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.

New structural motives for organosuperbases, that are easy to prepare and highly basic are urgently required in many areas of chemistry. The synthesis of N,N'-bis(imidazolyl)guanidine bases (BIG bases) is reported. Their pKα  values are determined as 26.1-29.3 in THF. They are thus probably the strongest known phosphorous-free organic bases both in solution and in the gas phase. Calculations he...

The very strong 1997–98 El Niño caused dramatic worldwide changes to weather patterns, such as drought in Indonesia, extreme rains in Peru and Ecuador, and a shutdown of the Atlantic hurricane season (Bell and Halpert 1998). While past El Niño events have also produced similar though not as large effects, this was the first El Niño in which national meteorological centers made accurate forecast...

S. Cox,1,2 J. C. Loudon,2 A. J. Williams,3 J. P. Attfield,3 J. Singleton,1 P. A. Midgley,2 and N. D. Mathur2 1National High Magnetic Field Laboratory, Ms-E536, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB2 3QZ, United Kingdom 3Centre for Science at Extreme Conditions, University of Edinbu...

The interpenetration function of some polymer mixture solutions in a good solvent is examined in the case of polymers of the same chemical species but with very different sizes. The results are compared to two theoretical models. In the first one, the polymers are considered as non-interpenetrating hard-spheres and, in the second one, a blob model of strongly interpenetrated chains is introduce...

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,...

We consider discrete time Heath–Jarrow–Morton type interest rate models, where the interest rate curves are driven by a geometric spatial autoregression field. Strong consistency and asymptotic normality of the maximum likelihood estimators of the parameters are proved for stable no-arbitrage models containing a general stochastic discounting factor, where explicit form of the ML estimators is ...

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.