S. Kathleen Lyons,* Felisa A. Smith, Peter J. Wagner, Ethan P. White and James H. Brown Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA Department of Geology, Field Museum of Natural History, Chicago, IL 60605, USA Present address: S. Kathleen Lyons, National Center for Ecological Analysis and Synthesis, University of California – Santa Barbara, Santa Barbara, CA 931...

We show that there exists a closed non-σ-porous set of extended uniqueness. We also give a new proof of Lyons’ theorem, which shows that the class of H(n)-sets is not large in U0.

Selected Reading McPherron, A.C., Lawler, A.M., and Lee, S.J. (1999). Nat. Genet. 22, 260–264. Bogdanovich, S., Krag, T.O.B., Barton, E.R., Morris, L.D., WhitteMcPherron, A.C., Lawler, A.M., and Lee, S.J. (1997). Nature 387, more, L., Ahima, R.S., and Khurana, T.S. (2002). Nature 420, 418–421. 83–90. Bullough, W.S. (1965). Cancer Res. 25, 1683–1727. Nakashima, M., Toyono, T., Akamine, A., and J...

We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nash, Moser, Aronson extend to this setting. It was then observed by Sturm that many proofs extend naturally to the setting of locally compact Dirichlet spaces. We relate these results to what is known as rough path theo...

1. This document is HS918, one of a series of the Horticultural Sciences Department, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. Publication date: May 2003. Please visit the EDIS Web site at http://edis.ifas.ufl.edu. 2. Daniel J. Cantliffe, professor and chair, Horticultural Sciences Department; John J. Vansickle, professor, Food an...

The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses Fuglede-Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove th...