An algebraic characterization ofB-convergent Runge-Kutta methods

Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung     

The combinatorics of the bar resolution in group cohomology

We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex K_n whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11].

We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.     

Molecular dynamics simulations of the oligonucleotide with the modified phosphate/phosphonate internucleotide linkage

Impact of the internucleotide linkage modification by inserting a methylene group to the P-O bond (—O—PO ₂ ^— —O— chain changed for —O—PO ₂ ^— —CH₂—O—), on the modified oligonucleotide binding ability to the natural DNA strand was studied by molecular dynamics simulation. Complex of (dT)₁₁ with a deoxyadenosine undecamer containing alternating modified and natural internucleotide linkage was studied as a model system. The Amber force field was completed by a set of new parameters needed to model the modified part of the nucleotide. The simulations confirmed existence of a double-helical complex the melting point of which is considerably higher than 300 K. While the thymidine (unmodified) strand possesses a B-type secondary structure, the conformation of the adenosine (modified) strand is not stable at 300 K. The -ggt conformation of the modified linkages is highly preferred, temporary jumps to the -g-gt and ggt conformations were, however, observed.     

A quasiconformal dynamic property of the disk

It is known that every conformai embedding of the disk into the extended complex plane possesses a r²-quasiconformal extension across eachr-level line (the r²-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther ²-property. Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.     

On operators and search space topology in multi-objective flow shop scheduling

Multi-objective optimization using evolutionary algorithms identifies Pareto-optimal alternatives or their close approximation by means of a sequence of successive local improvement moves. While several successful applications to combinatorial optimization problems are known, studies of underlying problem structures are still scarce.