Recent advances in scanning tunneling microscopy involving magnetic probes and samples

We report on recent developments in the field of STM performed with magnetic probes and samples. The choice of appropriate magnetic sensors and their in situ preparation will be described. We further focus on the information obtained in spin-polarized scanning tunneling microscopy (SPSTM) as well as on possible modes of operation for simultaneous acquisition of topographic and magnetic data. The prospects for SPSTM and related magnetic sensitive SXM techniques will be discussed.Permanent address: Forschungszentrum Jülich, ISI, W-5170 Jülich 1, Fed. Rep. Germany     

Young modules and filtration multiplicities for Brauer algebras

We define permutation modules and Young modules for the Brauer algebra B _k (r,δ), and show that if the characteristic of the field k is neither 2 nor 3 then every permutation module is a sum of Young modules, respecting an ordering condition similar to that for symmetric groups. Moreover, we determine precisely in which cases cell module filtration multiplicities are well-defined, as done by Hemmer and Nakano for symmetric groups. Supported by the European Community through Marie Curie fellowship MCFI 2002-01325 Supported by EPSRC grant GR/S18151/01     

Transvection free groups and invariants of polynomial tensor exterior algebras

Let :GGl(n, ) be a representation of a finite groupG over a field such that the ring of invariants is a polynomial algebra . It is known that in the nonmodular case (i.e., when the order of the group is not divisible by the characteristic of ), the invariants ofG acting on the tensor product of a polynomial and an exterior algebra are given by ,d denoting the exterior derivative. We show that in the modular case, the ring of invariants in is of this form if and only if is a polynomial algebra and all pseudoreflections in (G) are diagonalizable.     

The two‐variable fragment with counting and equivalence

We consider the two‐variable fragment of first‐order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NExpTime ‐complete. We further show that the corresponding problems for two‐variable first‐order logic with counting and two equivalences are both undecidable.     

Reaction of N-acylthioureas with electrophilic reagents : Synthesis of 1,3,5-oxadiazinium salts, 1,3,5-thiadiazinium salts, 1,2,4-dithiazolium salts and benzothiazoles

N-Acylthioureas 1 can be easily transformed into 2,4-diamino-6-aryl-1,3,5-oxadiazinium salts 12, 2,4-diamino-6-aryl-1,3,5-thiadiazinium salts 13,3-amino-5-aryl-1,2,4-dithiazolium salts 19 and 2-acylimino-benzothiazolines 22, respectively by reaction with different electrophiles. The structure of the compounds prepared is confirmed by analytical data as well as by chemical transformations.