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.

The acid-base status of the extracellular fluid is directly affected by the concentrations of strong basic cations and strong acid anions that are absorbed into the bloodstream from the diet. The objective of this study was to develop and characterize a model for dietary acid challenge in sheep by decreasing the dietary cation-anion difference (DCAD) using NutriChlor (HCl-treated canola meal), ...

  Background: The dried fruits of Silybum marianum (L.) Gaertn (Compositae) contain silymarin, an isomeric mixture of flavonolignans. Silymarin acts as a strong anti -hepatotoxic. This fruits contains a high amount of oil .  Objective: The objective of this study was to determine total lipid content, fatty acid composition and content of different kind of tocopherols in seed oils of S. marianum...

BACKGROUND: A limited number of studies have investigated the inclusion of amino acids in calf starter. OBJECTIVES: This study was aimed to evaluate different levels of crude protein in starter and supplement- ing some protected amino acids on efficiency, health status and blood metabolites of dairy calves and to com- pare it with unprotected amino acids. <st...

Background and objectives:Wild Sage(Salvia macrosiphon Boiss.) known as “Marvak” in Persian is one of the polymorphic and abundant plants of Lamiaceae. The plants whole seeds usually soaked or boiled in hot water are widely used for inflammatory ailments in folk medicine. Documents have shown that there is scant information on the chemical constituents of this...