In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.

Our proof (with Robertson and Thomas) of the strong perfect graph conjecture ran to 179 pages of dense matter; and the most impenetrable part was the final 55 pages, on what we called “wheel systems”. In this paper we give a replacement for those 55 pages, much easier and shorter, using “even pairs”. This is based on an approach of Maffray and Trotignon.

We introduce M -tensors. This concept extends the concept ofM -matrices. We denote Z-tensors as the tensors with nonpositive off-diagonal entries. We show that M -tensors must be Ztensors and the maximal diagonal entry must be nonnegative. The diagonal elements of a symmetric M -tensor must be nonnegative. A symmetric M -tensor is copositive. Based on the spectral theory of nonnegative tensors,...

In reliability or medical studies, we may only observe each ongoing renewal process for a certain period of time. When the underlying distribution F is arithmetic, Vardi (Ann. Statist. 10 (1982b), 772-785) developed the RT algorithm for nonparametric estimation. In this paper we extend the study to the nonarithmetic case and show that the choice of an arbitrary constant in the RT algorithm can ...

We consider the question of strong cosmic censorship in spatially compact, spatially locally homogeneous vacuum models. We show in particular that strong cosmic censorship holds in Bianchi IX vacuum space–times with spherical spatial topology.

To have a quality multimedia presentation through networks, its presentation lag needs to be controlled. One way to reduce the lag is to prefetch the media objects before their due dates. This paper explores techniques for optimizing the object sequence in a prefetch-enabled TV-like presentation. An optimal solution is the one with which the presentation lag is minimized. We formulate the probl...

 Events leading up to the release of toxic chemicals in the processing plants are one of the main hazards of chemical industries that can endanger employees and also people in neighborhood. In this study, DOW's Chemical Exposure Index (CEI) is used to determine hazard distances of possible toxic chemical releases in one of the South Pars gas refineries. To...