G-invariante Morse-funktionen

If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory.     

The ILUCP Preconditioner

We introduce a new incomplete LU‐type preconditioner which combines the advantages of Crout's formulation of Gaussian elimination with pivoting. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aggregation/Disaggregation Iterative Methods Applied to Leontev Systems and Markov Chains

The paper surveys some recent results on iterative aggregation/disaggregation methods (IAD) for computing stationary probability vectors of stochastic matrices and solutions of Leontev linear systems. A particular attention is paid to fast IAD methods.     

Running time experiments on some algorithms for solving propositional satisfiability problems

Satisfiability problems are of importance for many practical problems. They are NP-complete problems. However, some instances of the SAT problem can be solved efficiently. This paper reports on a study concerning the behaviour of a variety of algorithmic approaches to this problem tested on a set of problems collected at FAW. The results obtained give a lot of insight into the algorithms and problems, yet also show some general technical and methodological problems associated with such comparisons.     

Combining the use of solid‐supported transition metal catalysis with microwave irradiation in solution‐phase parallel library synthesis

Microwave heating methods have been combined with the use of solid-supported catalysts to produce small solution-phase libraries of medicinally-relevant compounds. Palladium supported on charcoal (Pd/C) has been used to produce libraries of pyrazole compounds for screening in COX II studies via Suzuki cross coupling reactions, while the same catalyst has been used also to produce styryl-based nAChR compounds using analogous chemistry. Although the reaction substrates are very different (aryl vs. vinyl), this catalyst system provided consistently good and reliable results. The use of a polystyrene-supported Ru catalyst for ring-closing metathesis (RCM) reactions was also evaluated to prepare benzolactam structures for evaluation as factor Xa inhibitors.     

Supershell structure in alkali metal nanowires

Nanowires are formed by indenting and subsequently retracting two pieces of sodium metal. Their cross section gradually reduces upon retraction and the diameters can be obtained from the conductance. In previous work we have demonstrated that when one constructs a histogram of diameters from large numbers of indentation-retraction cycles such histograms show a periodic pattern of stable nanowire diameters due to shell structure in the conductance modes. Here, we report the observation of a modulation of this periodic pattern, in agreement with predictions of a supershell structure.     

Yrast excitations in129Te

Using an 11.4MeV/u¹³⁶Xe beam of the UNILAC accelerator of GSI and a^natW target, A=184 isobars were produced and separated by using an on-line mass separator. A new isomeric state was found in¹⁸⁴Hf. This state decays with a half-life of 48(10) s and emits three -rays of 73, 482, and 555 keV as well as lower-lying cascade transitions. The hindrance of the 73 keV-E1 transition with K=8 is compared with those of other even-even hafnium isotopes. The half-life of¹⁸⁴Lu was estimated to be between 15 and 25s.     

A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast magnetic resonance (MR) images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained via DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.