Let G be the class of all graphs with no induced four-edge path or four-edge antipath. Hayward and Nastos [6] conjectured that every prime graph in G not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this paper we give a counterexample to their conjecture, and prove a slightly weaker version....

1 Institute for Manufacturing, University of Cambridge, 17 Charles Babbage Rd, Cambridge, CB3 4 0FS, UK 5 2 IMEC, Kapeldreef 75, 3001 Heverlee, Belgium, Department of Mechanical Engineering, Katholieke 6 Universiteit Leuven, 3001 Leuven, Belgium 7 3 Mechanosynthesis Group, Department of Mechanical Engineering, University of Michigan, 2350 8 Hayward Street, Ann Arbor, Michigan 48109 USA 9 4 Mech...

We consider two proposals for defining black hole entropy in spherical symmetry, where the horizon is defined locally as a trapping horizon. The first case, boundary terms in a dual-null form of the reduced action in two dimensions, gives a result that is proportional to the area. The second case, Wald’s Noether current method, is generalized to dynamic black holes, giving an entropy that is ju...

Received 25 September 2002; revised 22 October 2002; accepted 27 November 2002. For correspondence (fax þ6 351 7050; e-mail [email protected]). yPresent address: Crop and Food Research, Private Bag 11600, Palmerston North, New Zealand. zPresent address: Sygen International, Suite 130, 2929 Seventh Street, Berkeley, CA 94710, USA. Present address: Molecular Biology Department, University of ...

Y. Shu, Prof. B. Ma Department of Chemical and Biomedical Engineering Florida State University 95 Chieftan Way , Tallahassee , FL 32306 , USA E-mail: [email protected] J. Wang, Prof. S. Lin Department of Mechanical Engineering Florida State University 2525 Pottsdamer Street , Tallahassee , FL 32310 , USA E-mail: [email protected] Y. Tian, Prof. S. Lin, Prof. B. Ma Materials Science and Engineering Progra...