Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

Tuning Aqueous Supramolecular Polymerization by an Acid-Responsive Conformational Switch

Besides their widespread use in coordination chemistry, 2,2’-bipyridines are known for their ability to undergo cis–trans conformational changes in response to metal ions and acids, which has been primarily investigated at the molecular level. However, the exploitation of such conformational switching in self-assembly has remained unexplored. In this work, the use of 2,2’-bipyridines as acid-responsive conformational switches to tune supramolecular polymerization processes has been demonstrated. To achieve this goal, we have designed a bipyridine-based linear bolaamphiphile, 1 , that forms ordered supramolecular polymers in aqueous media through cooperative aromatic and hydrophobic interactions. Interestingly, addition of acid (TFA) induces the monoprotonation of the 2,2’-bipyridine moiety, leading to a switch in the molecular conformation from a linear (trans) to a V-shaped (cis) state. This increase in molecular distortion along with electrostatic repulsions of the positively charged bipyridine-H⁺ units attenuate the aggregation tendency and induce a transformation from long fibers to shorter thinner fibers. Our findings may contribute to opening up new directions in molecular switches and stimuli-responsive supramolecular materials.     

On the Homeomorphism Groups of Cantor's Discontinuum and the Spaces of Rational and Irrational Numbers

The paper shows that the homeomorphism groups of, respectively,Cantor's discontinuum, the rationals and the irrationals haveuncountable cofinality. It is well known that the homeomorphismgroup of Cantor's discontinuum is isomorphic to the automorphismgroup Aut B of the countable, atomless boolean algebra B. Soalso Aut B has uncountable cofinality, which answers a questionposed earlier by the first author and H. D. Macpherson. Thecofinality of a group G is the cardinality of the length ofa shortest chain of proper subgroups terminating at G. 2000Mathematics Subject Classification 20B22, 20E15.     

Investigation of lifetimes in dipole bands of 141Eu

Lifetimes have been measured for dipole bands in ¹⁴¹Eu using DSAM. The deduced B(M1) and B(E2) values as well as B(M1)/B(E2) ratios are compared with calculations in the framework of the TAC (Tilted Axis Cranking) and SPAC (Shears mechanism with Principal Axis Cranking) models. The dipole bands can be interpreted as magnetic rotational bands.Received: 6 April 2004, Revised: 14 May 2004, Published online: 13 July 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Re Collective levels - 21.10.Tg Lifetimes - 27.60. + j      

Uncountable cofinalities of automorphism groups of linear and partial orders

We demonstrate the uncountable cofinality of the automorphism groups of various linear and partial orders. We also relate this to the ‘Bergman’ property, and discuss cases where this may fail even though the cofinality is uncountable.     

Lifetimes and side-feeding population of the yrast band levels in 131La

Lifetimes of yrast levels with spins I^π = 23/2^--43/2^- in ¹³¹La populated in the ¹²²Sn(¹⁴N, 5n) reaction at a beam energy of 70MeV are measured by the Doppler Shift Attenuation method. A model of side-feeding population is presented. The model parameters are determined in an experiment based on the lineshape of γ-transitions from two highest spin levels and from the intensity distribution along the yrast band. The properties of the h_11/2 band in ¹³¹La are compared with the theoretical predictions obtained in the framework of the Core-Quasi-Particle Coupling and the self-consistent Total Routhian Surface models.     

New approach to doppler lifetime measurements

The modified procedure of RDM and DSAM data analysis applied to lifetime measurements in ¹¹⁹I presented. The main points are: the Recoil Distance Doppler Shift Attenuation Method, the evaluation of side-feeding time, and self-calibration of stopping-power parameters by “semi-thick” target method.