 (Si) wird eine Vakuumkammer eingesetzt, und die Dimensionen der Proben sind durch die Dimensionen dieser Vakuumkammer begrenzt, während für die Bestimmung der Elemente K bis U Proben jeder Größe, jeder Form oder jeden Gewichts verwendbar sind.