In my Diplomarbeit, written 1992 under Prof. Helmut Lenzing at the University of Paderborn, I developed a reduction formula for the characteristic polynomial of the Coxeter transformation of a path algebra and translated it into a MAPLE program. The detailed description and explanation as well as the estimation of the complexity of the program is contained in the Diplomarbeit.

Later I extended the results of the Diplomarbeit to quivers with
relations and wrote an article
titled "Methods to Determine Coxeter Polynomials"
which has been published in the *Journal for
Linear Algebra and its Applications* 230 (1995), p.151-164.

In August 96, I finished writing a paper with Martha Takane from UNAM,
Mexico City, about Coxeterpolynomials of unicyclic quivers. It has
since been published under the title "The spectral classes of unicyclic graphs" in the *Journal for Pure and
Applied Algebra* 133 (1998), no. 1-2, p.39-49.

My Ph.D. thesis, written under the direction of Prof. Birge Huisgen Zimmermann at the Math Department of the University of California at Santa Barbara, was finished in May 1996. It deals with uniserial modules over finite dimensional algebras, especially their patterns in the Auslander-Reiten quiver. It also contains the work on Coxeter polynomials.

A joint article with Ahmad Mojiri from the University of Ottawa containing some results about Auslander-Reiten sequences
involving uniserial modules was finished in February 2004. The preprint is available. It has since been published (with some modifications) as "On uniserial modules in the Auslander-Reiten quiver", *Journal of Algebra*, Volume 319, Issue 5, 1 March 2008, Pages 1825-1850.

The first article
deals with metric coordinate systems (a distinguished set of points of a metric space so that every other point can be uniquely identified
by the set of distances to the given points) and the solvability of
continuous dynamical systems specified in these coordinates. A preprint is
available. The article was published as "Metric Coordinate Systems" in *Communications in Mathematical Analysis*, Volume 6, Number 2, Pages 79-108, February 2009.

With Craig Calcaterra, I generalized the well-known flow-box theorem
from differential geometry to Lipschitz continuous vector fields on Banach spaces. A preprint is
available; it has since been published as "Lipschitz Flow-box Theorem" in the *Journal of Mathematical Analysis and Applications* 338 (2008), p. 1108-1115.

Craig Calcaterra and I also prepared the preprint Approximating with Gaussians (2008), in which we show that linear combinations of translations of the Gaussian function exp(-x^{2}) are dense in the space of square-integrable functions on the reals. This result entails that low-frequency trigonometric functions are also dense in a certain sense.

I wrote the article Extending Arxiv.org to Achieve Open Peer Review (2010), outlining a simple extension to the arxiv.org preprint archive. This proposed extension would allow us to establish an open peer review and open publishing process in the sciences. It was published in the *Journal of Scholarly Publishing*, Voluume 42, Number 2 (January 2011), pp. 238-242.

Last Change: 24-Feb-2011

Axel Boldt <axelboldt@yahoo.com>