Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities alg-rk(W) ≤ flat-rk(G) ≤ rk(|W|₀). Here, alg-rk(W) is the maximal Z-rank of abelian subgroups of W, and rk(|W|₀) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|₀. We can prove these inequalities under weaker assumptions. We also show that for any integer n ≥ 1 there is a simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G) = n and which is not linear.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Ramsey numbers for graphs with five vertices

The Ramsey numbers r(F¹, F²) are tabulated for essentially all but six pairs of graphs F¹ and F² with five vertices.     

Metal complexation of crosslinked polyacrylamide-supported dithiocarbamates: Effect of the molecular character and extent of crosslinking on complexation

Dithiocarbamate functions were incorporated into different polyacrylamide matrices crosslinked with a flexible and hydrophilic crosslinking agent, tetraethyleneglycol diacrylate (TEGDA), and their complexation behaviours were investigated. Crosslinked polyacrylamides with varying extents of the tetrafunctional TEGDA crosslinks were prepared by free radical solution polymerization at 60°C using potassium persulphate as initiator in ethanol. The dithiocarbamate functionality was incorporated into these polyacrylamides by a two-step polymer-analogous reaction involving (i)trans-amidation with ethylenediamine and (ii) dithiocarbamylation of the aminopolyacrylamide with carbon disulphide and alkali. The complexations of dithiocarbamate with Cu(II), Ni(II), Zn(II), Co(II) and Hg(II) ions were followed under different conditions. The metal ion intake varied with the extent of the crosslinking agent and the observed trend in complexation is Hg(II) > Cu(II)> Zn(II)> Co(II)> Ni (II). The time-course of complexation, the possibility of recycling, swelling characteristics, and spectral and thermal analyses were carried out. The thermal stability increases upon complexation with metal ions.     

Chemical imaging in biology and medicine using ion microscopy

The ability to quantitatively map the distribution of elements on the micrometer scale and smaller with high sensitivity and isotopic discrimination is unique to ion microscopy. The information contained in ion images can be crucial to the study of the solid state, where chemical heterogeneity is often directly related to observed behavior. The tools of digital image processing allow the extraction of quantitative information from the image data. These techniques coupled with improved instrumentation for the detection of ion images drastically increase the problem solving capabilities of the ion microscope. The use of such methods and instrumentation in the ion microscopic analyses of cell cultures and tissues of biological and biomedical relevance will be discussed.     

Edward Teller ninety

Edward Teller is a member of a very fortunate great generation. He was born into this exciting 20th century. As a university student he witnessed the birth of quantum mechanics, one of the boldest cultural venture of human spirit, and he actively participated in widening the realm of physics to chemistry and astrophysics. And he was one of the main actors in shaping the history of this century by realizing the potential power of modern physics. We greet him from his native country in the name of Hungarian physicists.     

Finite Abelian actions on surfaces

Edmonds showed that two free orientation preserving smooth actions φ₁ and φ₂ of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class [M,φ₁]=[M,φ₂] in the oriented bordism group Ω₂(G) of the group G. In this paper, we compute the bordism class [M,φ] for any such action of G on M and we determine for a given M, the bordism classes in Ω₂(G) that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form n(Z/pαZ)).