We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it is a Cantor set if G is countable), and give examples to show that the outer automorphism group of G does not always act faithfully on this space. Also, it ...

There are several graphs associated with finite groups which are currently of interest in the field. This subject of this project are graphs related to the element orders of a finite group. The best known such graph is the prime graph Γ(G) of the group G and is defined as follows. The vertices are the prime numbers dividing the order (=number of elements) of the group, and two such primes are l...

We present a method for the analytic solution of small x structure functions. The essential small x logarithms are summed to all orders in the anomalous dimensions and coefficient functions. Although we work at leading logarithmic accuracy, the method is general enough to allow the systematic inclusion of sub-leading logarithms. Results and predictions are presented for the gluon density, and t...

The radical cations generated from 4-methyl- and 4,7-dimethylindanone, as well as their deuterated isotopomers, isolated in Argon matrices, were found to undergo enolization to the corresponding enol radical cations at rates that differ by orders of magnitude. It is shown by quantum chemical calculations that the effect of the remote methyl group in the 4-position is of purely electronic nature...