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.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Luminescent Labels—More than Just an Alternative to Radioisotopes?

Chemical, chromatographic, or spectrometric methods are generally unsuitable for the detection of molecules in the nano and subnanogram region because of their low sensitivity. The radioimmunoassay (RIA) developed by Yalow and Berson in 1959 combined the high sensitivity of radioactively labeled substances with the high specificity of immunological reactions for the first time. In this way it was possible to detect quantitatively the tiniest traces of substances in the presence of an excess of other, in some cases, similar foreign substances without prior enrichment. Immunoassays have certainly developed to become the most valuable analytical tool of in vitro diagnostics and are today routinely employed for the detection of endogenous and exogenous substances (e.g. hormones, tumor-associated proteins, bacteria, viruses, toxins, drugs, etc). The many disadvantages of radioactivity such as the required handling licenses, disposal costs, precautions necessary to prevent risks to health, short shelf-life, and limited sensitivity soon led to the search for other nonradioactive labeling methods. Encouraged by the development of light measuring techniques and the commercial availability of highly sensitive apparatus, radioactive isotopes as labels are today being replaced increasingly by enzymes, fluorophores, or luminophores. Some of the new luminescent labels have, however, not only facilitated replacement of radioisotopes, but also a breakthrough into what has until now been unattainable levels of sensitivity. The following article reviews the methods of luminescent labeling and their applications mainly in the area of immunoassays.